Table of contents

The second International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE) took place at Prague, Czech Republic, from Sunday 1 September to Thursday 5 September 2013.

The Conference was attended by more than 280 participants and hosted about 400 oral, poster, and virtual presentations while counted more than 600 pre-registered authors. The second IC-MSQUARE consisted of different and diverging workshops and thus covered various research fields where Mathematical Modeling is used, such as Theoretical/Mathematical Physics, Neutrino Physics, Non-Integrable Systems, Dynamical Systems, Computational Nanoscience, Biological Physics, Computational Biomechanics, Complex Networks, Stochastic Modeling, Fractional Statistics, DNA Dynamics, Macroeconomics.

The scientific program was rather heavy since after the Keynote and Invited Talks in the morning, three parallel sessions were running every day. However, according to all attendees, the program was excellent with high level of talks and the scientific environment was fruitful, thus all attendees had a creative time.

We would like to thank the Keynote Speaker and the Invited Speakers for their significant contribution to IC-MSQUARE. We also would like to thank the Members of the International Advisory and Scientific Committees as well as the Members of the Organizing Committee.

Further information on the editors, speakers and committees is available in the attached pdf.

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

We consider the iterative method for solving a quadratic matrix equation with special coefficient matrices which arises in the quasi-birth-death problem. In this paper, we show that the elementwise minimal positive solvents to quadratic matrix equations can be obtained using Newton's method. We also prove that the convergence rate of the Newton iteration is quadratic if the Fréchet derivative at the elementwise minimal positive solvent is nonsingular. However, if the Fréchet derivative is singular, the convergence rate is at least linear. Numerical experiments of the convergence rate are given.(This is summarized a paper which is to appear in Honam Mathematical Journal.)

The article deals with the numerical simulation of the flow pattern around a moving body in a stratified fluid. The flow is assumed to be unsteady, incompressible and stratified. The mathematical model is based on the Boussinesq approximation of the Navier-Stokes equations for viscous incompressible flow wit non-constant density. The resulting set of PDE's is then solved by the AUSM MUSCLE scheme in finite volume approximation. For the time integration the three stage BDF method of the second order is used. Three different obstacle models were tested.

This work presents statistical analysis of data collected from laser interferometric detector "Dylkin-1" and nearby seismic stations. The final goal of Dylkin project consists in creating detector of theoretically predicted gravitational waves produced by binary relativistic astrophysical objects. Currently, works are underway to improve sensitivity of detector by 2-3 orders. The goals of this research were to test isolation of detector from noise caused by seismic waves and to find out whether it is sensitive to variations in the gradient of gravitational potential (acceleration of free fall) caused by free Earth oscillations. Noise isolation has been tested by comparing energy of signals during significant seismic events. Sensitivity to variations in acceleration of free fall has been tested by means of cross-spectral analysis.

In this study the estimation of parameters in dynamical systems governed by parameter-affine ordinary differential equations is explored. The described method by Mehrkanoon et al.~ in [1] is utilized as an initialization of the nonlinear optimization problem for parameter estimation. In contrast to existing convex initialization approaches [2] that use a first order Euler discretization, we do not require any integration method to simulate the dynamical system. Furthermore, a denoising scheme using LSSVM is proposed to first filter the measured data then proceed with the filtered signals for parameter estimation problem. Experimental results demonstrate the efficiency of the proposed method, compared to alternative approaches on different examples from the literature.

The dynamical simulation of rigid bodies can be gathered from the classical Newton-Euler differential equations, which commonly make use of the Euler angles parametrization. In this work, the initial value problem associated with motion is presented in terms of quaternion formulation instead of the Euler one. The reason why the quaternion parametrization is proposed lies on the possibility of avoiding singularities that can occur by considering Euler angles. Moreover, the strength of quaternions is represented by the linearity of their formulation, the easiness of their algebraic structure and, overall, on their stability and efficiency. Our proposed application is the mathematical modelling of a small Unmanned Aerial Vehicle dynamics. In particular a multirotor with six blades has been taken into account, its mathematical model is deduced and a comparison between the results obtained by implementing our formulation and the classical one is produced.

The structures of self-assembled monolayers (SAMs) of short (methyl) and long (hexyl) chain alkyl thiols on the clean gold (111) surface were modelled using for the Au-S interactions either the reactive ReaxFF potential or the well known non-reactive Morse potential, while for the Au-Au interactions either the ReaxFF potential or an embedded-atom method (EAM). Analysis of the MD trajectories of possible SAM structures suggests that disordering of interfacial Au atoms is definitely driven by the gold-sulphur interactions. Our MD results reveal a novel structure where two methanethiol molecules are bound to a gold adatom that has been lifted from the surface at 300 K, and the same kind of RS-Au-SR motif was also observed for hexanethiol at 600 K but not at 300 K. What is more, the above motif is only observed for the reactive ReaxFF potential. Moreover, these results are in clear agreement with recent experiments and more costly first principles-based MD simulations. These findings strongly support the use of reactive potentials such as ReaxFF for gathering an accurate description of Au-S interactions in inexpensive classical MD simulations.

Scatterometry is an indirect optical method for the determination of photomask geometry parameters from scattered light intensities by solving an inverse problem. The Bayesian approach is a powerful method to solve the inverse problem. In the Bayesian framework estimates of parameters and associated uncertainties are obtained from posterior distributions. The determination the probability distribution is typically based on Markov chain Monte Carlo (MCMC) methods. However, in scatterometry the evaluation of MCMC steps require solutions of partial differential equations that are computationally expensive and application of MCMC methods is thus impractical. In this article we introduce a surrogate model for scatterometry based on polynomial chaos that can be treated by Bayesian inference. We compare the results of the surrogate model with rigorous finite element simulations and demonstrate its convergence. The accuracy reaches a value of lower than one percent for a sufficient fine mesh and the speed up amounts more than two order of magnitudes. Furthermore, we apply the surrogate model to MCMC calculations and we reconstruct geometry parameters of a photomask.

This paper is the first step of generalization of the previously obtained full classification of the asymptotic behavior of the probability for Markov chain trajectories for the case of hidden Markov models. The main goal is to study the power (Zipf) and nonpower asymptotics of the frequency list of trajectories of hidden Markov frequencys and to obtain explicit formulae for the exponent of the power asymptotics. We consider several simple classes of hidden Markov models. We prove that the asymptotics for a hidden Markov model and for the corresponding Markov chain can be essentially different.

This paper is devoted to verifying of the empirical Zipf and Hips laws in natural languages using Google Books Ngram corpus data. The connection between the Zipf and Heaps law which predicts the power dependence of the vocabulary size on the text size is discussed. In fact, the Heaps exponent in this dependence varies with the increasing of the text corpus. To explain it, the obtained results are compared with the probability model of text generation. Quasi-periodic variations with characteristic time periods of 60-100 years were also found.

Digital image segmentation is a process in which one assigns distinct labels to different objects in a digital image. The MOFS (Multi Object Fuzzy Segmentation) algorithm has been successfully applied to the segmentation of images from several modalities. However, the traditional MOFS algorithm fails when applied to images whose composing objects are characterized by textures whose patterns cannot be successfully described by simple statistics computed over a very restricted area. Here, we present an extension of the MOFS algorithm that achieves the segmentation of textures by employing adaptive affinity functions that use the Skew Divergence as a measure of distance between two distributions. These affinity functions are called adaptive because their associated area (neighborhood) changes according to the characteristics of the texture being processed. We performed experiments on mosaic images composed by combining rock sample images which show the effectiveness of the adaptive skew divergence based fuzzy affinity functions.

Virus propagations in complex networks have been studied in the framework of discrete time Markov process dynamical systems. These studies have been carried out under the assumption of homogeneous transition rates, yielding conditions for virus extinction in terms of the transition probabilities and the largest eigenvalue of the connectivity matrix. Nevertheless the assumption of homogeneous rates is rather restrictive. In the present study we consider non-homogeneous transition rates, assigned according to a uniform distribution, with susceptible, infected and quarantine states, thus generalizing the previous studies. A remarkable result of this analysis is that the extinction depends on the weakest element in the network. Simulation results are presented for large free-scale networks, that corroborate our theoretical findings.

What is the ultimate fate of something that falls into a black hole? From this question arises one of the most intricate problems of modern theoretical physics: the black hole information loss paradox. Bekenstein and Hawking have been shown that the entropy in a black hole is proportional to the surface area of its event horizon, which should be quantized in a multiple of the Planck area. This led G.'t Hooft and L. Susskind to propose the holographic principle which states that all the information inside the black hole can be stored on its event horizon. From this results, one may think if the solution to the information paradox could lies in the quantum properties of the black hole horizon. One way to quantize the event horizon is to see it as a fuzzy sphere, which posses a closed relation with Hopf algebras. This relation makes possible a topology change process where a fuzzy sphere splits in two others. In this work it will be shown that, if one quantize the black hole event horizon as a fuzzy sphere taking into account its quantum symmetry properties, a topology change process to black holes can be defined without break unitarity or locality, and we can obtain a possible solution to the information paradox. Moreover, we show that this model can explain the origin of the black hole entropy, and why black holes obey a generalized second law of thermodynamics.

The Bloch-Torrey partial differential equation (PDE) describes the complex transverse water proton magnetization due to diffusion-encoding magnetic field gradient pulses. The integral of the solution of this PDE yields the diffusion magnetic resonance imaging (dMRI) signal. In a complex medium such as cerebral tissue, it is difficult to explicitly link the dMRI signal to biological parameters such as the cellular geometry or the cellular volume fraction. Studying the dMRI signal arising from a single neuron can provide insight into how the geometrical structure of neurons influences the measured signal. We formulate the Bloch-Torrey PDE inside a single neuron, under no water exchange condition with the extracellular space, and show how to reduce the 3D simulation in the full neuron to a 3D simulation around the soma and 1D simulations in the neurites. We show that this latter approach is computationally much faster than full 3D simulation and still gives accurate results over a wide range of diffusion times.

Tensor models in various forms are being studied as models of quantum gravity. Among them the canonical tensor model has a canonical pair of rank-three tensors as dynamical variables, and is a pure constraint system with first-class constraints. The Poisson algebra of the first-class constraints provides an algebraically consistent way of discretizing the Dirac algebra for general relativity. This paper successfully formulates the Wheeler-DeWitt quantization of the canonical tensor model. Formally one can obtain wave functions of the "universe" by solving the partial differential equations representing the constraints. For the simplest non-trivial case, the unique wave function is exactly and globally obtained. Although this case is far from being realistic, the wave function is physically interesting; locality is favored, and there exists a locus of configurations with features of the beginning of the universe.

Describing the combustion of log wood and others solid fuels with complex geometry, considerable water content and often heterogenous struture is a nontrivial task. Stochastic Cellular Automata models offer a promising approach for modelling such processes. Combustion models of this type exhibit several similarities to the well-known forest fire models, but there are also significant differences between those two types of models. These differences call for a detailed analysis and the development of supplementary modeling approaches. In this article we define a qualitative two-dimensional model of burning log wood, discuss the most important differences to classical forest fire models and present some preliminary results.

Quantum mechanics provide a detailed description of the physical and chemical behavior of molecules. However, with increasing size of the system the complexity rises exponentially, which is prohibitive for efficient dynamical simulation. In contrast, classical molecular dynamics procure a coarser description by using less degrees of freedom. Thus, it seems natural to seek for an adequate trade-off between accurateness and computational feasibility in the simulation of molecules. Here, we propose a novel method, which combines classical molecular simulations with quantum mechanics for molecular systems. For this we decompose the state space of the respective molecule into subsets, by employing a meshfree partition of unity. We show, that this partition allows us to localize an empirical force field and to run locally constrained classical trajectories. Within each subset, we compute the energy on the quantum level for a fixed number of spatial states (ab initio points). With these energy values from the ab initio points we have a local scattered data problem, which can be solved by the moving least squares method.

The application of appropriate transform pairs, such as the Fourier, the Laplace, the sine, the cosine and the Mellin transforms, provides the most well known method for constructing analytical solutions to a large class of physically significant boundary value problems. However, this method has several limitations. In particular, it requires the given PDE, domain and boundary conditions to be separable, and also may not be applicable if the given boundary value problem is non-self-adjoint. Furthermore, it expresses the solution as either an integral or an infinite series, neither of which are uniformly convergent on the boundary of the domain (for nonvanishing boundary conditions), which renders such expressions unsuitable for numerical computations. Here, we review a method recently introduced by the first author which can be applied to certain nonseparable and non-self-adjoint problems. Furthermore, this method expresses the solution as an integral in the complex plane which is uniformly convergent on the boundary of the domain. This method, which also suggests new numerical techniques, is illustrated for both evolution and elliptic PDEs. Athough this method was first applied to certain nonlinear PDEs called integrable and was originally formulated in terms of the so-called Lax pairs, it can actually be applied to linear PDEs without the need to analyse the associated Lax pair. The existence of Lax pairs is used here in order to motivate a related development, namely the emergence of a novel formalism for analysing certain inverse problems arising in medical imaging. Examples include PET and SPECT.

How many H₂O molecules are needed to form water? While the precise answer is not known, it is clear that the answer should be a finite number rather than infinity. We revisit with care the ideal Bose gas confined in a cubic box which is discussed in most statistical physics textbooks. We show that the isobar of the ideal gas zigzags on the temperature-volume plane featuring a boiling-like discrete phase transition, provided the number of particles is equal to or greater than a particular value: 7616. This demonstrates for the first time how a finite system can feature a mathematical singularity and realize the notion of 'Emergence', without resorting to the thermodynamic limit.

The primary goal of the NOνA neutrino oscillation experiment is to study the probabilities of transformation of muonic-neutrinos into electron-neutrinos. The experiment is currently under construction and will use a 700 kW accelerator-based NuMI beam (Neutrinos at the Main Injector) and two detectors. The Near Detector (329 t at Fermi National Accelerator Laboratory, Illinois) and the Far Detector (14 kt, Ash River, Minnesota) are aligned to 14 mrad off-axis and separated by 810 km. They are made of active liquid scintillator and readout by avalanche photo-diodes. Recent results from world-wide neutrino experiments indicate that NOνA is in the position to determine the neutrino mass hierarchy as it is also searching for the first hints of CP violation in neutrino sector. The design, the goals and the current status of the NOνA experiment are presented here with the current estimates of its sensitivity to the mass hierarchy measurement.

In image processing, edge detection is a valuable tool to perform the extraction of features from an image. This detection reduces the amount of information to be processed, since the redundant information (considered less relevant) can be disconsidered. The technique of edge detection consists of determining the points of a digital image whose intensity changes sharply. This changes are, for example, due to the discontinuities of the orientation on a surface. A well known method of edge detection is the Difference of Gaussians (DoG). The method consists of subtracting two Gaussians, where a kernel has a standard deviation smaller than the previous one. The convolution between the subtraction of kernels and the input image results in the edge detection of this image. This paper introduces a method of extracting edges using DoG with kernels based on the q-Gaussian probability distribution, derived from the q-statistic proposed by Constantino Tsallis. To demonstrate the method's potential, we compare the introduced method with the tradicional DoG using Gaussians kernels. The results showed that the proposed method can extract edges with more accurate details.

Using the method of the "average spin" a modelling study of magnetic and concentration phase transition in ultrathin antiferromagnetic of different crystalline structure has been carried out. It has been shown, that relative change of Neel temperature is subject to the power law with negative index which doesn't depend on the film's crystal kind. The calculation of the dependence of phase transition critical concentration in diluted magnetic material on the film thickness has been made out. The legitimacy of the use of the method developed for modelling of magnetic and concentration phase transition in different nanostructures is certified by accordance between the results of calculations and the experimental data.

Semi-supervised learning (SSL) stands out for using a small amount of labeled points for data clustering and classification. In this scenario graph-based methods allow the analysis of local and global characteristics of the available data by identifying classes or groups regardless data distribution and representing submanifold in Euclidean space. Most of methods used in literature for SSL classification do not worry about graph construction. However, regular graphs can obtain better classification accuracy compared to traditional methods such as k-nearest neighbor (kNN), since kNN benefits the generation of hubs and it is not appropriate for high-dimensionality data. Nevertheless, methods commonly used for generating regular graphs have high computational cost. We tackle this problem introducing an alternative method for generation of regular graphs with better runtime performance compared to methods usually find in the area. Our technique is based on the preferential selection of vertices according some topological measures, like closeness, generating at the end of the process a regular graph. Experiments using the global and local consistency method for label propagation show that our method provides better or equal classification rate in comparison with kNN.

Current Bayesian network software packages provide good graphical interface for users who design and develop Bayesian networks for various applications. However, the intended end-users of these networks may not necessarily find such an interface appealing and at times it could be overwhelming, particularly when the number of nodes in the network is large. To circumvent this problem, this paper presents an intuitive dashboard, which provides an additional layer of abstraction, enabling the end-users to easily perform inferences over the Bayesian networks. Unlike most software packages, which display the nodes and arcs of the network, the developed tool organises the nodes based on the cause-and-effect relationship, making the user-interaction more intuitive and friendly. In addition to performing various types of inferences, the users can conveniently use the tool to verify the behaviour of the developed Bayesian network. The tool has been developed using QT and SMILE libraries in C++.

We analize a parametric coupled KdV system and we find a Bäcklund transformation. For a positive value of the parameter the system reduces to two KdV decoupled equations. For negative value of the parameter the system has non trivial coupling and presents multisolitonic solutions generated by the Backlund transformation. We compare the results with the already known in the literature.

We discuss the bosonization of supersymmetric KdV as a first step on the construction of operatorial extensions of that system. We obtain the hamiltonian structure of those operatorial extensions using extended Miura tranformations. We also discuss their integrability properties in terms of extended Gardner tranformations. We give explicit examples of some operatorial extensions.

In this work we investigate the usefulness of node roles of complex systems in dynamical processes. More specifically, we use the characteristic equations of an SIS epidemic spreading in order to simulate an actual epidemic spreading. The equations that are used, encapsulate the degree correlations in comparison to the role distribution and the results are compared with an actual epidemic release simulation.

The following work uses the dynamic capabilities of an evolutionary algorithm in order to obtain an optimal immunization strategy in a user specified network. The produced algorithm uses a basic genetic algorithm with crossover and mutation techniques, in order to locate certain nodes in the inputted network. These nodes will be immunized in an SIR epidemic spreading process, and the performance of each immunization scheme, will be evaluated by the level of containment that provides for the spreading of the disease.

In this paper, we construct a three-phase model (that is, a system consisting of three homogeneous regions with various scattering length densities), which illustrate the behavior of small-angle scattering (SAS) scattering curves. Here two phases are a deterministic fractal embedded in another deterministic mass fractal, and they altogether are further embedded in a third phase, which can be a solution or solid matrix. We calculate SAS intensities, derive expressions for the crossover position (that is, the point where the power-law scattering exponent changes) as a function of control parameters, including size, concentration, and volumes of each phase. The corresponding SAS intensities from these models describe a succession of power-law regimes in momentum space where both regimes correspond to mass fractals. The models can be applied to SAS data where the absolute value of the scattering exponent of the first power-law regime is higher than that of the subsequent second power-law regime, that is, the scattering curve of "convex" kind near the crossover position.

Deflection of Cosmic Ray charged particles under the influence of magnetic fields (Galactic and Extragalactic) causes a nearly isotropic distribution of their observed fluxes especially in lower energy ranges. Anyhow, as very high energy cosmic rays experience less deflections in their paths, they may point out the direction of their sources within a few degrees. We used a Galactic magnetic field model to study the possible Galactic sources of these cosmic rays. The propagation of cosmic rays in this Galactic magnetic field is simulated to estimate average deflection angles into their straight-line paths from their sources. Pulsars with suitable characteristics are selected and deflection regions around them are defined. Compared with the observational data (i.e. detected directions of observed CRs), the possibility of a Galactic origin of ultra high energy cosmic rays is examined. We defined deflection angles in terms of energies for sources in a distance d into center and anti-center directions. The probability of observing cosmic rays of di?erent energies from the direction of a source in a distance d is studied and the possibility of a pulsar origin of very high energy cosmic rays due to some recent models, is discussed.

