critical finite size corrections for the sherrington kirkpatrick spin glass starting from the effective lagrangian of the sherrington kirkpatrick spin glass near the critical temperature the authors investigate the finite size effects for the free energy and the propagator above and at tc 1 they perform the calculation going up to the three loop diagrams for t to tc the cubic vertex only gives the leading term the inclusion of the quartic vertex gives the following terms the numerical coefficients in these terms are established by the different methods of the partial summation of perturbation series the comparison with numerical simulations is done

the role of network topology on extremism propagation with the relative agreement opinion dynamics abstract in deffuant et al j artif soc soc simulation 5 2002 4 we proposed a simple model of opinion dynamics which we used to simulate the influence of extremists in a population simulations were run without any specific interaction structure and varying the simulation parameters we observed different attractors such as predominance of centrism or of extremism we even observed in certain conditions that the whole population drifts to one extreme of the opinion even if initially there are an equal number of extremists at each extreme of the opinion axis in the present paper we study the influence of the social networks on the presence of such a dynamical behavior in particular we use small world networks with variable connectivity and randomness of the connections we find that the drift to a single extreme appears only beyond a critical level of connectivity which decreases when the randomness increases

calculation of the threshold surface for nerve equations in this paper calculations are presented for the threshold surface mathcal m in mckean s caricature for nerve conduction u t u xx u h u a and for the fitzhugh nagumo equation u t u xx u 1 u u a the previous construction of this surface gave no information about data on mathcal m or in particular the value of the amplitude which makes data critical this amplitude is computed by both a standard discretization of the partial differential equation and for mckean s equation by means of an asymptotic calculation for the integral equation satisfied by the free boundary m t defined by u m t t a on this numerical evidence it is conjectured that for a large class of initial data u 0 on mathcal m the value u 0 l 1 depends only ona

a rigorous theory of finite size scaling at first order phase transitions a large class of classical lattice models describing the coexistence of a finite number of stable states at low temperatures is considered the dependence of the finite volume magnetizationm per h l in cubes of sizel d under periodic boundary conditions on the external fieldh is analyzed for the case where two phases coexist at the infinite volume transition pointh t we prove that independent of the details of the model the finite volume magnetization per lattice site behaves likem per h t m tanh ml d h ht withm per h denoting the infinite volume magnetization and m 1 2 m per h t 0 m per h t 0 introducing the finite size transition pointh m l as the point where the finite volume susceptibility attains the maximum we show that in the case of asymmetric field driven transitions its shift ish t h m l o l 2d in contrast to claims in the literature starting from the obvious observation that the number of stable phases has a local maximum at the transition point we propose a new way of determining the pointh t from finite size data with a shift that is exponentially small inl finally the finite size effects are discussed also in the case where more than two phases coexist

polygonal approximation to the flow on the critical surface for the bistable equation abstract we present a method to follow the evolution of the flow on the stable manifold of the stationary wave for the bistable equation previous calculations indicated that a large class of initial data those whose support above threshold is kept away from 0 and on this surface are characterized by a constant value of their area the results presented here show that this is not sufficient to characterize data on threshold we have observed that the areas converge smoothly under the flow to the area of the standing wave we conjecture that the critical surface m is divided into three distinct regions in the first the critical multiplier is minimal in the second data has constant area and the third is a region containing the standing wave the procedure is an adaptation of euler s polygonal method for the solution of ordinary differential equations

high dimensional structure estimation in ising models local separation criterion we consider the problem of high dimensional ising graphical model selection we propose a simple algorithm for structure estimation based on the thresholding of the empirical conditional variation distances we introduce a novel criterion for tractable graph families where this method is efficient based on the presence of sparse local separators between node pairs in the underlying graph for such graphs the proposed algorithm has a sample complexity of n omega j min 2 log p where p is the number of variables and j min is the minimum absolute edge potential in the model we also establish nonasymptotic necessary and sufficient conditions for structure estimation

finite size scaling in the p state mean field potts glass a monte carlo investigation the p state mean field potts glass with bimodal bond distribution j is studied by monte carlo simulations both for p 3 and p 6 states for system sizes from n 5 to n 120 spins considering particularly the finite size scaling behavior at the exactly known glass transition temperature t c it is shown that for p 3 the moments q k of the spin glass order parameter satisfy a simple scaling behavior q k alpha n k 3 tilde f k n 1 3 1 t t c text k 1 2 3 tilde f k being the appropriate scaling function and t the temperature also the specific heat maxima have a similar behavior c v max alpha text const n 1 3 while moments of the magnetization scale as m k alpha n k 2 the approach of the positions t max of these specific heat maxima to t c as n is nonmonotonic for p 6 the results are compatible with a first order transition q k q jump k as n but since the order parameter q jump at t c is rather small a behavior q k n k 3 as n also is compatible with the data thus no firm conclusions on the finite size behavior of the order parameter can be drawn the specific heat maxima c v max behave qualitatively in the same way as for p 3 consistent with the prediction that there is no latent heat a speculative phenomenological discussion of finite size scaling for such transitions is given for small n n 15 for p 3 n 12 for p 6 the monte carlo data are compared to exact partition function calculations and excellent agreement is found we also discuss ratios r x equiv langle x rangle t langle x rangle t text av 2 text av langle x rangle t text av 2 for various quantities x to test the possible lack of self averaging at t c

