distributed time varying quadratic optimization for multiple agents under undirected graphs this paper considers a class of distributed quadratic optimization problem under an undirected and connected graph different from most of the existing distributed optimization works that consider the optimal solutions to be constants the optimal solution and the objective functions at the optimal solution are both assumed to be time varying for the case where there is no constraint on the decision variables gradient based searching methods are proposed to track the unknown optimal solution the tracking errors are proven to be asymptotically stable for the case where there exists a local compact convex constraint set for each agent projected gradient based methods are proposed for both neighboring coupled and generally coupled objective functions and the tracking errors are proven to be uniformly ultimately bounded with arbitrarily small bound

the attractor basin portrait of a cellular automaton local space time structures such as domains and the intervening dislocations dominate a wide class of cellular automaton ca behavior for such spatially extended dynamics regular domains vicinities and attractors are introduced as organizing principles to identify the discretized analogs of attractors basins and separatrices structures used in classifying dissipative continuous state dynamical systems we describe the attractor basin portrait of nonlinear elementary ca rule 18 whose global dynamics is largely determined by a single regular attracting domain the latter s basin is analyzed in terms of subbasin and portal structures associated with particle annihilation the conclusion is that the computational complexity of such ca is more apparent than real transducer machines are constructed that automatically identify domain and dislocation structures in space time count the number of dislocations in a spatial pattern and implement an isomorphism between rule 18 and rule 90 we use a transducer to trace dislocation trajectories and confirm that in rule 18 isolated dislocation trajectories as well as a dislocation gas agree extremely well with the classical model of annihilating diffusive particles the ca efficiently transforms randomness of an initial pattern ensemble into a random walk of dislocations in space time

self organized criticality resulting from minimization of perpetual disequilibration abstract a bootstrapping system is proposed in order to describe nonlogical properties of living systems in which the velocity of observation propagation is finite a cellular automaton ca model of the system combines two logics which are the a priori non boolean logic and the a posteriori boolean logic because of inconsistency between the two logics the system evolves perpetually generating disequilibrium and perpetually equilibrating the generated disequilibrium the system tends to self organize to the border between order and disorder and shows critical behaviours as class iv ca although the critical behaviors of the two systems are similar the bootstrapping ssstem has twice stronger undecidability than class iv ca or edge of chaos dynamics it is stressed that real living systems are not computable and should be described by strongly undecidable systems

hunting for the fractal dimension of the kauffman model abstract the kauffman model is a random mixture of all possible cellular automata on the square lattice with nearest neighbor interactions simulations give a fractal dimension d above 1 8 compatible with the usual scaling law d d for damage spreading

comments on distributed robust adaptive equilibrium computation for generalized convex games automatica 63 2016 82 91 abstract theorem 4 1 in zhu and frazzoli 2016 is incorrect algorithm 1 does not ensure convergence to a nash equilibrium

initiation of damage in the kauffman model an alternate method is presented for initiating damage to the kauffman model a numerical study suggests that this modification increases the efficiency of generating damage clusters without changing their fractal properties

learning generalized nash equilibria in a class of convex games we consider multiagent decision making where each agent optimizes its convex cost function subject to individual and coupling constraints the constraint sets are compact convex subsets of a euclidean space to learn nash equilibria we propose a novel distributed payoff based algorithm where each agent uses information only about its cost value and the constraint value with its associated dual multiplier we prove convergence of this algorithm to a nash equilibrium under the assumption that the game admits a strictly convex potential function in the absence of coupling constraints we prove convergence to nash equilibria under significantly weaker assumptions not requiring a potential function namely strict monotonicity of the game mapping is sufficient for convergence we also derive the convergence rate of the algorithm for strongly monotone game maps

