Table of contents

Spontaneous brain activity has been recently characterized by avalanche dynamics with critical features for systems in vitro and in vivo. In this contribution we present a review of experimental results on neuronal avalanches in cortex slices, together with numerical results from a neuronal model implementing several physiological properties of living neurons. Numerical data reproduce experimental results for avalanche statistics. The temporal organization of avalanches can be characterized by the distribution of waiting times between successive avalanches. Experimental measurements exhibit a non-monotonic behaviour, not usually found in other natural processes. Numerical simulations provide evidence that this behaviour is a consequence of the alternation between states of high and low activity, leading to a balance between excitation and inhibition controlled by a single parameter. During these periods both the single neuron state and the network excitability level, keeping memory of past activity, are tuned by homoeostatic mechanisms. Interestingly, the same homoeostatic balance is detected for neuronal activity at the scale of the whole brain. We finally review the learning abilities of this neuronal network. Learning occurs via plastic adaptation of synaptic strengths by a non-uniform negative feedback mechanism. The system is able to learn all the tested rules and the learning dynamics exhibits universal features as a function of the strength of plastic adaptation. Any rule could be learned provided that the plastic adaptation is sufficiently slow.

We review and investigate the general theory of the thermodynamics of computation, and derive the fundamental inequalities that set the lower bounds of the work requirement and the heat emission during a computation. These inequalities constitute the generalized Landauer principle, where the information contents are involved in the second law of thermodynamics. We discuss in detail the relationship between the thermodynamic and logical reversibilities; the former is related to the entropy production in the total system including a heat bath, while the latter is related to the entropy change only in the logical states of the memory. In particular, we clarify that any logically irreversible computation can be performed in a thermodynamically reversible manner in the quasi-static limit, which does not contradict the conventional Landauer principle. Our arguments would serve as the theoretical foundation of the thermodynamics of computation in terms of modern statistical physics.

We investigate the completeness of the solutions of the Bethe equations for the integrable spin-s isotropic (XXX) spin chain with periodic boundary conditions. Solutions containing the exact string is, i(s − 1), ..., −i(s − 1), −is are singular. For s > 1/2, there exist also 'strange' solutions with repeated roots, which nevertheless are physical (i.e., correspond to eigenstates of the Hamiltonian). We derive conditions for the singular solutions and the solutions with repeated roots to be physical. We formulate a conjecture for the number of solutions with pairwise distinct roots in terms of the numbers of singular and strange solutions. Using homotopy continuation, we solve the Bethe equations numerically for s = 1 and s = 3/2 up to eight sites, and find some support for the conjecture. We also present several examples of strange solutions.

We study the time evolution of the local magnetization in the critical Ising chain in a transverse field after a sudden change of the parameters at a defect. The relaxation of the defect magnetization is algebraic and the corresponding exponent, which is a continuous function of the defect parameters, is calculated exactly. In finite chains the relaxation is oscillating in time and its form is conjectured on the basis of precise numerical calculations.

We numerically investigate the stochastic resonance (SR) pheno menon in a groundwater-dependent plant ecosystem under the combined influence of environmental fluctuations, seasonal rainfall oscillation, and time delay. The effects of time delay and intrinsic and extrinsic fluctuations on the output signal-to-noise ratio (SNR) of the system are analyzed. The results indicate that the SNR exhibits a maximum as a function of the intensities of the intrinsic and extrinsic noises, identifying the occurrence of the SR effect. An increase of the delay time always suppresses the SR effect, while an increase of correlation strength between noises may suppress or enhance it. The SNR also shows a resonant behavior as a function of the correlation strength between noises, and it can be weakened by the time delay.

Complex networks considering both positive and negative links have gained considerable attention during the past several years. Community detection is one of the main challenges for complex network analysis. Most of the existing algorithms for community detection in a signed network aim at providing a hard-partition of the network where any node should belong to a community or not. However, they cannot detect overlapping communities where a node is allowed to belong to multiple communities. The overlapping communities widely exist in many real-world networks. In this paper, we propose a signed probabilistic mixture (SPM) model for overlapping community detection in signed networks. Compared with the existing models, the advantages of our methodology are (i) providing soft-partition solutions for signed networks; (ii) providing soft memberships of nodes. Experiments on a number of signed networks show that our SPM model: (i) can identify assortative structures or disassortative structures as the same as other state-of-the-art models; (ii) can detect overlapping communities; (iii) outperforms other state-of-the-art models at shedding light on the community detection in synthetic signed networks.

