Random point patterns are ubiquitous in nature, and statistical models such as point processes, i.e., algorithms that generate stochastic collections of points, are commonly used to simulate and interpret them. We propose an application of quantum computing to statistical modeling by establishing a connection between point processes and Gaussian boson sampling, an algorithm for photonic quantum computers. We show that Gaussian boson sampling can be used to implement a class of point processes based on hard-to-compute matrix functions which, in general, are intractable to simulate classically. We also discuss situations where polynomial-time classical methods exist. This leads to a family of efficient quantum-inspired point processes, including a fast classical algorithm for permanental point processes. We investigate the statistical properties of point processes based on Gaussian boson sampling and reveal their defining property: like bosons that bunch together, they generate collections of points that form clusters. Finally, we analyze properties of these point processes for homogeneous and inhomogeneous state spaces, describe methods to control cluster location, and illustrate how to encode correlation matrices.

Recent experimental findings on anomalous diffusion have demanded novel models that combine annealed (temporal) and quenched (spatial or static) disorder mechanisms. The comb model is a simplified description of diffusion on percolation clusters, where the comblike structure mimics quenched disorder mechanisms and yields a subdiffusive regime. Here we extend the comb model to simultaneously account for quenched and annealed disorder mechanisms. To do so, we replace usual derivatives in the comb diffusion equation by different fractional time-derivative operators and the conventional comblike structure by a generalized fractal structure. Our hybrid comb models thus represent a diffusion where different comblike structures describe different quenched disorder mechanisms, and the fractional operators account for various annealed disorder mechanisms. We find exact solutions for the diffusion propagator and mean square displacement in terms of different memory kernels used for defining the fractional operators. Among other findings, we show that these models describe crossovers from subdiffusion to Brownian or confined diffusions, situations emerging in empirical results. These results reveal the critical role of interactions between geometrical restrictions and memory effects on modeling anomalous diffusion.

Theoretical expressions for the distribution of the ratio of consecutive level spacings for quantum systems with transiting dynamics remain unknown. We propose a family of one-parameter distributions $P\left(r\right)\equiv P(r;\beta )$, where $\beta \in [0,+\infty )$ is a generalized Dyson index, that describes the eigenlevel statistics of a quantum system characterized by different symmetries and degrees of chaos. We show that this crossover strongly depends on the specific properties of each model, and thus the reduction of such a family to a universal formula, albeit desirable, is not possible. We use the information entropy as a criterion to suggest particular ansätze for different transitions, with a negligible associated error in the limits corresponding to standard random ensembles.

We consider time-average quantities of chaotic systems and their sensitivity to system parameters. When the parameters are random variables with a prescribed probability density function, the sensitivities are also random. The central aim of the paper is to study and quantify the uncertainty of the sensitivities; this is useful to know in robust design applications. To this end, we couple the nonintrusive polynomial chaos expansion (PCE) with the multiple shooting shadowing (MSS) method, and apply the coupled method to two standard chaotic systems, the Lorenz system and the Kuramoto-Sivashinsky equation. The method leads to accurate results that match well with Monte Carlo simulations (even for low chaos orders, at least for the two systems examined), but it is costly. However, if we apply the concept of shadowing to the system trajectories evaluated at the quadrature integration points of PCE, then the resulting regularization can lead to significant computational savings. We call the new method shadowed PCE (sPCE).

Many interdependent, real-world infrastructures involve interconnections between different communities or cities. Here we show how the effects of such interconnections can be described as an external field for interdependent networks experiencing a first-order percolation transition. We find that the critical exponents $\gamma$ and $\delta$, related to the external field, can also be defined for first-order transitions but that they have different values than those found for second-order transitions. Surprisingly, we find that both sets of different exponents (for first and second order) can even be found within a single model of interdependent networks, depending on the dependency coupling strength. Nevertheless, in both cases both sets satisfy Widom's identity, $\delta -1=\gamma /\beta$, which further supports the validity of their definitions. Furthermore, we find that both Erdős-Rényi and scale-free networks have the same values of the exponents in the first-order regime, implying that these models are in the same universality class. In addition, we find that in $k$-core percolation the values of the critical exponents related to the field are the same as for interdependent networks, suggesting that these systems also belong to the same universality class.