continuous time penalty methods for nash equilibrium seeking of a nonsmooth generalized noncooperative game in this paper we propose centralized and distributed continuous time penalty methods to find a nash equilibrium for a generalized noncooperative game with shared inequality and equality constraints and private inequality constraints that depend on the player itself by using the l 1 penalty function we prove that the equilibrium of a differential inclusion is a normalized nash equilibrium of the original generalized noncooperative game and the centralized differential inclusion exponentially converges to the unique normalized nash equilibrium of a strongly monotone game suppose that the players can communicate with their neighboring players only and the communication topology can be represented by a connected undirected graph based on a leader following consensus scheme and singular perturbation techniques we propose distributed algorithms by using the exact l 1 penalty function and the continuously differentiable squared l 2 penalty function respectively the squared l 2 penalty function method works for games with smooth constraints and the exact l 2 penalty function works for certain scenarios the proposed two distributed algorithms converge to an neighborhood of the unique normalized nash equilibrium and an neighborhood of an approximated nash equilibrium respectively with being a positive constant for each 0 and each initial condition there exists an varepsilon such that for each 0 varepsilon varepsilon the convergence can be guaranteed where varepsilon is a parameter in the algorithm

universality and complexity in cellular automata abstract cellular automata are discrete dynamical systems with simple construction but complex self organizing behaviour evidence is presented that all one dimensional cellular automata fall into four distinct universality classes characterizations of the structures generated in these classes are discussed three classes exhibit behaviour analogous to limit points limit cycles and chaotic attractors the fourth class is probably capable of universal computation so that properties of its infinite time behaviour are undecidable

distributed robust adaptive equilibrium computation for generalized convex games this paper considers a class of generalized convex games where each player is associated with a convex objective function a convex inequality constraint and a convex constraint set the players aim to compute a nash equilibrium through communicating with neighboring players the particular challenge we consider is that the component functions are unknown a priori to associated players we study two distributed computation algorithms and analyze their convergence properties in the presence of data transmission delays and dynamic changes of network topologies the algorithm performance is verified through demand response on the ieee 30 bus test system our technical tools integrate convex analysis variational inequalities and simultaneous perturbation stochastic approximation

criticality in cellular automata abstract using recent results obtained for the transition to turbulence via spatiotemporal intermittency in extended dynamical systems critical cellular automata rules are built thanks to a systematic procedure the continuous phase transition observed in a coupled map lattice is translated into a sequence of cellular automata rules for which the critical properties of the original system are reproduced as precisely as desired it is shown that criticality as understood from the point of view of statistical mechanics is intimately related to the various characteristics of wolfram s class iv rules this suggests in turn the picture of a critical surface in the space of rules and provides the basis for a discussion of the problem of classification schemes we review recent cellular automata studies where questions linked to criticality arise and argue that they are unified in light of our results leaving the relationship between computational and statistical characterizations of critical rules as the central problem for future studies on this subject

exploiting regularities in large cellular spaces abstract we informally describe a computer algorithm for simulating deterministic cellular automata it grows smarter by selectively recording intermediate computations while operating on a compressed representation of the cellular space time no information is lost because configurations do not actually evolve instead the simulator accomodates random exploration of place times in the future of initial configurations embedded in an effectively unbounded void we use conway s life automaton as a model but the idea extends easily to other geometries dimensions and number of states

distributed optimization for linear multiagent systems edge and node based adaptive designs this paper studies the distributed optimization problem for continuous time multiagent systems with general linear dynamics the objective is to cooperatively optimize a team performance function formed by a sum of convex local objective functions each agent utilizes only local interaction and the gradient of its own local objective function to achieve the cooperative goal a couple of fully distributed optimal algorithms are designed first an edge based adaptive algorithm is developed for linear multiagent systems with a class of convex local objective functions then a node based adaptive algorithm is constructed to solve the distributed optimization problem for a class of agents satisfying the bounded input bounded state stable property sufficient conditions are given to ensure that all agents reach a consensus while minimizing the team performance function finally numerical examples are provided to illustrate the theoretical results

distributed nash equilibrium seeking in networked graphical games abstract this paper considers a gossip approach for finding a nash equilibrium in networked games on graphs where a player s cost function may be affected by the actions of any subset of players an interference graph illustrates the partially coupled cost functions i e the asymmetric strategic interaction and information requirements an algorithm is proposed whereby players make decisions based only on the estimates of their interfering players actions given the interference graph not necessarily complete a communication graph is designed so that players exchange only their required information when the interference graph is sparse the algorithm can offer substantial savings in communication and computation almost sure convergence to a nash equilibrium is proved for diminishing step sizes the effect of the second largest eigenvalue of the expected communication matrix on the convergence rate is quantified

