can extra updates delay mixing we consider glauber dynamics starting from an extremal configuration in a monotone spin system and show that interjecting extra updates cannot increase the expected hamming distance or the total variation distance to the stationary distribution we deduce that for monotone markov random fields when block dynamics contracts a hamming metric single site dynamics mixes in o n log n steps on an n vertex graph in particular our result completes work of kenyon mossel and peres concerning glauber dynamics for the ising model on trees our approach also shows that on bipartite graphs alternating updates systematically between odd and even vertices cannot improve the mixing time by more than a factor of log n compared to updates at uniform random locations on an n vertex graph our result is especially effective in comparing block and single site dynamics it has already been used in works of martinelli toninelli sinclair mossel sly ding lubetzky and peres in various combinations

rigorous inequalities between length and time scales in glassy systems glassy systems are characterized by an extremely sluggish dynamics without any simple sign of long range order it is a debated question whether a correct description of such phenomenon requires the emergence of a large correlation length we prove rigorous bounds between length and time scales implying the growth of a properly defined length when the relaxation time increases our results are valid in a rather general setting which covers finite dimensional and mean field systems as an illustration we discuss the glauber heat bath dynamics of p spin glass models on random regular graphs we present the first proof that a model of this type undergoes a purely dynamical phase transition not accompanied by any thermodynamic singularity

simulating time harmonic flows with the lattice boltzmann method we simulate time harmonic flows by the lattice boltzmann method we propose a general scheme to choose simulation parameters under the constraints of fixed reynolds and womersley numbers and with a specified simulation error under these constraints parameters are chosen to minimize the execution time numerical stability is studied in a range of reynolds and womersley numbers as an example of time harmonic flow simulations results of blood flow in a human abdominal aorta are presented

robust reconstruction on trees is determined by the second eigenvalue consider a markov chain on an infinite tree t v e rooted at in such a chain once the initial root state is chosen each vertex iteratively chooses its state from the one of its parent by an application of a markov transition rule and all such applications are independent let j denote the resulting measure for j j is defined on configurations x x2v 2 a v where a is some finite set let n denote the restriction of to the sigma algebra generated by the variables x where x is at distance exactly n from letting n maxi j2a dtv n n where dtv denotes total variation distance we say that the reconstruction problem is solvable if liminfn 1 n 0 reconstruction solvability roughly means that the n th level of the tree contains a non vanishing amount of information on the root of the tree as n 1 in this paper we study the problem of robust reconstruction let be a non degenerate distribution on a and 0 let be chosen according to n and 0 be obtained from by letting for each node independently v 0 v with probability 1 and 0 v to be an independent sample from otherwise we denote by n the resulting measure on 0 the measure n is a perturbation of the measure n letting n maxi j2a dtv n n we say that the reconstruction problem is robust solvable if liminfn 1 n 0 for all 0 1 where 2 m is the second largest eigenvalue of m in absolute value then for all non degenerate the reconstruction problem is robust solvable we prove a converse and show that the reconstruction problem is not robust solvable if b 2 m 2 1 this proves a conjecture by the second author and peres we also consider other models of noise and general trees

decentralised coordination of a multi agent system based on intermittent data in this paper we present a novel decentralised and non cooperative algorithm for estimation and control of a multi agent system the control goal is to achieve a balanced formation on a generic closed curve different from previous work each agent only gathers a measurement of its euclidean distance from the other agents when they are in its proximity this distance is usually different from the controlled distance along the curve thus producing an uncertain and intermittent information on the actual spacing among agents this fleeting data flow is processed by an estimation algorithm to produce an interval estimate of the relative position which is then used by an interval feedback control law to steer the system dynamics the effectiveness of the approach and its performance are demonstrated through an extensive numerical analysis on two representative examples

evolutionary trees and the ising model on the bethe lattice a proof of steel s conjecture a major task of evolutionary biology is the reconstruction of phylogenetic trees from molecular data the evolutionary model is given by a markov chain on a tree given samples from the leaves of the markov chain the goal is to reconstruct the leaf labelled tree it is well known that in order to reconstruct a tree onn leaves sample sequences of length log n are needed it was conjectured by m steel that for the cfn ising evolutionary model if the mutation probability on all edges of the tree is less thanp p 2 1 2 3 2 then the tree can be recovered from sequences of length o logn the value p is given by the transition point for the extremality of the free gibbs measure for the ising model on the binary tree steel s conjecture was proven by the second author in the special case where the tree is balanced the second author also proved that if all edges have mutation probability larger thanp then the length needed isn 1 here we show that steel s conjecture holds true for general trees by giving a reconstruction algorithm that recovers the tree from o logn length sequences when the mutation probabilities are discretized and less than p our proof and results demonstrate that extremality of the free gibbs measure on the infinite binary tree which has been studied before in probability statistical physics and computer science determines how distinguishable are gibbs measures on finite binary trees

