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In a multi-robot system consisting of numerous agents, it may be impractical to individually identify each agent. Consequently, issuing specific commands to each agent might not be feasible. We therefore, introduce the concept of a Statistical multi-robot system (SMRS). Such systems comprises a very large number of agents that cannot be identified or located individually. Moreover, Since it is impractical to track and communicate the complete configuration of an SMRS, we resort to statistical physics methods, specifically gas kinetic knowledge, to extract their distribution. But unlike in Thermodynamics, we employ the fact robotic agents can sense their environment, communicate their microscopic state, and change their local behavior to enable control. The concept of an SMRS suggests that the comprising agents should be as simple as possible, for practical reasons. In this study, we demonstrate how an SMRS comprised of single-degree-of-freedom agents can be controlled by a global controller. Using the same rationale, we define a successful mission of an SMRS as one in which a sufficient portion of the agents accomplish the mission. To demonstrate the efficacy of our approach, we provide a motion planner and exemplify our formalism in both simulations and real-world experiments.One-Sentence Summary: To control huge multi robotic systems we resort to the theory of statistical-physics and utilize its macroscopic properties.

Fast simulation technology is very important to explore the consequences of air traffic management decision. Although a variety of simulation tools have been developed to make decisions for air traffic controllers, the cognitive process of air traffic controllers is not effectively integrated into these tools. This article studies a probabilistic cellular automata (CA) model for air traffic flow simulation. By introducing the safety distance parameter into the CA model, the equilibrium property of air traffic system is studiedusing the statistical physics method. The simulation results show that the data are in good agreement with the measured results. [ABSTRACT FROM AUTHOR]

Disordered complex networks are of fundamental interest in statistical physics, and they have attracted recent interest as stochastic models for information transmission over wireless networks. While mathematically tractable, a network based on the regulation Poisson point process model offers challenges vis-a-vis network efficiency. Strongly correlated alternatives, such as networks based on random matrix spectra (the Ginibre network), on the other hand offer formidable challenges in terms of tractability and robustness issues. In this work, we demonstrate that network models based on random perturbations of Euclidean lattices interpolate between Poisson and rigidly structured networks, and allow us to achieve the best of both worlds: significantly improve upon the Poisson model in terms of network efficacy measured by the Signal to Interference plus Noise Ratio (abbrv. SINR) and the related concept of coverage probabilities, at the same time retaining a considerable measure of mathematical and computational simplicity and robustness to erasure and noise. We investigate the optimal choice of the base lattice in this model, connecting it to the celebrated problem optimality of Euclidean lattices with respect to the Epstein Zeta function, which is in turn related to notions of lattice energy. This leads us to the choice of the triangular lattice in 2D and face centered cubic lattice in 3D, whose Gaussian perturbations we consider. We provide theoretical analysis and empirical investigations to demonstrate that the coverage probability decreases with increasing strength of perturbation, eventually converging to that of the Poisson network. In the regime of low disorder, our studies suggest an approximate statistical behaviour of the coverage function near a base station as a log-normal distribution with parameters depending on the Epstein Zeta function of the lattice, and related approximate dependencies for a power-law constant that governs the network coverage probability at large thresholds. In 2D, we determine the disorder strength at which the perturbed triangular lattice (abbrv. PTL) and the Ginibre networks are the closest measured by comparing their network topologies via a comparison of their Persistence Diagrams in the total variation as well as the symmetrized nearest neighbour distances. We demonstrate that, at this very same disorder, the PTL and the Ginibre networks exhibit very similar coverage probability distributions, with the PTL performing at least as well as the Ginibre. Thus, the PTL network at this disorder strength can be taken to be an effective substitute for the Ginibre network model, while at the same time offering the advantages of greater tractability both from theoretical and empirical perspectives. [ABSTRACT FROM AUTHOR]