predecessors and garden of eden configurations in parallel dynamical systems on maxterm and minterm boolean functions abstract in this work we solve the classical predecessor problems for parallel dynamical systems on maxterm and minterm boolean functions actually we solve analytically the predecessor existence problem by giving a characterization to have a predecessor for any given configuration as a consequence we also get a characterization of the garden of eden configurations of these systems moreover the structure of the predecessors found out allows us to give a solution to the unique predecessor problem the coexistence of predecessors problem and the number of predecessors problem

boolean dynamics of networks with scale free topology the dynamics of boolean networks with scale free topology are studied the existence of a phase transition from ordered to chaotic dynamics governed by the value of the scale free exponent of the network is shown analytically by analyzing the overlap between two distinct trajectories the phase diagram shows that the phase transition occurs for values of the scale free exponent in the open interval 2 2 5 since the boolean networks under study are directed graphs the scale free topology of the input connections and that of the output connections are studied separately ultimately these two topologies are shown to be equivalent a numerical study of the attractor structure of the configuration space reveals that this structure is similar in both networks with scale free topologies and networks with homogeneous random topologies however an important result of this work is that the fine tuning usually required to achieve stability in the dynamics of networks with homogeneous random topologies is no longer necessary when the network topology is scale free finally based on the results presented in this work it is hypothesized that the scale free topology favors the evolution and adaptation of network functioning from a biological perspective

characterization of random fluctuation based computation in cellular automata a brownian cellular automaton bca is an asynchronous cellular automaton aca in which the timing of the local cell state transitions approaches a poisson point process and the global transitions between cell configurations can be formulated as an irreducible and reversible markov chain bcas exploit fluctuations to find solutions of a computation via a stochastic search process this characteristic has been shown to contribute to a decreased complexity of bcas lee and peper 2008 as compared to non brownian acas with equivalent functionality this paper proposes a computationally universal bca that is based on a conventional aca rather than the previously employed block cellular automata which have transition rules that update each cell simultaneously with its neighboring cells the proposed allows for a more natural update model in which no need arises to locally synchronize the cells in a neighborhood the resulting bca is significantly less complex than equivalent non block non brownian acas which demonstrates that random fluctuations can serve as a powerful resource for efficient computation on cellular automata

relaxation and limit cycles in a global version of the quenched kauffman model abstract a combinatorial method is used to investigate all possible cellular automata defined on a finite set of w global configurations relaxation time is defined as the number of steps before entering a fixed point or a cycle for given w we derive an analytical formula for the distribution of relaxation times t pw t w ww 1 k 0w t 1 wk k the same distribution is proved to be valid for the length of limit cycles the results have some relevance to the quenched kauffman model

fictitious mass element in structural dynamics fictitious masses are used to improve the accuracy and efficiency of modal based structural analyses that involve substructure synthesis local excitation and local structural changes new formulations which allow easy applications in various subsequent analyses are given for two categories of fictitious masses regular and very large regular masses are of the order of entire substructures whereas very large ones are several orders of magnitude larger the regular fictitious masses are added to selected coordinates of the finite element model for normal mode analysis and then removed in a way that produces modes with local deformations near the selected points in addition to the nominal natural vibration modes subsequent analyses of local nature can then be performed in the standard way very large masses are used to generate static constraint modes for fixed boundary modal coupling and broken modes are used for representing rigid body relative motion between structural segments with application to loads analysis the inclusion of fictitious masses as optional elements in standard structural dynamic procedures is facilitated

parametric flutter margin method for aeroservoelastic stability analysis a new parametric flutter margin method for linear and nonlinear stability analysis of aeroservoelastic systems is presented the method is based on frequency response calculations with the system s

distributed nash equilibrium seeking for aggregative games with coupled constraints abstract in this paper we study a distributed continuous time design for aggregative games with coupled constraints in order to seek the generalized nash equilibrium by a group of agents via simple local information exchange to solve the problem we propose a distributed algorithm based on projected dynamics and non smooth tracking dynamics even for the case when the interaction topology of the multi agent network is time varying moreover we prove the convergence of the non smooth algorithm for the distributed game by taking advantage of its special structure and also combining the techniques of the variational inequality and lyapunov function