on the general consensus protocol of multi agent systems with double integrator dynamics in this paper a general consensus protocol is considered for multi agent systems with double integrator dynamics the advantage of this protocol is that different consensus dynamics including linear periodic and positive exponential dynamics can be realized by choosing different gains necessary and sufficient conditions for solving the consensus problem with the considered general protocol are obtained namely all the gains realizing the consensus can be described the design method of the consensus protocol is constructively given moreover a periodic consensus protocol is obtained as a special case and it is revealed that the maximum convergence speed can be achieved by choosing suitable gains

dynamic behaviors in directed networks motivated by the abundance of directed synaptic couplings in a real biological neuronal network we investigate the synchronization behavior of the hodgkin huxley model in a directed network we start from the standard model of the watts strogatz undirected network and then change undirected edges to directed arcs with a given probability still preserving the connectivity of the network a generalized clustering coefficient for directed networks is defined and used to investigate the interplay between the synchronization behavior and underlying structural properties of directed networks we observe that the directedness of complex networks plays an important role in emerging dynamical behaviors which is also confirmed by a numerical study of the sociological game theoretic voter model on directed networks

phase transitions in phylogeny we apply the theory of markov random fields on trees to derive a phase transition in the number of samples needed in order to reconstruct phylogenies we consider the cavender farris neyman model of evolution on trees where all the inner nodes have degree at least 3 and the net transition on each edge is bounded by e motivated by a conjecture by m steel we show that if 2 1 2 2 1 then for balanced trees the topology of the underlying tree having n leaves can be reconstructed from o logn samples characters at the leaves on the other hand we show that if 2 1 2 2 1 then there exist topologies which require at least n 1 samples for reconstruction our results are the first rigorous results to establish the role of phase transitions for markov random fields on trees as studied in probability statistical physics and information theory for the study of phylogenies in mathematical biology

a manifold of pure gibbs states of the ising model on the lobachevsky plane in this paper we construct many new gibbs states of the ising model on the lobachevsky plane the millefeuilles unlike the usual states on the integer lattices our foliated states have infinitely many interfaces the interfaces are rigid and fill the lobachevsky plane with positive density we also construct analogous states on the cayley trees

improved bounds for sampling colorings we consider the problem of sampling uniformly at random from the set of proper k colorings of a graph with maximum degree our main result is the design of a simple markov chain that converges in o nk log n time to the desired distribution when k 116

phase ordering after a deep quench the stochastic ising and hard core gas models on a tree consider a low temperature stochastic ising model in the phase coexistence regime with markov semigroup p t a fundamental and still largely open problem is the understanding of the long time behavior of p t when the initial configuration is sampled from a highly disordered state e g a product bernoulli measure or a high temperature gibbs measure exploiting recent progresses in the analysis of the mixing time of monte carlo markov chains for discrete spin models on a regular b ary tree open image in new window we study the above problem for the ising and hard core gas independent sets models on open image in new window if is a biased product bernoulli law then under various assumptions on the bias and on the thermodynamic parameters we prove almost sure weak convergence of p t to an extremal gibbs measure pure phase and show that the limit is approached at least as fast as a stretched exponential of the time t in the context of randomized algorithms and if one considers the glauber dynamics on a large finite tree our results prove fast local relaxation to equilibrium on time scales much smaller than the true mixing time provided that the starting point of the chain is not taken as the worst one but it is rather sampled from a suitable distribution

sampled data based consensus of continuous time multi agent systems with time varying topology this technical note studies consensus problems of multiple agents with continuous time second order dynamics where each agent can obtain its positions and velocities relative to its neighbors only at sampling instants it is assumed that the sampling period of each agent is independent of the others and the interaction topology among agents is time varying where the associated direct graphs may not have spanning trees if the union graph of all direct graphs has a spanning tree then there exist controller gains and sampling periods such that consensus is reached moreover two approaches are presented to design such controller gains and sampling periods simulations are performed to validate the theoretical results