For the long-range one-dimensional Ising spin-glass with random couplings decaying as J(r) ∝ r^−σ, the scaling of the effective coupling defined as the difference between the free energies corresponding to periodic and antiperiodic boundary conditions J^R(N) ≡ F^(P)(N) − F^(AP)(N) ∼ N^θ(σ) defines the droplet exponent θ(σ). Here we study numerically the instability of the renormalization flow of the effective coupling J^R(N) with respect to magnetic, disorder and temperature perturbations respectively, in order to extract the corresponding chaos exponents ζ_H(σ), ζ_J(σ) and ζ_T(σ) as a function of σ. Our results for ζ_T(σ) are interpreted in terms of the entropy exponent θ_S(σ) ≃ 1/3 which governs the scaling of the entropy difference S^(P)(N) − S^(AP)(N) ∼ N^θ_S(σ). We also study the instability of the ground state configuration with respect to perturbations, as measured by the spin overlap between the unperturbed and the perturbed ground states, in order to extract the corresponding chaos exponents $\zeta ^{\rm overlap}_H(\sigma )$ and $\zeta ^{\rm overlap}_J(\sigma )$.

We present new numerical simulations of the random field Ising model in three dimensions at zero temperature. The critical exponents are found to agree with previous results. We study the magnetic susceptibility by applying a small magnetic field perturbation. We find the critical amplitude ratio of the magnetic susceptibilities to be very large, equal to 233.1 ± 1.5. We find strong sample to sample fluctuations which obey finite size scaling. The probability distribution of the size of small energy excitations is maximally non-self-averaging, obeying a double peak distribution, and is finite size scaling invariant. We also study the approach to the thermodynamic limit of the ground state magnetization at the phase transition.

Despite extensive work on the interplay between traffic dynamics and epidemic spreading, the control of epidemic spreading by routing strategies has not received adequate attention. In this paper, we study the impact of an efficient routing protocol on epidemic spreading. In the case of infinite node-delivery capacity, where the traffic is free of congestion, we find that that there exist optimal values of routing parameter, leading to the maximal epidemic threshold. This means that epidemic spreading can be effectively controlled by fine tuning the routing scheme. Moreover, we find that an increase in the average network connectivity and the emergence of traffic congestion can suppress the epidemic outbreak.

The full set of vibrational energies {E_υ} and the maximum vibrational quantum number υ_max generated by an algebraic method (AM) are suggested to implement classical statistical thermodynamic formulae. This protocol is applied to study the molar vibrational internal energy, molar vibrational entropy and molar vibrational heat capacity of a macro-system consisting of the ground electronic state X¹Σ⁺ of CO molecules. Comparisons of theoretical results with experimental measurements show that the AM statistical thermodynamic quantities are much better than those generated using beautiful analytical formulae that are based on the traditional simple harmonic oscillator (SHO) vibrational model, and that the suggested protocol can be extended to study statistical thermodynamic properties of any macro-diatomic system.

We consider the time evolution following a quantum quench in spin-1/2 chains. It is well known that local conservation laws constrain the dynamics and, eventually, the stationary behavior of local observables. We show that some widely studied models, such as the quantum XY model, possess extra families of local conservation laws in addition to the translation invariant ones. As a consequence, the additional charges must be included in the generalized Gibbs ensemble that describes the stationary properties. The effects go well beyond a simple redefinition of the stationary state. The time evolution of a non-translation-invariant state under a (translation-invariant) Hamiltonian with a perturbation that weakly breaks the hidden symmetries underlying the extra conservation laws exhibits pre-relaxation. In addition, in the limit of small perturbation, the time evolution following pre-relaxation can be described by means of a time-dependent generalized Gibbs ensemble.