So-called the instant coffee effect is well known in the field of the physics education. The effect is explained that the sound yielded by touching the cup with a spoon is shifted to low-pitched by adulterating bubble owing to putting a spoon of instant coffee into hot water. The phenomenon has been interpreted with the averaged density and compressibility of the fluid in the macroscopic relation for the sound velocity, . We introduce the linear coupled oscillator model with finite oscillators including the impurity air-mass oscillator. The model may well reproduce the increase in the shift of the eigen frequency accompanying with the amount of bubble.

It is shown that the R-matrix theory of nuclear reactions is a viable mathematical theory for the description of the fine, intermediate and gross structure observed in the time-dependence of economic indices in general, and the daily Dow Jones Industrial Average in particular. A Lorentzian approximation to R-matrix theory is used to analyze the complex structures observed in the Dow Jones Industrial Average on a typical trading day. Resonant structures in excited nuclei are characterized by the values of their fundamental strength function, (average total width of the states)/(average spacing between adjacent states). Here, values of the ratios (average lifetime of individual states of a given component of the daily Dow Jones Industrial Average)/(average interval between the adjacent states) are determined. The ratios for the observed fine and intermediate structure of the index are found to be essentially constant throughout the trading day. These quantitative findings are characteristic of the highly statistical nature of many-body, strongly interacting systems, typified by daily trading. It is therefore proposed that the values of these ratios, determined in the first hour-or-so of trading, be used to provide valuable information concerning the likely performance of the fine and intermediate components of the index for the remainder of the trading day.

A system of linearized equations of the (1+1)-dimensional Sine-Gordon (SG) equation and its Bäcklund transformation are given to determine not only nonlocal symmetries but also nonlocal conservation laws of the SG equation. Through the parameter expansion procedure, a sequence of infinitely many nonlocal symmetries and a sequence of infinitely many nonlocal conservation laws are obtained.

The solvent-gradient simulated moving bed process (SG-SMB) is the new tendency in the performance improvement if compared to the traditional isocratic solvent conditions. In such SG-SMB process the modulation of the solvent strength leads to significant increase in the purities and productivity followed by reduction in the solvent consumption. A stepwise modelling approach was utilized in the representation of the interconnected chromatographic columns of the system combined with a lumped mass transfer model between the solid and liquid phase. The influence of the solvent modifier was considered applying the Abel model which takes into account the effect of modifier volume fraction over the partition coefficient. Correlation models of the mass transfer parameters were obtained through the retention times of the solutes according to the volume fraction of modifier. The modelling and simulations were carried out and compared to the experimental SG-SMB separation unit of the amino acids Phenylalanine and Tryptophan. The simulation results showed the great potential of the proposed modelling approach in the representation of such complex systems. The simulations showed great agreement fitting the experimental data of the amino acids concentrations both at the extract as well as at the raffinate. A new optimization strategy was proposed in the determination of the best operating conditions which uses the phi-plot concept.

It is calculated that in single-particle states events with a fermion have positive energy and occurrences with an antifermion have negative energy. In double-particle states events with pair of antifermions have negative energy and events with pair of fermions and with fermion-antifermion pair have positive energy. An event with positive energy transfers this energy photons which carries it on recorders observers. Observers know that this event occurs, not before it happens. But event with negative energy should absorb this energy from observers. Consequently, observers know that this event happens before it happens. Since time is irreversible then only the events with positive energy can occur.

We consider the interaction of hydrogen atom with a very intense low frequency laser pulse. The Henneberger-Kramers representation of the time-dependent Schrödinger equation is the most appropriate one for this purpose. It is shown that in the case of very low frequencies, the quantum dispersion of the electron wave packet plays a dominant role in the dynamics of the atom.

The complex permittivity spectra for tert-butyl alcohol(TB) with n-propanol(nP) were determined over the frequency range of 10 MHz to 20 GHz using the time domain reflectometry (TDR) in the temperature range of 25°C to 55°C for 11 different concentrations of the system. The static dielectric constant (ε₀) and relaxation time (τ) have been determined these spectra using the Debye model. Excess properties and Kirkwood correlation factor of the mixtures have been determined. The excess permittivity is found to be positive in the tart-butyl alcohol rich region and negative in the n-Propanol rich region. However, the excess inverse relaxation time has different trend. The static dielectric constants for the mixtures have also been fitted with the modified Bruggeman model by assuming an additional parameter in the model.

The problem of constructing a physically based hardening laws of mono- and polycrystalline samples in multi-level theories using crystal plasticity is considered, these hardening laws should allow describing the process of the defect structure evolution of the material due to the intensive inelastic deformations. It is also should be applicable to the description of simple and cyclic loading. An approach to the construction of a general and a particular form of hardening law is proposed, which takes into account the interaction of full and split dislocations with each other, forming and destruction of dislocation barriers, annihilation of dislocations during reverse loading. Using the obtained hardening law, the known experimental effects of simple and cyclic loading are described.

We consider a generalized angle in complex normed vector spaces. Its definition corresponds to the definition of the well known Euclidean angle in real inner product spaces. Not surprisingly it yields complex values as 'angles'. This 'angle' has some simple properties, which are known from the usual angle in real inner product spaces. But to do ordinary Euclidean geometry real angles are necessary. We show that even in a complex normed space there are many pure real valued 'angles'. The situation improves yet in inner product spaces. There we can use the known theory of orthogonal systems to find many pairs of vectors with real angles, and to do geometry which is based on the Greeks 2000 years ago.

We obtain an analytical expression for the energy eigenvalues of the Hyperbolical potential using an approximation of the centrifugal term. In order to obtain the l-states solutions, we use the the Feynman path integral approach to quantum mechanics. We show that by performing nonlinear space-time transformations in the radial path integral, we can derive a transformation formula that relates the original path integral to the Green function of a new quantum solvable system. The explicit expression of bound state energy is obtained and the eigenfunctions are given in terms of hypergeometric functions. The present results are consistent with those obtained by others methods.

A Multi-Layer Perceptron (MLP) defines a family of artificial neural networks often used in TS modeling and forecasting. Because of its "black box" aspect, many researchers refuse to use it. Moreover, the optimization (often based on the exhaustive approach where "all" configurations are tested) and learning phases of this artificial intelligence tool (often based on the Levenberg-Marquardt algorithm; LMA) are weaknesses of this approach (exhaustively and local minima). These two tasks must be repeated depending on the knowledge of each new problem studied, making the process, long, laborious and not systematically robust. In this paper a pruning process is proposed. This method allows, during the training phase, to carry out an inputs selecting method activating (or not) inter-nodes connections in order to verify if forecasting is improved. We propose to use iteratively the popular damped least-squares method to activate inputs and neurons. A first pass is applied to 10% of the learning sample to determine weights significantly different from 0 and delete other. Then a classical batch process based on LMA is used with the new MLP. The validation is done using 25 measured meteorological TS and cross-comparing the prediction results of the classical LMA and the 2-stage LMA.

Establishing a mathematical supply-chain model is a proposition that has received attention due to its inherent benefits of evolving global supply-chain efficiencies. This paper discusses the prevailing relationships found within apparel supply-chain environments, and contemplates the complex issues indicated for constituting a mathematical model. Principal results identified within the data suggest, that the multifarious nature of global supply-chain activities require a degree of simplification in order to fully dilate the necessary factors which affect, each sub-section of the chain. Subsequently, the research findings allowed the division of supply-chain components into sub-sections, which amassed a coherent method of product development activity. Concurrently, the supply-chain model was found to allow systematic mathematical formulae analysis, of cost and time, within the multiple contexts of each subsection encountered. The paper indicates the supply-chain model structure, the mathematics, and considers how product analysis of cost and time can improve the comprehension of product lifecycle management.

We give an interaction between a drift and a fractional power of a degenerated Laplacian such that the involved semi-group has a density by using the Malliavin Calculus for boundary processes translated by ourself in semi-group theory in [1].

Vehicle Routing Problem (VRP) is an important management problem in the field of distribution and logistics. In VRPs, routes from a distribution point to geographically distributed points are designed with minimum cost and considering customer demands. All points should be visited only once and by one vehicle in one route. Total demand in one route should not exceed the capacity of the vehicle that assigned to that route. VRPs are varied due to real life constraints related to vehicle types, number of depots, transportation conditions and time periods, etc. Heterogeneous fleet vehicle routing problem is a kind of VRP that vehicles have different capacity and costs. There are two types of vehicles in our problem. In this study, it is used the real world data and obtained from a company that operates in LPG sector in Turkey. An optimization model is established for planning daily routes and assigned vehicles. The model is solved by GAMS and optimal solution is found in a reasonable time.

We analyze initial value problems for ordinary differential equations with infinitely many derivatives such as (linearized versions of) nonlocal field equations of motion appearing in particle physics, nonlocal cosmology and string theory. We show that the corresponding initial value problem on a half line is well-posed and that it requires only a finite number of initial conditions. We also investigate nonlinear pseudo-equations defined by functions of the Laplace operator, that is, nonlinear partial differential equations with infinitely many derivatives.

We present a molecular dynamics (MD) simulation of nanoscale gas flow due to thermal creep at cryogenic temperatures. Helium is considered because its low liquefying temperature allows a wide range of cryogenic analysis. The thermal creep flow along a nanochannel is generated by applying temperature differences along the channel. Pressure and density variations are measured at various rarefaction conditions, covering the slip flow to the free molecular regimes. Thermo molecular pressure difference (TMPD) values are also calculated. Our results are compared with those in the literature.

Continuous times series {f(x)} such as a depth of water is written f(x) = T(x)+P(x)+S(x)+C(x) in hydrological science where T(x),P(x),S(x) and C(x) are called the trend, periodic, stochastic and catastrophic components respectively. We simplify this model and apply it to the local temperature data such as given E. Halley (1693), the UK (1853-2010), Germany (1880-2010), Japan (1876-2010). We also apply the model to CO₂ data. The model coefficients are evaluated by a symbolic computation by using a standard personal computer. The accuracy of obtained nonlinear curve is evaluated by the arithmetic mean of relative errors between the data and estimations. E. Halley estimated the temperature of Gresham College from 11/1692 to 11/1693. The simplified model shows that the temperature at the time rather cold compared with the recent of London. The UK and Germany data sets show that the maximum and minimum temperatures increased slowly from the 1890s to 1940s, increased rapidly from the 1940s to 1980s and have been decreasing since the 1980s with the exception of a few local stations. The trend of Japan is similar to these results.

We study atomic and molecular (AM) stationary systems and electrodynamic (ED) systems, composed of an electron interacting with an electromagnetic field. We show that the Schrödinger and Klein-Gordon equations written for these systems have a secondary solution, which is the wave function associated to a classical system. For AM systems, the wave surfaces (S surfaces) and their normals (C curves) are solutions of the Hamilton-Jacobi equation, written for the same system. The S surfaces have a periodical motion and the C curves are closed. The integral relation of the Schrödinger equation on the C curve has a solution identical to the wave function associated to the classical motion. This solution leads to the generalized Bohr quantization relation and to the generalized de Broglie relations, which are valid in the space of the electron coordinates. An identical wave function verifies the Klein-Gordon equation, in the case of the EM systems. The above properties lead to a central field method for calculation of the energetic values and symmetry properties for AM systems, whose accuracy is comparable to the accuracy of the Hartree-Fock method. They also lead to an accurate method for modeling EM systems, which is verified by experimental data from the literature. The above properties are deduced without using any approximation.

The oxidation of CO on Pt-group metal surfaces has attracted widespread attention since a long time due to its interesting oscillatory kinetics and spatiotemporal behavior. The use of STM in conjunction with other experimental data has confirmed the validity of the surface reconstruction (SR) model under low pressure and the more recent surface oxide (SO) model which is possible under sub-atmospheric pressure conditions [1]. In the SR model the surface is periodically reconstructed below a certain low critical CO-coverage and this reconstruction is lifted above a second, higher critical CO-coverage. Alternatively the SO model proposes periodic switching between a low-reactivity metallic surface and a high-reactivity oxide surface. Here we present an overview of our recent kinetic Monte Carlo (KMC) simulation studies on the oscillatory kinetics of surface catalyzed CO oxidation. Different modifications of the lattice gas Ziff-Gulari-Barshad (ZGB) model have been utilized or proposed for this purpose. First we present the effect of desorption on the ZGB reactive to poisoned irreversible phase transition in the SR model. Next we discuss our recent research on KMC simulation of the SO model. The ZGB framework is utilized to propose a new model incorporating not only the standard Langmuir-Hinshelwood (LH) mechanism, but also introducing the Mars-van Krevelen (MvK) mechanism for the surface oxide phase [5]. Phase diagrams, which are plots between long time averages of various oscillating quantities against the normalized CO pressure, show two or three transitions depending on the CO coverage critical threshold (CT) value beyond which all adsorbed oxygen atoms are converted to surface oxide.

We present analytic solutions of the Feynman propagator with the Rosen-Morse potential. To do that, an approximation of the centrifugal potential is used and nonlinear space-time transformations are applied. A relation between the original path integral and the Green function of a new quantum soluble system is derived. Explicit expressions of the bound state energy spectra and the eigenfunctions are obtained and compared to those of Schrodinger formalism.

Molecular simulations, such as Monte Carlo (MC) and molecular dynamics (MD) have been recently used for understanding the forces between colloidal nanoparticles that determine the dispersion and stability of nanoparticle suspensions. Herein we review the current status of research in the area of nanoparticles immersed in L-J solvents. The first study by Shinto et al. used large smooth spheres to depict nanoparticles in L-J and soft sphere solvents. The nanoparticles were held fixed at a particular interparticle distance and only the solvents were allowed to equilibrate. Both Van-der-waals and solvation forces were computed at different but fixed interparticle separation. Later Qin and Fitchthorn improved on this model by considering the nanoparticles as collection of molecules, thus taking into the account the effect of surface roughness of nanoparticles. Although the inter particle distance was fixed, the rotation of such nanoparticles with respect to each other was also investigated. Recently, in keeping with the experimental situation, we modified this model by allowing the nanoparticles to move and rotate freely. Solvophilic, neutral and solvophobic interactions between the solvent atoms and those that make up the nanoparticles were modelled. While neutral and solvophobic nanoparticles coalesce even at intermediate distances, solvophilic nanoparticles are more stable in solution due to the formation of a solvent shield.

The singly-excited states of He and He-like atomic ions in the manifold of the n = 3 principal shell have been studied replying on the full configuration interaction wave function focusing on the origin of the first Hund rule. The probability density distributions of the singlet-triplet pairs of states for the three orbital configurations of (1s)(3s), (1s)(3p), and (1s)(3d) have been examined in detail in the internal space (r₁,r₂,ϕ₋). The structure of the genuine and conjugate Fermi holes for the (1s)(3s) and (1s)(3p) configurations has shown similar characteristics to those for the respective (1s)(2s) and (1s)(2p) configurations examined in an earlier study. A significantly smaller size of the genuine and conjugate Fermi holes for the (1s)(3d) singlet-triplet pair of states rationalizes the much smaller singlet-triplet energy gap of this pair than those for the (1s)(3s) and (1s)(3p) pairs of states.

Reproductive success and survival are influenced by wealth in human populations. Wealth is transmitted to offsprings and strategies of transmission vary over time and among populations, the main variation being how equally wealth is transmitted to children. Here we propose a model where we simulate both the dynamics of wealth in a population and the evolution of a trait that determines how wealth is transmitted from parents to offspring, in a darwinian context.

In this study, design and kinematic analysis of a crank-slider mechanism for a crank press is studied. The crank-slider mechanism is the commonly applied one as direct and indirect drive alternatives in practice. Since inexpensiveness, flexibility and controllability are getting more and more important in many industrial applications especially in automotive industry, a crank press with servo actuator (servo crank press) is taken as an application. Design and kinematic analysis of representative mechanism is presented with geometrical analysis for the inverse kinematic of the mechanism by using desired motion concept of slider. The mechanism is modelled in MATLAB/Simulink platform. The simulation results are presented herein.

In this paper, we propose a dipole simulation method for two-dimensional potential problems. The proposed method is a modification of the charge simulation method (the method of fundamental solutions), which is a numerical solver for potential problems, and it gives an approximate solution as a superposition of the potentials due to electric dipoles positioned outside the problem region instead of point charges as in the charge simulation method. We find that the proposed method achieves high accuracy under some conditions from a numerical example. Besides, it is advantageous to the charge simulation method in approximating complex analytic functions. We also show the dipole simulation method for two-dimensional potential problems with one-dimensional periodicity.

A quantum measuring device is introduced through a projective operator of any complete set of states that span the Hilbert space. Consequently, even a "bizarre" basis such as a basis of states composed of superpositions between location states, is legitimate despite its incomprehensible interpretation of a particle located in some places simultaneously.

The collapse scenario that lies in the essence of any quantum measuring device, suggests that measurement is actually an interpretation process that translate reality into the predefined concepts determined by the particular selection of the basis of states. The very fact that there are bases that contradict "common sense" suggests that our brain by serving as a measuring and interpreting "device", selects only unique measuring processes. We suggest a procedure of nonlinear recursive maps that dominant an evolution of states toward few selected bases of states.

Flow through a narrow bent channel may induce topological rearrangements in a two-dimensional monodispersed dry liquid foam. We use the Cellular Potts Model to simulate a foam under a variable driving force in order to investigate the strain-rate response from these rearrangements. We observe a set of foams' behaviors ranging from elastic, viscoelastic to fluid regime. Bubble's topological rearrangements are localized and their cumulative rearrangements change linearly with time, thus non avalanches critical behavior is found. The strain-rate affects the rate of topological rearrangements, its dependence on the drag force is nonlinear, obeying a Herschel-Bulkley like relationship below the foam's flow point.

In the present work we consider the inverse problem of identification the spherical cavity of small relative size in the isotropic elastic cylinder. Based on the methods of perturbation theory, analytical formulas for determining the parameters of the cavity have been obtained using information concerning corrections to the natural frequencies. A series of numerical experiments has been carried out.

We study some equations used in the analysis of the materials of the Raman spectrum. Some equations are, phonon lifetime, related to the full width at half maximum (FWHM), the size of the nanoparticles, as explained with the equation of the intensity of Raman Spectrum; the Grüneisen parameter isothermal and isobaric explained by the frequency shift of the Raman scattered light; it is directly related to the structural properties of the material. The frequency shift may be dependent upon the application of temperature, hydrostatic pressure and the composition of the material itself. Furthermore, it is possible to obtain the behavior of anharmonic material using the Raman scattering frequency shift.

The elastic properties and structural stability in ruthenium under pressure are investigated. The analysis is performed in the framework of Landau theory and nonlinear elasticity. For this purpose the definition of effective elastic constants (EC) of n-th (n≥2) order characterizing elastic properties of loaded crystal and the relations between effective EC and corresponding EC of Bragger type for hcp crystals is given. The conditions of hcp lattice stability to the uniform shear strain under the pressure P are expressed in terms of the second order effective EC. The method of effective EC calculations for hcp crystals under hydrostatic pressure is presented. The equation of state and EC of second and third order and phonon dispersion relations in high-symmetry directions in the pressure range of 0 – 600 GPa are calculated in the framework of the density functional theory (DFT) and the density functional perturbation theory (DFPT) respectively. EC are in the good agreement with available experimental data and increase monotonically with pressure, no softening or stability condition violation are observed. Softening of phonon frequencies near the Brillion zone center is also not observed.

Very recently in the work "Simple Iterative Method for Solving Problems for Plates with Partial Internal Supports, Journal of Engineering Mathematics, DOI: 10.1007/s10665-013-9652-7 (in press)", we proposed a numerical method for solving some problems of plates on one and two line partial internal supports (LPIS). In the essence they are problems with strongly mixed boundary conditions for biharmonic equation. Using this method we reduced the problems to a sequence of boundary value problems for the Poisson equation with weakly mixed boundary conditions, which are easily solved numerically. The advantages of the method over other ones were shown.