analyzing glauber dynamics by comparison of markov chains a popular technique for studying random properties of a combinatorial set is to design a markov chain monte carlo algorithm for many problems there are natural markov chains connecting the set of allowable configurations which are based on local moves or glauber dynamics typically these single site update algorithms are difficult to analyze so often the markov chain is modified to update several sites simultaneously recently there has been progress in analyzing these more complicated algorithms for several important combinatorial problems in this work we use the comparison technique of diaconis and saloff coste to show that several of the natural single point update algorithms are efficient the strategy is to relate the mixing rate of these algorithms to the corresponding nonlocal algorithms which have already been analyzed this allows us to give polynomial time bounds for single point update algorithms for problems such as generating planar tilings and random triangulations of convex polygons we also survey several other comparison techniques along with specific applications which have been used in the context of estimating mixing rates of markov chains

formation stability analysis of unmanned multi vehicles under interconnection topologies in this paper the overall formation stability of an unmanned multi vehicle is mathematically presented under interconnection topologies a novel definition of formation error is first given and followed by the proposed formation stability hypothesis based on this hypothesis a unique extension decomposition aggregation scheme is then employed to support the stability analysis for the overall multi vehicle formation under a mesh topology it is proved that the overall formation control system consisting of n number of nonlinear vehicles is not only asymptotically stable but also exponentially stable in the sense of lyapunov within a neighbourhood of the desired formation this technique is shown to be applicable for a mesh topology but is equally applicable for other topologies a simulation study of the formation manoeuvre of multiple aerosonde uavs unmanned aerial vehicles in 3 d space is finally carried out verifying the achieved formation stability result

glauber dynamics on trees and hyperbolic graphs we study continuous time glauber dynamics for random configurations with local constraints e g proper coloring ising and potts models on finite graphs with n vertices and of bounded degree we show that the relaxation time defined as the reciprocal of the spectral gap 1 2 for the dynamics on trees and on planar hyperbolic graphs is polynomial in n for these hyperbolic graphs this yields a general polynomial sampling algorithm for random configurations we then show that for general graphs if the relaxation time 2 satisfies 2 o 1 then the correlation coefficient and the mutual information between any local function which depends only on the configuration in a fixed window and the boundary conditions decays exponentially in the distance between the window and the boundary for the ising model on a regular tree this condition is sharp

the tightness of the kesten stigum reconstruction bound of symmetric model with multiple mutations it is well known that reconstruction problems as the interdisciplinary subject have been studied in numerous contexts including statistical physics information theory and computational biology to name a few we consider a 2q state symmetric model with two categories of q states in each category and 3 transition probabilities the probability to remain in the same state the probability to change states but remain in the same category and the probability to change categories we construct a nonlinear second order dynamical system based on this model and show that the kesten stigum reconstruction bound is not tight when q ge 4

average consensus in networks of dynamic agents with switching topologies and multiple time varying delays in this paper we discuss average consensus problem in undirected networks of dynamic agents with fixed and switching topologies as well as multiple time varying communication delays by employing a linear matrix inequality method we prove that all the nodes in the network achieve average consensus asymptotically for appropriate communication delays if the network topology is connected particularly several feasible linear matrix inequalities are established to determine the maximal allowable upper bound of time varying communication delays numerical examples are given to demonstrate the effectiveness and the sharpness of the theoretical results

chaotic synchronization by the intermittent feedback method this paper studies the synchronization of chaotic systems by the intermittent feedback method which is efficient a sufficient synchronization criterion for a general intermittent linear state error feedback control is obtained by using a lyapunov function and differential inequalities numerical simulations for the chaotic chua oscillator are presented to illustrate the theoretical results

the ising partition function zeros and deterministic approximation we study the problem of approximating the partition function of the ferromagnetic ising model with both pairwise as well as higher order interactions equivalently in graphs as well as hypergraphs our approach is based on the classical lee yang theory of phase transitions along with a new lee yang theorem for the ising model with higher order interactions and on an extension of ideas developed recently by barvinok and patel and regts that can be seen as an algorithmic realization of the lee yang theory our first result is a deterministic polynomial time approximation scheme an fptas for the partition function in bounded degree graphs that is valid over the entire range of parameters beta the interaction and lambda the external field except for the case left lambda right 1 the zero field case a polynomial time randomized approximation scheme fpras for all graphs and all beta lambda based on markov chain monte carlo simulation has long been known unlike most other deterministic approximation algorithms for problems in statistical physics and counting our algorithm does not rely on the decay of correlations property but as pointed out above on lee yang theory this approach extends to the more general setting of the ising model on hypergraphs of bounded degree and edge size where no previous algorithms even randomized were known for a wide range of parameters in order to achieve this latter extension we establish a tight version of the lee yang theorem for the ising model on hypergraphs improving a classical result of suzuki and fisher