Recent empirical analyses of some realistic dynamical networks have demonstrated that their degree distributions are stable scale-free (SF), but the instantaneous well-connected hubs at one point of time can quickly become weakly connected. Motivated by these empirical results, we propose a simple toy dynamical agent-to-agent contact network model, in which each agent stays at one node of a static underlay network and the nearest neighbors swap their positions with each other. Although the degree distribution of the dynamical network model at any one time is equal to that in the static underlay network, the numbers and identities of each agent's contacts will change over time. It is found that the dynamic interaction tends to suppress epidemic spreading in terms of larger epidemic threshold, smaller prevalence (the fraction of infected individuals) and smaller velocity of epidemic outbreak. Furthermore, the dynamic interaction results in the prevalence to undergo a phase transition at a finite threshold of the epidemic spread rate in the thermodynamic limit, which is in contradiction to the absence of an epidemic threshold in static SF networks. Some of these findings obtained from heterogeneous mean-field theory are in good agreement with numerical simulations.

We investigate a minimal model of the plastic deformation of amorphous materials. The material elements are assumed to exhibit ideally plastic behavior (J2 plasticity). Structural disorder is considered in terms of random variations of the local yield stresses. Using a finite element implementation of this simple model, we simulate the plane strain deformation of long thin rods loaded in tension. The resulting strain patterns are statistically characterized in terms of their spatial correlation functions. Studies of the corresponding surface morphology reveal a non-trivial Hurst exponent H ≈ 0.8, indicating the presence of long-range correlations in the deformation patterns. The simulated deformation patterns and surface morphology exhibit persistent features which emerge already at the very onset of plastic deformation, while subsequent evolution is characterized by growth in amplitude without major morphology changes. The findings are compared to experimental observations.

Various applications like finding Web communities, detecting the structure of social networks, and even analyzing a graph's structure to uncover Internet attacks are just some of the applications for which community detection is important. In this paper, we propose an algorithm that finds the entire community structure of a network, on the basis of local interactions between neighboring nodes and an unsupervised distributed hierarchical clustering algorithm. The novelty of the proposed approach, named SCCD (standing for synthetic coordinate community detection), lies in the fact that the algorithm is based on the use of Vivaldi synthetic network coordinates computed by a distributed algorithm. The current paper not only presents an efficient distributed community finding algorithm, but also demonstrates that synthetic network coordinates could be used to derive efficient solutions to a variety of problems. Experimental results and comparisons with other methods from the literature are presented for a variety of benchmark graphs with known community structure, derived from varying a number of graph parameters and real data set graphs. The experimental results and comparisons to existing methods with similar computation cost on real and synthetic data sets demonstrate the high performance and robustness of the proposed scheme.

The dynamics of stochastic systems, both classical and quantum, can be studied by analysing the statistical properties of dynamical trajectories. The properties of ensembles of such trajectories for long, but fixed, times are described by large-deviation (LD) rate functions. These LD functions play the role of dynamical free energies: they are cumulant generating functions for time-integrated observables, and their analytic structure encodes dynamical phase behaviour. This 'thermodynamics of trajectories' approach is to trajectories and dynamics what the equilibrium ensemble method of statistical mechanics is to configurations and statics. Here we show that, just like in the static case, there are a variety of alternative ensembles of trajectories, each defined by their global constraints, with that of trajectories of fixed total time being just one of these. We show how the LD functions that describe an ensemble of trajectories where some time-extensive quantity is constant (and large) but where total observation time fluctuates can be mapped to those of the fixed-time ensemble. We discuss how the correspondence between generalized ensembles can be exploited in path sampling schemes for generating rare dynamical trajectories.

We evaluate the exact energy current and scaled cumulant generating function (related to the large-deviation function) in non-equilibrium steady states with energy flow, in any integrable model of relativistic quantum field theory (IQFT) with diagonal scattering. Our derivations are based on various recent results of Bernard and Doyon. The steady states are built by connecting homogeneously two infinite halves of the system thermalized at different temperatures T_l, T_r, and waiting for a long time. We evaluate the current J(T_l, T_r) using the exact QFT density matrix describing these non-equilibrium steady states and using Zamolodchikov's method of the thermodynamic Bethe ansatz (TBA). The scaled cumulant generating function is obtained from the extended fluctuation relations which hold in integrable models. We verify our formula in particular by showing that the conformal field theory (CFT) result is obtained in the high-temperature limit. We analyze numerically our non-equilibrium steady-state TBA equations for three models: the sinh-Gordon model, the roaming trajectories model, and the sine-Gordon model at a particular reflectionless point. Based on the numerics, we conjecture that an infinite family of non-equilibrium c-functions, associated with the scaled cumulants, can be defined, which we interpret physically. We study the full scaled distribution function and find that it can be described by a set of independent Poisson processes. Finally, we show that the 'additivity' property of the current, which is known to hold in CFT and was proposed to hold more generally, does not hold in general IQFT—that is, J(T_l, T_r) is not of the form f(T_l) − f(T_r).

