Biological neuronal networks exhibit highly variable spiking activity. Balanced networks offer a parsimonious model of this variability in which strong excitatory synaptic inputs are canceled by strong inhibitory inputs on average, and irregular spiking activity is driven by fluctuating synaptic currents. Most previous studies of balanced networks assume a homogeneous or distance-dependent connectivity structure, but connectivity in biological cortical networks is more intricate. We use a heterogeneous mean-field theory of balanced networks to show that heterogeneous in-degrees can break balance. Moreover, heterogeneous architectures that achieve balance promote lower firing rates in neurons with larger in-degrees, consistent with some recent experimental observations.

The growth of multicomponent structures in simulations and experiments often results in kinetically trapped, nonequilibrium objects. In such cases we have no general theoretical framework for predicting the outcome of the growth process. Here we use computer simulations to study the growth of two-component structures within a simple lattice model. We show that kinetic trapping happens for many choices of growth rate and intercomponent interaction energies, and that qualitatively distinct kinds of kinetic trapping are found in different regions of parameter space. In a region in which the low-energy structure is an “antiferromagnet” or “checkerboard,” we show that the grown nonequilibrium structure displays a component-type stoichiometry that is different from the equilibrium one but is insensitive to growth rate and solution conditions. This robust nonequilibrium stoichiometry can be predicted via a mapping to the jammed random tiling of dimers studied by Flory, a finding that suggests a way of making defined nonequilibrium structures in experiment.

Within the point-vortex model, we compute the probability distribution function of the velocity fluctuations induced by same-sign vortices scattered within a disk according to a fractal distribution of distances to the origin $\sim r^{-\alpha }$. We show that the different random configurations of vortices induce velocity fluctuations that are broadly distributed and follow a power-law tail distribution $P\left(V\right)\sim V^{\alpha -2}$ with a scaling exponent determined by the $\alpha$ exponent of the spatial distribution. We also show that the range of the power-law scaling regime in the velocity distribution is set by the mean density of vortices and the exponent $\alpha$ of the vortex density distribution.

This works reports the use of a complex network approach to produce a phylogenetic classification tree of a simple evolutionary model. This approach has already been used to treat proteomic data of actual extant organisms, but an investigation of its reliability to retrieve a traceable evolutionary history is missing. The used evolutionary model includes key ingredients for the emergence of groups of related organisms by differentiation through random mutations and population growth, but purposefully omits other realistic ingredients that are not strictly necessary to originate an evolutionary history. This choice causes the model to depend only on a small set of parameters, controlling the mutation probability and the population of different species. Our results indicate that for a set of parameter values, the phylogenetic classification produced by the used framework reproduces the actual evolutionary history with a very high average degree of accuracy. This includes parameter values where the species originated by the evolutionary dynamics have modular structures. In the more general context of community identification in complex networks, our model offers a simple setting for evaluating the effects, on the efficiency of community formation and identification, of the underlying dynamics generating the network itself.

The multidimensional energy surface of a cholesteric liquid crystal in a planar cell is investigated as a function of spherical coordinates determining the director orientation. Minima on the energy surface correspond to the stable states with particular director distribution. External electric and magnetic fields deform the energy surface and positions of minima. It can lead to the transitions between states, known as the Fréedericksz effect. Transitions can be continuous or discontinuous depending on parameters of the liquid crystal which determine an energy surface. In a case of discontinuous transition when a barrier between stable states is comparable with the thermal energy, the activation transitions may occur, and it leads to the modification of characteristics of the Fréedericksz effect with temperature without explicit temperature dependencies of liquid crystal parameters. A minimum energy path between stable states on the energy surface for the Fréedericksz transition is found using the geodesic nudged elastic band method. Knowledge of this path, which has maximal statistical weight among all other paths, gives the information about a barrier between stable states and configuration of director orientation during the transition. It also allows one to estimate the stability of states with respect to the thermal fluctuations and their lifetime when the system is close to the Fréedericksz transition.