In this paper we apply the method to plates on internal supports of more complicated configurations. Namely, we consider the case of three LPIS and the case of the cross support. The convergence of the method is established theoretically and its efficiency is confirmed on numerical experiments.

In this paper we show that the classical definition and the associated characterizations of wide-sense Markov (WSM) signals are not valid for improper complex signals. For that, we propose an extension of the concept of WSM to a widely linear (WL) setting and the study of new characterizations. Specifically, we introduce a new class of signals, called widely linear Markov (WLM) signals, and we analyze some of their properties based either on second-order properties or on state-space models from a WL processing standpoint. The study is performed in both the forwards and backwards directions of time. Thus, we provide two forwards and backwards Markovian representations for WLM signals. Finally, different estimation recursive algorithms are obtained for these models.

A Finsler geometric surface model for membranes is studied by using the Monte Carlo simulation technique on connection-fixed triangle lattices with sphere topology. An in-plane three-dimensional unit vector σ is assumed to be the in-plane tilt variable of the surface. The interaction with σ is described by the XY-model Hamiltonian. Since this variable σ is considered as a vector field on the surface, a Finsler metric is defined by using σ. We find that the model has three different phases. They change from the para-magnetic phase to the ferromagnetic and to the glass phases when the strength of the XY interaction increases. Both the para-magnetic and the glass phases are characterized by random configuration of σ; the variable σ randomly fluctuates in the para-magnetic phase while it is randomly frozen in the glass phase. We also find that the surface becomes spherical in both phases. On the contrary, in the ferro-magnetic phase the surface shape becomes tubular or discotic due to the anisotropic bending rigidity and surface tension coefficient, which are dynamically generated by ordered configurations of σ.

This is a preliminary theoretical discussion on the computational requirements of the state of the art smoothed particle hydrodynamics (SPH) from the optics of pattern recognition and artificial intelligence. It is pointed out in the present paper that, when including anisotropy detection to improve resolution on shock layer, SPH is a very peculiar case of unsupervised machine learning. On the other hand, the free particle nature of SPH opens an opportunity for artificial intelligence to study particles as agents acting in a collaborative framework in which the timed outcomes of a fluid simulation forms a large knowledge base, which might be very attractive in computational astrophysics phenomenological problems like self-propagating star formation.

The quantum Hall effect (QHE) and high temperature superconductivity (HTSC) have remarkable common features. They occur only in two-dimensional (2D) solids. The critical temperature T_c of some HTSC exceeds 160K while the room temperature QHE is observed in graphene. The cause of both QHE and HTSC is the phonon exchange attraction. We develop a theoretical model for the QHE in terms of the composite bosons (fermions), each containing an electron and an odd (even) number of fluxons (magnetic flux quanta). The composite particles (boson, fermion) are bound by the phonon exchange attraction. If the Bose-Einstein condensation (BEC) of the composite (c)- bosons occurs, then the system exhibits zero resistivity and the associated Hall conductivity plateau. The Hall conductivity is calculated rigorously without averaging. The mystery of the fractional charge carried by the c-bosons is resolved in our model.

We focus on the simulation of flexible and semiflexible polymer systems using the multicanonical Monte Carlo method where we study their thermodynamic properties and conformational behavior. First, we investigate transition signatures of flexible homopolymer chains where monomers interact through a standard Lennard-Jones potential. In the second time, we introduce a square well potential that produces helical structures. The idea behind the use of those different potentials is to construct a phase diagram where we can characterize the liquid, solid, crystalline and helical phases.

This study deals with numerical solution of a 2D and 3D unsteady flows of a compressible viscous fluid in 2D and 3D channel for low inlet airflow velocity. The unsteadiness of the flow is caused by a prescribed periodic motion of a part of the channel wall, nearly closing the channel during oscillations. The channels shape is a simplified geometry of the glottal space in the human vocal tract. Goal is numerical simulation of flow in the channels which involves attributes of real flow causing acoustic perturbations. The system of Navier-Stokes equations closed with static pressure expression for ideal gas describes the unsteady laminar flow of compressible viscous fluid. The numerical solution is implemented using the finite volume method and the predictor-corrector MacCormack scheme with artificial viscosity using a grid of quadrilateral cells. The unsteady grid of quadrilateral cells is considered in the form of conservation laws using Arbitrary Lagrangian-Eulerian method. The application of developed method for numerical simulations of flow fields in the 2D and 3D channels, acquired from a developed program, are presented for inlet velocity u=4.12 m/s, inlet Reynolds number Re=4481 and the wall motion frequency 100 Hz.

In this paper, the use of Fire Dynamics Simulator (FDS) and its evacuation module, Evac for modelling fire and people evacuation in a road tunnel is illustrated. For given fire scenario and traffic situation in the tunnel, behaviour of individual evacuees as well as groups of evacuees is analyzed in order to demonstrate the impact of fire on people evacuation. Some specific features of the use of FDS+Evac for simulation of people evacuation in case of tunnel fire are also discussed.

Graph model of interdisciplinary connections, and method of calculation quantitative parameters of model have described. The application of quantitative method to content of physics and mathematics has already done in this paper. The hierarchy of mathematical concepts used by the general physics course is established co according to two parameters – the bond strength (frequency of use) and the bond length (duration of use).

In this paper we revise the main features of pseudospin and spin symmetries of the Dirac equation with scalar and vector potentials and mention several of its applications to physical systems. These symmetries have been extensively researched in the last 15 years, especially pseudospin symmetry, mainly in its application in understanding certain nuclear structure features of heavy nuclei. The realization of both symmetries has also been studied using several mean-field scalar and vector potentials. For many classes of potentials, these symmetries allow to have analytical solutions of the Dirac equation which otherwise would not have been possible. We report here some recent results related to anti-fermions, Coulomb and confining potentials.

Neutrino detectors at the accelerator machines of the Intensity Frontier in particle physics are becoming commonplace. As their capabilities are being understood, they seem to have the potential for studies beyond the neutrino oscillations measurements. Besides these primary neutrino physics goals, a number of exotic searches can be done with such detectors in general, and the NOvA detectors that we present here, as a particular example. Specifically, we focus on simulating signatures in NOvA experiment's Near-Detector (300 ton, 900 m from the NuMI target of Fermilab) that correspond to beam-generated new physics states from hidden sectors, dark sectors, axion-like particles, heavy or sterile neutrinos, and heavy photons. As there are no physics generators that can inherently include such states, along with the mainstream production branches, we present here the initial stages of an effort to incorporate these signatures manually in the overall simulation framework of the NOvA experiment. For this, we discuss examples and examine the potential and challenges for detecting such signatures.

A new treatment is presented for land use planning problems by means of extremal optimization in conjunction to cell-based neighborhood local search. Extremal optimization, inspired by self-organized critical models of evolution has been applied mainly to the solution of classical combinatorial optimization problems. Cell-based local search has been employed by the author elsewhere in problems of spatial resource allocation in combination with genetic algorithms and simulated annealing. In this paper it complements extremal optimization in order to enhance its capacity for a spatial optimization problem. The hybrid method thus formed is compared to methods of the literature on a specific characteristic problem. It yields better results both in terms of objective function values and in terms of compactness. The latter is an important quantity for spatial planning. The present treatment yields significant compactness values as emergent results.

The approximation of the normal distribution by means of a chaotic expression is achieved by means of Weierstrass function, where, for a certain set of parameters, the density of the derived recurrence renders good approximation of the bell curve.

In studying the high-temperature plasma physics, the researcher is faced with the need to process large amounts of semi-structured data. Dozens of multi-channel diagnostics, the results of which are multi-million ensembles of time samples of plasma signals, are usually installed at the same time in thermonuclear devices. These samples contain information necessary to understand the mechanisms of relation between plasma macroparameters (plasma density and temperature, plasma current, magnetic field, auxiliary heating power, etc) and plasma microparameters determined by turbulence (energy, spectral composition, amplitude density distribution, etc). The methods of analysis of plasma signals based on the processing of a single time realization of turbulence cannot be used as a basis for comparison with macroparameters and identification of new patterns of plasma containment in a magnetic trap. The main objective of this work is to obtain information about the relationship between the macro- and microparameters of the plasma based on the structuring of the acquired data and its multi-parameter processing using the modern software and hardware.

The evolution of computers, more specifically regarding the increased storage and data processing capacity, allowed the construction of computational tools for the simulation of physical and chemical phenomena. Thus, practical experiments are being replaced, in some cases, by computational ones. In this context, we can highlight models used to simulate different phenomena on atomic scale. The construction of these simulators requires, by developers, the study and definition of accurate and reliable models. This complexity is often reflected in the construction of complex simulators, which simulate a limited group of structures. Such structures are sometimes expressed in a fixed manner using a limited set of geometric shapes. This work proposes a computational tool that aims to generate a set of crystal structures. The proposed tool consists of a) a programming language, which is used to describe the structures using for this purpose their characteristic functions and CSG (Constructive Solid Geometry) operators, and b) a compiler/interpreter that examines the source code written in the proposed language, and generates the objects accordingly. This tool enables the generation of an unrestricted number of structures, which can be incorporated in simulators such as the Monte Carlo Spin Engine, developed by our group at UFJF.

The development of computational systems that mimics the physiological response of organs or even the entire body is a complex task. One of the issues that makes this task extremely complex is the huge computational resources needed to execute the simulations. For this reason, the use of parallel computing is mandatory. In this work, we focus on the simulation of temporal and spatial behaviour of some human innate immune system cells and molecules in a small three-dimensional section of a tissue. To perform this simulation, we use multiple Graphics Processing Units (GPUs) in a shared-memory environment. Despite of high initialization and communication costs imposed by the use of GPUs, the techniques used to implement the HIS simulator have shown to be very effective to achieve this purpose.

This work presents new methods for constructing orthonormal wavelets from certain families of Hardy functions. Inner functions and the corresponding backward shift invariant subspaces are in the core of the structure of these families. The new algorithms focus on the local shape of the wavelets, a property making them especially useful for pattern recognition.

All thermonuclear controlled fusion devices under construction or design have such high performances to require a special care in the dimensioning of various components, specifically from the electromagnetic point of view. To this purpose, it is fundamental to develop models which are both accurate (i.e. able to describe the physical phenomena) and predictive (i.e. useful not only to explain what happens in running experiments, but also to reliably extrapolate to other range of parameters).

The dynamics of fusion plasmas is often conveniently described by Magneto-Hydro-Dynamics (MHD) equations, which predict that some unstable evolution modes may exist. On the other hand, the complexity of the intrinsically 3D model of the interactions between a realistic unstable plasma, the surrounding passive structures (important to guarantee a good MHD stability) and the active conductors (coils) require the numerical solution of challenging electromagnetic problems.

In this work a discrete geometric formulation for eddy-current problems in the frequency domain is developed; the magnetic fields produced by a typical active coil system is calculated in the presence of 3D conductive structures.

In magnetic confinement fusion devices, during abnormal operations (disruptions) the plasma begins to move rapidly towards the vessel wall in a vertical displacement event (VDE), producing plasma current asymmetries, vessel eddy currents and open field line halo currents, each of which can exert potentially damaging forces upon the vessel and in-vessel components. This paper presents a methodology to estimate electromagnetic loads, on three-dimensional conductive structures surrounding the plasma, which arise from the interaction of halo-currents associated to VDEs with a magnetic field of the order of some Tesla needed for plasma confinement. Lorentz forces, calculated by complementary formulations, are used as constraining loads in a linear static structural analysis carried out on a detailed model of the mechanical structures of a representative machine.

Segmentation of anatomical structures from medical image series is an ongoing field of research. Although, organs of interest are three-dimensional in nature, slice-by-slice approaches are widely used in clinical applications because of their ease of integration with the current manual segmentation scheme. To be able to use slice-by-slice techniques effectively, adjacent slice information, which represents likelihood of a region to be the structure of interest, plays critical role. Recent studies focus on using distance transform directly as a feature or to increase the feature values at the vicinity of the search area. This study presents a novel approach by constructing a higher order neural network, the input layer of which receives features together with their multiplications with the distance transform. This allows higher-order interactions between features through the non-linearity introduced by the multiplication. The application of the proposed method to 9 CT datasets for segmentation of the liver shows higher performance than well-known higher order classification neural networks.

The regularization of ill-posed problems has become a useful tool in studying initial value problems that do not adhere to certain desired properties such as continuous dependence of solutions on initial data. Because direct computation of the solution becomes difficult in this situation, many authors have alternatively approximated the solution by the solution of a closely-defined well-posed problem. In this paper, we demonstrate this process of regularization for the backward heat equation with a time-dependent diffusion coefficient, among other nonautonomous ill-posed problems. In the process, we provide two different approximate well-posed models and numerically compare convergence rates of their solutions to a known solution of the original ill-posed problem.

Principal component analysis (PCA) is an important tool in exploring data. The conventional approach to PCA leads to a solution which favours the structures with large variances. This is sensitive to outliers and could obfuscate interesting underlying structures. One of the equivalent definitions of PCA is that it seeks the subspaces that maximize the sum of squared pairwise distances between data projections. This definition opens up more flexibility in the analysis of principal components which is useful in enhancing PCA. In this paper we introduce scales into PCA by maximizing only the sum of pairwise distances between projections for pairs of datapoints with distances within a chosen interval of values [l,u]. The resulting principal component decompositions in Multiscale PCA depend on point (l,u) on the plane and for each point we define projectors onto principal components. Cluster analysis of these projectors reveals the structures in the data at various scales. Each structure is described by the eigenvectors at the medoid point of the cluster which represent the structure. We also use the distortion of projections as a criterion for choosing an appropriate scale especially for data with outliers. This method was tested on both artificial distribution of data and real data. For data with multiscale structures, the method was able to reveal the different structures of the data and also to reduce the effect of outliers in the principal component analysis.

This case study tests the possibility of prediction for 'success' (or 'winner') components of four stock & shares market indices in a time period of three years from 02-Jul-2009 to 29-Jun-2012.We compare their performance ain two time frames: initial frame three months at the beginning (02/06/2009-30/09/2009) and the final three month frame (02/04/2012-29/06/2012).To label the components, average price ratio between two time frames in descending order is computed. The average price ratio is defined as the ratio between the mean prices of the beginning and final time period. The 'winner' components are referred to the top one third of total components in the same order as average price ratio it means the mean price of final time period is relatively higher than the beginning time period. The 'loser' components are referred to the last one third of total components in the same order as they have higher mean prices of beginning time period. We analyse, is there any information about the winner-looser separation in the initial fragments of the daily closing prices log-returns time series.The Leave-One-Out Cross-Validation with k-NN algorithm is applied on the daily log-return of components using a distance and proximity in the experiment. By looking at the error analysis, it shows that for HANGSENG and DAX index, there are clear signs of possibility to evaluate the probability of long-term success. The correlation distance matrix histograms and 2-D/3-D elastic maps generated from ViDaExpert show that the 'winner' components are closer to each other and 'winner'/'loser' components are separable on elastic maps for HANGSENG and DAX index while for the negative possibility indices, there is no sign of separation.

Considering the advantages of the press process as compared to the machining process, the making good utilization of work piece materials and the saving of production time, the Press machine associated with press form tooling is increasingly served for complicated shape parts production. The sheet-extrusion is the most important metal-forming process, which controls the material flow to fulfil the extruded shape. By using this process, the complicated extruded-shape parts could be manufactured without the machining process. Owing to the piping defect, however, the complicated extruded-shape parts are limited in the sheet-extrusion process. In this study, the finite element method (FEM) is used to investigate the piping feature. In addition, a relationship between extruded shape and piping defect is also examined. The laboratory experiments are performed to validate the accuracy of FEM simulation results. Based on the stress distribution and velocity analysis, the relationship between extruded shape and piping defect could be clearly identified. Furthermore, The FEM simulation results show good agreement with the experimental results with reference to the extruded shape and piping defect.

A simple mathematical model is presented for the generation of mass via the spontaneous confinement of elementary particles, e.g. electrons, neutrinos or quarks, in bound rotational states with relativistic particle velocities. In this simple mechanism, which is operative both in chemical and in physical systems, the new mass which is created corresponds to the kinetic energy of the trapped particles. It is shown that the ratio of the new mass created to the initial mass is very small for chemical systems but can be very high in the case of gravitational confinement of neutrinos in rotational states with relativistic particle velocities.

This study proposes the application of fractal descriptors method to the discrimination of microscopy images of plant leaves. Fractal descriptors have demonstrated to be a powerful discriminative method in image analysis, mainly for the discrimination of natural objects. In fact, these descriptors express the spatial arrangement of pixels inside the texture under different scales and such arrangements are directly related to physical properties inherent to the material depicted in the image. Here, we employ the Bouligand-Minkowski descriptors. These are obtained by the dilation of a surface mapping the gray-level texture. The classification of the microscopy images is performed by the well-known Support Vector Machine (SVM) method and we compare the success rate with other literature texture analysis methods. The proposed method achieved a correctness rate of 89%, while the second best solution, the Co-occurrence descriptors, yielded only 78%. This clear advantage of fractal descriptors demonstrates the potential of such approach in the analysis of the plant microscopy images.

Here we compare the Boltzmann-Gibbs-Shannon (standard) with the Tsallis entropy on the pattern recognition and segmentation of colored images obtained by satellites, via "Google Earth". By segmentation we mean particionate an image to locate regions of interest. Here, we discriminate and define an image partition classes according to a training basis. This training basis consists of three pattern classes: aquatic, urban and vegetation regions. Our numerical experiments demonstrate that the Tsallis entropy, used as a feature vector composed of distinct entropic indexes q outperforms the standard entropy. There are several applications of our proposed methodology, once satellite images can be used to monitor migration form rural to urban regions, agricultural activities, oil spreading on the ocean etc.

We demonstrate the reconstruction of f(R) modified gravity theory with late-time accelerated cosmic expansion. A second-order differential equation for Lagrangian density is obtained from the field equation, and is solved as a function of the cosmic scale factor in two cases. First we begin with the case of a wCDM cosmological model, in which a dark-energy equation-of-state parameter w is constant, for simplicity. Next we extend the method to a case in which the parameter w is epoch-dependent and is expressed as the Chevallier-Polarski-Linder parametrization. Thus we can represent Lagrangian density of f(R) modified gravity theory in terms of dark energy parameters.

Given an n-dimensional natural Hamiltonian L on a Riemannian or pseudo-Riemannian manifold, we call "extension" of L the n+1 dimensional Hamiltonian H = ½p²_u + α(u)L + β(u) with new canonically conjugated coordinates (u,p_u). For suitable L, the functions α and β can be chosen depending on any natural number m such that H admits an extra polynomial first integral in the momenta of degree m, explicitly determined in the form of the m-th power of a differential operator applied to a certain function of coordinates and momenta. In particular, if L is maximally superintegrable (MS) then H is MS also. Therefore, the extension procedure allows the creation of new superintegrable systems from old ones. For m=2, the extra first integral generated by the extension procedure determines a second-order symmetry operator of a Laplace-Beltrami quantization of H, modified by taking in account the curvature of the configuration manifold. The extension procedure can be applied to several Hamiltonian systems, including the three-body Calogero and Wolfes systems (without harmonic term), the Tremblay-Turbiner-Winternitz system and n-dimensional anisotropic harmonic oscillators. We propose here a short review of the known results of the theory and some previews of new ones.

A mathematical model for fibrous structures using a direction dependent scaling law is presented. The orientation of fibrous nets (e.g. paper) is analysed with a method based on the curvelet transform. The curvelet-based orientation analysis has been tested successfully on real data from paper samples: the major directions of fibrefibre orientation can apparently be recovered. Similar results are achieved in tests on data simulated by the new model, allowing a comparison with ground truth.