kauffman boolean model in undirected scale free networks we investigate analytically and numerically the critical line in undirected random boolean networks with arbitrary degree distributions including the scale free topology of connections p k ensuremath sim k ensuremath ensuremath gamma we explain that the unattainability of the critical line in numerical simulations of classical random graphs is due to percolation phenomena we suggest that recent findings of discrepancy between simulations and theory in directed random boolean networks might have the same reason we also show that in infinite scale free networks the transition between frozen and chaotic phases occurs for 3l ensuremath gamma l3 5 since most critical phenomena in scale free networks reveal their nontrivial character for ensuremath gamma l3 the position of the critical line in the kauffman model seems to be an important exception to the rule

1 f fluctuation in the game of life abstract the fourier power spectra are examined for the game of life and its variants the results show that only the game of life exhibits fluctuation by means of observing patterns and measuring entropy and difference pattern spreading rate we conclude that the game of life only belongs to wolfram s class iv cellular automata which are thought to be capable of supporting universal computation this predicts a connection between fluctuation and computational universality

time evolution of damage in the ising model the time evolution of the damage in the ising model with the heat bath and glauber dynamics has been investigated with the damage spreading method the damage density d t and the average distance r t of damaged sites from the origin have been measured numerically from the simulational data the scaling forms have been established as d t tx r t t1z and d t r t df and the corresponding exponents x z and df have been estimated

spontaneous emergence of spatio temporal order in class 4 automata abstract we report surprisingly regular behaviors observed for a class 4 cellular automaton the totalistic rule 20 starting from disordered initial configurations the automaton produces patterns which are periodic not only in time but also in space this is the first evidence that different types of spatio temporal order can emerge under specific conditions out of disorder in the same discrete rule based algorithm

applications of ergodic theory and sofic systems to cellular automata abstract we indicate a mathematical framework for analysing the evolution of cellular automata those automata obeying an additive rule are shown to be the same as endomorphisms of a compact abelian group and therefore their statistical and dynamical behavior can be told exactly by using fourier analysis and ergodic theory those obeying certain nonlinear rules are closely tied to a finitely described object called a sofic system but the underlying statistics appear to be more complicated and interesting we conclude by formulating several conjectures about one such system

evolution by damage spreading in kauffman model in kauffman s boolean automata model on the square lattice the darwinian fitness of survival can be defined as the fraction of elements which do not change from one iteration to the next biological mutations are simulated by filpping one bit in the rule of one site selection of the fitter mutant then optimizes the whole lattice completely this optimization is particularly effective near the critical point of the transition to chaos but is in itself not a critical phenomenon also a two dimensional spin glass can be optimized in this way

smooth lyapunov functions for hybrid systems part i existence is equivalent to robustness hybrid systems are dynamical systems where the state is allowed to either evolve continuously flow on certain subsets of the state space or evolve discontinuously jump from other subsets of the state space for a broad class of such systems characterized by mild regularity conditions on the data we establish the equivalence between the robustness of stability with respect to two measures and a characterization of such stability in terms of a smooth lyapunov function this result unifies and generalizes previous results for differential and difference inclusions with outer semicontinuous and locally bounded right hand sides furthermore we give a description of forward completeness of a hybrid system in terms of a smooth lyapunov like function

distributed nash equilibrium seeking this paper presents an asynchronous gossip based algorithm for finding a nash equilibrium ne of a game in a distributed multi player network the algorithm is designed in such a way that players make decisions based on estimates of the other players actions obtained from local neighbors using a set of standard assumptions on the cost functions and communication graph the paper proves almost sure convergence to a ne for diminishing step sizes for constant step sizes an error bound on expected distance from a ne is established the effectiveness of the proposed algorithm is demonstrated via simulation for both diminishing and constant step sizes