Of the two approaches of density-functional theory molecular dynamics, quantum molecular dynamics is limited at high temperature by computational cost whereas orbital-free molecular dynamics, based on an approximation of the kinetic electronic free energy, can be implemented in this domain. In the case of deuterium, it is shown how orbital-free molecular dynamics can be regarded as the limit of quantum molecular dynamics at high temperature for the calculation of the equation of state. To this end, accurate quantum molecular dynamics calculations are performed up to 20 eV at mass densities as low as $0.5\mathrm{g}/{\mathrm{cm}}^3$ and up to 10 eV at mass densities as low as $0.2\mathrm{g}/{\mathrm{cm}}^3$. As a result, the limitation in temperature so far attributed to quantum molecular dynamics is overcome and an approach combining quantum and orbital-free molecular dynamics is used to construct an equation of state of deuterium. The thermodynamic domain addressed is that of the fluid phase above 1 eV and $0.2\mathrm{g}/{\mathrm{cm}}^3$. Both pressure and internal energy are calculated as functions of temperature and mass density, and various exchange-correlation contributions are compared. The generalized gradient approximation of the exchange-correlation functional, corrected to approximately include the influence of temperature, is retained and the results obtained are compared to other approaches and to experimental shock data; in parts of the thermodynamic domain addressed, these results significantly differ from those obtained in other first-principles investigations which themselves disagree. The equations of state of hydrogen and tritium above 1 eV and above, respectively, $0.1\mathrm{g}/{\mathrm{cm}}^3$ and $0.3\mathrm{g}/{\mathrm{cm}}^3$, can be simply obtained by mass density scaling from the results found for deuterium. This ab initio approach allows one to consistently cover a very large domain of temperature on the domain of mass density outlined above.

We propose a version of the pure temporal epidemic type aftershock sequences (ETAS) model: the ETAS model with correlated magnitudes. As for the standard case, we assume the Gutenberg-Richter law to be the probability density for the magnitudes of the background events. Instead, the magnitude of the triggered shocks is assumed to be probabilistically dependent on that of the relative mother events. This probabilistic dependence is motivated by some recent works in the literature and by the results of a statistical analysis made on some seismic catalogs [Spassiani and Sebastiani, J. Geophys. Res. 121, 903 (2016)]. On the basis of the experimental evidences obtained in the latter paper for the real catalogs, we theoretically derive the probability density function for the magnitudes of the triggered shocks proposed in Spassiani and Sebastiani and there used for the analysis of two simulated catalogs. To this aim, we impose a fundamental condition: averaging over all the magnitudes of the mother events, we must obtain again the Gutenberg-Richter law. This ensures the validity of this law at any event's generation when ignoring past seismicity. The ETAS model with correlated magnitudes is then theoretically analyzed here. In particular, we use the tool of the probability generating function and the Palm theory, in order to derive an approximation of the probability of zero events in a small time interval and to interpret the results in terms of the interevent time between consecutive shocks, the latter being a very useful random variable in the assessment of seismic hazard.

A fundamental connection between thermodynamics and information theory arises from the fact that correlations exhibit an inherent work value. For noninteracting systems this translates to a work cost for establishing correlations. Here we investigate the relationship between work and correlations in the presence of interactions that cannot be controlled or removed. For such naturally coupled systems, which are correlated even in thermal equilibrium, we determine general strategies that can reduce the work cost of correlations, and illustrate these for a selection of exemplary physical systems.

The Granger causality (GC) analysis is an effective approach to infer causal relations for time series. However, for data obtained by uniform sampling (i.e., with an equal sampling time interval), it is known that GC can yield unreliable causal inference due to aliasing if the sampling rate is not sufficiently high. To solve this unreliability issue, we consider the nonuniform sampling scheme as it can mitigate against aliasing. By developing an unbiased estimation of power spectral density of nonuniformly sampled time series, we establish a framework of spectrum-based nonparametric GC analysis. Applying this framework to a general class of pulse-coupled nonlinear networks and utilizing some particular spectral structure possessed by these nonlinear network data, we demonstrate that, for such nonlinear networks with nonuniformly sampled data, reliable GC inference can be achieved at a low nonuniform mean sampling rate at which the traditional uniform sampling GC may lead to spurious causal inference.

