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With the prevalence of COVID-19, the modeling of epidemic propagation and its analyses have played a significant role in controlling epidemics. However, individual behaviors, in particular the self-protection and migration, which have a strong influence on epidemic propagation, were always neglected in previous studies. In this paper, we mainly propose two models from the individual and population perspectives. In the first individual model, we introduce the individual protection degree that effectively suppresses the epidemic level as a stochastic variable to the SIRS model. In the alternative population model, an open Markov queueing network is constructed to investigate the individual number of each epidemic state, and we present an evolving population network via the migration of people. Besides, stochastic methods are applied to analyze both models. In various simulations, the infected probability, the number of individuals in each state and its limited distribution are demonstrated. [ABSTRACT FROM AUTHOR]

This paper presents a systematic method to analyze the stability of systems with single delay in which the coefficient polynomials of the characteristic equation depend on the delay. Such systems often arise in, for example, life science and engineering systems. A method to analyze such systems was presented by Beretta and Kuang in a 2002 paper, but with some very restrictive assumptions. This paper extends their results to the general case with the exception of some degenerate cases. It is found that a much richer behavior is possible when the restrictive assumptions are removed. The interval of interest for the delay is partitioned into subintervals so that the magnitude condition generates a fixed number of frequencies as functions of the delay within each subinterval. The crossing conditions are expressed in a general form, and a simplified derivation for the first-order derivative criterion is obtained. Illustrative examples are also presented in this paper. [ABSTRACT FROM AUTHOR]

This paper presents the integration of reinforcement learning-based differential evolution (DE) with the cooperative coevolution (R-CCDE) method in a compensatory neuro-fuzzy controller (CNFC). The CNFC model employs compensatory fuzzy operations, which increase the adaptability and effectiveness of the controller. The R-CCDE method was used to determine an adequate control policy for nonlinear system problems. The evolution of a population involved the use of DE with cooperative coevolution to adjust CNFC parameters, and the fitness function of the R-CCDE method is used by a reinforcement signal to determine the controller that can be used to solve the control problem. This paper identified the best performing controller to solve nonlinear system problems. The simulation results of the proposed R-CCDE method were compared with those of various DE methods and the performance of the proposed R-CCDE method was superior to that of the other methods. [ABSTRACT FROM AUTHOR]

As the integrated circuit (IC) technology advances into smaller nanometre feature sizes, a fixed-error noise known as device mismatch is introduced owing to the dissimilarity between transistors, and this degrades the accuracy of analog circuits. In this paper, we present an analog co-processor that uses this fixed-pattern noise to its advantage to perform complex computation. This circuit is an extension of our previously published trainable analogue block (TAB) framework and uses multiple inputs that substantially increase functionality. We present measurement results of our two-input analogue co-processor built using a 130-nm process technology and show its learning capabilities for regression and classification tasks. We also show that the co-processor, comprised of 100 neurons, is a low-power system with a power dissipation of only 1.1~\mu \textW . The IC fabrication process contributes to randomness and variability in ICs, and we show that random device mismatch is favorable for the learning capability of our system as it causes variability among the neuronal tuning curves. The low-power capability of our framework makes it suitable for use in various battery-powered applications ranging from biomedical to military as a front-end analog co-processor. [ABSTRACT FROM AUTHOR]

Pairwise-interaction graphical games have been widely used in the study and design of strategic interaction in multiagent systems. With regard to this issue, one entitative problem is actually to understand how the interaction structure of agents affects the strategy configuration of Nash equilibria. This paper intends to study the effect of interaction networks on Nash equilibria in pairwise-interaction graphical games. We first show that interaction networks may induce new strategy equilibria in pairwise-interaction graphical games and then provide graphical conditions for the existence of these network-induced equilibria. Furthermore, to determine Nash equilibria of pairwise-interaction graphical games, a graphical replicator dynamics model is formulated, and its connection with graphical games is established. In detail, it is shown that every Nash equilibrium of the graphical games corresponds to a fixed point of the graphical replicator dynamics and that every asymptotically stable fixed point of the graphical replicator dynamics corresponds to a strict pure Nash equilibrium of the graphical games. The obtained results are applied in understanding coordination in complex networks and determination of structural conflicts in signed graphs. This work may provide new insights into understanding and designing strategy equilibria and dynamics in games on networks. [ABSTRACT FROM AUTHOR]