Gaussian-type orbitals (GTOs) are the most common choice of basis functions in calculations of electronic structure of molecules, i.e. for the description of bound electrons. The main advantage of this approach is the analytic form of the multicentre molecular integrals. For the same reason GTOs have been adopted as basis functions for the description of the unbound particle in many ab-initio calculations of electron, positron and laser fields interacting with molecules. However, the accurate description of the unbound particle using GTOs may become very difficult and in some cases numerically unstable. We describe an approach for the representation of the continuum in which the unbound particle is described using a mixed GTO and B-spline basis set in a manner which exploits the best features of these functions. Analytical expressions for the GTO-only molecular integrals allow us to accurately represent the part of the wavefunction close to the target, while the B-splines enable us to represent accurately the wavefunction's tail, corresponding to the unbound particle, over a wide range of kinetic energies. The main challenge posed by this approach is the accurate and rapid numerical evaluation of a large number of mixed BTO/GTO molecular integrals. We propose a scheme for this integral calculation in which the overlap integrals between GTOs and B-spline functions play a central role and demonstrate that they can be calculated rapidly and accurately.

The wave function of a moderately cold atom in a stationary near-resonant standing light wave delocalizes very fast due to wave packet splitting. However, frequency modulation of the field may suppress packet splitting for some atoms having specific velocities in a narrow range. These atoms remain localized in a small space for a long time. We show that modulated field can not only trap, but also cool the atoms. We perform a numerical experiment with a large atomic ensebmble having wide initial velocity and energy distribution. During the experiment, most of atoms leave the wave while trapped atoms have narrow energy distribution

The hybrid Monte Carlo algorithm (HMCA) is applied for Bayesian parameter estimation of the realized stochastic volatility (RSV) model. Using the 2nd order minimum norm integrator (2MNI) for the molecular dynamics (MD) simulation in the HMCA, we find that the 2MNI is more efficient than the conventional leapfrog integrator. We also find that the autocorrelation time of the volatility variables sampled by the HMCA is very short. Thus it is concluded that the HMCA with the 2MNI is an efficient algorithm for parameter estimations of the RSV model.

The work deals with mathematical models of turbulent flow through turbine cascade in 2D and 3D. It is based on the Favre-averaged Navier-Stokes equations with SST or EARSM turbulence models. A two-equation model of transition to turbulence is considered too. The solution is obtained by implicit AUSM finite volume method. The 2D and 3D results are shown flow through the SE1050 cascade including simulation of a range of off-design angles of attack.

The embedding of time series provides a valuable, and sometimes indispensable, tool in order to analyze the dynamical properties of a chaotic system. To this purpose, the choice of the embedding dimension and lag is decisive. The scientific literature describes several methods for selecting the most appropriate parameter pairs. Unfortunately, no conclusive criterion to decide which method – and thus which embedding pair – is the best has been so far devised. A widely employed quantity to compare different methods is the maximum Lyapunov exponent (MLE) because, for chaotic systems that have explicit analytic representations, MLE can be numerically evaluated independently of the embedding dimension and lag. Within this framework, we investigated the dependence on the calculated MLE on the embedding dimension and lag in the case of three dynamical systems that are also widespreadly used as reference systems, namely the Lorenz, Rössler and Mackey-Glass attractors. By also taking into account the statistical fluctuations of the calculated MLE, we propose a new method to assess which systems provide suitable test benches for the comparison of different embedding methods via MLE calculation. For example we found that, despite of its popularity in this scientific context, the Rössler attractor is not a reliable workbench to test the validity of an embedding method.

A mechanical structure supported by nonlinear springs subjected to an external load is considered. If all mechanical parameters of the system were known, the displacement of the system subjected to this load could be easily calculated. If not all of the parameters are known, but the load and the displacement are measured at one location, an inverse problem exists. In the presented problem the nonlinear springs are unknown and have to be determined. At first glance a problem needs to be solved, which is underdetermined due to the number of unknown variables. However, evolutionary computing can be applied to solve this inverse, nonlinear and multimodal problem. Sometimes a prior knowledge exists on certain system properties, which is difficult to implement into analytical or numerical solver. This knowledge can play a decisive role in identifying the system properties and it can be easily included as boundary condition when applying evolutionary algorithm. This article examines how and under what conditions the spring resistances can be identified. The procedure is exemplified at a mechanical system of a pile foundation.

Negative masses arise naturally from dynamic groups, as shown in 1970 by the French mathematician Jean-Marie Souriau. We recall this, based on the coadjoint action of the Poincaré group on its momentum. Negative populations include negative energy photons. If we admit that positive and negative masses cannot interact through virtual photons, they only interact through gravitational force. Two particles whose masses display the same sign attract each other through Newton law. Two particles of opposite signs repel each-other through "anti-Newton" law. Then the two populations tend to separate. If the mass density of the negative material is much larger, it first forms clusters by gravitational instability. Then the positive matter is repelled in the remnant place, shaped like adjoining bubbles, which looks like VLS. To illustrate this scheme, we provide 2D simulation results. In addition this model provides a new insight on the galaxies' birth mechanism.

Hermite Collocation is a high order finite element method for Boundary Value Problems modelling applications in several fields of science and engineering. Application of this integration free numerical solver for the solution of linear BVPs results in a large and sparse general system of algebraic equations, suggesting the usage of an efficient iterative solver especially for realistic simulations. In part I of this work an efficient parallel algorithm of the Schur complement method coupled with Bi-Conjugate Gradient Stabilized (BiCGSTAB) iterative solver has been designed for multicore computing architectures with a Graphics Processing Unit (GPU). In the present work the proposed algorithm has been extended for high performance computing environments consisting of multiprocessor machines with multiple GPUs. Since this is a distributed GPU and shared CPU memory parallel architecture, a hybrid memory treatment is needed for the development of the parallel algorithm. The realization of the algorithm took place on a multiprocessor machine HP SL390 with Tesla M2070 GPUs using the OpenMP and OpenACC standards. Execution time measurements reveal the efficiency of the parallel implementation.

A systematic study of the binding energy of the ground state of a hydrogenic off-axis donor in a cylindrical quantum wire containing two quantum wells in a section of the tube layer is calculated in the presence of a uniform magnetic field applied parallel to the wire axis with different potential shape. We express the wave function as a product of combinations of s and p subband wave functions and an envelope function that depends only on the electron-ion separation . By using the variational principle we derive a differential equation for the envelope function, which we solve numerically. Two peaks in the curves for the dependence of the ground-state binding energies on the donor distance from the axis are presented and it is shown that the increasing the magnetic field increasing the binding energy while the impurity is located in the QW1, whereas the opposite occurs when the impurity is located in the QW2.

We report on microtube with double quantum well and large radius of curvature. Method for calculating the ground-state energy of light hole exciton and density of states confined in a square potential model that consist of a narrow well, which is produced by a symmetrical structure. The exciton trial function is taken as a product of the ground state wave functions of both the unbound electron and hole in the heterostructure, with an arbitrary correlation function that depends only on electron-hole separation. A renormalized Schrödinger equation for the correlation function is derived and coincides with the corresponding equation for a hydrogen atom in an effective and space-isotropic homogeneous. The binding energy of the ground state to an exciton in this heterostructure, the contribution to the energy given by the sublevels and the density of states is determined as a function of the width of the well, the aluminum concentration and confinement potential profile is obtained by solving the equation calculated by the variational model proposed.

Considering the limited availability of laboratories for physics teaching and the difficulties this causes in the learning of school students in Santa Marta Colombia, we have developed software in order to generate greater student interaction with the phenomena physical and improve their understanding. Thereby, this system has been proposed in an architecture Model/View- View- Model (MVVM), sharing the benefits of MVC. Basically, this pattern consists of 3 parts: The Model, that is responsible for business logic related. The View, which is the part with which we are most familiar and the user sees. Its role is to display data to the user and allowing manipulation of the data of the application. The ViewModel, which is the middle part of the Model and the View (analogous to the Controller in the MVC pattern), as well as being responsible for implementing the behavior of the view to respond to user actions and expose data model in a way that is easy to use links to data in the view. .NET Framework 4.0 and editing package Silverlight 4 and 5 are the main requirements needed for the deployment of physical simulations that are hosted in the web application and a web browser (Internet Explorer, Mozilla Firefox or Chrome). The implementation of this innovative application in educational institutions has shown that students improved their contextualization of physical phenomena.

The Nosé-Hoover scheme demonstrates that molecular dynamics simulations can be used to calculate the properties of systems at constant temperature (i.e. canonical ensemble averages). There is interest in deterministic generalizations of Nosé-Hoover dynamics which are ergodic even for simple systems like the harmonic oscillator. Prompted by parallels with studies of the Duffing oscillator within control theory, we have investigated a non-autonomous version of the Nosé-Hoover oscillator in which the temperature is replaced by a weakly time-dependent function. This function is chosen so that its average over time coincides with the temperature desired. Calculations are facilitated by graphical programming with a MATLAB-Simulink platform. A time series analysis of our simple non-autonomous system yields the position and momentum distributions expected for the harmonic oscillator.

The fundamental result, obtained by Dirac, that the dynamical system, which consists of the ensemble of identical bosons is equivalent to the dynamical system, which consists of the ensemble of oscillators, was used to show, that the presence of scalar charge function ρ(, t) to be peer force characteristic of electromagnetic (EM) field along with vector force characteristics (,t), (,t), that was established earlier, agrees with charge neutrality of photons. The simplest analogue in its mathematical description in the physics of condensed matter is the chain of bosonic (spin S = 1) carbon atoms in trans-polyacetylene. It has been shown, that neutral photons are topological relativistic solitons with nonzero spin value, which is equal to ½ instead of prevalent viewpoint, that the photons possess by spin S = 1. Naturally, they have nonzero size, that is, they cannot be considered to be point objects. At the same time, the main excitations in so called "doped" rest massless "boson-atomic" structure of EM-field will be charged spinless EM-solitons. It seems to be reasonable to suggest, that "doping" can be effective by propagation of EM-field in the medium like to rain-clouds, although detailed mechanism has to be additionally studied.

The representation of photons to be the result of spin-charge separation effect in rest massless "boson-atomic" structure of EM-field makes substantially more clear the nature of corpuscular-wave dualism.

This study aims to subjectively detect and classify similar gestures using a red-green-blue-depth camera. Human gesture recognition is one of the crucial components for realizing natural user interfaces (NUIs) using computers and machines. The quality of the NUI highly depends on the robustness of the achieved gesture recognition. We, therefore, propose a gesture classification method using singular spectrum transformation. Using this method, we can robustly classify gestures and behavior.

Telematics form an important technology enabler for intelligent transportation systems. By deploying on-board diagnostic devices, the signatures of vehicle vibration along with its location and time are recorded. Detailed analyses of the collected signatures offer deep insights into the state of the objects under study. Towards that objective, we carried out experiments by deploying telematics device in one of the office bus that ferries employees to office and back. Data is being collected from 3-axis accelerometer, GPS, speed and the time for all the journeys. In this paper, we present initial results of the above exercise by applying statistical methods to derive information through systematic analysis of the data collected over four months. It is demonstrated that the higher order derivative of the measured Z axis acceleration samples display the properties Weibull distribution when the time axis is replaced by the amplitude of such processed acceleration data. Such an observation offers us a method to predict future behaviour where deviations from prediction are classified as context-based aberrations or progressive degradation of the system. In addition we capture the relationship between speed of the vehicle and median of the jerk energy samples using regression analysis. Such results offer an opportunity to develop a robust method to model road-vehicle interaction thereby enabling us to predict such like driving behaviour and condition based maintenance etc.

Investigations of superheavy elements (SHE) have received much attention in the last two decades, due to the successful syntheses of SHE. In particular, α-decay of SHEs has a great importance because most synthesized SHE have a-decay and the experimentalists have evaluated the theoretical predictions of the a-decay half-life during the experimental design. Because of this, the correct prediction of α-decay half-life is important to investigate superheavy nuclei as well as heavy nuclei. In this work, artificial neural networks (ANN) have been employed on experimental a-decay half-lives of superheavy nuclei. Statistical modeling of a-decay half-life of superheavy nuclei have been found as to be successful.

Constrained Hartree-Fock-Bogoliubov theory with SLy5 Skyrme force has been applied for even-even ^142-164Nd isotopes to investigate the structural evolution of Nd isotopic chain. In this work, ground-state energies and charge radii of Nd isotopes have been carried out as in good agreement with the experimental data. The systematic investigation of ground-state shape evolution between spherical U(5) and axially deformed SU(3) for ^142-164Nd has been studied by using potential energy curves.

We study both the short term and long term effects of solar activity on the large transformers (150kV and 400kV) of the Greek national electric grid. We use data analysis and various analytic and statistical methods and models. Contrary to the common belief in PPC Greece, we see that there are considerable both short term (immediate) and long term effects of solar activity onto large transformers in a mid-latitude country like Greece. Our results can be summarized as follows: For the short term effects: During 1989-2010 there were 43 "stormy days" (namely days with for example Ap ≥ 100) and we had 19 failures occurring during a stormy day plus or minus 3 days and 51 failures occurring during a stormy day plus or minus 7 days. All these failures can be directly related to Geomagnetically Induced Currents (GIC's). Explicit cases are presented. For the long term effects we have two main results:

The maximum number of transformer failures occur 3-4 years after the maximum of solar activity.

There is statistical correlation between solar activity expressed using various newly defined long term solar activity indices and the annual number of transformer failures. These new long term solar activity indices were defined using both local (from geomagnetic stations in Greece) and global (planetary averages) geomagnetic data. Applying both linear and non-linear statistical regression we compute the regression equations and the corresponding coefficients of determination.

There are many types of respiratory infectious diseases caused by germs, virus, mycetes and parasites. Researchers recently have tried to develop mathematical models to predict the epidemic of infectious diseases. However, with the development of ground transportation system in modern society, the spread of infectious diseases became faster and more complicated in terms of the speed and the pathways. The route of infectious diseases during Vancouver Olympics was predicted based on the Susceptible-Infectious-Recovered (SIR) model. In this model only the air traffic as an essential factor for the intercity migration of infectious diseases was involved. Here, we propose a multi-city transmission model to predict the infection route during 2018 Winter Olympics in Korea based on the pre-existing SIR model. Various types of transportation system such as a train, a car, a bus, and an airplane for the interpersonal contact in both inter- and intra-city are considered. Simulation is performed with assumptions and scenarios based on realistic factors including demographic, transportation and diseases data in Korea. Finally, we analyze an economic profit and loss caused by the variation of the number of tourists during the Olympics.

The water self-diffusion in the root segments of winter wheat plantlet after their cutting off from the intact plants during continued "adaptive aging" was investigated by PGSE technique. The diffusion decay of the stimulated echo relative amplitude under the diffusion times 10 ms, 155 ms, 350 ms may be described by the sum of three exponents. Strongly marked correlated dependences of diffusion coefficients and population of the diffusion decay components on the sample lifetime have been revealed. These dependences may be caused by the change of diffusion direction of water molecules running through the tonoplast aquaporin channels in the different cell compartments. This change of direction seems to be the important mechanism of the cell water homeostasis maintenance and it is considered as the part of the general stress roots reaction.

Quality of service (QoS) for internet traffic management requires good traffic models and good estimation of sharing network resource.

A link of a network processes all traffic and it is designed with certain capacity C and buffer size B.

A Generalized Markov Fluid model (GMFM), introduced by Marrón (2011), is assumed for the sources because describes in a versatile way the traffic, allows estimation based on traffic traces, and also consistent effective bandwidth estimation can be done.

QoS, interpreted as buffer overflow probability, can be estimated for GMFM through the effective bandwidth estimation and solving the optimization problem presented in Courcoubetis (2002), the so call inf-sup formulas.

In this work we implement a code to solve the inf-sup problem and other optimization related with it, that allow us to do traffic engineering in links of data networks to calculate both, minimum capacity required when QoS and buffer size are given or minimum buffer size required when QoS and capacity are given.

This work deals with the numerical solution of viscous and viscoelastic fluids flow. The governing system of equations is based on the system of balance laws for mass and momentum for incompressible laminar fluids. Different models for the stress tensor are considered. For viscous fluids flow Newtonian model is used. For the describing of the behaviour of the mixture of viscous and viscoelastic fluids Oldroyd-B model is used. Numerical solution of the described models is based on cell-centered finite volume method in conjunction with artificial compressibility method. For time integration an explicit multistage Runge-Kutta scheme is used. In the case of unsteady computation dual-time stepping method is considered. The principle of dual-time stepping method is following. The artificial time is introduced and the artificial compressibility method in the artificial time is applied.

Saltwater intrusion in freshwater aquifers is a problem of increasing significance in areas nearby the coastline. Apart from natural disastrous phenomena, such as earthquakes or floods, intense pumping human activities over the aquifer areas may change the chemical composition of the freshwater aquifer. Working towards the direction of real time management of freshwater pumping from coastal aquifers, we have considered the deployment of the stochastic optimization Algorithm of Pattern Extraction (ALOPEX), coupled with several penalty strategies that produce convenient management policies. The present study, which further extents recently derived results, considers the analytical solution of a classical model for underground flow and the ALOPEX stochastic optimization technique to produce an efficient approach for pumping management over coastal aquifers. Numerical experimentation also includes a case study at Vathi area on the Greek island of Kalymnos, to compare with known results in the literature as well as to demonstrate different management strategies.

Proposed and studied in a multivariate discrete probability model of distribution of processes distortion of radiation from remote sensing data. Introduce the concept of the most appropriate evaluation of the set of unbiased, which has good asymptotic properties.

Several interesting phenomena have been observed simulating two-dimensional decaying turbulence in bounded domains. In this paper an overview is given about our observations obtained by simulating freely decaying turbulence in different regular polygon shaped containers with no-slip walls. For these simulations the lattice Boltzmann method has been used as a numerical approach. The initial Reynolds number based on the container dimension was in the order of 1000. The initial condition was the same in each simulation, therefore, we were able to compare the effect of geometrical constraints on the evolution of relevant physical quantities such as the kinetic energy and the enstrophy.

The battery sustainable time has been an active research topic recently for the development of battery powered embedded products such as tablets and smart phones, which are determined by the battery capacity and power consumption. Despite numerous efforts on the improvement of battery capacity in the field of material engineering, the power consumption also plays an important role and easier to ameliorate in delivering a desirable user-experience, especially considering the moderate advancement on batteries for decades. In this study, a new Top-Down modelling method, User-Experience-Oriented Battery Powered Embedded System Design Paradigm, is proposed to estimate the target average power consumption, to guide the hardware and software design, and eventually to approach the theoretical lowest power consumption that the application is still able to provide the full functionality. Starting from the 10-hour sustainable time standard, average working current is defined with battery design capacity and set as a target. Then an implementation is illustrated from both hardware perspective, which is summarized as Auto-Gating power management, and from software perspective, which introduces a new algorithm, SleepVote, to guide the system task design and scheduling.

Based on a detailed analysis of explosive electron emission in high-current electronic devices, we formulate a system of equations that describes the expansion of the cathode plasma and the generation of high-current electron beams. The system underlies the numerical algorithm for the hybrid code which enables simulating the charged particles' dynamics in high-current vircators with open resonators. Using the Gabor-Morlet transform, we perform the time-frequency analysis of vircator radiation.

Diffusion magnetic resonance imaging (dMRI) probes the diffusion characteristics of a sample via the application of magnetic field gradient pulses. The dMRI signal from a heterogeneous sample includes the water proton magnetization from all spatial positions in a voxel. If the voxel consists of different diffusion compartments with weak exchange, while the duration of the diffusion-encoding gradient pulses is short compared to the diffusion time (the narrow pulse approximation), the dMRI signal can be approximated by the Karger model. A new macroscopic ODE model for the dMRI signal was recently derived mathematically from the microscopic multiple compartments Bloch-Torrey partial differential equation (PDE) without the narrow pulse restriction. We illustrate by numerical simulations that this ODE model accurately approximates the dMRI signal in a domain containing spherical cells of various sizes, and show preliminary results on solving the inverse problem to estimate the cellular volume fraction and surface area.