glauber dynamics on trees boundary conditions and mixing time we give the first comprehensive analysis of the effect of boundary conditions on the mixing time of the glauber dynamics in the so called bethe approximation specifically we show that the spectral gap and the log sobolev constant of the glauber dynamics for the ising model on an n vertex regular tree with boundary are bounded below by a constant independent of n at all temperatures and all external fields this implies that the mixing time is o logn in contrast to the free boundary case where it is not bounded by any fixed polynomial at low temperatures in addition our methods yield simpler proofs and stronger results for the spectral gap and log sobolev constant in the regime where the mixing time is insensitive to the boundary condition our techniques also apply to a much wider class of models including those with hard core constraints like the antiferromagnetic potts model at zero temperature proper colorings and the hard core lattice gas independent sets

second order leader following consensus of nonlinear multi agent systems via pinning control abstract without assuming that the interaction diagraph is strongly connected or contains a directed spanning tree this paper studies the second order leader following consensus problem of nonlinear multi agent systems with general network topologies based on graph theory matrix theory and lasalle s invariance principle a pinning control algorithm is proposed to achieve leader following consensus in a network of agents with nonlinear second order dynamics furthermore a pinning consensus protocol is developed for coupled double integrators with a constant reference velocity in particular this paper addresses what kind of agents and how many agents should be pinned and establishes some sufficient conditions to guarantee that all agents asymptotically follow the virtual leader numerical simulations are given to verify the theoretical analysis

consensus tracking for second order nonlinear multi agent systems with switching topologies and a time varying reference state abstractin this study the authors consider the consensus tracking problem for second order nonlinear multi agent systems with switching topologies and a time varying reference state the dynamics of each agent consists of nonlinear inherent dynamics in order to reach consensus tracking a class of nonsmooth control protocols is proposed which only depends on the agent s own information and its neighbours information with the aid of algebraic graph theory matrix theory and lyapunov theory some corresponding sufficient conditions guaranteeing consensus tracking under the proposed control protocols are derived finally the numerical simulations are given to illustrate the effectiveness of the developed theoretical results

some results on the forced pendulum equation abstract this paper is devoted to the study of the forced pendulum equation in the presence of friction namely u a u sin u f t with a r and f l 2 0 t using a shooting type argument we prove the existence of at least two essentially different t periodic solutions under appropriate conditions on t and f we also prove the existence of solutions decaying with a fixed rate 0 1 by the leray schauder theorem finally we prove the existence of a bounded solution on 0 using a diagonal argument

leader following consensus of multi agent systems under fixed and switching topologies the leader following consensus problem of higher order multi agent systems is considered in the system the dynamics of each agent and the leader is a linear system the control of each agent using local information is designed and detailed analysis of the leader following consensus is presented for both fixed and switching interaction topologies which describe the information exchange between the multi agent systems the design technique is based on algebraic graph theory riccati inequality and lyapunov inequality simulations indicate the capabilities of the algorithms

multi vehicle consensus with a time varying reference state in this paper we study the consensus problem in multi vehicle systems where the information states of all vehicles approach a time varying reference state under the condition that only a portion of the vehicles e g the unique team leader have access to the reference state and the portion of the vehicles might not have a directed path to all of the other vehicles in the team we first analyze a consensus algorithm with a constant reference state using graph theoretical tools we then propose consensus algorithms with a time varying reference state and show necessary and sufficient conditions under which consensus is reached on the time varying reference state the time varying reference state can be an exogenous signal or evolve according to a nonlinear model these consensus algorithms are also extended to achieve relative state deviations among the vehicles an application example to multi vehicle formation control is given as a proof of concept