In dynamic optimization problems (DOPs), as the environment changes through time, the optima also dynamically change. How to adapt to the dynamic environment and quickly find the optima in all environments is a challenging issue in solving DOPs. Usually, a new environment is strongly relevant to its previous environment. If we know how it changes from the previous environment to the new one, then we can transfer the information of the previous environment, e.g., past solutions, to get new promising information of the new environment, e.g., new high-quality solutions. Thus, in this paper, we propose a neural network (NN)-based information transfer method, named NNIT, to learn the transfer model of environment changes by NN and then use the learned model to reuse the past solutions. When the environment changes, NNIT first collects the solutions from both the previous environment and the new environment and then uses an NN to learn the transfer model from these solutions. After that, the NN is used to transfer the past solutions to new promising solutions for assisting the optimization in the new environment. The proposed NNIT can be incorporated into population-based evolutionary algorithms (EAs) to solve DOPs. Several typical state-of-the-art EAs for DOPs are selected for comprehensive study and evaluated using the widely used moving peaks benchmark. The experimental results show that the proposed NNIT is promising and can accelerate algorithm convergence. [ABSTRACT FROM AUTHOR]

Mean field game theory has been developed largely following two routes. One of them, called the direct approach, starts by solving a large-scale game and next derives a set of limiting equations as the population size tends to infinity. The second route is to apply mean field approximations and formalize a fixed point problem by analyzing the best response of a representative player. This paper addresses the connection and difference of the two approaches in a linear quadratic (LQ) setting. We first introduce an asymptotic solvability notion for the direct approach, which means for all sufficiently large population sizes, the corresponding game has a set of feedback Nash strategies in addition to a mild regularity requirement. We provide a necessary and sufficient condition for asymptotic solvability and show that in this case the solution converges to a mean field limit. This is accomplished by developing a re-scaling method to derive a low-dimensional ordinary differential equation (ODE) system, where a non-symmetric Riccati ODE has a central role. We next compare with the fixed point approach which determines a two-point boundary value (TPBV) problem, and show that asymptotic solvability implies feasibility of the fixed point approach, but the converse is not true. We further address non-uniqueness in the fixed point approach and examine the long time behavior of the non-symmetric Riccati ODE in the asymptotic solvability problem. [ABSTRACT FROM AUTHOR]

Active learning (AL) is a machine-learning approach for reducing the data labeling effort. Given a pool of unlabeled samples, it tries to select the most useful ones to label so that a model built from them can achieve the best possible performance. This paper focuses on pool-based sequential AL for regression (ALR). We first propose three essential criteria that an ALR approach should consider in selecting the most useful unlabeled samples: informativeness, representativeness, and diversity, and compare four existing ALR approaches against them. We then propose a new ALR approach using passive sampling, which considers both the representativeness and the diversity in both the initialization and subsequent iterations. Remarkably, this approach can also be integrated with other existing ALR approaches in the literature to further improve the performance. Extensive experiments on 11 University of California, Irvine, Carnegie Mellon University StatLib, and University of Florida Media Core data sets from various domains verified the effectiveness of our proposed ALR approaches. [ABSTRACT FROM AUTHOR]