We develop a mathematical model to describe the system where a dilute granular flow is deflected by an oblique smooth wall. Both particles in the granular flow and the oblique wall experience inelastic collisions with other particles. An analytical solution for the mean force experienced by the wall is obtained through the derivation based on the mathematical model and probability theory. Our theory shows that large angle between the wall and the granular flow may decrease the force experienced by the wall. This is opposite to one's intuition that large deflected angle implies large force. It is probable particle collisions and scattering after the deflection that prevent the wall from experiencing a further strong impact, thus the wall experience less force.

In (photo) electrochemical oscillations, the discretization of phase oscillators leads to a sequence of time dependent oscillator density functions which describe the passing of the oscillators through their minimum at each cycle. Two consecutive oscillator density functions are connected by a Markov process represented by a linear integral equation of second order which is homogeneous in the case of sustained oscillations. The kernel of the integral equation is a normalized Greens Function and represents the probability density for the periods of the oscillators. Both together, the oscillator density function and the two-dimensional probability density for the periods of the oscillators define a random walk. The relation of the model to the holographic principle is discussed briefly. Further, a detailed analysis of a kernel of the integral equation leads to a frequency distribution g for the period length. Additionally, it is possible to determine the energy E in dependence on the period length from the electrochemical process. The product g E shows qualitatively the same behaviour as the radiation of a black body, indicating that the discretization of phase oscillators, when represented by phase space analysis, show an analogy to quantum processes.

Phononic crystal is a structured media with periodic modulation of its physical properties that influences the propagation of elastic waves and leads to a peculiar behaviour, for instance the phononic band gap effect by which elastic waves cannot propagate in certain frequency ranges. The formulation of the problem leads to a second order partial differential equation with periodic coefficients; different methods exist to determine the structure of the eigenmodes propagating in the material, both in the real or Fourier domain. Brillouin explains the periodicity of the band structure as a direct result of the discretization of the crystal in the real domain. Extending the Brillouin vision, we introduce digital signal processing tools developed in the frame of distribution functions theory. These tools associate physical meaning to mathematical expressions and reveal the correspondence between real and Fourier domains whatever is the physical domain under consideration. We present an illustrative practical example concerning two dimensions phononic crystals and highlight the appreciable shortcuts brought by the method and the benefits for physical interpretation.

In this paper we report some recent progresses and open problems in the determination of the first quantum correction at strong coupling of the dressing phases appearing in the Bethe Ansatz equation which have been conjectured to describe the spectrum of string theory on the AdS₃ × S³ × T⁴ background.

Recent progress which relates non-abelian T-duality of N = 1 SuGra solutions to the powerful techniques of Generalised geometry is reviewed. It is shown that SU(3) structure solutions are mapped to SU(2) structures and the transformation rule of the corresponding pure spinors is presented. This constitutes an important step on the road towards the utility of the duality within holography, showing for example, how smeared sources must transform and so how to add flavour to the T-duals.

We consider anisotropic gravity at the conformal point of the kinetic term of the Hořava Gravity. This value is protected under quantum corrections by the constraints of the theory. The symmetry of the z = 3 interacting terms, z being the time scale, which ensure the renormalizability of the theory is softly broken by z = 1 interacting terms. We show that the resulting theory has the same number of physical degrees of freedom as General Relativity. Moreover the linearized theory around the Minkowski solution is exactly equivalent to General Relativity. We also study the spherically symmetric solutions to the fields equations. We find a close expression for the solutions. It terms out that the solutions are structurally stable from the right and unstable from the left around the value of the coupling constant corresponding to the Schwarzchild solution of General Relativity.

Here we present a mathematical model of binocular vision that maps a visible physical world to a subjective perception of it. The subjective space is a set of 4-D vectors whose components are outputs of four monocular neurons from each of the two eyes. Monocular neurons have one of the four types of concentric receptive fields with Gabor-like weighting coefficients. Next this vector representation of binocular vision is implemented as a pool of neurons where each of them is selective to the object's particular location in a 3-D visual space. Formally each point of the visual space is being projected onto a 4-D sphere. Proposed model allows determination of subjective distances in depth and direction, provides computational means for determination of Panum's area and explains diplopia and allelotropia.

In vitro production has been employed in bovine embryos and quantification of lipids is fundamental to understand the metabolism of these embryos. This paper presents a unsupervised segmentation method for histological images of bovine embryos. In this method, the anisotropic filter was used in the differents RGB components. After pre-processing step, the thresholding technique based on maximum entropy was applied to separate lipid droplets in the histological slides in different stages: early cleavage, morula and blastocyst. In the postprocessing step, false positives are removed using the connected components technique that identify regions with excess of dye near pellucid zone. The proposed segmentation method was applied in 30 histological images of bovine embryos. Experiments were performed with the images and statistical measures of sensitivity, specificity and accuracy were calculated based on reference images (gold standard). The value of accuracy of the proposed method was 96% with standard deviation of 3%.

Collective behavior is a fascinating phenomenon and ubiquitous in nature. A large variety of complex dynamic structures from swarming to turbulence arise in active particle systems. In recent investigations a set of minimal continuum equations was proposed to model mesoscale bacterial turbulence. Numerical solutions are validated with experimental data of Bacillus subtilis bacteria. In this short paper we present a recently used pseudo-spectral operator splitting method that directly solves the nonlinear equations in the turbulent regime. In two and three spatial dimensions we show the resulting typical velocity and vorticity fields as well as energy spectra to highlight the strong difference between turbulence in ordinary fluids and in bacterial suspensions.

This paper presents a comparison of two methods for features extraction of mammograms based in completed local binary pattern (CLBP) and wavelet transform. In first part, CLBP was applied in digitized mammograms. In second part, we applied CLBP in the sub-bands obtained from the wavelet multi-resolution representation of the mammographies. In this study, we evaluated the CLBP in the image in the spatial domain and in the sub-bands obtained with wavelet transform. Then, the statistical technique of variance analysis (ANOVA) was used to reduce the number of features. Finally, the classifier Support Vector Machine (SVM) was applied in the samples. The proposed methods were tested on 720 mammographies which 240 was diagnosed as normal samples, 240 as benign lesion and 240 as malign lesion. The images were obtained randomly of the Digital Database for Screening Mammography (DDSM). The system effectiveness was evaluated using the area under the ROC curve (AUC). The experiments demonstrate that the textural feature extraction of the multi-resolution representation was more relevant with value of AUC=1.0. In our experiments, CLBP in the spatial domain resulted in value of AUC=0.89. The proposed method demonstrated promising results in the classification of different classes of mammographic lesions.

PET imaging is an important nuclear medicine modality that measures in vivo distribution of imaging agents labeled with positron-emitting radionuclides. Image reconstruction is an essential component in tomographic medical imaging. In this study, we present the mathematical formulation and an improved numerical implementation of an analytic, 2D, reconstruction method called SRT, Spline Reconstruction Technique. This technique is based on the numerical evaluation of the Hilbert transform of the sinogram via an approximation in terms of 'custom made' cubic splines. It also imposes sinogram thresholding which restricts reconstruction only within object pixels. Furthermore, by utilizing certain symmetries it achieves a reconstruction time similar to that of FBP. We have implemented SRT in the software library called STIR and have evaluated this method using simulated PET data. We present reconstructed images from several phantoms. Sinograms have been generated at various Poison noise levels and 20 realizations of noise have been created at each level. In addition to visual comparisons of the reconstructed images, the contrast has been determined as a function of noise level. Further analysis includes the creation of line profiles when necessary, to determine resolution. Numerical simulations suggest that the SRT algorithm produces fast and accurate reconstructions at realistic noise levels. The contrast is over 95% in all phantoms examined and is independent of noise level.

We have developed a numerical model that simulates the growth of small avascular solid tumors. At its core lies a set of partial differential equations that describe diffusion processes as well as transport and reaction mechanisms of a selected number of nutrients. Although the model relies on a restricted subset of molecular pathways, it compares well with experiments, and its emergent properties have recently led us to uncover a metabolic scaling law that stresses the common mechanisms that drive tumor growth. Now we plan to expand the biochemical model at the basis of the simulator to extend its reach. However, the introduction of additional molecular pathways requires an extensive revision of the reaction-diffusion part of the C++ code to make it more modular and to boost performance. To this end, we developed a novel computational abstract model where the individual molecular species represent the basic computational building blocks. Using a simple two-dimensional toy model to benchmark the new code, we find that the new implementation produces a more modular code without affecting performance. Preliminary results also show that a factor 2 speedup can be achieved with OpenMP multithreading, and other very preliminary results indicate that at least an order-of-magnitude speedup can be obtained using an NVidia Fermi GPU with CUDA code.

Mackerel is an infravalored fish captured by European fishing vessels. A manner to add value to this specie can be achieved by trying to classify it attending to its sex. Colour measurements were performed on Mackerel females and males (fresh and defrozen) extracted gonads to obtain differences between sexes. Several linear and non linear classifiers such as Support Vector Machines (SVM), k Nearest Neighbors (k-NN) or Diagonal Linear Discriminant Analysis (DLDA) can been applied to this problem. However, theyare usually based on Euclidean distances that fail to reflect accurately the sample proximities. Classifiers based on non-Euclidean dissimilarities misclassify a different set of patterns. We combine different kind of dissimilarity based classifiers. The diversity is induced considering a set of complementary dissimilarities for each model. The experimental results suggest that our algorithm helps to improve classifiers based on a single dissimilarity.

The Finite Element Method (FEM) is a way of numerical solution applied in different areas, as simulations used in studies to improve cardiac ablation procedures. For this purpose, the meshes should have the same size and histological features of the focused structures. Some methods and tools used to generate tetrahedral meshes are limited mainly by the use conditions. In this paper, the integration of Open Source Softwares is presented as an alternative to solid modeling and automatic mesh generation. To demonstrate its efficiency, the cardiac structures were considered as a first application context: atriums, ventricles, valves, arteries and pericardium. The proposed method is feasible to obtain refined meshes in an acceptable time and with the required quality for simulations using FEM.

Several radiobiological models mimic the biologic effect of one single radiation dose on a living tissue. However, the actual fractionated radiotherapy requires accounting for a new magnitude, i.e., time. Here, we explore the biological consequences posed by the mathematical prolongation of a previous single radiation model to fractionated treatment. The survival fraction is obtained, together with the equivalent physical dose, in terms of a time dependent factor (similar to a repair coefficient) describing the tissue trend to recovering its radioresistance. The model describes how dose fractions add up to obtain the equivalent dose and how the repair coefficient poses a limit to reach an equivalent dose equal to the critical one that would completely annihilate the tumor. On the other hand, the surrounding healthy tissue is a limiting factor to treatment planning. This tissue has its own repair coefficient and thus should limit the equivalent dose of a treatment. Depending on the repair coefficient and the critical dose of each tissue, unexpected results (failure to fully remove the tumor) can be obtained. To illustrate these results and predictions, some realistic example calculations will be performed using parameter values within actual clinical ranges. In conclusion, the model warns about treatment limitations and proposes ways to overcome them.

Fisher's equation has been widely used to model the biological invasion of single-species communities in homogeneous one dimensional habitats. In this study we develop high order numerical methods to accurately capture the spatiotemporal dynamics of the generalized Fisher equation, a nonlinear reaction-diffusion equation characterized by density dependent non-linear diffusion. Working towards this direction we consider strong stability preserving Runge-Kutta (RK) temporal discretization schemes coupled with the Hermite cubic Collocation (HC) spatial discretization method. We investigate their convergence and stability properties to reveal efficient HC-RK pairs for the numerical treatment of the generalized Fisher equation. The Hadamard product is used to characterize the collocation discretized non linear equation terms as a first step for the treatment of generalized systems of relevant equations. Numerical experimentation is included to demonstrate the performance of the methods.

We report a theoretical/computational approach for modeling the current-voltage characteristics of sensing proteins. The modeling is applied to a couple of transmembrane proteins, bacteriorhodopsin and proteorhodopsin, sensitive to visible light and promising biomaterials for the development of a new generation of photo-transducers. The agreement between theory and experiments sheds new light on the microscopic interpretation of charge transfer in proteins and biological materials in general.

One out of four dogs will develop cancer in their lifetime and 20% of those will be lymphoma cases. PetScreen developed a lymphoma blood test using serum samples collected from several veterinary practices. The samples were fractionated and analysed by mass spectrometry. Two protein peaks, with the highest diagnostic power, were selected and further identified as acute phase proteins, C-Reactive Protein and Haptoglobin. Data mining methods were then applied to the collected data for the development of an online computer-assisted veterinary diagnostic tool. The generated software can be used as a diagnostic, monitoring and screening tool. Initially, the diagnosis of lymphoma was formulated as a classification problem and then later refined as a lymphoma risk estimation. Three methods, decision trees, kNN and probability density evaluation, were used for classification and risk estimation and several preprocessing approaches were implemented to create the diagnostic system. For the differential diagnosis the best solution gave a sensitivity and specificity of 83.5% and 77%, respectively (using three input features, CRP, Haptoglobin and standard clinical symptom). For the screening task, the decision tree method provided the best result, with sensitivity and specificity of 81.4% and >99%, respectively (using the same input features). Furthermore, the development and application of new techniques for the generation of risk maps allowed their user-friendly visualization.

The role of Magnetic Resonance Imaging (MRI) as an alternative protocol for screening of breast cancer has been intensively investigated during the past decade. Preliminary research results have indicated that gadolinium-agent administrative MRI scans may reveal the nature of breast lesions by analyzing the contrast-agent's uptake time. In this study, we attempt to deduce the same conclusion, however, from a different perspective by investigating, using image processing, the vascular network of the breast at two different time intervals following the administration of gadolinium. Twenty cases obtained from a 3.0-T MRI system (SIGNA HDx; GE Healthcare) were included in the study. A new modification of the Seeded Region Growing (SRG) algorithm was used to segment vessels from surrounding background. Delineated vessels were investigated by means of their topology, morphology and texture. Results have shown that it is possible to estimate the nature of the lesions with approximately 94.4% accuracy, thus, it may be claimed that the breast vascular network does encodes useful, patterned, information, which can be used for characterizing breast lesions.

The aim of this study was to design a pattern recognition system for assisting the diagnosis of breast lesions, using image information from Ultrasound (US) and Digital Mammography (DM) imaging modalities. State-of-art computer technology was employed based on commercial Graphics Processing Unit (GPU) cards and parallel programming. An experienced radiologist outlined breast lesions on both US and DM images from 59 patients employing a custom designed computer software application. Textural features were extracted from each lesion and were used to design the pattern recognition system. Several classifiers were tested for highest performance in discriminating benign from malignant lesions. Classifiers were also combined into ensemble schemes for further improvement of the system's classification accuracy. Following the pattern recognition system optimization, the final system was designed employing the Probabilistic Neural Network classifier (PNN) on the GPU card (GeForce 580GTX) using CUDA programming framework and C++ programming language. The use of such state-of-art technology renders the system capable of redesigning itself on site once additional verified US and DM data are collected. Mixture of US and DM features optimized performance with over 90% accuracy in correctly classifying the lesions.

Hyperthermia has been widely used in cancer treatment to destroy tumors. The main idea of the hyperthermia is to heat a specific region like a tumor so that above a threshold temperature the tumor cells are destroyed. This can be accomplished by many heat supply techniques and the use of magnetic nanoparticles that generate heat when an alternating magnetic field is applied has emerged as a promise technique. In the present paper, the Pennes bioheat transfer equation is adopted to model the thermal tumor ablation in the context of magnetic nanoparticles. Numerical simulations are carried out considering different injection sites for the nanoparticles in an attempt to achieve better hyperthermia conditions. Explicit finite difference method is employed to solve the equations. However, a large amount of computation is required for this purpose. Therefore, this work also presents an initial attempt to improve performance using OpenMP, a parallel programming API. Experimental results were quite encouraging: speedups around 35 were obtained on a 64-core machine.

The aim of the present study was to propose a comprehensive method for PET scanners image quality assessment, by the simulation of a thin layer chromatography (TLC) flood source with a previous validated Monte-Carlo (MC) model. The model was developed by using the GATE MC package and reconstructed images were obtained using the STIR software, with cluster computing. The PET scanner simulated was the GE Discovery-ST. The TLC source was immersed in 18F-FDG bath solution (1MBq) in order to assess image quality. The influence of different scintillating crystals on PET scanner's image quality, in terms of the MTF, the NNPS and the DQE, was investigated. Images were reconstructed by the commonly used FBP2D, FPB3DRP and the OSMAPOSL (15 subsets, 3 iterations) reprojection algorithms. The PET scanner configuration, incorporating LuAP crystals, provided the optimum MTF values in both 2D and 3DFBP whereas the corresponding configuration with BGO crystals was found with the higher MTF values after OSMAPOSL. The scanner incorporating BGO crystals were also found with the lowest noise levels and the highest DQE values after all image reconstruction algorithms. The plane source can be also useful for the experimental image quality assessment of PET and SPECT scanners in clinical practice.

Biological models of an apoptotic process are studied using models describing a system of differential equations derived from reaction kinetics information. The mathematical model is re-formulated in a state-space robust control theory framework where parametric and dynamic uncertainty can be modelled to account for variations naturally occurring in biological processes. We propose to handle the nonlinearities using neural networks.

We discuss the modelling of dielectric responses of amorphous biological samples. Such samples are commonly encountered in impedance spectroscopy studies as well as in UV, IR, optical and THz transient spectroscopy experiments and in pump-probe studies. In many occasions, the samples may display quenched absorption bands. A systems identification framework may be developed to provide parsimonious representations of such responses. To achieve this, it is appropriate to augment the standard models found in the identification literature to incorporate fractional order dynamics. Extensions of models using the forward shift operator, state space models as well as their non-linear Hammerstein-Wiener counterpart models are highlighted. We also discuss the need to extend the theory of electromagnetically excited networks which can account for fractional order behaviour in the non-linear regime by incorporating nonlinear elements to account for the observed non-linearities. The proposed approach leads to the development of a range of new chemometrics tools for biomedical data analysis and classification.

This paper discusses ECG signal classification after parametrizing the ECG waveforms in the wavelet domain. Signal decomposition using perfect reconstruction quadrature mirror filter banks can provide a very parsimonious representation of ECG signals. In the current work, the filter parameters are adjusted by a numerical optimization algorithm in order to minimize a cost function associated to the filter cut-off sharpness. The goal consists of achieving a better compromise between frequency selectivity and time resolution at each decomposition level than standard orthogonal filter banks such as those of the Daubechies and Coiflet families. Our aim is to optimally decompose the signals in the wavelet domain so that they can be subsequently used as inputs for training to a neural network classifier.

Motivated by proliferation-diffusion mathematical models for studying highly diffusive brain tumors, that also take into account the heterogeneity of the brain tissue, in the present work we consider a multi-domain linear reaction-diffusion equation with a discontinuous diffusion coefficient. For the solution of the problem at hand we implement Fokas transform method by directly following, and extending in this way, our recent work for a white-gray-white matter brain model pertaining to high grade gliomas. Fokas's novel approach for the solution of linear PDE problems, yields novel integral representations of the solution in the complex plane that, for appropriately chosen integration contours, decay exponentially fast and converge uniformly at the boundaries. Combining these method-inherent advantages with simple numerical quadrature rules, we produce an efficient method, with fast decaying error properties, for the solution of the discontinuous reaction-diffusion problem.

The aim of the present study was to implement a pattern recognition system for the discrimination of healthy from malignant prostate tumors from proteomic Mass Spectroscopy (MS) samples and to identify m/z intervals of potential biomarkers associated with prostate cancer. One hundred and six MS-spectra were studied in total. Sixty three spectra corresponded to healthy cases (PSA < 1) and forty three spectra were cancerous (PSA > 10). The MS-spectra are publicly available from the NCI Clinical Proteomics Database. The pre-processing comprised the steps: denoising, normalization, peak extraction and peak alignment. Due to the enormous number of features that rose from MS-spectra as informative peaks, and in order to secure optimum system design, the classification task was performed by programming in parallel the multiprocessors of an nVIDIA GPU card, using the CUDA framework. The proposed system achieved 98.1% accuracy. The identified m/z intervals displayed significant statistical differences between the two classes and were found to possess adequate discriminatory power in characterizing prostate samples, when employed in the design of the classification system. Those intervals should be further investigated since they might lead to the identification of potential new biomarkers for prostate cancer.