In this paper we consider a biased velocity jump process with excluded-volume interactions for chemotaxis, where we account for the size of each particle. Starting with a system of $N$ individual hard rod particles in one dimension, we derive a nonlinear kinetic model using two different approaches. The first approach is a systematic derivation for small occupied fraction of particles based on the method of matched asymptotic expansions. The second approach, based on a compression method that exploits the single-file motion of hard core particles, does not have the limitation of a small occupied fraction but requires constant tumbling rates. We validate our nonlinear model with numerical simulations, comparing its solutions with the corresponding noninteracting linear model as well as stochastic simulations of the underlying particle system.

In the nuclear pore complex, intrinsically disordered nuclear pore proteins (FG Nups) form a selective barrier for transport into and out of the cell nucleus, in a way that remains poorly understood. The collective FG Nup behavior has long been conceptualized either as a polymer brush, dominated by entropic and excluded-volume (repulsive) interactions, or as a hydrogel, dominated by cohesive (attractive) interactions between FG Nups. Here we compare mesoscale computational simulations with a wide range of experimental data to demonstrate that FG Nups are at the crossover point between these two regimes. Specifically, we find that repulsive and attractive interactions are balanced, resulting in morphologies and dynamics that are close to those of ideal polymer chains. We demonstrate that this property of FG Nups yields sufficient cohesion to seal the transport barrier, and yet maintains fast dynamics at the molecular scale, permitting the rapid polymer rearrangements needed for transport events.

We focus on a dilute uniform suspension of magnetic nanoparticles in a nematic-filled micron-sized shallow well with tangent boundary conditions as a paradigm system with two coupled order parameters. This system exhibits spontaneous magnetization without magnetic fields. We numerically obtain the stable nematic and associated magnetization morphologies, induced purely by the geometry, the boundary conditions, and the coupling between the magnetic nanoparticles and the host nematic medium. Our most striking observations pertain to domain walls in the magnetization profile, whose location can be manipulated by the coupling and material properties, and stable interior and boundary nematic defects, whose location and multiplicity can be tailored by the coupling too. These tailored morphologies are not accessible in uncoupled systems and can be used for multistable systems with singularities and stable interfaces.

Bistable nonequilibrium systems are realized in catalytic reaction-diffusion processes, biological transport and regulation, spatial epidemics, etc. Behavior in spatially continuous formulations, described at the mean-field level by reaction-diffusion type equations (RDEs), often mimics that of classic equilibrium van der Waals type systems. When accounting for noise, similarities include a discontinuous phase transition at some value, $p_{\mathrm{eq}}$, of a control parameter, $p$, with metastability and hysteresis around $p_{\mathrm{eq}}$. For each $p$, there is a unique critical droplet of the more stable phase embedded in the less stable or metastable phase which is stationary (neither shrinking nor growing), and with size diverging as $p\to p_{\mathrm{eq}}$. Spatially discrete analogs of these mean-field formulations, described by lattice differential equations (LDEs), are more appropriate for some applications, but have received less attention. It is recognized that LDEs can exhibit richer behavior than RDEs, specifically propagation failure for planar interphases separating distinct phases. We show that this feature, together with an orientation dependence of planar interface propagation also deriving from spatial discreteness, results in the occurrence of entire families of stationary droplets. The extent of these families increases approaching the transition and can be infinite if propagation failure is realized. In addition, there can exist a regime of generic two-phase coexistence where arbitrarily large droplets of either phase always shrink. Such rich behavior is qualitatively distinct from that for classic nucleation in equilibrium and spatially continuous nonequilibrium systems.

In order to understand the dynamics of granular flows, one must have knowledge about the solid volume fraction. However, its reliable experimental estimation is still a challenging task. Here, we present the application of a stochastic-optical method (SOM) [L. Sarno et al., Granul. Matter 18, 80 (2016)] to an array of spheres arranged according to faced-centered cubic lattices, where spheres' locations are known a priori. The purpose of this study is to test the robustness of the image binarization algorithm, introduced in the SOM for the indirect estimation of the near-wall volume fraction through an optically measurable quantity, defined as two-dimensional volume fraction. A comprehensive range of volume fractions and illumination conditions are numerically and experimentally investigated. The proposed binarization algorithm is found to yield reasonably accurate estimations of the two-dimensional volume fraction with a root-mean-square error smaller than 0.03 for all investigated illumination conditions. A slightly worse performance is observed for samples with relatively low volume fractions (<0.3), where the binarization algorithm occasionally cannot identify the surface elements in the second and third layers of the regular lattice.