This paper presents a discrete-time distributed and noncooperative routing algorithm, which is proved, via Lyapunov arguments, to asymptotically converge to a specific equilibrium condition among the traffic flows over the network paths, known as Wardrop equilibrium. This convergence result improves the discrete-time algorithms in the literature, which achieve approximate convergence to the Wardrop equilibrium. Numerical simulations show the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper studies the linear–quadratic mean-field game (MFG) for a class of stochastic delayed systems. We consider a large-population system, where the dynamics of each agent is modeled by a stochastic differential delayed equation. The consistency condition is derived through an auxiliary system, which is an anticipated forward–backward stochastic differential equation with delay (AFBSDDE). The wellposedness of such an AFBSDDE system can be obtained using a continuation method. Thus, the MFG strategies can be defined on an arbitrary time horizon, not necessary on a small time horizon by a commonly used contraction mapping method. Moreover, the decentralized strategies are verified to satisfy the $\epsilon$ -Nash equilibrium property. For illustration, three special cases of delayed systems are further explored, for which the closed-loop and open-loop MFG strategies are derived, respectively. [ABSTRACT FROM AUTHOR]

Most learning methods contain optimization as a substep, where the nondifferentiability and multimodality of objectives push forward the interplay of evolutionary optimization algorithms and machine learning models. The recently emerged evolutionary multimodal optimization (MMOP) technique enables the learning of diverse sets of effective parameters for the models simultaneously, providing new opportunities to the applications requiring both accuracy and diversity, such as ensemble, interactive, and interpretive learning. Targeting at locating multiple optima simultaneously in the multimodal landscape, this paper develops an efficient neighborhood-based niching algorithm. Bare-bones differential evolution is used as the baseline. Further, using Gaussian mutation with local mean and standard deviations, the neighborhoods capture niches that match well with the contours of peaks in the landscape. To increase diversity and enhance global exploration, the proposed algorithm embeds a diversity preserving operator to reinitialize converged or overlapped neighborhoods. The experimental results verify that the proposed algorithm has superior and consistent performance for a wide range of MMOP problems. Further, the algorithm has been successfully applied to train neural network ensembles, which validates its effectiveness and benefits of learning multimodal parameters. [ABSTRACT FROM AUTHOR]

Within the realm of smart buildings and smart cities, dynamic response management is playing an ever-increasing role, thus attracting the attention of scientists from different disciplines. Dynamic demand response management involves a set of operations aiming at decentralizing the control of loads in large and complex power networks. Each single appliance is fully responsive and readjusts its energy demand to the overall network load. A main issue is related to mains frequency oscillations resulting from an unbalance between supply and demand. In a nutshell, this paper contributes to the topic by equipping each consumer with strategic insight. In particular, we highlight three main contributions and a few other minor contributions. First, we design a mean-field game for a population of thermostatically controlled loads, study the mean-field equilibrium for the deterministic mean-field game, and investigate on asymptotic stability for the microscopic dynamics. Second, we extend the analysis and design to uncertain models, which involve both stochastic or deterministic disturbances. This leads to robust mean-field equilibrium strategies guaranteeing stochastic and worst-case stability, respectively. Minor contributions involve the use of stochastic control strategies rather than deterministic and some numerical studies illustrating the efficacy of the proposed strategies. [ABSTRACT FROM PUBLISHER]

The purpose of this paper is to show how insight obtained from a mean-field model can be used to create an architecture for approximate dynamic programming (ADP) for a certain class of games comprising of a large number of agents. The general technique is illustrated with the aid of a mean-field oscillator game model introduced in our prior work. The states of the model are interpreted as the phase angles for a collection of nonhomogeneous oscillators, and in this way the model may be regarded as an extension of the classical coupled oscillator model of Kuramoto. The paper introduces ADP techniques for design and adaptation (learning) of approximately optimal control laws for this model. For this purpose, a parameterization is proposed, based on an analysis of the mean-field PDE model for the game. In an offline setting, a Galerkin procedure is introduced to choose the optimal parameters while in an online setting, a steepest descent algorithm is proposed. The paper provides a detailed analysis of the optimal parameter values as well as the Bellman error with both the Galerkin approximation and the online algorithm. Finally, a phase transition result is described for the large population limit when each oscillator uses the approximately optimal control law. A critical value of the control penalty parameter is identified: above this value, the oscillators are incoherent; and below this value (when control is sufficiently cheap) the oscillators synchronize. These conclusions are illustrated with results from numerical experiments. [ABSTRACT FROM AUTHOR]