nash equilibrium computation in subnetwork zero sum games with switching communications in this paper we investigate a distributed nash equilibrium computation problem for a time varying multi agent network consisting of two subnetworks where the two subnetworks share the same objective function we first propose a subgradient based distributed algorithm with heterogeneous stepsizes to compute a nash equilibrium of a zero sum game we then prove that the proposed algorithm can achieve a nash equilibrium under uniformly jointly strongly connected ujsc weight balanced digraphs with homogenous stepsizes moreover we demonstrate that for weighted unbalanced graphs a nash equilibrium may not be achieved with homogenous stepsizes unless certain conditions on the objective function hold we show that there always exist heterogeneous stepsizes for the proposed algorithm to guarantee that a nash equilibrium can be achieved for ujsc digraphs finally in two standard weight unbalanced cases we verify the convergence to a nash equilibrium by adaptively updating the stepsizes along with the arc weights in the proposed algorithm

distributed learning for stochastic generalized nash equilibrium problems this paper examines a stochastic formulation of the generalized nash equilibrium problem where agents are subject to randomness in the environment of unknown statistical distribution we focus on fully distributed online learning by agents and employ penalized individual cost functions to deal with coupled constraints three stochastic gradient strategies are developed with constant step sizes we allow the agents to use heterogeneous step sizes and show that the penalty solution is able to approach the nash equilibrium in a stable manner within o mu text max for small step size value mu text max and sufficiently large penalty parameters the operation of the algorithm is illustrated by considering the network cournot competition problem

consensus seeking in multiagent systems under dynamically changing interaction topologies this note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies both discrete and continuous update schemes are proposed for information consensus this note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves

on the effect of memory in one dimensional k 4 automata on networks the effect of implementing memory in cells of one dimensional ca and on nodes of various types of automata on networks with increasing degrees of random rewiring is studied in this article paying particular attention to the case of four inputs as a rule memory induces a moderation in the rate of changing nodes and in the damage spreading albeit in the latter case memory turns out to be ineffective in the control of the damage as the wiring network moves away from the ordered structure that features proper one dimensional ca this article complements the previous work done in the two dimensional context

algebraic properties of cellular automata cellular automata are discrete dynamical systems of simple construction but complex and varied behaviour algebraic techniques are used to give an extensive analysis of the global properties of a class of finite cellular automata the complete structure of state transition diagrams is derived in terms of algebraic and number theoretical quantities the systems are usually irreversible and are found to evolve through transients to attractors consisting of cycles sometimes containing a large number of configurations

dynamic aeroservoelastic response with nonlinear structural elements linear structural dynamics unsteady aerodynamics control system and actuator models are combined for linear aeroservoelastic equations of motion that are augmented with nonlinear feedback loops based on the increased order modeling approach although the linear equations are formulated in the frequency domain for best combined efficiency accuracy and robustness in industrial environment the nonlinear feedback loops are modeled in the time domain to provide maximal flexibility in adding nonlinear effects in all the involved disciplines the linear equations are solved first to provide a baseline response to deterministic or stochastic gusts maneuver commands or direct force excitations using fast fourier transform techniques nonlinear effects are then added in a time marching process that modifies the linear solution using convolution integrals the numerical process was used in the dynresp code that was recently developed as a framework for industrial applications and research in the area of nonl

computational mechanics of cellular automata an example abstract we illustrate and extend the techniques of computational mechanics in explicating the structures that emerge in the space time behavior of elementary one dimensional cellular automaton rule 54 the dominant regular domain of the cellular automation is identified and a domain filter is constructed to locate and classify defects in the domain the primary particles are identified and a range of interparticle interactions is studied the deterministic equation of motion of the filtered space time behavior is derived filters of increasing sophistication are constructed for the efficient gathering of particle statistics and for the identification of higher level defects particle interactions and secondary domains we define the emergence time at which the space time behavior condenses into configurations consisting only of domains particles and particle interactions taken together these techniques serve as the basis for the investigation of pattern evolution and self organization in this representative system

towards the classification of all boolean cellular automata abstract a classification scheme for all boolean cellular automata models involving an arbitrary number of inputs is proposed the scheme is based upon counting the number of stable points for a given rule i e points whose time development is stable with respect to small perturbations when applied to all cellular automata with 2 3 4 or 5 boolean inputs the latter involving more than 4000 million cases it yields in each case a nontrivial classification i e there is no single class in which nearly all the rules lie in addition it is shown how rules satisfying a given boolean differential equation can easily be obtained