We argue that when a social convergence mechanism exists and is strong enough, one should expect the emergence of a well-defined 'field', i.e. a slowly evolving, local quantity around which individual attributes fluctuate in a finite range. This condensation phenomenon is well illustrated by the Deffuant–Weisbuch opinion model for which we provide a natural extension to allow for spatial heterogeneities. We show analytically and numerically that the resulting dynamics of the emergent field is a noisy diffusion equation that has a slow dynamics. This random diffusion equation reproduces the long-ranged, logarithmic decrease of the correlation of spatial voting patterns empirically found in Borghesi and Bouchaud (2010 Eur. Phys. J. B 75 395) and Borghesi et al (2012 PLoS One 7 e36289). Interestingly enough, we find that when the social cohesion mechanism becomes too weak, cultural cohesion breaks down completely, in the sense that the distribution of intentions/opinions becomes infinitely broad. No emerging field exists in this case. All these analytical findings are confirmed by numerical simulations of an agent-based model.

We address the effect of disorder geometry on the critical force in disordered elastic systems. We focus on the model system of a long-range elastic line driven in a random landscape. In the collective pinning regime, we compute the critical force perturbatively. Not only does our expression for the critical force confirm previous results on its scaling with respect to the microscopic disorder parameters, but it also provides its precise dependence on the disorder geometry (represented by the disorder two-point correlation function). Our results are successfully compared with the results of numerical simulations for random field and random bond disorders.

It is well known that most real-world complex networks, such as the Internet and the World Wide Web, are evolving networks. An interesting fundamental question is: how do some important functions or dynamical behaviors of complex networks evolve with increasing network scale? This paper aims at investigating the scalability of the synchronizability for ring or chain networks with dense clusters as the network size increases. We discover some interesting phenomena as follows: (i) the synchronizability of ring or chain networks with clusters decreases with increasing network scale regardless of the inner structures of all communities; (ii) for the same network scale, the network synchronizability decreases more quickly with increasing number of cluster blocks than with increasing number of nodes within the cluster block; (iii) the number of rings or chains has a much more significant influence on the network synchronizability than the size of the rings or chains. Our results indicate that network synchronizability can be maintained with increasing network scale by avoiding ring and chain structures.

A fundamental question related to innovation diffusion is how the structure of the social network influences the process. Empirical evidence regarding real-world networks of influence is very limited. On the other hand, agent-based modeling literature reports different, and at times seemingly contradictory, results. In this paper we study innovation diffusion processes for a range of Watts–Strogatz networks in an attempt to shed more light on this problem. Using the so-called Sznajd model as the backbone of opinion dynamics, we find that the published results are in fact consistent and allow us to predict the role of network topology in various situations. In particular, the diffusion of innovation is easier on more regular graphs, i.e. with a higher clustering coefficient. Moreover, in the case of uncertainty—which is particularly high for innovations connected to public health programs or ecological campaigns—a more clustered network will help the diffusion. On the other hand, when social influence is less important (i.e. in the case of perfect information), a shorter path will help the innovation to spread in the society and—as a result—the diffusion will be easiest on a random graph.

Monte Carlo simulations of colloidal aggregation were performed showing that, by increasing the range or the height of a repulsive barrier of non-negligible width between the particles, the fractal dimension of the formed clusters decreases, at least for not very large clusters. This result offers an explanation of old experimental findings of 2D aggregates, with a low fractal dimensionality, made of silica colloids confined on the air–water interface, as well as of very recent experimental results of low fractal dimensionality of clusters of diverse colloids in 3D, when the size of the primary particles is increased. This second case was studied through an analysis of the Derjaguin–Landau–Verwey–Overbeek (DLVO) potential between the particles.