We study the spreading of two mutually cooperative diseases on different network topologies, and with two microscopic realizations, both of which are stochastic versions of a susceptible-infected-removed type model studied by us recently in mean field approximation. There it had been found that cooperativity can lead to first order transitions from spreading to extinction. However, due to the rapid mixing implied by the mean field assumption, first order transitions required nonzero initial densities of sick individuals. For the stochastic model studied here the results depend strongly on the underlying network. First order transitions are found when there are few short but many long loops: (i) No first order transitions exist on trees and on 2-d lattices with local contacts. (ii) They do exist on Erdős-Rényi (ER) networks, on $d$-dimensional lattices with $d\ge 4$, and on 2-d lattices with sufficiently long-ranged contacts. (iii) On 3-d lattices with local contacts the results depend on the microscopic details of the implementation. (iv) While single infected seeds can always lead to infinite epidemics on regular lattices, on ER networks one sometimes needs finite initial densities of infected nodes. (v) In all cases the first order transitions are actually “hybrid”; i.e., they display also power law scaling usually associated with second order transitions. On regular lattices, our model can also be interpreted as the growth of an interface due to cooperative attachment of two species of particles. Critically pinned interfaces in this model seem to be in different universality classes than standard critically pinned interfaces in models with forbidden overhangs. Finally, the detailed results mentioned above hold only when both diseases propagate along the same network of links. If they use different links, results can be rather different in detail, but are similar overall.

On the basis of experimental data and mathematical equations in the literature, we remodel the ionic dynamics of smooth muscle cells (SMCs) as an eigensystem formulation, which is valid for investigating finite variations of variables from the equilibrium such as in common experimental operations. This algorithm provides an alternate viewpoint from frequency-domain analysis and enables one to probe functionalities of SMCs' rhythm by means of a resonance-related mechanism. Numerical results show three types of calcium oscillations of SMCs in mesenteric arterioles: spontaneous calcium oscillation, agonist-dependent calcium oscillation, and agonist-dependent calcium spike. For simple single and double SMCs, we demonstrate properties of synchronization among complex signals related to calcium oscillations, and show different correlation relations between calcium and voltage signals for various synchronization and resonance conditions. For practical cell clusters, our analyses indicate that the rhythm of SMCs could (1) benefit enhancements of signal communications among remote cells, (2) respond to a significant calcium peaking against transient stimulations for triggering globally oscillating modes, and (3) characterize the globally oscillating modes via frog-leap (non-molecular-diffusion) calcium waves across inhomogeneous SMCs.

Backward stimulated Raman and Brillouin scattering (SRS and SBS) are experimentally investigated by using two successive 1-μm, 1.5-ps FWHM laser pulses. The collinear pulses, separated by 3 or 6 ps and of moderate laser intensities $\left(\sim 2\times {10}^{16}\mathrm{W}\mathrm{c}{\mathrm{m}}^{-2}\right)$, are fired into a preionized He plasma of density $\sim 2.5-6\times {10}^{19}\mathrm{c}{\mathrm{m}}^{-3}$. The electron plasma waves and ion acoustic waves, respectively driven by SRS and SBS, are analyzed through space- and time-resolved Thomson scattering. Depending on the laser and plasma parameters, we observe the effect of the first pulse on the time-resolved SRS and SBS signals of the second pulse. The measurements are found to qualitatively agree with the results of a large-scale particle-in-cell simulation.