Tsallis and Rényi entropies, which are monotone transformations of each other, are deformations of the celebrated Shannon entropy. Maximization of these deformed entropies, under suitable constraints, leads to the $q$ -exponential family which has applications in non-extensive statistical physics, information theory and statistics. In previous information-geometric studies, the $q$ -exponential family was analyzed using classical convex duality and Bregman divergence. In this paper, we show that a generalized $\lambda $ -duality, where $\lambda = 1 - q$ is to be interpreted as the constant information-geometric curvature, leads to a generalized exponential family which is essentially equivalent to the $q$ -exponential family and has deep connections with Rényi entropy and optimal transport. Using this generalized convex duality and its associated logarithmic divergence, we show that our $\lambda $ -exponential family satisfies properties that parallel and generalize those of the exponential family. Under our framework, the Rényi entropy and divergence arise naturally, and we give a new proof of the Tsallis/Rényi entropy maximizing property of the $q$ -exponential family. We also introduce a $\lambda $ -mixture family which may be regarded as the dual of the $\lambda $ -exponential family, and connect it with other mixture-type families. Finally, we discuss a duality between the $\lambda $ -exponential family and the $\lambda $ -logarithmic divergence, and study its statistical consequences. [ABSTRACT FROM AUTHOR]

Reconfigurable intelligent surface (RIS) stands out as a promising technology by enhancing the electromagnetic wave propagation environment with its passive reflecting elements. In this paper, we focus on the ergodic sum-rate analysis and maximization of the RIS-assisted uplink multiuser multiple-input multiple-output (MIMO) multiple-access channel (MAC) under Rician fading by exploiting full statistical channel state information (CSI). The spatial correlations at the base station, the users, and the RIS are also considered. By using the replica method originated in statistical physics, the closed-form asymptotic ergodic sum-rate of the system is first derived in the large-system regime on the account of the unique channel structure of the RIS-assisted MIMO-MAC system. Then, based on the derived asymptotic ergodic sum-rate, we propose an alternating optimization (AO) algorithm to jointly design the transmit covariance matrix of users and the phase-shifting matrix of RIS with full statistical CSI. Simulation results are also demonstrated to verify the accuracy of the derived asymptotic ergodic sum-rate and the superiority of the proposed AO algorithm. The results reveal that the derived closed-form asymptotic ergodic sum-rate matches very well with the Monte Carlo results even for a small number of antennas, and the proposed AO algorithm can achieve up to 10 bps/Hz gain at high signal-to-noise (SNR) regime, which is therefore valuable for future RIS-assisted MIMO-MAC system designs. [ABSTRACT FROM AUTHOR]

The hardcore model on a graph $G$ with parameter $\lambda > 0$ is a probability measure on the collection of all independent sets of $G$ , that assigns to each independent set $I$ a probability proportional to $\lambda ^{|I|}$. In this paper we consider the problem of estimating the parameter $\lambda $ given a single sample from the hardcore model on a graph $G$. To bypass the computational intractability of the maximum likelihood method, we use the maximum pseudo-likelihood (MPL) estimator, which for the hardcore model has a surprisingly simple closed form expression. We show that for any sequence of graphs $\{G_{N}\}_{N \geq 1}$ , where $G_{N}$ is a graph on $N$ vertices, the MPL estimate of $\lambda $ is $\sqrt {N}$ -consistent (that is, it converges to the true parameter at rate $1/\sqrt {N}$), whenever the graph sequence has uniformly bounded average degree. We then extend our methods to obtain estimates for the vector of activity parameters in general $H$ -coloring models, in which restrictions between adjacent colors are encoded by a constraint graph $H$. These constitute an important class of Markov random fields that includes all hard-constraint models, which arise in a broad array of fields including combinatorics, statistical physics, and communication networks. Given a single sample from an $H$ -coloring model, we derive sufficient conditions under which the MPL estimate is $\sqrt {N}$ -consistent. Moreover, we verify the sufficient conditions for $H$ -coloring models for which there is at least one ‘unconstrained’ color (that is, there exists at least one vertex in the constraint graph $H$ that is connected to all vertices), as long as the graph sequence has uniformly bounded average degree. This applies to many $H$ -coloring examples such as the Widom-Rowlinson and multi-state hard-core models. On the other hand, for the $q$ -coloring model, which falls outside this class, we show that the condition can fail and consistent estimation may be impossible even for graphs with bounded average degree. Nevertheless, we show that the MPL estimate is $\sqrt {N}$ -consistent in the $q$ -coloring model when $\{G_{N}\}_{N \geq 1}$ has bounded average double neighborhood. The presence of hard constraints, as opposed to soft constraints, leads to new challenges, and our proofs entail applications of the method of exchangeable pairs as well as combinatorial arguments that employ the probabilistic method. [ABSTRACT FROM AUTHOR]