Huang (2010) and Nguyen and Huang (2012) solved the linear quadratic mean field systems and control problem in the case where there is a major agent (i.e. non-asymptotically vanishing as the population size goes to infinity) together with a population of minor agents (i.e. individually asymptotically negligible). The new feature in this case is that the mean field becomes stochastic and then, by minor agent state extension, the existence of $\epsilon$-Nash equilibria together with the individual agents' control laws that yield the equilibria may be established. This paper presents results initially announced by Caines and Kizilkale (2013, 2014) where it is shown that if the major agent's state is partially observed by the minor agents, and if the major agent completely observes its own state, all agents can recursively generate estimates (in general individually distinct) of the major agent's state and the mean field, and thence generate feedback controls yielding $\epsilon$ -Nash equilibria. [ABSTRACT FROM PUBLISHER]

This paper concerns state estimation problems in a mean field control setting. In a finite population model, the goal is to estimate the joint distribution of the population state and the state of a typical individual. The observation equations are a noisy measurement of the population. The general results are applied to demand dispatch for regulation of the power grid, based on randomized local control algorithms. In prior work by the authors it is shown that local control can be designed so that the aggregate of loads behaves as a controllable resource, with accuracy matching or exceeding traditional sources of frequency regulation. The operational cost is nearly zero in many cases. The information exchange between grid and load is minimal, but it is assumed in the overall control architecture that the aggregate power consumption of loads is available to the grid operator. It is shown that the Kalman filter can be constructed to reduce these communication requirements, and to provide the grid operator with accurate estimates of the mean and variance of quality of service (QoS) for an individual load. [ABSTRACT FROM AUTHOR]

Natural systems are inextricably affected by noise. Within recent decades, the manner in which noise affects the collective behavior of self-organized systems, specifically, has garnered considerable interest from researchers and developers in various fields. To describe the collective motion of multiple interacting particles, Vicsek et al. proposed a well-known self-propelled particle (SPP) system, which exhibits a second-order phase transition from disordered to ordered motion in simulation; due to its non-equilibrium, randomness, and strong coupling nonlinear dynamics, however, there has been no rigorous analysis of such a system to date. To decouple systems consisting of deterministic laws and randomness, we propose a general method which transfers the analysis of these systems to the design of cooperative control algorithms. In this study, we rigorously analyzed the original Vicsek model under both open and periodic boundary conditions for the first time, and developed extensions to heterogeneous SPP systems (including leader-follower models) using the proposed method. Theoretical results show that SPP systems switch an infinite number of times between ordered and disordered states for any noise intensity and population density, which implies that the phase transition indeed takes a nontraditional form. We also investigated the robust consensus and connectivity of these systems. Moreover, the findings presented in this paper suggest that our method can be used to predict possible configurations during the evolution of complex systems, including turn, vortex, bifurcation, and flock merger phenomena as they appear in SPP systems. [ABSTRACT FROM PUBLISHER]

This paper presents an enhanced rank-order-based learning algorithm, called SpikeTemp, for spiking neural networks (SNNs) with a dynamically adaptive structure. The trained feed-forward SNN consists of two layers of spiking neurons: 1) an encoding layer which temporally encodes real-valued features into spatio-temporal spike patterns and 2) an output layer of dynamically grown neurons which perform spatio-temporal classification. Both Gaussian receptive fields and square cosine population encoding schemes are employed to encode real-valued features into spatio-temporal spike patterns. Unlike the rank-order-based learning approach, SpikeTemp uses the precise times of the incoming spikes for adjusting the synaptic weights such that early spikes result in a large weight change and late spikes lead to a smaller weight change. This removes the need to rank all the incoming spikes and, thus, reduces the computational cost of SpikeTemp. The proposed SpikeTemp algorithm is demonstrated on several benchmark data sets and on an image recognition task. The results show that SpikeTemp can achieve better classification performance and is much faster than the existing rank-order-based learning approach. In addition, the number of output neurons is much smaller when the square cosine encoding scheme is employed. Furthermore, SpikeTemp is benchmarked against a selection of existing machine learning algorithms, and the results demonstrate the ability of SpikeTemp to classify different data sets after just one presentation of the training samples with comparable classification performance. [ABSTRACT FROM PUBLISHER]