We investigate the computational hardness of spin-glass instances on a square lattice, generated via a recently introduced tunable and scalable approach for planting solutions. The method relies on partitioning the problem graph into edge-disjoint subgraphs and planting frustrated, elementary subproblems that share a common local ground state, which guarantees that the ground state of the entire problem is known a priori. Using population annealing Monte Carlo, we compare the typical hardness of problem classes over a large region of the multidimensional tuning parameter space. Our results show that the problems have a wide range of tunable hardness. Moreover, we observe multiple transitions in the hardness phase space, which we further corroborate using simulated annealing and simulated quantum annealing. By investigating thermodynamic properties of these planted systems, we demonstrate that the harder samples undergo magnetic ordering transitions which are also ultimately responsible for the observed hardness transitions on changing the sample composition.

The critical dynamics of ‘model A” of Hohenberg and Halperin has been studied by the Monte Carlo method. Simulations have been carried out in the three-dimensional (3d) simple cubic Ising model for lattices of sizes $L=16$ to $L=512$. Using Wolff's cluster algorithm, the critical temperature is precisely found as ${\beta }_c=0.22165468\left(5\right)$. By Fourier transform of the lattice configurations, the critical scattering intensities $I\left(\vec{q}\right)$ can be obtained. After circular averaging, the static simulations with $L=256$ and $L=512$ provide an estimate of the critical exponent $\gamma /\nu =2-\eta =1.9640\left(5\right)$. The $|\vec{q}|$-dependent distribution of $I\left(\vec{q}\right)$ showed an exponential distribution, corresponding to a Gaussian distribution of the scattering amplitudes for a large $q$ domain. The time-dependent intensities were then used for the study of the critical dynamics of 3d lattices at the critical point. To simulate results of an x-ray photon correlation spectroscopy experiment, the time-dependent correlation function of the intensities was studied for each $|\vec{q}|$-value. In the $q$ region where $I\left(\vec{q}\right)$ had an exponential distribution, the time correlations can be fit to a stretched exponential, where the exponent $\mu =\gamma /\nu z\simeq 0.975$ provides an estimate of the dynamic exponent $z$. This corresponds to $z=2.0145$, in agreement with the observed variations of the characteristic fluctuation time of the intensity: $\tau \left(q\right)\propto q^{-z}$, which gives $z=2.015$. These results agree with the $\epsilon$ expansion of field-theoretical methods (2.017). In this paper, the need to take account of the anomalous time behavior ($\mu <1$) in the dynamics is exemplified. This dynamics reflects a nonlinear time behavior of model A, and its large time extension is discussed in detail.

On the basis of a self-consistent cluster effective-medium approximation for random trapping transport, we study the problem of self-averaging of the diffusion coefficient in a nonstationary formulation. In the long-time domain, we investigate different cases that correspond to the increasing degree of disorder. In the regular and subregular cases the diffusion coefficient is found to be a self-averaging quantity—its relative fluctuations (relative standard deviation) decay in time in a power-law fashion. In the subdispersive case the diffusion coefficient is self-averaging in three dimensions (3D) and weakly self-averaging in two dimensions (2D) and one dimension (1D), when its relative fluctuations decay anomalously slowly logarithmically. In the dispersive case, the diffusion coefficient is self-averaging in 3D, weakly self-averaging in 2D, and non-self-averaging in 1D. When non-self-averaging, its fluctuations remain of the same order as, or larger than, its average value. In the irreversible case, the diffusion coefficient is non-self-averaging in any dimension. In general, with the decreasing dimension and/or increasing disorder, the self-averaging worsens and eventually disappears. In the cases of weak self-averaging and, especially, non-self-averaging, the reliable reproducible experimental measurements are highly problematic. In all the cases under consideration, asymptotics with prefactors are obtained beyond the scaling laws. Transition between all cases is analyzed as the disorder increases.