The present article aims to study the effect of external parameters, such as the action of a constant force and the action of an external harmonic potential, on the trajectory of a charged particle in Brownian motion in a time-dependent magnetic field. The approach presented here builds on methods of statistical physics and produces an analytical and numerical general solution for the stochastic differential equations of motion. [ABSTRACT FROM AUTHOR]

Recently, a new adaptive path interpolation method has been developed as a simple and versatile scheme to calculate exactly the asymptotic mutual information of Bayesian inference problems defined on dense factor graphs. These include random linear and generalized estimation, sparse superposition codes, and low-rank matrix / tensor estimation. For all these systems, the adaptive interpolation method directly proves that the replica-symmetric prediction is exact, in a simple and unified manner. When the underlying factor graph of the inference problem is sparse the replica prediction is considerably more complicated, and rigorous results are often lacking or obtained by rather complicated methods. In this work we show how to extend the adaptive path interpolation method to sparse systems. We concentrate on a censored block model, where hidden variables are measured through a binary erasure channel, for which we fully prove the replica prediction. [ABSTRACT FROM AUTHOR]

When users in online social networks make a decision, they are often affected by their neighbors. Social recommendation models utilize social information to reveal the impact of neighbors on user preferences, and this impact is often described by the linear superposition of neighbor preferences or by global trust propagation. Further exploration needs to be undertaken to determine whether the influence pattern of other users from online interaction behaviors is adequately described. In this paper, we introduce evolutionary opinion dynamics from the field of statistical physics into recommender systems, characterizing the impact of other users. We propose an opinion dynamic model by evolutionary game theory. To describe online user interactions, we define the strategies during an interaction between two users, and present the payoff for each strategy in terms of errors of estimated ratings. Therefore, user behaviors are associated with their preferences and ratings. In addition, we measure user influence according to their topological roles in the social network. We incorporate evolutionary opinion dynamics and user influence into the recommendation framework for the prediction of unknown ratings. Experiment results on two real-world datasets demonstrate that our method outperforms state-of the-art models in terms of accuracy, and it also performs well for cold-start users. Our method reduces the divergence of user preferences, in accordance with online opinion interactions. Furthermore, our method has approximate computational complexity with matrix factorization, and results in less computation than state-of-the-art models. Our method is quite general, and indicates that studies in social physics, statistics, and other research fields may be involved in recommendation to improve the performance. [ABSTRACT FROM AUTHOR]