gibbs rapidly samples colorings of g n d n gibbs sampling also known as glauber dynamics is a popular technique for sampling high dimensional distributions defined on graphs of special interest is the behavior of gibbs sampling on the erd s renyi random graph g n d n where each edge is chosen independently with probability d n and d is fixed while the average degree in g n d n is d 1 o 1 it contains many nodes of degree of order log n log log n the existence of nodes of almost logarithmic degrees implies that for many natural distributions defined on g n d n such as uniform coloring with a constant number of colors or the ising model at any fixed inverse temperature the mixing time of gibbs sampling is at least n 1 1 log log n with high probability high degree nodes pose a technical challenge in proving polynomial time mixing of the dynamics for many models including coloring almost all known sufficient conditions in terms of number of colors needed for rapid mixing of gibbs samplers are stated in terms of the maximum degree of the underlying graph in this work we consider sampling q colorings and show that for every d 1 where the number of colors does not depend on n they also provide a rare example where one can prove a polynomial time mixing of gibbs sampler in a situation where the actual mixing time is slower than npolylog n in previous work we have shown that similar results hold for the ferromagnetic ising model however the proof for the ising model crucially relied on monotonicity arguments and the weitz tree both of which have no counterparts in the coloring setting our proof presented here exploits in novel ways the local treelike structure of erd s renyi random graphs block dynamics spatial decay properties and coupling arguments our results give the first polynomial time algorithm to approximately sample colorings on g n d n with a constant number of colors they extend to much more general families of graphs which are sparse in some average sense and to much more general interactions in particular they apply to any graph for which there exists an 0 such that every vertex v of the graph has a neighborhood n v of radius o log n in which the induced sub graph is the union of a tree and at most o 1 edges and where each simple path of length o log n satisfies sum u in gamma sum v neq u alpha d u v o rm log n the results also generalize to the hard core model at low fugacity and to general models of soft constraints at high temperatures

glauber dynamics on the cycle is monotone we study heat bath glauber dynamics for the ferromagnetic ising model on a finite cycle a graph where every vertex has degree two we prove that the relaxation time 2 is an increasing function of any of the couplings j xy we also prove some further inequalities and obtain exact asymptotics for 2 at low temperatures

decentralized dynamics for finite opinion games game theory studies situations in which strategic players can modify the state of a given system in the absence of a central authority solution concepts such as nash equilibrium have been defined in order to predict the outcome of such situations in multi player settings it has been pointed out that to be realistic a solution concept should be obtainable via processes that are decentralized and reasonably simple accordingly we look at the computation of solution concepts by means of decentralized dynamics these are algorithms in which players move in turns to decrease their own cost and the hope is that the system reaches an equilibrium quickly we study these dynamics for the class of opinion games recently introduced by bindel et al 10 these are games important in economics and sociology that model the formation of an opinion in a social network we study best response dynamics and show upper and lower bounds on the convergence to nash equilibria we also study a noisy version of best response dynamics called logit dynamics and prove a host of results about its convergence rate as the noise in the system varies to get these results we use a variety of techniques developed to bound the mixing time of markov chains including coupling spectral characterizations and bottleneck ratio

approximating the permanent a randomised approximation scheme for the permanent of a 0 1s presented the task of estimating a permanent is reduced to that of almost uniformly generating perfect matchings in a graph the latter is accomplished by simulating a markov chain whose states are the matchings in the graph for a wide class of 0 1 matrices the approximation scheme is fully polynomial i e runs in time polynomial in the size of the matrix and a parameter that controls the accuracy of the output this class includes all dense matrices those that contain sufficiently many 1 s and almost all sparse matrices in some reasonable probabilistic model for 0 1 matrices of given density for the approach sketched above to be computationally efficient the markov chain must be rapidly mixing informally it must converge in a short time to its stationary distribution a major portion of the paper is devoted to demonstrating that the matchings chain is rapidly mixing apparently the first such result for a markov chain with genuinely c

a new look at survey propagation and its generalizations this article provides a new conceptual perspective on survey propagation which is an iterative algorithm recently introduced by the statistical physics community that is very effective in solving random k sat problems even with densities close to the satisfiability threshold we first describe how any sat formula can be associated with a novel family of markov random fields mrfs parameterized by a real number 0 1 we then show that applying belief propagation a well known message passing technique for estimating marginal probabilities to this family of mrfs recovers a known family of algorithms ranging from pure survey propagation at one extreme e 1 to standard belief propagation on the uniform distribution over sat assignments at the other extreme e 0 configurations in these mrfs have a natural interpretation as partial satisfiability assignments on which a partial order can be defined we isolate cores as minimal elements in this partial ordering which are also fixed points of survey propagation and the only assignments with positive probability in the mrf for e 1 our experimental results for k e 3 suggest that solutions of random formulas typically do not possess non trivial cores this makes it necessary to study the structure of the space of partial assignments for 0 can be viewed as a smoothed version of the uniform distribution over satisfying assignments e 0 finally we isolate properties of gibbs sampling and message passing algorithms that are typical for an ensemble of k sat problems