In this paper, we analyze a reaction–diffusion (R–D) system with a double negative feedback loop and find cases where self diffusion alone cannot lead to Turing pattern formation but cross diffusion can. Specifically, we first derive a set of sufficient conditions for Turing instability by performing linear stability analysis, then plot two bifurcation diagrams that specifically identify Turing regions in the parameter phase plane, and finally numerically demonstrate representative Turing patterns according to the theoretical predictions. Our analysis combined with previous studies actually implies an interesting fact that Turing patterns can be generated not only in a class of monostable R–D systems where cross diffusion is not necessary but also in a class of bistable R–D systems where cross diffusion is necessary. In addition, our model would be a good candidate for experimentally testing Turing pattern formation from the viewpoint of synthetic biology.

We investigate the behaviour of the mean size of directed compact percolation clusters near a damp wall in the low-density region, where sites in the bulk are wet (occupied) with probability p while sites on the wall are wet with probability p_w. Methods used to find the exact solution for the dry case (p_w = 0) and the wet case (p_w = 1) turn out to be inadequate for the damp case. Instead we use a series expansion for the p_w = 2p case to obtain a second-order inhomogeneous differential equation satisfied by the mean size, which exhibits a critical exponent γ = 2, in common with the wet wall result. For the more general case of p_w = rp, with r rational, we use a modular arithmetic method for finding ordinary differential equations (ODEs) and obtain a fourth-order homogeneous ODE satisfied by the series. The ODE is expressed exactly in terms of r. We find that in the damp region 0 < r < 2 the critical exponent γ^damp = 1, which is the same as the dry wall result.

This paper provides a complete analytical solution to the Brownian motion of a self-propelled particle that moves in two spatial dimensions in the overdamped limit by satisfying kinematic constraints. The analytical expression of any-order moment of the probability distribution is obtained by a direct integration of the Langevin equation. Each moment is expressed as a multiple integral of the active motion performed by the particle. This allows us to obtain any-order moment for any active motion, i.e. when the particle is propelled by arbitrary time-dependent force and torque. For the special case when the ratio between the force and the torque is constant, the multiple integrals can be easily analytically solved and expressed as the real or the imaginary parts of suitable analytic functions. As an application of the derived analytical results, the paper investigates the diffusivity of the considered Brownian motion for constant and for arbitrary time-dependent force and torque.

We consider non-equilibrium quantum steady states in conformal field theory (CFT) on star-graph configurations, with a particular, simple connection condition at the vertex of the graph. These steady states occur after a large time as a result of initially thermalizing the legs of the graph at different temperatures, and carry energy flows. Using purely Virasoro algebraic calculations we evaluate the exact scaled cumulant generating function for these flows. We show that this function satisfies a generalization of the usual non-equilibrium fluctuation relations. This extends results by two of the authors to the case of more than two legs. It also provides an alternative derivation centered on Virasoro algebra operators rather than local fields, hence an alternative regularization scheme, thus confirming the validity and universality of the scaled cumulant generating function. Our derivation shows how the usual Virasoro algebra leads, in large volumes, to a continuous-index Virasoro algebra for which we develop diagrammatic principles, which may be of interest in other non-equilibrium contexts as well. Finally, our results shed light on the Poisson-process interpretation of the long-time energy transfer in CFT.

Physical reasons for a crucial difference between the results of a three-phase theory developed recently (Kerner 2011 Phys. Rev. E 84 045102(R); 2013 Europhys. Lett. 102 28010; 2014 Physica A 397 76) and the classical theory are explained. Microscopic characteristics of traffic passing a traffic signal during the green signal phase and their dependence on the duration of the green phase have been found. It turns out that a moving synchronized flow pattern (MSP), which occurs in under-saturated traffic at the signal, causes 'compression' of traffic flow: the rate of MSP discharge can be considerably larger than the saturation flow rate of the classical traffic theory of city traffic. This leads to a considerably larger rate of traffic passing the signal in comparison with the saturation flow rate. This effect together with traffic behavior at the upstream queue front explains the metastability of under-saturated traffic with respect to a random time-delayed traffic breakdown.