Within the field of systems biology, revealing the control systems functioning during embryogenesis is an important task. To clarify the mechanisms controlling sequential events, the relationships between various factors and the expression of specific genes should be determined. In this study, we applied a method based on Structural Equation Modeling (SEM), combined with factor analysis. SEM can include the latent variables within the constructed model and infer the relationships among the latent and observed variables, as a network model. We improved a method for the construction of initial models for the SEM calculation, and applied our approach to estimate the regulatory network for Antero-Posterior (AP) pattern formation in D. melanogaster embryogenesis. In this new approach, we combined cross-correlation and partial correlation to summarize the temporal information and to extract the direct interactions from the gene expression profiles. In the inferred model, 18 transcription factor genes were regulated by not only the expression of other genes, but also the estimated factors. Since each factor regulated the same type of genes, these factors were considered to be involved in maternal effects or spatial morphogen distributions. The interpretation of the inferred network model allowed us to reveal the regulatory mechanism for the patterning along the head to tail axis in D. melanogaster.

In this paper we introduce a computational modelling that reproduces the breast compression processes used to obtain the mammogram. The main result is a programme in which one can track the first steps of virtual mammography. On the one hand, our modelling enables addition of structures that represent different tissues, muscles and glands in the breast. On the other hand, we shall validate and implement it by means of laboratory tests with phantoms. To the best of our knowledge, these two characteristics do confer originality to our research. This is because their interrelation seems not to be properly established elsewhere yet. We conclude that our model reproduces the same shapes and measurements really taken by the volunteer's breasts.

Aspartic acid (Asp) residues in peptides and proteins (L-Asp) can undergo spontaneous, nonenzymatic reactions under physiological conditions by which abnormal L-β-Asp, D-Asp, and/or D-β-Asp residues are formed. These altered Asp residues may affect the three-dimensional structures of the peptides and proteins and hence their properties and functions. In fact, the altered Asp residues are relevant to age-related diseases such as cataract and Alzheimer's disease. Most of the above reactions of the L-Asp residue proceed via a cyclic succinimide intermediate. In this paper, I propose a detailed mechanism of cyclization of an Asp residue (forming a precursor of the succinimide) by the B3LYP/6-31+G(d,p) density functional theory calculations carried out for a small Asp-containing model compound complexed with three water molecules which act as general acid-base catalysts in proton transfers. In the proposed mechanism, the amide group on the C-terminal side of the Asp residue is first converted to the tautomeric iminol form. Then, successive reorientation of a water molecule and conformational change occur followed by the nucleophilic attack of the iminol nitrogen atom on the carboxyl carbon atom of the Asp side chain to form a five-membered ring. A satisfactory agreement was obtained between the calculated and experimental energetics.

The inverse Radon transform and his straightforward implementation, known as filtered backprojection (also known as FBP), has become a powerful algorithm for solving a tomographic inverse problem. It has a wide range of applications, including geophysics, medicine and synchrotrons, and from kilo to centi to micro scale respectively. Such a classical inversion has a major computational disadvantage: increasing slowness proportionally to the data size. An ordinary implementation of this algorithm relies on a simple integral that has to be done pixelwise. Many accelerating techniques were proposed in the literature so as to make this part of the inversion as fast as possible. One the most promising strategies is converting the backprojection as a convolution operator (at log-polar coordinates). The generalized backprojector has many applications, for instance in the analytical inversion of single-photon emission tomography or x-ray fluorescence tomography. Our aim in this paper is to show how these ideas can be used for other inversion methods, the iterative ones; which deal much better with noise.

In this article, we give a different mathematical approach for background aspects of grazing incidence x-ray fluorescence, GIXRF for short. Our contribution comes from an applied point of view, in order to have a computer program to simulate the fluorescence intensity from a stacking of thin layer films. A typical ill-posed inverse problem is formulated. Our aim is to reconstruct the fluorescence intensity for a variety of grazing angle measurements. We rederive some classical equations pointing out the numerical aspects of the inversion procedure and giving new directions for direct in inverse algorithms.

We have recently developed an atomistic model of the B-DNA configuration, up to the 30-nm chromatin fiber. This model is intended to be used in Monte Carlo simulations of the DNA-radiation interaction, specifically in conjunction with the Geant4-DNA extension of the Geant4 Monte Carlo toolkit. In this work, 11449 parallel chromatin fibers have been arranged within a cube mimicking a cell nucleus containing about 6.5×10⁹ base pairs. Each atom in the model is represented by a sphere with the corresponding van der Waals radius. Direct single, double and total DNA strand break yields due to the impact of protons and alpha particles with LET ranging from 4.57 to 207.1 keV/μm have been determined. Also, the corresponding site-hit probabilities have been calculated.

In this paper we presente a classification system that uses a combination of texture features from stromal regions: Haralick features and Local Binary Patterns (LBP) in wavelet domain. The system has five steps for classification of the tissues. First, the stromal regions were detected and extracted using segmentation techniques based on thresholding and RGB colour space. Second, the Wavelet decomposition was applied in the extracted regions to obtain the Wavelet coefficients. Third, the Haralick and LBP features were extracted from the coefficients. Fourth, relevant features were selected using the ANOVA statistical method. The classication (fifth step) was performed with Radial Basis Function (RBF) networks. The system was tested in 105 prostate images, which were divided into three groups of 35 images: normal, hyperplastic and cancerous. The system performance was evaluated using the area under the ROC curve and resulted in 0.98 for normal versus cancer, 0.95 for hyperplasia versus cancer and 0.96 for normal versus hyperplasia. Our results suggest that texture features can be used as discriminators for stromal tissues prostate images. Furthermore, the system was effective to classify prostate images, specially the hyperplastic class which is the most difficult type in diagnosis and prognosis.

In the context of loop quantum cosmology, we provide a complete quantization of an inhomogeneous inflationary model consisting of a perturbed Friedmann-Lemaître-Robertson-Walker universe filled with a minimally coupled massive scalar field. We focus on the case of flat, compact spatial sections. After fixing the local gauge freedom, the kinematical Hilbert space is constructed by combining the representation used in loop quantum cosmology for the homogeneous sector with a preferred Fock quantization of the inhomogeneities. We characterize the physical states annihilated by the quantum Hamiltonian constraint and discuss the evolution of the inhomogeneities in the presence of an emergent relational time.

The possibility of photon-photon scattering is a striking difference between classical and quantum electrodynamics. This genuinely quantum feature is made possible by the fluctuations of charged fields, and it makes quantum vacuum a nonlinear optical medium. Photon-photon scattering is thus a delicate probe into the structure of quantum electrodynamics and any departure from the expected behavior would be a powerful signal of "new physics". To date this process has never been observed – except as a radiative correction to other processes – and several experiments are trying to detect it at very low energy, in the scattering of real photons in powerful light beams off the virtual photons of intense magnetic fields. Here we briefly review the experimental state-of-the-art, with special emphasis on the PVLAS experiment, and we describe a new proposal to observe photon-photon scattering in the range 1 – 2 MeV.

The simplest quantum composite body, a hydrogen atom, is considered in the presence of a weak external gravitational field. We define an operator for the passive gravitational mass of the atom in the post-Newtonian approximation of the general relativity and show that it does not commute with its energy operator. Nevertheless, the equivalence between the expectation values of the mass and energy is shown to survive at a macroscopic level for stationary quantum states. Breakdown of the equivalence between passive gravitational mass and energy at a microscopic level for stationary quantum states can be experimentally detected by studying unusual electromagnetic radiation, emitted by the atoms, supported by and moving in the Earth's gravitational field with constant velocity, using spacecraft or satellite.

The strong-field region inside a black hole needs special attention during numerical simulation. One approach for handling the problem is the moving puncture method, which has become an important tool in numerical relativity since it allows long term simulations of binary black holes. An essential component of this method is the choice of the '1+log'-slicing condition. We present an investigation of this slicing condition in rotating black hole spacetimes. We discuss how the results of the stationary Schwarzschild '1+log'-trumpet change when spin is added. This modification enables a simple and cheap algorithm for determining the spin of a non-moving black hole for this particular slicing condition. Applicability of the algorithm is verified in simulations of single black hole, binary neutron star and mixed binary simulations.

A relativistic approach of the Hill Problem is presented by using an approximate binary system metric obtained from the first post-Newtonian expansion (1PN). We employ Poincaré maps and Lyapunov exponents to study the stability of bounded orbits of the system for different mass arrangements, and compare with the classical problem based on Newtonian dynamics. We find that for larger masses the system become totally stable, a striking behaviour that is not predicted by the Newtonian dynamics.

We show how a mass mixing matrix can be generated dynamically, for two massless fermion flavours coupled to a Lorentz invariance violating (LIV) gauge field. The LIV features play the role of a regulator for the gap equations, and the non-analytic dependence of the dynamical masses, as functions of the gauge coupling, allows to consider the limit where the LIV gauge field eventually decouples from the fermions. Lorentz invariance is then recovered, to describe the oscillation between two free fermion flavours, and we check that the finite dynamical masses are the only effects of the original LIV theory.

The structure and thermal conductivity of the sodium chloride (NaCl) aqueous solution in similar concentration to the seawater with saturated carbon dioxide (CO₂) have been investigated by molecular dynamics simulation. The effects of pressure have been investigated under various pressures corresponding to the depth of the sea from 40m to 10000m. The negative pressure dependence of the thermal conductivity has been detected in the depth of more than 8000m, whereas that of NaCl aqueous solution without CO₂ shows the positive pressure dependence.

We present the results of investigation of electron excitations in various carbon-based nanoscale systems in the process of photoionization. As a case study, we consider a number of highly symmetric fullerenes, namely C₂₀, C₆₀ and C₈₀, as well as aromatic hydrocarbons – benzene (C₆H₆) and coronene (C₂₄H₁₂). The calculations are performed within the ab initio TDDFT framework and model approach, based on the plasmon resonance approximation. Analysis of the results demonstrates that the main contribution to the photoionization spectra of nanoscale carbon systems is due to collective excitations of delocalized electrons, known as plasmons. Results of the model-based calculations are in close agreement with those of the more accurate quantum-chemical calculations and correspond also to the existing experimental data.

In this paper, we have analysed an effect of quantum nature of the hydrogen molecule on its thermodynamic and transport properties using molecular dynamics (MD) method based on the path integral method. We performed NVE constant MD simulation and the quantum effect on the molecular mechanism was analysed. The simulation results were compared with experimental data. As a result, we clarified that the quantum nature makes the virial pressure larger than in classical mechanics and taking account the quantum nature makes smaller intermolecular interaction energy and larger repulsive force than classical representation. Besides, we have confirmed that the path-integral-based MD method well reproduces the thermal conductivity and quantum effect on the transport properties is also large.

This article theoretically analyzes the cutting depth and material removal rate of an atomic force microscope (AFM) cantilever during nanomachining. An analytical expression for the vibration frequency and displacement of the cantilever has been obtained by using the modified couple stress theory. The theory includes one additional material length scale parameter revealing the micro-scale effect. According to the analysis, the results show that the effect of size-dependent on the vibration behavior of the AFM cantilever is obvious. The maximum displacement of nanomachining with the AFM cantilever represents the cutting depth. The area under the displacement-time curve is related to the material removal rate. When the excitation frequency is closer to the nature frequency of the cantilever, a larger material removal rate is obtained.

Recent frequency-modulated atomic force microscopy (FM-AFM) can measure the three-dimensional force distribution between a probe and a sample surface in liquid. The force distribution is currently regarded to approximate the solvation structure on the surface, because shapes of the force distribution and the solvation structure are somewhat similar to each other. However, the force distribution is never the solvation structure. Therefore, we propose a method that converts the force distribution to the solvation structure. (This conversion is an example of inverse calculations.) A new benefit of the method is that it can perform the inverse calculation without any simplifications of the shape and the solvation affinity of the actual probe tip in a three-dimensional system.

Numerical approaches to the study of the magnetic states, properties, and phase transitions in the Ising spin systems with the long-range exchange interaction is presented. The Monte Carlo calculations have been performed for a system of Ising spins on a square lattice with long-range RKKY interaction. It is shown that the Monte Carlo simulation systems RKKY interaction leads to the formation of a complex of the magnetic structure. We compared the results of simulation with experimental images of domain structure of garnet ferrite films.

The idea that the properties of nano materials depend on their crystalline structure and the form and geometric sizes of them is discussed in this paper. The progress in the growth area of nano magnetic devices attracts the interest from both experimental and theoretical study of the nano structures for potential applications in industry. In various fields of electronics there is need to have nano materials with a wide range of magnetic properties. In this case theoretical research could provide a way to get the nano compounds with the required characteristics. In this paper we present the results of Monte Carlo simulations of magnetic nanodisks, which are based on simple cubic and body-centered cubic unit cell. The magnetization of spin, magnetic susceptibility and specific heat are investigated for nanodisks with the different diameters, thicknesses and for different values of the ratio of the correlation constants. The combination of dipolar and Heisenberg model interaction are considered for ferromagnetic case and are show that the magnetic and thermodynamic properties of the nanostructures are strongly dependent on their geometry. The structures with body-centered cubic unit cell demonstrate stronger dependences on the thickness of the disks and also higher critical temperature and wider hysteresis loop.

In this paper the two-sublattice crystalline ferromagnet in the approximation of the Ising model was investigated. In each sub-lattice density of magnetic atoms can vary from 0 to 1. The exchange interactions within each sublattice and between the spins of different sublattices are considered as given. The case of direct exchange was investigated and the conditions for the occurrence of ferromagnetism, antiferromagnetism and ferrimagnetism, depending on the concentration of magnetic atoms in each sublattice were established.

Two-level models of different polycrystalline metal's inelastic deformation based on crystal plasticity and describing viscoplastic intragranular dislocations slip, lattice rotation with an explicit consider of dislocation slip incompatibility in neighboring grains, and fragmentation of crystallites are developed. The homogenization of constitutive equations at various scale levels is used, which allows to connect the same type of characteristics of different scale levels and leads to an unambiguous description of geometric nonlinearity on the macro level by specifying the corotational derivative of Cauchy stress tensor. An algorithm for solving boundary value problems in FEM package Abaqus with using proposed models to describe the behavior of the material is developed, corresponding computational modules are created. Numerical investigation of different loading of samples from various polycrystalline metals with a description of the evolving internal structure is done.

The authors propose and numerically examine a two-component design of an optical nanocavity. The design utilizes the effective medium theory. Such a nanocavity consists, first, of a photonic crystal nanobeam, in which the photonic crystal unit cell is not changed. Second, the cavity contains a fragment of some supplementary material of the size of several or several tens of photonic crystal unit cells. This paper describes the cavity model in which the both components have an equal thickness and can be fabricated from the same silicon wafer. While combining the two components, the defect has formed, in which the resonant mode can be excited. The advantages of the proposed cavity model are reported, particularly the easiness with which the cavities array can be fabricated and the possibility of implementing electrically pumped light sources and amplifiers. The fabrication tolerances of the proposed nanocavity were investigated. It has been found that existing structural layers alignment technologies can be used for fabricating the suggested cavity.

Small magnetic particles placed in a relatively soft polymer (with elastic modulus E ~ 10 ÷ 100 kPa) are magnetically soft elastomers. The external magnetic field acts on each particle which leads to microscopic deformation of the material and consequently to changing of its shape – magnetostriction. For purposes of studying of magnetostriction the model of movable cellular automata (MCA), in which a real heterogeneous material is an ensemble of interacting elements of finite size – automata, is used. It's supposed to be that the motion of each automata can be described by Newton's Second law. The force acting on the i-th automata consists of the following components: volume-dependent force acting on the automata i which is caused by pressure from the surrounding automata; force of an external magnetic field acting on the i-th automata with some magnetic moment; and normal and tangential interaction force between a pair of i and j automata. This approach was used for modeling of magnetostriction elastomer.

A number of experiments show that helium plasma constructs filament (fuzz) structures whose diameter is in nanometer-scale on the tungsten material under the suitable experimental condition. In this paper, binary-collision-approximation-based simulation is performed to reveal the mechanism and the conditions of fuzz formation of tungsten material under plasma irradiation. The irradiation of the plasma of hydrogen, deuterium, and tritium, and also the plasma of noble gas such as helium, neon, and argon atoms are investigated. The possibility of fuzz formation is discussed on the simulation result of penetration depth of the incident atoms.

In this article, by using the first principle calculations based on the density functional theory, we present a detailed investigation of the energy band and density of states of armchair graphene nanoribbons (AGNRs) with bare and H-terminated edges. Based on the structural optimization results, we compute the energy band and density of states of considered nanoribbons. The results show that there is a direct band gap for bare and H-terminated edges AGNRs, and indicate AGNRs have semiconductor properties for both cases our calculated. There are localized states turns up at -2.520eV for the case of bare edges, after modification of hydrogen atoms, the localized states disappeared, the band gap is widened form 0.535eV for the bare edges to 0.722eV for H-terminated edges, at the same time, and the energy band degeneracy appeared.

The electronic band structure and phonon dispersion of wurtzite BN are studied by the first principle calculations. The local density approximation (LDA) and the generalized gradient approximation (GGA) exchange-correlation potentials are applied in the calculations and compared. The computational results for the band structure and density of states with indirect band gaps as well as the phonon dispersive curves and density of states are obtained. The corresponding dielectric and thermodynamic properties are discussed. The conclusions are consistent with other theoretical results and experimental data.

Lattice parameters and band structure of the ternary mixed crystal Al_xGa_1-xAs of zinc blende structure are calculated by first-principle calculations within the framework of the density functional theory. The results for the equilibrium lattice parameters and band gaps of Al_xGa_1-xAs for the Al-composition varying from 0.0 to 1.0 by step of 0.125 are presented and discussed. The results show that the lattice constants vary with the composition almost linearly following the Vegard's law. The electron band gap at Gamma; point exhibits non-linear behavior versus the composition. The Al-3s, 3p states shift to high energy region in the conduction band with increasing the Al concentration. It leads to an increase of the band gap and the blue shift phenomenon.

Three semiempirical algorithms for electronic levels calculations of polar nanosystems with the partial self-consistency are discussed. These algorithms are based on the model of pointlike polarized ions and on the self-consistent modification of semiempirical tight-binding theory of Slater and Koster. The basic feature of this work is the use of partial self-consistency which allows to simplify a mathematical formalism and to accelerate considerably the process of the calculations for nanosystems containing "whole ions". The obtained results for such systems, as was shown, are in rather good qualitative agreement with the results of non-empirical calculations. The presented algorithms can be effectively used for calculations of the electronic structure of polar nanosystems containing ~ 10⁴ and more ions.

The main characteristics of MM-wave image detector were simulated by means of accurate numerical modelling of thermophysical processes in a metamaterial MM-to-IR converter. The converter represents a multilayer structure consisting of an ultra thin resonant metamaterial absorber and a perfect emissive layer. The absorber consists of a dielectric self-supporting film that is metallized from both sides. A micro-pattern is fabricated from one side. Resonant absorption of the MM waves induces the converter heating that yields enhancement of IR emission from the emissive layer. IR emission is detected by IR camera. In this contribution an accurate numerical model for simulation of the thermal processes in the converter structure was created by using COMSOL Multiphysics software. The simulation results are in a good agreement with experimental results that validates the model. The simulation shows that the real time operation is provided for the converter thickness less than 3 micrometers and time response can be improved by decreasing of the converter thickness. The energy conversion efficiency of MM waves into IR radiation is over 80%. The converter temperature increase is a linear function of a MM-wave radiation power within three orders of the dynamic range. The blooming effect and ways of its reducing are also discussed. The model allows us to choose the ways of converter structure optimization and improvement of image detector parameters.