With the explosion of social media networks, many modern applications are concerning about people's connections, which leads to the so-called social computing. An elusive question is to study how opinion communities form and evolve in real-world networks with great individual diversity and complex human connections. In this scenario, the classic K-means technique and its extended versions could not be directly applied, as they largely ignore the relationship among interactive objects. On the other side, traditional community detection approaches in statistical physics would be neither adequate nor fair: they only consider the network topological structure but ignore the heterogeneous-objects’ attributive information. To this end, we attempt to model a realistic social media network as a discrete-time dynamical system, where the opinion matrix and the community structure could mutually affect each other. In this paper, community detection in social media networks is naturally formulated as a multi-objective optimization problem (MOOP), i.e., finding a set of densely connected components with similar opinion vectors. We propose a novel and powerful graph K-means framework, which is composed of three coupled phases in each discrete-time period. Specifically, the first phase uses a fast heuristic approach to identify those opinion leaders who have relatively high local reputation; the second phase adopts a novel dynamic game model to find the locally Pareto-optimal community structure; and the final phase employs a robust opinion dynamics model to simulate the evolution of the opinion matrix. We conduct a series of comprehensive experiments on real-world benchmark networks to validate the performance of GK-means through comparisons with the state-of-the-art graph clustering technologies. [ABSTRACT FROM AUTHOR]

We consider the estimation of a signal from the knowledge of its noisy linear random Gaussian projections. A few examples where this problem is relevant are compressed sensing, sparse superposition codes, and code division multiple access. There has been a number of works considering the mutual information for this problem using the replica method from statistical physics. Here we put these considerations on a firm rigorous basis. First, we show, using a Guerra-Toninelli type interpolation, that the replica formula yields an upper bound to the exact mutual information. Secondly, for many relevant practical cases, we present a converse lower bound via a method that uses spatial coupling, state evolution analysis and the I-MMSE theorem. This yields a single letter formula for the mutual information and the minimal-mean-square error for random Gaussian linear estimation of all discrete bounded signals. In addition, we prove that the low complexity approximate message-passing algorithm is optimal outside of the so-called hard phase, in the sense that it asymptotically reaches the minimal-mean-square error. In this work spatial coupling is used primarily as a proof technique. However our results also prove two important features of spatially coupled noisy linear random Gaussian estimation. First there is no algorithmically hard phase. This means that for such systems approximate message-passing always reaches the minimal-mean-square error. Secondly, in the limit of infinitely long coupled chain, the mutual information associated to spatially coupled systems is the same as the one of uncoupled linear random Gaussian estimation. [ABSTRACT FROM AUTHOR]

The large-system performance of maximum-a-poste-rior estimation is studied considering a general distortion function when the observation vector is received through a linear system with additive white Gaussian noise. The analysis considers the system matrix to be chosen from the large class of rotationally invariant random matrices. We take a statistical mechanical approach by introducing a spin glass corresponding to the estimator, and employing the replica method for the large-system analysis. In contrast to earlier replica based studies, our analysis evaluates the general replica ansatz of the corresponding spin glass and determines the asymptotic distortion of the estimator for any structure of the replica correlation matrix. Consequently, the replica symmetric as well as the replica symmetry breaking ansatz with $b$ steps of breaking is deduced from the given general replica ansatz. The generality of our distortion function lets us derive a more general form of the maximum-a-posterior decoupling principle. Based on the general replica ansatz, we show that for any structure of the replica correlation matrix, the vector-valued system decouples into a bank of equivalent decoupled scalar systems followed by maximum-a-posterior estimators. The structure of the decoupled system is further studied under both the replica symmetry and the replica symmetry breaking assumptions. For $b$ steps of symmetry breaking, the decoupled system is found to be an additive system with a non-Gaussian noise term given as the sum of an independent Gaussian random variable with $b$ non-Gaussian impairment terms which depend on the input symbol. The general decoupling property of the maximum-a-posterior estimator leads to the idea of a replica simulator which represents the replica ansatz through the state evolution of a transition system described by its corresponding decoupled system. As an application of our study, we investigate large compressive sensing systems by considering the $\ell _{p}$ norm minimization recovery schemes. Our numerical investigations show that the replica symmetric ansatz for $\ell _{0}$ norm recovery fails to give an accurate approximation of the mean square error as the compression rate grows, and therefore, the replica symmetry breaking ansätze are needed in order to assess the performance precisely. [ABSTRACT FROM AUTHOR]