tight bounds for mixing of the swendsen wang algorithm at the potts transition point we study two widely used algorithms for the potts model on rectangular subsets of the hypercubic lattice mathbb z d heat bath dynamics and the swendsen wang algorithm and prove that under certain circumstances the mixing in these algorithms is torpid or slow in particular we show that for heat bath dynamics throughout the region of phase coexistence and for the swendsen wang algorithm at the transition point the mixing time in a box of side length l with periodic boundary conditions has upper and lower bounds which are exponential in ld 1 this work provides the first upper bound of this form for the swendsen wang algorithm and gives lower bounds for both algorithms which significantly improve the previous lower bounds that were exponential in l log l 2

a uniqueness condition for gibbs measures with application to the 2 dimensional ising antiferromagnet a uniqueness condition for gibbs measures is given this condition is stated in terms of absence of a certain type of percolation involving two independent realisations this result can be applied in certain concrete situations by comparison with ordinary percolation in this way we prove that the ising antiferromagnet on a square lattice has a unique gibbs measure if 4 h 1 2ln pc 1 pc whereh denotes the external magnetic field the inverse temperature andpc the critical probability for site percolation on that lattice sincepc is larger than 1 2 this extends a result by dobrushin kolafa and shlosman whose proof was computer assisted

brief paper second order consensus in multi agent dynamical systems with sampled position data this paper studies second order consensus in multi agent dynamical systems with sampled position data a distributed linear consensus protocol with second order dynamics is designed where both the current and some sampled past position data are utilized it is found that second order consensus in such a multi agent system cannot be reached without any sampled position data under the given protocol while it can be achieved by appropriately choosing the sampling period a necessary and sufficient condition for reaching consensus of the system in this setting is established based on which consensus regions are then characterized it is shown that if all the eigenvalues of the laplacian matrix are real then second order consensus in the multi agent system can be reached for any sampling period except at some critical points depending on the spectrum of the laplacian matrix however if there exists at least one eigenvalue of the laplacian matrix with a nonzero imaginary part second order consensus cannot be reached for sufficiently small or sufficiently large sampling periods in such cases one nevertheless may be able to find some disconnected stable consensus regions determined by choosing appropriate sampling periods finally simulation examples are given to verify and illustrate the theoretical analysis

polynomial time approximation algorithms for the ising model the paper presents a randomised algorithm which evaluates the partition function of an arbitrary ferromagnetic ising system to any specified degree of accuracy the running time of the algorithm in

accuracy of the lattice boltzmann method based on analytical solutions in this paper a simple method is proposed to obtain steady analytical solutions for the lattice boltzmann method based on such analytical results it is demonstrated how the accuracy of the lattice boltzmann method can depend on the relative orientation of the lattice and the flow field it is also demonstrated that the method can be useful to obtain a general class of analytical solutions for the lattice boltzmann method finally a simple relation is given between the compressibility error and the velocity field

nonsmooth leader following formation control of nonidentical multi agent systems with directed communication topologies this paper presents two nonsmooth leader following formation protocols for nonidentical lipschitz nonlinear multi agent systems with directed communication network topologies one protocol is used to achieve finite time formation for first order systems and the other to achieve asymptotic formation for second order systems in these protocols the states of all the agents including the leader and the followers are available only locally within their neighborhoods some sufficient conditions for reaching formations are derived for nonidentical nonlinear systems satisfying locally lipschitz conditions to prove the stability a new nonsmooth lyapunov function is constructed with stability conditions derived under a nonsmooth analysis framework the proposed formation protocols are applied to multi spacecraft systems in deep space exploration with numerical simulations demonstrating the effectiveness of the theoretical results