Acousto-optic coupling mechanisms within simultaneous photonic and phononic crystal cavities are theoretically studied. The structure considered is a silicon slab drilled periodically with air holes arranged on a square lattice; the cavity is obtained by removing one hole from the ideal crystal structure. Two acousto-optic coupling mechanisms are taken into account: the classical photo-elastic effect and the opto-mechanic effect which arises from the moving boundaries. The coupling mechanisms are computed according to the finite element method. The results reveal that the mechanisms can sustain each other or act with counteracted effects.

A mathematical model of a new type of liquid crystal (LC) based diffraction grating for the terahertz frequency range is proposed. Numerical time-integration by the finite-difference time-domain (FDTD) method of Maxwell-equation systems, describing the proposed structure, has been performed. The partial differential equation, describing the electro-optical induced orientation of the LC molecule in the external electric field, is calculated by the method of lines (MOL). The dependence of induced birefringence vs. external control voltage is obtained for 6CB nematic liquid crystal (NLC).

The light propagation in an anisotropic periodic media, such us circular diffraction waveplate (CDW) by a finite-difference time-domain (FDTD) technique is studied. The FDTD numerical simulation and the subsequent Fourier transform of the diffracted electric near field was been used for study of ability of CDW to diffract a laser beam and simultaneously convert polarization state. The FDTD simulation results used to restore the diffracted electric far field at the CDW output. an abstract.

We report the numerical analysis of p-GaAs/n-GaAs tunnel junction employing InAs as the intermediate layer at the junction. Incorporation of this intermediate layer introduces an intermediate level at the junction bandgap leading to enhanced tunneling of carriers. By doing so, we obtain a two order of enhancement in the tunnel current. Furthermore, the performance of GaInP/GaAs dual-junction solar cells using the TJ with InAs intermediate layer is calculated under concentrated suns condition and it shows a conversion efficiency exceeding 30% under 1800 suns condition.

We have simulated distribution of electromagnetic waves through the system composed of miter bends by Finite-Difference Time-Domain (FDTD) simulation. We develop the interactive visualization system using a new interactive GUI system which is composed of the virtual reality system and android tablet to analyze the FDTD simulation. The effect of the waveguide system with grooves have been investigated to quantitatively by visualization system. Comparing waveguide system with grooves and without grooves, grooves have been confirmed to suppress the surface current at the metal surface. The surface current at complex shape such as the miter bend have been investigated.

In this paper the method for modelling of word usage frequency time series is proposed. An artificial feedforward neural network was used to predict word usage frequencies. The neural network was trained using the maximum likelihood criterion. The Google Books Ngram corpus was used for the analysis. This database provides a large amount of data on frequency of specific word forms for 7 languages. Statistical modelling of word usage frequency time series allows finding optimal fitting and filtering algorithm for subsequent lexicographic analysis and verification of frequency trend models.

We propose a new model about diffusion of a product which includes a memory of how many adopters or advertisements a non-adopter met, where (non-)adopters mean people (not) possessing the product. This effect is lacking in the Bass model. As an application, we utilize the model to fit the iPod sales data, and so the better agreement is obtained than the Bass model.

Firm size data usually do not show the normality that is often assumed in statistical analysis such as regression analysis. In this study we focus on two firm size data: the number of employees and sale. Those data deviate considerably from a normal distribution. To improve the normality of those data we transform them by the Box-Cox transformation with appropriate parameters. The Box-Cox transformation parameters are determined so that the transformed data best show the kurtosis of a normal distribution. It is found that the two firm size data transformed by the Box-Cox transformation show strong linearity. This indicates that the number of employees and sale have the similar property as a firm size indicator. The Box-Cox parameters obtained for the firm size data are found to be very close to zero. In this case the Box-Cox transformations are approximately a log-transformation. This suggests that the firm size data we used are approximately log-normal distributions.

The connection between the micro and macro-arrow of time is discussed in the frame of the stochastic quantum hydrodynamic analogy (SQHA). The presence of fluctuations that in the case on non-linear interactions leads to the breaking of the quantum mechanics on large scale and then to the macroscopic irreversibility with a defined arrow of time, gives also rise to the time reversal breaking in the micro-scale quantum evolution (micro-arrow of time). The quantum irreversibility with time reversal asymmetry is briefly discussed.

We consider particles with repulsive nearest-neighbor interactions in a periodically modulated tilted-sine potential as a model for a peristaltic ratchet system. Using the Markov chain approach to kinetics (MCAK), the collective transport behavior is investigated with respect to the modulation period, interaction strength, and applied mechanical bias (tilt amplitude). In the stationary state, a maximum is found in the period-averaged particle current and transport efficiency as function of both the mechanical bias and the modulation period. The efficiency can be enhanced when the interaction strength is increased. While the maximal current arises for fast modulation, maximum efficiency is obtained for comparatively slow modulation.

The development of efficient artificial nanodevices poses challenges which are of fundamental and technological nature. Recent progress has been made in the context of finite-time thermodynamics. A central question in finite-time thermodynamics is to identify the optimal procedure to extract the greatest amount of work from a system operating under well-defined constraints. For externally controlled small systems, the optimal driving protocol maximizes the mean work spend in a finite-time transition between two given system states under the constraints of given initial and final energy values, and a fixed total operation time. For simplicity we consider an externally controlled single level system, which is embedded in a thermal environment and coupled to a particle reservoir. The optimal protocols are calculated from a master equation approach for different system-reservoir couplings. For open systems, the system-reservoir couplings are shown to have a striking influence on the optimal driving setup. We point out that the optimal protocols have discontinuous jumps at the initial and final times. Finally, this work provides a first attempt to extend these calculations to larger system sizes.

Based on the spatial factor other than the temporal accumulation, the hidden tree model was built up to model scale-free networks. This paper further assumed that a node has multiple roles in different hidden trees, and explored the multi-role hidden tree model. The experimental results showed that multi-role hidden tree model can also produce scale-free networks. This conclusion indicates that the hidden tree model is robust with multiple roles.

We analyze emotionally annotated massive data from BBC Forum and examine properties of the isolation phenomenon of negative and positive users. Our results show the existence of a percolation threshold dependent on the average emotional value in the network of negatively charged nodes.

Epidemics have been known to persist in the form of recurrence cycles. Despite intervention efforts through vaccination and targeted social distancing, infectious diseases like influenza continue to appear intermittently over time. I have undertaken an analysis of a stochastic epidemic model to explore the hypothesis that intervention efforts actually drive epidemic cycles. Time series from simulations of the model reveal oscillations exhibiting a similar temporal signature as influenza epidemics. The power-spectral density indicates a resonant frequency, which approximately corresponds to the apparent annual seasonality of influenza in temperate zones. Asymptotic solution to the backward Kolmogorov equation of the dynamics corresponds to an exponentially-decaying mean-exit time as a function of the intervention rate. Intervention must be implemented at a sufficiently high rate to extinguish the infection. The results demonstrate that intervention efforts can induce epidemic cycles, and that the temporal signature of cycles can provide early warning of imminent outbreaks.

We investigate a stochastic model of network formation where short-cut edges are assumed to be created between vertices in traces of random walkers. The network initially starts from a tree-like structure (Bethe lattice) with a finite number of shells, and develops into a complex network with many circuits generated by the movement of random walkers. We show that the resulting network has a power-law in the degree distribution with an exponent smaller than 2, and demonstrate the robustness against attacks on hubs in the networks. While scale-free networks without a degree correlation are usually vulnerable to attacks on its hubs, the robustness of the network connectivity in this model comes from a self-similar structure of the network. It is interesting that a simple stochastic process like random walks can cause various structures widely seen in real networks on tree-like graphs which play an important role in the graph theory.

Since peer-to-peer file-sharing systems have become familiar recently, the information traffic in the networks is increasing. Therefore it causes various traffic problems in peer-to-peer networks. In this paper, we model some features of the peer-to-peer networks, and investigate the traffic problems. Peer-to-peer networks have two notable characters. One is that each peer frequently searches for a file and download it from a peer who has the requested file. To decide whether a peer has the requested file or not in modelling of the search and download process, we introduce file-parameter P_j, which expresses the amount of files stored in peer j. It is assumed that if P_j is large, peer j has many files and can meet other peers' requests with high probability. The other character is that peers leave and join into the network repeatedly. Many researchers address traffic problems of data transfer in computer communication networks. To our knowledge, however, no reports focus on those in peer-to-peer networks whose topology changes with time. For routing paths of data transfer, generally, the shortest paths are used in usual computer networks. In this paper, we introduce a new optimal routing strategy which uses weights of peers to avoid traffic congestion. We find that the new routing strategy is superior to the shortest path strategy in terms of congestion frequency in data transfer.

Consideration is given to results of experimental and theoretical investigations how alpha-epsilon- phase transition in the unalloyed iron and the 30KhGSA steel and its absence in the austenitic 12Kh18N10T stainless steel influence processes under explosive deformation of spheres made of these materials. Polymorphous transition is shown to significantly effect on:

- amount of explosion-products energy transferred to a sphere,

- evolution of the converging-wave structure and its parameters, profiles of stress wave and temperature T(R,t) for some Lagrangian particles along the sphere radius,

- character of energy cumulation under spherical convergence of waves.

To pursue VNIIEF-VNIITF joint investigations, this paper briefly describes the experimental setup and provides numerical 3D-computation results (LEGAK-3D technique) on special features in the convergence dynamics of steel shells under their quasi-spherical explosive loading in the system with the 40-mm outer radius of the explosive layer.

The computation results were compared with the data experimentally registered for shells of the high-purity and technical-purity unalloyed iron, the 30KhGSA steel, both as-received and quenched to HRC 35...40, and the austenitic 12Kh18N10T stainless steel. The comparison was also made with laser-interferometry results obtained directly under explosive loading, as well as with gamma-tomography and scanning electron microscopy investigations of the recovered shells.

The simplex algorithm is a popular algorithm for solving linear programming problems. If the origin point satisfies all constraints then the simplex can be started. Otherwise, artificial variables will be introduced to start the simplex algorithm. If we can start the simplex algorithm without using artificial variables then the simplex iterate will require less time. In this paper, we present the artificial-free technique for the simplex algorithm by mapping the problem into the objective plane and splitting constraints into three groups. In the objective plane, one of variables which has a nonzero coefficient of the objective function is fixed in terms of another variable. Then it can split constraints into three groups: the positive coefficient group, the negative coefficient group and the zero coefficient group. Along the objective direction, some constraints from the positive coefficient group will form the optimal solution. If the positive coefficient group is nonempty, the algorithm starts with relaxing constraints from the negative coefficient group and the zero coefficient group. We guarantee the feasible region obtained from the positive coefficient group to be nonempty. The transformed problem is solved using the simplex algorithm. Additional constraints from the negative coefficient group and the zero coefficient group will be added to the solved problem and use the dual simplex method to determine the new optimal solution. An example shows the effectiveness of our algorithm.

Evolvable Hardware is facing the problems of scalability and stalling effect. This paper proposed a novel Orthogonal Neighbourhood Mutation (ONM) operator in Cartesian genetic programming (CGP), to reduce the stalling effect in CGP and improve the efficiency of the algorithms.The method incorporates with Differential Evolution strategy. Demonstrated by experiments on benchmark, the proposed Orthogonal Neighbourhood Search can jump out of Local optima, reduce the stalling effect in CGP and the algorithm convergence faster.

In this paper, a ITO algorithm inspired by ITO stochastic process is proposed for Traveling Salesmen Problems (TSP), so far, many meta-heuristic methods have been successfully applied to TSP, however, as a member of them, ITO needs further demonstration for TSP. So starting from designing the key operators, which include the move operator, wave operator, etc, the method based on ITO for TSP is presented, and moreover, the ITO algorithm performance under different parameter sets and the maintenance of population diversity information are also studied.

The simplex method is used to solve linear programming problem by improving the current basic feasible solution. It uses a pivot rule to guide the search in the feasible region. The pivot rule is used to select an entering index in simplex method. Nowadays, many pivot rule have been presented, but no pivot rule shows superior performance than other. Therefore, this is still an active research in linear programming. In this research, we present the max-out-in pivot rule with Dantzig's safeguarding for simplex method. This rule is based on maximum improvement of objective value of the current basic feasible point similar to the Dantzig's rule. We can illustrate by Klee and Minty problems that our rule outperforms that of Dantzig's rule by the number of iterations for solving linear programming problems.

Quantum theory is thought to explain the periodic law which underlies the periodic table (PT); however, the lengths of the periods remain unexplained. Also, this explanation depends on two empirical rules, namely Madelung's n+l rule and Hund's rule. Furthermore, even Madelung's rule fails to explain the ground state configuration for many elements. Toward achieving an explanation of the periodic table, the Hartree-Fock (HF) method has been applied in this paper to calculate energies of various possible configurations of transition metals in the fourth and fifth periods. These calculations for Cr, Cu and Ni do not agree with the spectroscopically observed ground state configurations. We further calculated the nonrelativistic and relativistic energies of the various possible configurations of second row transition metals such as niobium, palladium, molybdenum and silver for which Madelung's rule predicts the wrong ground state configuration. In contrast to Cr and Cu, the observed ground state configuration of these elements is found to be associated with the lowest energy by HF calculations.

Quantum dynamics in a curved spacetime can be studied using a modified Lagrangian approach directly in terms of the spacetime variables [Mirza, B.M., Quantum Dynamics in Black Hole Spacetimes, IC-MSQUARE 2012]. Here we investigate the converse problem of determining the nature of the background spacetime when quantum dynamics of a test particle is known. We employ the quantum potential formalism here to obtain the modifications introduced by the quantum effects to the background spacetime. This leads to a novel geometry for the spacetime in which a test particle modifies the spacetime via interaction through the quantum potential. We present here the case of a Gaussian wave packet, and a localized quantum soliton, representing the test particle, and determine the corresponding geometries that emerge.

In the present work, bound state solutions for a class of multiparameter exponential-type potential are obtained in the frame of the Greene and Aldrich approximation for the centrifugal term. The proposal is general and their usefulness is exemplified with the treatment of the Eckart, Manning-Rosen, Hulthen and Deng Fan potentials that are obtained straightforwardly without resorting to specialized methods of solution for each specific potential, as usually is done. Furthermore, the proposal admits other approximations for the centrifugal term indicating an improvement to procedures developed with the same objective. So, our proposal can be considered as an unified treatment of the ℓ-state solutions for exponential-type potentials and can be used to find new solvable potentials.

The biological effect of ionizing radiation is mediated practically always by the clusters of radicals formed by densely ionizing track ends of primary or secondary particles. In the case of low-LET radiation the direct effect may be practically neglected and the radical clusters meet a DNA molecule always some time after their formation. The corresponding damage effect (formation of DSB) depends then on the evolution running in individual clusters, being influenced by present chemical agents. Two main parallel processes influence then final effect: diffusion of corresponding radical clusters (lowering radical concentrations) and chemical reactions of all chemical substances present in the clusters. The processes running in the corresponding radical clusters will be modeled with the help of continuous Petri net, which enables us to study the concurrent influence of both the processes: lowering concentration of radicals due diffusion and due chemical reactions. The given model may be helpful especially when the effect of radicals on DSB formation (DNA damage) at the presence of different substances influencing radiobiological effect is to be studied.

In this work, the quantum operator approach is applied to both, the position-dependent mass Schrödinger equation (PDMSE) and the Schrodinger equation with constant mass (CMSE). This fact enable us to find the factorization operators that relates both Hamiltonians by means of a kinetic energy operator that comes from the proposal of Morrow and Brownstein. With this approach is possible to find the exactly-solvable PDMSE, for any value of the parameters α and γ in the von Roos's Hamiltonian. For that, our proposal can be considered as a unified treatment of the PDMSE because it contains as particular cases, the kinetic energy operators of various authors such as BenDaniel-Duke, Gora-Williams, Zhu-Kroemer and Li-Kuhn among others. To show the usefulness of our result, we show the solvable PDMSE that comes from the harmonic oscillator potential model for the CMSE. The proposal is general and can easily be extended to other potential models and mass distributions which will be given in the extended paper.

A fast and efficient numerical-analytical approach is proposed for description of complex behaviour in non-equilibrium ensembles in the BBGKY framework. We construct the multiscale representation for hierarchy of partition functions by means of the variational approach and multiresolution decomposition. Numerical modeling shows the creation of various internal structures from fundamental localized (eigen)modes. These patterns determine the behaviour of plasma. The localized pattern (waveleton) is a model for energy confinement state (fusion) in plasma.

The Peyrard-Bishop model is a mesoscopic approximation to model DNA and RNA molecules. Several variants of this model exists, from 3D Hamiltonians, including torsional angles, to simpler 2D versions. Currently, we are able to parametrize the 2D variants of the model which allows us to extract important information about the molecule. For example, with this technique we were able recently to obtain the hydrogen bonds of RNA from melting temperatures, which previously were obtainable only from NMR measurements. Here, we take the 3D torsional Hamiltonian and set the angles to zero. Curiously, in doing this we do not recover the traditional 2D Hamiltonians. Instead, we obtain a different 2D Hamiltonian which now includes a base pair step distance, commonly known as rise. A detailed knowledge of the rise distance is important as it determines the overall length of the DNA molecule. This 2D Hamiltonian provides us with the exciting prospect of obtaining DNA structural parameters from melting temperatures. Our results of the rise distance at low salt concentration are in good qualitative agreement with those from several published x-ray measurements. We also found an important dependence of the rise distance with salt concentration. In contrast to our previous calculations, the elastic constants now show little dependence with salt concentrations which appears to be closer to what is seen experimentally in DNA flexibility experiments.

The purpose of this work is to derive an automated system that provides advantageous drawings of energy spectra for quantum systems (nuclei, atoms, molecules, etc.) required in various physical sciences. The automation involves the development of appropriate computational code and graphical imaging system based on raw data insertion, theoretical calculations and experimental or bibliographic data insertion. The system determines the appropriate scale to depict graphically with the best possible way in the available space. The presently developed code operates locally and the results are displayed on the screen and can be exported to a PostScript file. We note its main features to arrange and visualize in the available space the energy levels with their identity, taking care the existence in the final diagram the least auxiliary deviations. Future improvements can be the use of Java and the availability on the Internet. The work involves the automated plotting of energy levels in molecules, atoms, nuclei and other types of quantized energy spectra. The automation involves the development of an appropriate computational code and graphical imaging system.

In the present work we investigate a class of numerical techniques, that take advantage of discrete variational principles, for the numerical solution of multi-symplectic PDEs arising at various physical problems. The resulting integrators, which use the nonstandard finite difference framework, are also multisymplectic. For the derivation of those integrators, the necessary discrete Lagrangian is expressed at the appropriate discrete jet bundle using triangle and square discretization. The preliminary results obtained by the resulting numerical schemes show that for the case of the linear wave equation the discrete multisymplectic structure is preserved.

Granular materials may exhibit different pattern forming behaviors, depending on the average energy per grain. Various granular flow PDE models exist, each capturing different behaviors of the physical phenomenon. In the present work we investigate the model and parameter identification problem of different continuous granular flow models as an encapsulated optimization problem. The identification problem is then split in a series of inverse problems. For the discrimination of the different models, the Fisher information matrix is used and different optimality criteria are discussed. Basic concepts of algorithmic differentiation (AD), which is used for the computation of the sensitivity matrix, are also given. The PDEs are discretized by the finite element method.

The class of particulate composites with cross-linked hyperelastic polymer matrix and non-deformable filler particles represents many important biopolymer and engineering materials. At application conditions, the matrix is either in the swollen state, or the swollen state is utilized for matrix characterization. In this contribution, a numerical model for simulation of equilibrium stress-strain and swelling behavior of this composite material was developed based on finite element method using COMSOL Multiphysics® software. In the constitutive equations (Gibbs energy), the elastic contribution is based on statistical-mechanical model of a network composed of freely jointed chains of finite extensibility and polymer-solvent mixing term is derived from the Flory-Huggins lattice model. A perfect adhesion of matrix-to-particle is assumed. The adhesion of matrix to stiff surface generates stress and degree-of-swelling fields in the composite. The existence of these fields determines the mechanical and swelling properties of the composite. Spatial distribution of filler particles in the composite plays an important role.