This article presents contact resistivity variability (CRV) in metal-semiconductor (MS) and metal-interfacial layer (IL)-semiconductor (MIS) contacts on Ge and Si source/drain regions resulting from process-induced random dopant fluctuation (RDF) and IL thickness variation (ILTV). CRV is modeled by combining the effect of RDF and ILTV in statistical simulations incorporating Fermi-level pinning physics. CRV is also shown to have a direct and significant impact on 7-nm FinFET On-current variability. The choice of contact architecture depends strongly on the source/drain doping. RDF dominates at low doping and MIS contacts provide lower CRV as well as lower resistivity ($\rho _{c}$) due to a lower contact barrier height. Impact of RDF decreases and that of ILTV increases with increasing doping resulting in lower CRV with comparable $\rho _{c}$ for MS contacts. [ABSTRACT FROM AUTHOR]

This paper considers the fundamental limit of random linear estimation for i.i.d. signal distributions and i.i.d. Gaussian measurement matrices. Its main contribution is a rigorous characterization of the asymptotic mutual information (MI) and minimum mean-square error (MMSE) in this setting. Under mild technical conditions, our results show that the limiting MI and MMSE are equal to the values predicted by the replica method from statistical physics. This resolves a well-known problem that has remained open for over a decade. [ABSTRACT FROM AUTHOR]

In this correspondence, by adopting the Coulomb gas analogy that is an analytical approach from statistical physics, we derive a closed-form approximation of the cumulative distribution function (CDF) of the largest eigenvalue of a random Gram matrix $ \boldsymbol {H}^{H} \boldsymbol {H}$ , where $\boldsymbol {H}$ denotes the channel matrix of a multiple-input multiple-output (MIMO) system. The expression of approximation has a simple structure in terms of several elementary functions, which is derived by assuming that the entries of $\boldsymbol {H}$ have Nakagami- $m$ distributed amplitude with an independent phase. This assumption is made because it applies in two common cases of the Nakagami- $m$ distributions, i.e., with a uniformly distributed phase and a complex signal model. Simulation results indicate that the theoretical expression also provides a good approximation to the CDF for Rice and Hoyt distributions when the CDF is within a near-one range. This range takes the form of $(P_{no}, 1)$ , where we assume $P_{no} = 10^{-3}$ by default in this study. The derived approximation can find many uses for the performance analysis of MIMO beamforming and singular value decomposition MIMO systems, e.g., evaluating the outage probability for these systems. [ABSTRACT FROM AUTHOR]

The employment of social similarity (SS) aware device-to-device (D2D) user equipment (UE)-to-network (UE-NW) relay helps to improve system capacity and UEs’ accessability to the evolved Node B (eNB), where a crucial aspect is the design of the relay helper UE (HUE) selection process. However, few existing studies jointly consider the diverse impacts from various design criteria on the performance of HUE selection. In this paper, we formulate the SS-aware D2D UE-NW relay selection (RS) issue as a multiobjective binary integer linear programming (MOBILP) problem under the constraints of several criteria. Then, we propose a new two-stage D2D UE-NW selection scheme. Specifically, a joint algorithm exploiting the intuitionistic fuzzy analytic hierarchy process and the entropy weight generation method is designed for stage one, which provides both subjective and objective preferences for assisting decision making. In stage two, with the constructed decision weights, the MOBILP can be transformed to a simpler binary integer linear programming problem and thus be solved distributively through an efficient message passing method. Based on realistic social data traces, our simulation results validate the benefits of the proposed two-stage scheme, which ensures high system performances in terms of throughput, fairness and energy efficiency. [ABSTRACT FROM AUTHOR]