Bombardment of a solid surface with a broad, obliquely incident ion beam frequently produces nanoscale surface ripples. The primary obstacle that prevents the adoption of ion bombardment as a nanofabrication tool is the high density of defects in the patterns that are typically formed. Our simulations indicate that ion bombardment can produce nearly defect-free ripples on the surface of an elemental solid if the sample is concurrently and periodically rocked about an axis orthogonal to the surface normal and the incident beam direction. We also investigate the conditions necessary for rocking to produce highly ordered ripples and discuss how the results of our simulations can be reproduced experimentally. Finally, our simulations show that periodic temporal oscillations of coefficients in the Kuramoto-Sivashinsky equation can suppress spatiotemporal chaos and lead to patterns with a high degree of order.

The recently developed extended local equilibrium approach to stochastic thermodynamics is applied to reactive systems. The properties of the fluctuating entropy and entropy production are analyzed for general linear and for prototypical nonlinear kinetic processes. It is shown that nonlinear kinetics typically induces deviations of the mean entropy production from its value in the deterministic (mean-field) limit. The probability distributions around the mean are derived and shown to qualitatively differ in thermodynamic equilibrium, under nonequilibrium conditions and in the vicinity of criticalities associated to the onset of multistability. In each case large deviation-type properties are shown to hold. The results are compared with those of alternative approaches developed in the literature.

We estimate the critical thresholds of bond and site percolation on nonplanar, effectively two-dimensional graphs with chimeralike topology. The building blocks of these graphs are complete and symmetric bipartite subgraphs of size $2n$, referred to as $K_{n,n}$ graphs. For the numerical simulations we use an efficient union-find-based algorithm and employ a finite-size scaling analysis to obtain the critical properties for both bond and site percolation. We report the respective percolation thresholds for different sizes of the bipartite subgraph and verify that the associated universality class is that of standard two-dimensional percolation. For the canonical chimera graph used in the D-Wave Systems Inc. quantum annealer ($n=4$), we discuss device failure in terms of network vulnerability, i.e., we determine the critical fraction of qubits and couplers that can be absent due to random failures prior to losing large-scale connectivity throughout the device.

Recent years have witnessed major advances in our understanding of nonequilibrium processes. The Jarzynski equality, for example, provides a link between equilibrium free energy differences and finite-time nonequilibrium dynamics. We propose a generalization of this relation to non-Hamiltonian dynamics, relevant for active matter systems, continuous feedback, and computer simulation. Surprisingly, this relation allows us to calculate the free energy difference between the desired initial and final equilibrium states using arbitrary dynamics. As a practical matter, this dissociation between the dynamics and the initial and final states promises to facilitate a range of techniques for free energy estimation in a single universal expression.

In the Yule-Simon process, creation and selection of words follows the preferential attachment mechanism, resulting in a power-law growth in the cumulative number of individual word occurrences as well as the power-law population distribution of the vocabulary. This is derived using mean-field approximation, assuming a continuum limit of both the time and number of word occurrences. However, time and word occurrences are inherently discrete in the process, and it is natural to assume that the cumulative number of word occurrences has a certain fluctuation around the average behavior predicted by the mean-field approximation. We derive the exact and approximate forms of the probability distribution of such fluctuation analytically, and confirm that those probability distributions are well supported by the numerical experiments.

Stochastic processes wherein the size of the state space is changing as a function of time offer models for the emergence of scale-invariant features observed in complex systems. I consider such a sample-space reducing (SSR) stochastic process that results in a random sequence of strictly decreasing integers $\left\{x\right(t\left)\right\},0\le t\le \tau$, with boundary conditions $x\left(0\right)=N$ and $x\left(\tau \right)$ = 1. This model is shown to be exactly solvable: ${\mathcal{P}}_N\left(\tau \right)$, the probability that the process survives for time $\tau$ is analytically evaluated. In the limit of large $N$, the asymptotic form of this probability distribution is Gaussian, with mean and variance both varying logarithmically with system size: $\langle \tau \rangle \sim lnN$ and ${\sigma }_{\tau }^2\sim lnN$. Correspondence can be made between survival-time statistics in the SSR process and record statistics of independent and identically distributed random variables.