This paper introduces the backward mean-field (MF) linear-quadratic-Gaussian (LQG) games (for short, BMFLQG) of weakly coupled stochastic large-population system. In contrast to the well-studied forward mean-field LQG games, the individual state in our large-population system follows the backward stochastic differential equation (BSDE) whose terminal instead initial condition should be prescribed. Two classes of BMFLQG games are discussed here and their decentralized strategies are derived through the consistency condition. In the first class, the individual agents of large-population system are weakly coupled in their state dynamics and the full information can be accessible to all agents. In the second class, the coupling structure lies in the cost functional with only partial information structure. In both classes, the asymptotic near-optimality property (namely, $\epsilon$- Nash equilibrium) of decentralized strategies are verified. To this end, some estimates to BSDE, are presented in the large-population setting. [ABSTRACT FROM AUTHOR]

This paper considers decentralized control and optimization methodologies for large populations of systems, consisting of several agents with different individual behaviors, constraints and interests, and influenced by the aggregate behavior of the overall population. For such large-scale systems, the theory of aggregative and mean field games has been established and successfully applied in various scientific disciplines. While the existing literature addresses the case of unconstrained agents, we formulate deterministic mean field control problems in the presence of heterogeneous convex constraints for the individual agents, for instance arising from agents with linear dynamics subject to convex state and control constraints. We propose several model-free feedback iterations to compute in a decentralized fashion a mean field Nash equilibrium in the limit of infinite population size. We apply our methods to the constrained linear quadratic deterministic mean field control problem. [ABSTRACT FROM PUBLISHER]

An accurate and noninvasive stress assessment from human physiology is a strenuous task. In this paper, a pattern recognition system to learn complex correlates between heart rate variability (HRV) features and salivary stress biomarkers is proposed. Using the Trier social stress test, heart rate and salivary measurements were obtained from volunteers under varying levels of stress induction. Measurements of salivary alpha-amylase and cortisol were used as objective measures of stress, and were correlated with the HRV features using fuzzy ARTMAP (FAM). In improving the predictive ability of the ARTMAPs, techniques, such as genetic algorithms for parameter optimization and voting ensembles, were employed. The ensemble of FAMs can be used for predicting stress responses of salivary alpha-amylase or cortisol using heart rate measurements as the input. Using alpha-amylase as the stress indicator, the ensemble was able to classify stress from heart rate features with 75% accuracy, and 80% accuracy when cortisol was used. [ABSTRACT FROM AUTHOR]

The increasing liberalization of European electricity markets, the growing proportion of intermittent renewable energy being fed into the energy grids, and also new challenges in the patterns of energy consumption (such as electric mobility) require flexible and intelligent power grids capable of providing efficient, reliable, economical, and sustainable energy production and distribution. From the supplier side, particularly, the integration of renewable energy sources (e.g., wind and solar) into the grid imposes an engineering and economic challenge because of the limited ability to control and dispatch these energy sources due to their intermittent characteristics. Time-series prediction of wind speed for wind power production is a particularly important and challenging task, wherein prediction intervals (PIs) are preferable results of the prediction, rather than point estimates, because they provide information on the confidence in the prediction. In this paper, two different machine learning approaches to assess PIs of time-series predictions are considered and compared: 1) multilayer perceptron neural networks trained with a multiobjective genetic algorithm and 2) extreme learning machines combined with the nearest neighbors approach. The proposed approaches are applied for short-term wind speed prediction from a real data set of hourly wind speed measurements for the region of Regina in Saskatchewan, Canada. Both approaches demonstrate good prediction precision and provide complementary advantages with respect to different evaluation criteria. [ABSTRACT FROM PUBLISHER]