The electromagnetic resonant structures and their perturbations have been found their way in many applications in microwave engineering. Analysis of these structures using finite element method results in a generalized eigenvalue problem, where the eigenvalues correspond to the resonant frequencies, and the eigenvectors correspond to the resonant modes. The perturbations of resonant structures yield perturbed eigenvalue problem and can be solved by eigenvalue perturbation methods, effectively. Combining finite element method with step by step eigenvalue perturbation method yields parametric history with respect to perturbation parameter. In this study perturbation of a microwave ring resonator placed in a metalic enclosure has been examined, combining the vector finite element and the step-by-step generalized eigenvalue perturbation methods.

The problem of the propagation of an electrical discharge between a spherical electrode and a plane has been solved by means of finite element methods (FEM) using a fluid approximation and assuming weak ionization and local equilibrium with the electric field. The numerical simulation of this type of problems presents the usual difficulties of convection-diffusion-reaction problems, in addition to those associated with the nonlinearities of the charged species velocities, the formation of steep gradients of the electric field and particle densities, and the coexistence of very different temporal scales. The effect of using different temporal discretizations for the numerical integration of the corresponding system of partial differential equations will be here investigated. In particular, the so-called θ-methods will be used, which allows to implement implicit, semi-explicit and fully explicit schemes in a simple way.

In fusion devices strongly localized intensive sources of impurities may arise unexpectedly or can be created deliberately through impurity injection. The spreading of impurities from such sources is essentially three-dimensional and non-stationary phenomenon involving physical processes of extremely different time scales. Numerical modeling of such events is still a very challenging task even by using most modern computers. To diminish drastically the calculation time a "shell" model has been elaborated that allows to reduce equations for particle, parallel momentum and energy balances of various ion species to one-dimensional equations describing the time evolution of radial profiles for several most characteristic parameters. The assumptions of the "shell" approach are verified by comparing its predictions with a numerical solution of one-dimensional time dependent diffusion equation.

Pure metals and special alloys obtained by electron beam melting and refining (EBMR) in vacuum, using electron beams as a heating source, have a lot of applications in nuclear and airspace industries, electronics, medicine, etc. An analytical optimization problem for the EBMR process based on mathematical heat model is proposed. The used criterion is integral functional minimization of a partial derivative of the temperature in the metal sample. The investigated technological parameters are the electron beam power, beam radius, the metal casting velocity, etc. The optimization problem is discretized using a non-stationary heat model and corresponding adapted Pismen-Rekford numerical scheme, developed by us and multidimensional trapezional rule. Thus a discrete optimization problem is built where the criterion is a function of technological process parameters. The discrete optimization problem is heuristically solved by cluster optimization method. Corresponding software for the optimization task is developed. The proposed optimization scheme can be applied for quality improvement of the pure metals (Ta, Ti, Cu, etc.) produced by the modern and ecological-friendly EBMR process.

Vibro-acoustic analysis plays a vital role on the design of aircrafts, spacecrafts, land vehicles and ships produced from thin plates backed by closed cavities, with regard to human health and living comfort. For this type of structures, it is required a coupled solution that takes into account structural-acoustic interaction which is crucial for sensitive solutions. In this study, coupled vibro-acoustic analyses of plates produced from composite materials have been performed by using finite element analysis software. The study has been carried out for E-glass/Epoxy, Kevlar/Epoxy and Carbon/Epoxy plates with different ply angles and numbers of ply. The effects of composite material, ply orientation and number of layer on coupled vibro-acoustic characteristics of plates have been analysed for various combinations. The analysis results have been statistically examined and assessed.

We analyze the diffraction of the laser beam with a vortex phase singularity on the basis of the finite-difference time-domain method (FDTD). It is shown that, when incident beam has phase singularity, increase of the micro-axicon radius leads to extension of the light needle consisting of longitudinal electric field component. The numerical investigations held of the near-field diffraction for the most common and easily implemented types of polarization of the incident beam – linear and circular.

The Explicit Green's approach is an effective method for solving initial-boundary value problems in any kind of medium and geometry. This is due to the fact that numerical Green's functions are adopted instead of analytical ones, rendering a more general approach. When the Explicit Green's approach is applied to the scalar wave equation and Green's functions are computed by the finite element method (FEM) in conjunction with the central difference time integration scheme, unstable results are observed. To circumvent this drawback, the present paper discusses the application of a time substep procedure to the central difference time integration for the Green's functions computation. The substep procedure has the advantage of stabilizing the solution as well as increasing the accuracy order in the time domain from two to four. Numerical examples that demonstrate the accuracy and effectiveness of the proposed methodology are provided.

Friction Stir Welding (FSW) is a solid state welding process that can be modelled using a Computational Fluid Dynamics (CFD) approach. These models use adjustable parameters to control the heat transfer and the heat input to the weld. These parameters are used to calibrate the model and they are generally determined using the conventional trial and error approach. Since this method is not very efficient, we used the Differential Evolution (DE) algorithm to successfully determine these parameters. In order to improve the success rate and to reduce the computational cost of the method, this work studied different characteristics of the DE algorithm, such as the evolution strategy, the objective function, the mutation scaling factor and the crossover rate. The DE algorithm was tested using a friction stir weld performed on a UNS S32205 Duplex Stainless Steel.

We demonstrate the creation of nontrivial (meta) stable states (patterns), localized, chaotic, entangled or decoherent, from the basic localized modes in various collective models arising from the quantum hierarchy described by Wigner-like equations. The numerical simulation demonstrates the formation of various (meta) stable patterns or orbits generated by internal hidden symmetry from generic high-localized fundamental modes. In addition, we can control the type of behaviour on the pure algebraic level by means of properly reduced algebraic systems (generalized dispersion relations).

The thermodynamical properties of a thin superconducting film with a central square hole are found theoretically. It is assumed that two opposite outer edges of the sample are in contact with a thin layer of metallic material while the other two edges are in contact with a thin layer of superconducting material, its configuration allows to control the vortex entry in the sample. In this work, we solve numerically the Ginzburg Landau equations with general boundary conditions using the Link variable method extended to multiply connected domains. It is shown that the value of the magnetization, the first vortex entry field, and the free energy are sensitive to the material in contact with the inner edge of the hollow.

The vortex state in a thin mesoscopic superconducting disk with a concave/convex surface is found theoretically. It is assumed that the outer edge of the sample is in contact with a metallic material. This configuration decreases the Bean-Livingston surface barrier energy, that is, it allows the vortex entry into the sample at lower magnetic field. In this work, we solve numerically the Ginzburg Landau equations with the metal/superconducting boundary condition using the link variable method in polar coordinates. It is shown that for a determined value for the deGennes parameter the superconductor becomes a type I superconductor and the irregular surface allows the vortex giant formation. The value of the thermodynamical properties decreases with this boundary condition and kind of surface.

The generalized Bogolubov-de Gennes (BdG) theory, including explicitly the Zeeman energy of electrons, is developed for nanoscale superconductors. To this end the system of four BdG equations is derived, corresponding to four coherent functions (instead of two in conventional BdG theory), two for electron-like excitations and two for hole-like excitations. These equations are transformed into matrix equations by using the basis set of particle-in-the-box problem and solved self-consistently with the equation for the order parameter and the chemical potential. The proposed microscopic approach is suitable for the study of unconventional vortex states and the appearance of FFLO phase in thin nanoscale superconductors.

The recently proposed approach for the solution of Ginzburg-Landau (GL) problem for 2D samples of arbitrary shape is, in this article, extended over 3D samples having the shape of (i) a prism with arbitrary base and (ii) a solid of revolution with arbitrary profile. Starting from the set of Laplace operator eigenfunctions of a 2D object, we construct an approximation to or the exact eigenfunctions of the Laplace operator of a 3D structure by applying an extrusion or revolution to these solutions. This set of functions is used as the basis to construct the solutions of the linearized GL equation. These solutions are then used as basis for the non-linear GL equation much like the famous LCAO method. To solve the non-linear equation, we used the Newton-Raphson method starting from the solution of the linear equation, i.e., the nucleation distribution of superconducting condensate. The vector potential approximations typically used in 2D cases, i.e., considering it as corresponding to applied constant field, are in the 3D case harder to justify. For that reason, we use a locally corrected Nystrom method to solve the second Ginzburg-Landau equation. The complete solution of GL problem is then achieved by solving self-consistently both equations.

In order to study the anisotropic superconductivity in two dimensional lattices, it has been recently proposed a generalized Hubbard model based on first- and second-neighbour correlated-hopping interactions. After considering this Hamiltonian within the BCS formalism, we obtain a system of two coupled integral equations, whose solution gives the superconducting gap and the chemical potential for each temperature and electronic density. This system of equations is usually solved in a numerical way, but the involved integrals over the first Brillouin zone (1BZ) consume a large amount of computing time since the integrand functions are extremely sharp around the Fermi surface (FS) especially for small pairing interactions. In this work, we report a new efficient way to carry out these integrals by dividing the 1BZ in regions delimited by curves close to the FS.

The generalized quantum Monte Carlo algorithm is developed and used to calculate the energy, occupation numbers, and correlation functions of finite FeAs clusters in the two-orbital model at finite temperatures. The coding of quantum states made it possible to take into account complex exchange terms between the orbitals. The results for the calculation of the thermodynamic characteristics of finite two-dimensional FeAs clusters simulating iron-based superconductors have been obtained.

Asymptotic cones are structures that encode how a metric space appears when seen from far away. We discuss their meaning and potential significance for quantum gravity.

We consider some generalization of the theory of quantum states and demonstrate that the consideration of quantum states as sheaves can provide, in principle, more deep understanding of some well-known phenomena. The key ingredients of the proposed construction are the families of sections of sheaves with values in the proper category of the functional realizations of infinite-dimensional Hilbert spaces with special (multiscale) filtrations decomposed into the (entangled) orbits generated by actions/representations of internal hidden symmetries. In such a way, we open a possibility for the exact description and reinterpretation of a lot of quantum phenomena.

Analysis of experimental data has one of the most important roles in High Energy Physics. Commonly used multivariate techniques such as Boosted Decision Trees or Bayesian Neural Networks are based on learning algorithms using Monte Carlo generated samples. We implemented a new Model Based Clustering method using Bayesian statistics and a modified iterative Expectation-Maximization algorithm for weighted data that have never been applied in this area. This greatly promising method was developed especially for the data collected from the DØ experiment, which was one of two large particle physics experiments at the Tevatron proton-antiproton collider at Fermilab. We optimized and tested the proposed method in the single top search using a data sample of 9.7 fb⁻¹ of integrated luminosity, which corresponds to the entire Run II DØ dataset.

Low-energy strong interactions are a major source of background at hadron colliders, and methods of subtracting the associated energy flow are well established in the field. Traditional approaches treat the contamination as diffuse, and estimate background energy levels either by averaging over large data sets or by restricting to given kinematic regions inside individual collision events. On the other hand, more recent techniques take into account the discrete nature of background, most notably by exploiting the presence of substructure inside hard jets, i.e. inside collections of particles originating from scattered hard quarks and gluons. However, none of the existing methods subtract background at the level of individual particles inside events. We illustrate the use of an algorithm that will allow particle-by-particle background discrimination at the Large Hadron Collider, and we envisage this as the basis for a novel event filtering procedure upstream of the official reconstruction chains. Our hope is that this new technique will improve physics analysis when used in combination with state-of-the-art algorithms in high-luminosity hadron collider environments.

We report on an investigation of the self-similar structure of particle showers recorded at a highly-granular calorimeter. On both simulated and experimental data, a strong correlation between the number of hits and the spatial scale of the readout channels is observed, from which we define the shower fractal dimension. The measured fractal dimension turns out to be strongly dependent on particle type, which enables new approaches for particle identification. A logarithmic dependence of the particle energy on the fractal dimension is also observed.

Tau leptons play an essential role in the physics program at the LHC. They are used in the studies for the recently-observed Higgs boson as well as in electroweak measurements and are one of the key ingredients to search for processes predicted by theories beyond the Standard Model. Identifying hadronically decaying tau leptons with a good performance is an essential part of these analyses. The techniques of tau lepton reconstruction and identification used with the ATLAS detector are presented. The misidentification probabilities of QCD jets and electrons are determined from ATLAS data collected in 2012 and from Monte Carlo simulation.

The analysis and interpretation of data collected by the Large Hadron Collider (LHC) requires advanced statistical tools in order to quantify the agreement between observation and theoretical models. RooStats is a project providing a statistical framework for data analysis with the focus on discoveries, confidence intervals and combination of different measurements in both Bayesian and frequentist approaches. It employs the RooFit data modelling language where mathematical concepts such as variables, (probability density) functions and integrals are represented as C++ objects. RooStats and RooFit rely on the persistency technology of the ROOT framework. The usage of a common data format enables the concept of digital publishing of complicated likelihood functions. The statistical tools have been developed in close collaboration with the LHC experiments to ensure their applicability to real-life use cases. Numerous physics results have been produced using the RooStats tools, with the discovery of the Higgs boson by the ATLAS and CMS experiments being certainly the most popular among them. We will discuss tools currently used by LHC experiments to set exclusion limits, to derive confidence intervals and to estimate discovery significances based on frequentist statistics and the asymptotic behaviour of likelihood functions. Furthermore, new developments in RooStats and performance optimisation necessary to cope with complex models depending on more than 1000 variables will be reviewed.

The traceability of measurements to SI units requires a traceable calibration of the measurement devices employed. In the calibration for time-dependent measurements the mathematical model typically consists of a system of ODEs with constant parameters. The calibration then requires the estimation of these parameters from measurements of corresponding trajectories, and the assignment of reliable uncertainties to the obtained parameter estimates. Many approaches to parameter estimation in ODEs are available. However, the evaluation of a reliable uncertainty associated with the corresponding parameter estimates is challenging. The reasons are, for instance, the existence of many local minima, numerical instabilities or the non-identifiability of parameters from the available measurement data. Here we discuss some general approaches to ODE parameter estimation and demonstrate practical issues for the example of calibrating force sensors from shock force measurements.

Currently acute problem of developing new technologies by reducing the noise of aircraft engines, including the directional impact on the noise on the basis of the interaction of plasma disturbances and sound generation pulsations. One of the devices built on this principle being developed in GPI RAS. They are plasma actuators (group of related to each other gaps, built on the perimeter of the nozzle) of various shapes and forms. In this paper an algorithm was developed which allows to separate impulses from the received experimental data, acquired during the work of plasma actuator flush-mounted in the model plane nozzle. The algorithm can be adjusted manually under a variety of situations (work of actuator in a nozzle with or without airflow, adjustment to different frequencies and pulse duration of the actuator). And program complex is developed on the basis of MatLab software, designed for building sustainable robust spectral and autocovariation functions of acoustic signals recorded during the experiments with the model of a nozzle with working actuator.

We introduce the method of minimal subtraction in the computation of critical exponents of Lifshitz type generic competing systems using massless fields. We first treat the anisotropic cases, when several independent momentum scales define the renormalization group invariance of the scalar fields. In addition, we analyze the isotropic sector. We compute critical exponents using diagrammatic techniques at least up to two-loop level and show their equivalence with other methods presented in the literature.

The symmetry study of main differential equations of mechanics and electrodynamics has shown, that differential equations, which are invariant under transformations of groups, which are symmetry groups of mathematical numbers (considered in the frame of the number theory) determine the mathematical nature of the quantities, incoming in given equations. It allowed to proof the main postulate of quantum mechanics, that to any mechanical quantity can be set up into the correspondence the Hermitian matrix by quantization. High symmetry of Maxwell equations allows to show, that to EM-field funcions, incoming in given equations, can be set up into the correspondence the Quaternion (twice-Hermitian) matrices by their quantization.

We review Davydychev method for calculating Feynman integrals for massive and no massive propagators, by employing Mellin-Barnes transformation and integration-dimensionally continuous, same that lead to hypergeometric functions. In particular an example is calculated explicitly from such a method.

Some years ago we initiated a program to define Noncommutative Topological Quantum Field Theory (see [1]). The motivation came both from physics and mathematics: On the one hand, as far as physics is concerned, following the well-known holography principle of 't Hooft (which in turn appears essentially as a generalisation of the Hawking formula for black hole entropy), quantum gravity should be a topological quantum field theory. On the other hand as far as mathematics is concerned, the motivation came from the idea to replace the moduli space of flat connections with the Gabai moduli space of codim-1 taut foliations for 3 dim manifolds. In most cases the later is finite and much better behaved and one might use it to define some version of Donaldson-Floer homology which, hopefully, would be easier to compute. The use of foliations brings noncommutative geometry techniques immediately into the game. The basic tools are two: Cyclic cohomology of the corresponding foliation C*-algebra and the so called "tangential cohomology" of the foliation. A necessary step towards this goal is to develop some sort of Hodge theory both for cyclic (and Hochschild) cohomology and for tangential cohomology. Here we present a method to develop a Hodge theory for tangential cohomology of foliations by mimicing Witten's approach to ordinary Morse theory by perturbations of the Laplacian.

Some years ago we initiated a program to define Noncommutative Topological Quantum Field Theory (see [1]). The motivation came both from physics and mathematics: On the one hand, as far as physics is concerned, following the well-known holography principle of 't Hooft (which in turn appears essentially as a generalisation of the Hawking formula for black hole entropy), quantum gravity should be a topological quantum field theory. On the other hand as far as mathematics is concerned, the motivation came from the idea to replace the moduli space of flat connections with the Gabai moduli space of codim-1 taut foliations for 3 dim manifolds. In most cases the later is finite and much better behaved and one might use it to define some version of Donaldson-Floer homology which, hopefully, would be easier to compute. The use of foliations brings noncommutative geometry techniques immediately into the game. The basic tools are two: Cyclic cohomology of the corresponding foliation C*-algebra and the so called "tangential cohomology" of the foliation. A necessary step towards this goal is to develop some sort of Hodge theory both for cyclic (and Hochschild) cohomology and for tangential cohomology. Here we present a method to develop a Hodge theory for cyclic and Hochschild cohomology for the corresponding C*-algebra of a foliation.

Dirichlet-to-Neumann map is a powerful mathematical instrument that has proved to be useful in the analysis of the 2D and 3D solid state structures when described by the Schrödinger equation. In this paper we apply the DN-map approach to the analysis and numerical calculation of the dispersion relation for periodic quasi-2D layers constructed with unit 3D cells. Basically the dispersion relation is obtained using the methods of quantum scattering theory. The infinite-dimensional matching problem on the interfaces of the cells will be replaced by a finite-dimensional contact subspace that can always be selected so as to provide sufficient accuracy for the calculation of the dispersion relation. The techniques we present also require less computational resource than that of the direct finite-element solution of the Schrodinger equation with quasi-periodic boundary condition.

For the first time, the 1PN J₂c⁻² effects could be measured by the Juno mission in the gravitational field of Jupiter during its nearly yearlong science phase thanks to the high eccentricity (e = 0.947) of the spacecraft's orbit and to the huge oblateness of Jupiter (J₂ = 1.47 × 10⁻²). A numerical analysis shows that the expected J₂c⁻² range-rate signal for Juno should be as large as ≈ 280 microns per second (μm s⁻¹) during a typical 6 h pass at its closest approach to Jupiter. The radio science apparatus of Juno should reach an accuracy in Doppler range-rate measurements of ≈ 1 – 5 μm s⁻¹ over such passes. The range-rate signature of the classical even zonal perturbations is different from the J₂c⁻² one. Thus, further investigations, based on covariance analyses of simulated Doppler data and dedicated parameters estimation, are worth of further consideration.

We develop a framework for constraining a certain class of theories of nonminimally coupled (NMC) gravity with Solar System observations.