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

cooperative enclosing control for multiple moving targets by a group of agents in this paper the enclosing control problem of second order multi agent systems is considered where the targets can be either stationary or moving the objective is to achieve an equidistant circular formation for a group of agents to enclose a team of targets in order to do so we first introduce a formal definition explaining certain basic properties of the exploring relation between the agents and the targets we then construct the estimator of the centre of the targets which is used to build the control protocol to achieve equidistant circular enclosing using a lyapunov function and lasalle s invariance principle the convergency of the estimator and control protocol are respectively established we then construct a smooth function to approximate the discontinuous term in the estimator finally the simulations for stationary targets and moving targets are given to verify the validity of the results obtained

critical ising on the square lattice mixes in polynomial time the ising model is widely regarded as the most studied model of spin systems in statistical physics the focus of this paper is its dynamic stochastic version the glauber dynamics introduced in 1963 and by now the most popular means of sampling the ising measure intensive study throughout the last three decades has yielded a rigorous understanding of the spectral gap of the dynamics on mathbb z 2 everywhere except at criticality while the critical behavior of the ising model has long been the focus for physicists mathematicians have only recently developed an understanding of its critical geometry with the advent of sle cle and new tools to study conformally invariant systems

analytical solution of axi symmetrical lattice boltzmann model for cylindrical couette flows abstract analytical solution for the axi symmetrical lattice boltzmann model is obtained for the low mach number cylindrical couette flows in the hydrodynamic limit the present solution is in excellent agreement with the result of the navier stokes equation since the kinetic boundary condition is used the present analytical solution using nine discrete velocities can describe flows with the knudsen number up to 0 1 meanwhile the comparison with the simulation data obtained by the direct simulation monte carlo method shows that higher order lattice boltzmann models with more discrete velocities are needed for highly rarefied flows

brief paper some necessary and sufficient conditions for second order consensus in multi agent dynamical systems this paper studies some necessary and sufficient conditions for second order consensus in multi agent dynamical systems first basic theoretical analysis is carried out for the case where for each agent the second order dynamics are governed by the position and velocity terms and the asymptotic velocity is constant a necessary and sufficient condition is given to ensure second order consensus and it is found that both the real and imaginary parts of the eigenvalues of the laplacian matrix of the corresponding network play key roles in reaching consensus based on this result a second order consensus algorithm is derived for the multi agent system facing communication delays a necessary and sufficient condition is provided which shows that consensus can be achieved in a multi agent system whose network topology contains a directed spanning tree if and only if the time delay is less than a critical value finally simulation examples are given to verify the theoretical analysis

zero temperature glauber dynamics on mathbb z d we study zero temperature glauber dynamics on mathbb z d which is a dynamic version of the ising model of ferromagnetism spins are initially chosen according to a bernoulli distribution with density p and then the states are continuously and randomly updated according to the majority rule this corresponds to the sudden quenching of a ferromagnetic system at high temperature with an external field to one at zero temperature with no external field define p c mathbb z d to be the infimum over p such that the system fixates at with probability 1 it is a folklore conjecture that p c mathbb z d 1 2 for every 2 le d in mathbb n we prove that p c mathbb z d to 1 2 as d

synchronization of coupled harmonic oscillators with local interaction this paper studies synchronization of coupled second order linear harmonic oscillators with local interaction we analyze convergence conditions over respectively directed fixed and switching network topologies by using tools from algebraic graph theory matrix theory and nonsmooth analysis it is shown that the coupled harmonic oscillators can be synchronized under mild network connectivity conditions examples are given to validate the convergence conditions the theoretical result is also applied to synchronized motion coordination of multi agent systems as a proof of concept

explicit isoperimetric constants and phase transitions in the random cluster model the random cluster model is a dependent percolation model that has applications in the study of ising and potts models in this paper several new results are obtained for the random cluster model on nonamenable graphs with cluster parameter q geq 1 among these the main ones are the absence of percolation for the free random cluster measure at the critical value and examples of planar regular graphs with regular dual where p mathrm c mathrm free q p mathrm u mathrm wired q for q large enough the latter follows from considerations of isoperimetric constants and we give the first nontrivial explicit calculations of such constants such considerations are also used to prove nonrobust phase transition for the potts model on nonamenable regular graphs