Collaboration enables weak species to survive in an environment where different species compete for limited resources. Cooperative coevolution (CC) is a nature-inspired optimization method that divides a problem into subcomponents and evolves them while genetically isolating them. Problem decomposition is an important aspect in using CC for neuroevolution. CC employs different problem decomposition methods to decompose the neural network training problem into subcomponents. Different problem decomposition methods have features that are helpful at different stages in the evolutionary process. Adaptation, collaboration, and competition are needed for CC, as multiple subpopulations are used to represent the problem. It is important to add collaboration and competition in CC. This paper presents a competitive CC method for training recurrent neural networks for chaotic time-series prediction. Two different instances of the competitive method are proposed that employs different problem decomposition methods to enforce island-based competition. The results show improvement in the performance of the proposed methods in most cases when compared with standalone CC and other methods from the literature. [ABSTRACT FROM PUBLISHER]

In 1960, Science published a paper by Heinz von Foerster predicting that on Friday, 13 November 2026, the “human population will approach infinity if it grows as it has grown in the last two millennia.” Just a few years after this preposterous doomsday alarm, the annual growth of global population peaked at about 2.1 percent and immediately began to decline. By 2020 the growth rate stood at just a bit more than 1 percent, the result of the steadily declining total fertility rate (TFR), the number of children born to a woman during her reproductive period. [ABSTRACT FROM AUTHOR]

The multivalued neuron with periodic activation function (MVN-P) was proposed by Aizenberg for solving classification problems. The boundaries between two distinct categories are crisply specified in MVN-P, which may result in slow convergence or being unable to converge at all in the learning process. In this paper, we propose a revised model of MVN-P based on the idea of unsharp boundaries. In this revised model, a fuzzy buffer is provided around a boundary between two distinct categories, allowing incorrect assignments with membership degree less than a threshold to be tolerated in the training phase. Genetic algorithms are applied to derive optimal values for the parameters involved in this model, alleviating the burden of setting them manually by the user. Besides, MVN-P has difficulties solving the classification problems having a large number of categories. A tree structure is developed to overcome these difficulties. Simulation results demonstrate the effectiveness of our proposed ideas. [ABSTRACT FROM AUTHOR]

Feature extraction is the first and most critical step in image classification. Most existing image classification methods use hand-crafted features, which are not adaptive for different image domains. In this paper, we develop an evolutionary learning methodology to automatically generate domain-adaptive global feature descriptors for image classification using multiobjective genetic programming (MOGP). In our architecture, a set of primitive 2-D operators are randomly combined to construct feature descriptors through the MOGP evolving and then evaluated by two objective fitness criteria, i.e., the classification error and the tree complexity. After the entire evolution procedure finishes, the best-so-far solution selected by the MOGP is regarded as the (near-)optimal feature descriptor obtained. To evaluate its performance, the proposed approach is systematically tested on the Caltech-101, the MIT urban and nature scene, the CMU PIE, and Jochen Triesch Static Hand Posture II data sets, respectively. Experimental results verify that our method significantly outperforms many state-of-the-art hand-designed features and two feature learning techniques in terms of classification accuracy. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of risk-sensitive mean-field stochastic differential games. We show that under appropriate regularity conditions, the mean-field value of the stochastic differential game with exponentiated integral cost functional coincides with the value function satisfying a Hamilton –Jacobi– Bellman (HJB) equation with an additional quadratic term. We provide an explicit solution of the mean-field best response when the instantaneous cost functions are log-quadratic and the state dynamics are affine in the control. An equivalent mean-field risk-neutral problem is formulated and the corresponding mean-field equilibria are characterized in terms of backward-forward macroscopic McKean–Vlasov equations, Fokker–Planck–Kolmogorov equations, and HJB equations. We provide numerical examples on the mean field behavior to illustrate both linear and McKean–Vlasov dynamics. [ABSTRACT FROM PUBLISHER]