quantifying the complexity of geodesic paths on curved statistical manifolds through information geometric entropies and jacobi fields abstract we characterize the complexity of geodesic paths on a curved statistical manifold m s through the asymptotic computation of the information geometric complexity v m s and the jacobi vector field intensity j m s the manifold m s is a 2 l dimensional gaussian model reproduced by an appropriate embedding in a larger 4 l dimensional gaussian manifold and endowed with a fisher rao information metric g with non trivial off diagonal terms these terms emerge due to the presence of a correlational structure embedding constraints among the statistical variables on the larger manifold and are characterized by macroscopic correlational coefficients r k first we observe a power law decay of the information geometric complexity at a rate determined by the coefficients r k and conclude that the non trivial off diagonal terms lead to the emergence of an asymptotic information geometric compression of the explored macrostates on m s finally we observe that the presence of such embedding constraints leads to an attenuation of the asymptotic exponential divergence of the jacobi vector field intensity

damage spreading in non frustrated phase of a triangular antiferromagnet abstract we investigate a first order phase transition from a non magnetic phase to a non frustrated phase of a two dimensional triangular lattice with antiferromagnetic bonds a cellular automaton is defined which chooses a magnetic state of subsequent lattice sites where an interphase boundary arrives as to minimise the local energy the ground state magnetic state is found to be unstable with respect to the point defects of magnetic structure

phase transition in nk kauffman networks and its correction for boolean irreducibility abstract in a series of articles published in 1986 derrida and his colleagues studied two mean field treatments the quenched and the annealed for nk kauffman networks their main results lead to a phase transition curve k c 2 p c 1 p c 1 0 p c 1 for the critical average connectivity k c in terms of the bias p c of extracting a 1 for the output of the automata values of k bigger than k c correspond to the so called chaotic phase while k k c to an ordered phase in zertuche 2009 a new classification for the boolean functions called boolean irreducibility permitted the study of new phenomena of nk kauffman networks in the present work we study once again the mean field treatment for nk kauffman networks correcting it for boolean irreducibility a shifted phase transition curve is found in particular for p c 1 2 the predicted value k c 2 by derrida et al changes to k c 2 62140224613 we support our results with numerical simulations

continuous time integral dynamics for a class of aggregative games with coupling constraints we consider continuous time equilibrium seeking in a class of aggregative games with strongly convex cost functions and affine coupling constraints we propose simple semidecentralized integral dynamics and prove their global asymptotic convergence to a variational generalized aggregative or nash equilibrium the proof is based on lyapunov arguments and invariance techniques for differential inclusions

penalty methods for the solution of generalized nash equilibrium problems the generalized nash equilibrium problem gnep is an extension of the classical nash equilibrium problem where both the objective functions and the constraints of each player may depend on the rivals strategies this class of problems has a multitude of important engineering applications and yet solution algorithms are extremely scarce in this paper we analyze in detail a globally convergent penalty method that has favorable theoretical properties we also consider strengthened results for a particular subclass of problems very often considered in the literature basically our method reduces the gnep to a single penalized and nonsmooth nash equilibrium problem we suggest a suitable method for the solution of the latter penalized problem and present extensive numerical results

on singular perturbations due to fast actuators in hybrid control systems a stability result is given for hybrid control systems singularly perturbed by fast but continuous actuators if a hybrid control system has a compact set globally asymptotically stable when the actuator dynamics are omitted or equivalently are infinitely fast then the same compact set is semiglobally practically asymptotically stable in the finite speed of the actuator dynamics this result which generalizes classical results for differential equations justifies using a simplified plant model that ignores fast but continuous actuator dynamics even when using a hybrid feedback control algorithm

parallel dynamical systems over directed dependency graphs abstract in this work we analyze the orbit structure of parallel discrete dynamical systems over directed dependency graphs with boolean functions as global functions in this sense for the cases corresponding to the simplest boolean functions and and or it is proved that only fixed or eventually fixed points appear as occurs over undirected dependency graphs however for general boolean functions it is shown that any period can appear so breaking the pattern found for the undirected case where only eventually fixed points or 2 periodic orbits can exist