Given a sufficient statistic for a parametric family of distributions, one can estimate the parameter without access to the data. However, the memory or code size for storing the sufficient statistic may nonetheless still be prohibitive. Indeed, for $n$ independent samples drawn from a k$ -nomial distribution with d=k-1$ degrees of freedom, the length of the code scales as d\log n+O(1) . We consider errors measured according to the relative entropy and variational distance criteria. For the code constructions, we leverage Rissanen’s minimum description length principle, which yields a non-vanishing error measured according to the relative entropy. For the converse parts, we use Clarke and Barron’s formula for the relative entropy of a parameterized distribution and the corresponding mixture distribution. However, this method only yields a weak converse for the variational distance. We develop new techniques to achieve vanishing errors, and we also prove strong converses. The latter means that even if the code is allowed to have a non-vanishing error, its length must still be at least ({d}/{2})\log n . [ABSTRACT FROM AUTHOR]

This paper is about deriving lower bounds on the error exponents for the two-user interference channel under the random coding regime for several ensembles. Specifically, we first analyze the standard random coding ensemble, where the codebooks are comprised of independently and identically distributed (i.i.d.) codewords. For this ensemble, we focus on optimum decoding, which is in contrast to other, suboptimal decoding rules that have been used in the literature (e.g., joint typicality decoding, treating interference as noise, and so on). The fact that the interfering signal is a codeword, rather than an i.i.d. noise process, complicates the application of conventional techniques of performance analysis of the optimum decoder. In addition, unfortunately, these conventional techniques result in loose bounds. Using analytical tools rooted in statistical physics, as well as advanced union bounds, we derive single-letter formulas for the random coding error exponents. We compare our results with the best known lower bound on the error exponent, and show that our exponents can be strictly better. Then, in the second part of this paper, we consider more complicated coding ensembles and find a lower bound on the error exponent associated with the celebrated Han–Kobayashi random coding ensemble, which is based on superposition coding. [ABSTRACT FROM AUTHOR]

We rigorously study a channel that maps sequences from a finite alphabet to self-avoiding walks in the 2-D grid, inspired by a model of protein folding from statistical physics and studied empirically by biophysicists. This channel, which we call the Boltzmann sequence-structure channel, is characterized by a Boltzmann/Gibbs distribution with a free parameter corresponding to temperature. In our previous work, we verified empirically that the channel capacity appears to have a phase transition for small temperature and decays to zero for high temperature. In this paper, we make some progress toward theoretically explaining these phenomena. We first estimate the conditional entropy between the input sequence and the output fold, giving an upper bound which exhibits a phase transition with respect to temperature. Next, we formulate a class of parameter settings under which the dependence between walk energies is governed by their number of shared contacts. In this setting, we derive a lower bound on the conditional entropy. This lower bound allows us to conclude that the mutual information tends to zero in a nontrivial regime of high temperature, giving some support to the empirical fact regarding capacity. Finally, we construct an example setting of the parameters of the model for which the conditional entropy is exactly calculable and which does not exhibit a phase transition. [ABSTRACT FROM AUTHOR]

The impact of cloud impairments on satellite links is increasing with the employment of higher frequency bands. In this paper, a model for predicting cloud attenuation statistics for satellite communication systems operating from $Ka$ -band to optical range is presented. The cloud attenuation must be accurately quantified for the reliable design of satellite communication systems. A stochastic dynamic model for the generation of integrated liquid water content (ILWC) fields is proposed. The model is based on the stochastic differential equations and incorporates the spatial and temporal behavior of ILWC. Classifying the cloud types based on the cloud vertical extent and using the microphysical properties of clouds, the well-known Mie scattering theory and the global statistics for ILWC by International Telecommunications Union–Radio (ITU-R), a unified space-time model for the prediction of induced attenuation due to clouds for frequencies above $Ka$ -band up to optical range is presented. The proposed model is tested in terms of first order statistics, compared first with ITU-R P.840-6 model and then with data obtained in the literature, showing encouraging results. Moreover, the probability of cloud occurrence for optical satellite single and site diversity system is calculated. Finally, the limitations and the applicability of the proposed model are discussed. [ABSTRACT FROM AUTHOR]