We consider a continuum of phase oscillators on the circle interacting through an impulsive instantaneous coupling. In contrast with previous studies on related pulse-coupled models, the stability results obtained in the continuum limit are global. For the nonlinear transport equation governing the evolution of the oscillators, we propose (under technical assumptions) a global Lyapunov function which is induced by a total variation distance between quantile densities. The monotone time evolution of the Lyapunov function completely characterizes the dichotomic behavior of the oscillators: either the oscillators converge in finite time to a synchronous state or they asymptotically converge to an asynchronous state uniformly spread on the circle. The results of the present paper apply to popular phase oscillators models (e.g., the well-known leaky integrate-and-fire model) and show a strong parallel between the analysis of finite and infinite populations. In addition, they provide a novel approach for the (global) analysis of pulse-coupled oscillators. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to synthesize initial mean consensus behavior of a set of agents from the fundamental optimization principles of i) stochastic dynamic games, and ii) optimal control. In the stochastic dynamic game model each agent seeks to minimize its individual quadratic discounted cost function involving the mean of the states of all other agents. In this formulation we derive the limiting infinite population mean field equation system and explicitly compute its unique solution. The resulting mean field (MF) control strategies drive each agent to track the overall population's initial state distribution mean, and by applying these decentralized strategies, any finite population system reaches mean consensus asymptotically as time goes to infinity. Furthermore, these control laws possess an \varepsilonN-Nash equilibrium property where \varepsilonN goes to zero as the population size N goes to infinity. Finally, the analysis is extended to the case of random mean field couplings. In the social cooperative formulation the basic objective is to minimize a social cost as the sum of the individual cost functions containing mean field coupling. In this formulation we show that for any individual agent the decentralized mean field social (MF Social) control strategy is the same as the mean field Nash (MF Nash) equilibrium strategy. Hence $MF-Nash\ Controls\ UNash^N=\rm MF-Social\ Controls\ USoc^N.$On the other hand, the solution to the centralized LQR optimal control formulation yields the Standard Consensus (SC) algorithm whenever the graph representing the corresponding topology of the network is Completely Connected (CC). Hence $Cent.\ LQR\ Controls\ UCent^N=\rm SC-CC\ Controls\ USC^N.$Moreover, a system with centralized control laws reaches consensus on the initial state distribution mean as time and population size N go to infinity. Hence, asymptotically in time $\eqalignno&MF-Nash\ Controls\ UNash^N\!=\!\,\rm MF-Social\ Controls\ USoc^N\cr&\!=\!\,\rm Cent.\ \rm LQR\ Controls\ UCent^\infty \!=\! \,\rm SC-CC\ Controls\ USC^\infty.$Finally, the analysis is extended to the long time average (LTA) cost functions case. [ABSTRACT FROM AUTHOR]

Random device mismatch that arises as a result of scaling of the CMOS (complementary metal-oxide semi-conductor) technology into the deep submicrometer regime degrades the accuracy of analog circuits. Methods to combat this increase the complexity of design. We have developed a novel neuromorphic system called a trainable analog block (TAB), which exploits device mismatch as a means for random projections of the input to a higher dimensional space. The TAB framework is inspired by the principles of neural population coding operating in the biological nervous system. Three neuronal layers, namely input, hidden, and output, constitute the TAB framework, with the number of hidden layer neurons far exceeding the input layer neurons. Here, we present measurement results of the first prototype TAB chip built using a 65 nm process technology and show its learning capability for various regression tasks. Our TAB chip is tolerant to inherent randomness and variability arising due to the fabrication process. Additionally, we characterize each neuron and discuss the statistical variability of its tuning curve that arises due to random device mismatch, a desirable property for the learning capability of the TAB. We also discuss the effect of the number of hidden neurons and the resolution of output weights on the accuracy of the learning capability of the TAB. We show that the TAB is a low power system—the power dissipation in the TAB with 456 neuron blocks is 1.38 \mu\textW. [ABSTRACT FROM AUTHOR]