Modeling thermal transport through interfaces has been one of the most challenging problems in nanoscale heat transfer. Although continuous theoretical efforts have been made, there has been no consensus on how to rigorously incorporate temperature effect and anharmonicity. In this paper, we adopt the self-consistent anharmonic phonon concept for nonlinear lattices to investigate phonon propagation within the materials as well as across interfaces based on equilibrium molecular dynamics simulations. Based on linear response theory, we propose an efficient method to calculate the frequency-dependent transmission coefficient in a nonlinear lattice. The transmission spectrum is extracted directly from velocity correlations, which naturally includes anharmonic effects. Phonon renormalization at finite temperature can also be easily handled using the proposed method. Our results are consistent with the atomistic Green's function method at the limit of weak anharmonicity. For nonlinear lattices under high temperatures, the anharmonicity is found to increase the cutoff frequency of the transmission coefficient due to phonon renormalization. Further analysis shows that the anharmonicity also promotes interfacial thermal conductance by causing the redistribution of the spectral flux of the excited vibrational waves during their propogation.

The entanglement of eigenstates in two coupled, classically chaotic kicked tops is studied in dependence of their interaction strength. The transition from the noninteracting and unentangled system toward full random matrix behavior is governed by a universal scaling parameter. Using suitable random matrix transition ensembles we express this transition parameter as a function of the subsystem sizes and the coupling strength for both unitary and orthogonal symmetry classes. The universality is confirmed for the level spacing statistics of the coupled kicked tops and a perturbative description is in good agreement with numerical results. The statistics of Schmidt eigenvalues and entanglement entropies of eigenstates is found to follow a universal scaling as well. Remarkably, this is not only the case for large subsystems of equal size but also if one of them is much smaller. For the entanglement entropies a perturbative description is obtained, which can be extended to large couplings and provides very good agreement with numerical results. Furthermore, the transition of the statistics of the entanglement spectrum toward the random matrix limit is demonstrated for different ratios of the subsystem sizes.

Multiple organs in a living system respond to environmental changes, and the signals from the organs regulate the physiological environment. Inspired by this biological feedback, we propose a simple autonomous system of active rotators to explain how multiple units are synchronized under a fluctuating environment. We find that the feedback via an environment can entrain rotators to have synchronous phases for specific conditions. This mechanism is markedly different from the simple entrainment by a common oscillatory external stimulus that is not interacting with systems. We theoretically examine how the phase synchronization depends on the interaction strength between rotators and environment. Furthermore, we successfully demonstrate the proposed model by realizing an analog electric circuit with microelectronic devices. This bioinspired platform can be used as a sensor for monitoring varying environments and as a controller for amplifying signals by their feedback-induced synchronization.

Variability in the dynamical function of nodes comprising a complex network impacts upon cascading failures that can compromise the network's ability to operate. Node types correspond to sources, sinks, or passive conduits of a current flow, applicable to renewable electrical power microgrids containing a variable number of intermittently operating generators and consumers of power. The resilience to cascading failures of ensembles of synthetic networks with different topology is examined as a function of the edge current carrying capacity and mix of node types, together with exemplar real-world networks. While a network with a homogeneous composition of node types can be resilient to failure, onewith an identical topology but with heterogeneous nodes can be strongly susceptible to failure. For networks with similar numbers of sources, sinks, and passive nodes the mean resilience decreases as networks become more disordered. Nevertheless all network topologies have enhanced regions of resilience, accessible by the manipulation of node composition and functionality.

We present an ensemble Monte Carlo growth method to sample the equilibrium thermodynamic properties of random chains. The method is based on the multicanonical technique of computing the density of states in the energy space. Such a quantity is temperature independent, and therefore microcanonical and canonical thermodynamic quantities, including the free energy, entropy, and thermal averages, can be obtained by reweighting with a Boltzmann factor. The algorithm we present combines two approaches: The first is the Monte Carlo ensemble growth method, where a “population” of samples in the state space is considered, as opposed to traditional sampling by long random walks, or iterative single-chain growth. The second is the flat-histogram Monte Carlo, similar to the popular Wang-Landau sampling, or to multicanonical chain-growth sampling. We discuss the performance and relative simplicity of the proposed algorithm, and we apply it to known test cases.