a synthesis approach of distributed model predictive control for homogeneous multi agent system with collision avoidance for the tracking and formation problem of multi agent systems with collision avoidance a synchronous distributed model predictive control dmpc algorithm is proposed we consider the deterministic linear time invariant and homogeneous dynamics for all agents in the synchronous dmpc all the agents solve their optimisation problems synchronously taking advantage of their neighbours assumed predictive information to obtain the current optimal inputs considering the uncertain deviation existing between the assumed and actual predictive information of each agent we contribute to design a deviation dependent collision avoidance constraint which is imposed in the individual optimisation problem to guarantee the safety of each agent we constrain the uncertain deviation by designing a time varying compatibility constraint in the two norm form which is imposed in the individual optimisation problem to play an important role in both the collision avoidance and exponential stability by applying the pr

second order consensus for multi agent systems with switching topology and communication delay in this paper two kinds of consensus problems for second order agents under directed and arbitrarily switching topologies are investigated that is the cases without and with communication delay for the former by constructing a new kind of digraph and employing a new graphic method we can specify the least convergence rate for all the agents to reach consensus for the latter in virtue of a matrix inequality method a sufficient condition in the form of feasible matrix inequalities is presented for all the agents to reach consensus this on the other hand shows that consensus can be reached if the delay is small enough finally two numerical examples are given to demonstrate the effectiveness and advantages of the proposed results

consensus of multi agent systems with unbounded time varying delays in this note the consensus problem with infinite time varying delays for linearly coupled static network is investigated the delay affects only the off diagonal terms in continuous time equations at first we define an effective consensus ability index then by using the graph theory and a new concept of consensus we prove that under some mild conditions the network can realize consensus an example is given to show the validity of obtained results

gibbs measures over locally tree like graphs and percolative entropy over infinite regular trees consider a statistical physical model on the d regular infinite tree t d described by a set of interactions phi let g n be a sequence of finite graphs with vertex sets v n that locally converge to t d from phi one can construct a sequence of corresponding models on the graphs g n let mu n be the resulting gibbs measures here we assume that mu n converges to some limiting gibbs measure mu on t d in the local weak sense and study the consequences of this convergence for the specific entropies v n 1 h mu n we show that the limit supremum of v n 1 h mu n is bounded above by the percolative entropy h textit perc mu a function of mu itself and that v n 1 h mu n actually converges to h textit perc mu in case phi exhibits strong spatial mixing on t d when it is known to exist the limit of v n 1 h mu n is most commonly shown to be given by the bethe ansatz percolative entropy gives a different formula and we do not know how to connect it to the bethe ansatz directly we discuss a few examples of well known models for which the latter result holds in the high temperature regime

consensus problems in networks of agents with double integrator dynamics and time varying delays in this article we consider consensus problems in networks of agents with double integrator dynamics and non uniform time varying delays the agent dynamics is adopted as a typical point mass model based on newton s law without assuming that the weighting factors in the information update schemes are non negative we propose two protocols such that both the state and the velocity of agents achieve consensus an equivalent reduced order system is introduced to analyse the convergence of the protocols some necessary and or sufficient conditions for consensus are established in terms of linear matrix inequalities simulation results are provided that demonstrate the effectiveness of our theoretical results

on the hardness of sampling independent sets beyond the tree threshold we consider local markov chain monte carlo algorithms for sampling from the weighted distribution of independent sets with activity where the weight of an independent set i is i a recent result has established that gibbs sampling is rapidly mixing in sampling the distribution for graphs of maximum degree d and c it is np hard to approximate the above weighted sum over independent sets to within a factor polynomial in the size of the graph

leader following formation control of multi agent systems under fixed and switching topologies in this article two kinds of leader following formation control problems for second order nonlinear multi agent systems are investigated that is the cases with fixed topology and with switching topology for the former by constructing an appropriate lyapunov functional and utilising linear matrix inequality lmi method we propose a formation control algorithm which makes the nonlinear multi agent systems converge to a desired formation in addition a formation control algorithm is also developed for coupled double integrators with a constant reference velocity then we extend these results to the case when the interaction topology is switching numerical simulations are presented finally to demonstrate the effectiveness of the proposed results

the critical ising model on trees concave recursions and nonlinear capacity we consider the ising model on a general tree under various boundary conditions all plus free and spin glass in each case we determine when the root is influenced by the boundary values in the limit as the boundary recedes to infinity we obtain exact capacity criteria that govern behavior at critical temperatures for plus boundary conditions an l 3 capacity arises in particular on a spherically symmetric tree that has n b n vertices at level n up to bounded factors we prove that there is a unique gibbs measure for the ferromagnetic ising model at the relevant critical temperature if and only if 1 2 our proofs are based on a new link between nonlinear recursions on trees and l p capacities