new results on stability analysis for systems with discrete distributed delay the integral inequality technique is widely used to derive delay dependent conditions and various integral inequalities have been developed to reduce the conservatism of the conditions derived in this study a new integral inequality was devised that is tighter than existing ones it was used to investigate the stability of linear systems with a discrete distributed delay and a new stability condition was established the results can be applied to systems with a delay belonging to an interval which may be unstable when the delay is small or nonexistent three numerical examples demonstrate the effectiveness and the smaller conservatism of the method

rational group decision making a random field ising model at t 0 abstract a modified version of a finite random field ising ferromagnetic model in an external magnetic field at zero temperature is presented to describe group decision making fields may have a non zero average a postulate of minimum inter individual conflicts is assumed interactions then produce a group polarization along one very choice which is however randomly selected a small external social pressure is shown to have a drastic effect on the polarization individual bias related to personal backgrounds cultural values and past experiences are introduced via quenched local competing fields they are shown to be instrumental in generating a larger spectrum of collective new choices beyond initial ones in particular compromise is found to results from the existence of individual competing bias conflict is shown to weaken group polarization the model yields new psychosociological insights about consensus and compromise in groups

stationary filter for linear minimum mean square error estimator of discrete time markovian jump systems we derive in this paper a stationary filter for the linear minimum mean square error estimator lmmse of discrete time markovian jump linear systems mjlss we obtain the convergence of the error covariance matrix of the lmmse to a stationary value under the assumption of mean square stability of the mjls and ergodicity of the associated markov chain it is shown that there exists a unique solution for the stationary riccati filter equation and moreover this solution is the limit of the error covariance matrix of the lmmse the advantage of this scheme is that it is very easy to implement and all calculations can be performed off line leading to a linear time invariant filter

ultimate fate of constrained voters we examine the ultimate fate of individual opinions in a socially interacting population of leftists centrists and rightists in an elemental interaction between agents a centrist and a leftist can both become centrists or both become leftists with equal rates and similarly for a centrist and a rightist however leftists and rightists do not interact this interaction step between pairs of agents is applied repeatedly until the system can no longer evolve in the mean field limit we determine the exact probability that the system reaches consensus either leftist rightist or centrist or a frozen mixture of leftists and rightists as a function of the initial composition of the population we also determine the mean time until the final state is reached some implications of our results for the ultimate fate in a limit of the axelrod model are discussed

further results on exponential estimates of markovian jump systems with mode dependent time varying delays this technical note studies the problem of exponential estimates for markovian jump systems with mode dependent interval time varying delays a novel lyapunov krasovskii functional lkf is constructed with the idea of delay partitioning and a less conservative exponential estimate criterion is obtained based on the new lkf illustrative examples are provided to show the effectiveness of the proposed results

output feedback control of markovian jump repeated scalar nonlinear systems this paper is concerned with the induced l2 dynamic output feedback controller dofc design problem for discrete time markovian jump repeated scalar nonlinear systems by employing both the switching sequence dependent lyapunov function approach and the positive definite diagonally dominant lyapunov function technique a sufficient condition is first established which guarantees the underlying system to be stochastically stable with an induced l2 disturbance attenuation performance then the desired full or reduced order dofcs are designed by using projection approach cone complementarity linearization procedure is employed to cast the nonconvex feasibility problem into a sequential minimization problem finally a numerical example is presented to show the effectiveness of the proposed methods

technical communique sliding mode control with bounded l 2 gain performance of markovian jump singular time delay systems in this paper we investigate the problem of sliding mode control smc of markovian jump singular time delay systems the aim is to consider the bounded 2 gain performance in the analysis of sliding mode dynamics thus to improve the transient performance of the smc system firstly a delay dependent bounded real lemma is proposed for the underlying system to be stochastically admissible while achieving the prescribed bounded 2 gain performance condition an integral type switching surface function is designed by taking the singular matrix into account thus the resulting sliding mode dynamics is a full order singular markovian jump time delay system then the sliding mode dynamics is analyzed and the solvability condition for the desired switching surface function is derived moreover an smc law is synthesized to drive the system trajectories onto the predefined switching surface in a finite time finally a numerical example is provided to illustrate the effectiveness of the proposed techniques

locally self similar phase diagram of the disordered potts model on the hierarchical lattice we study the critical behavior of the random q state potts model in the large q limit on the diamond hierarchical lattice with an effective dimensionality d eff 2 by varying the temperature and the strength of the frustration the system has a phase transition line between the paramagnetic and the ferromagnetic phases which is controlled by four different fixed points according to our renormalization group study the phase boundary in the vicinity of the multicritical point is self similar it is well represented by a logarithmic spiral we expect an infinite number of reentrances in the thermodynamic limit consequently one cannot define standard thermodynamic phases in this region

mean field theory and fluctuations in potts spin glasses i a short range potts spin glass is studied a stable non marginal mean field theory is found with one level of replica symmetry breaking and a discontinuous transition for p 4 a complete stability analysis is provided and two different correlation lengths are found above eight dimensions the fluctuations in the ordered phase around this solution are incorporated in a renormalisation group approach and it is found that for a small range of the parameters they restore scaling close to the upper critical dimension for the three state case it appears that fluctuations destroy the stability of the solution for d or 8 and cause the system to undergo a first order phase transition non universal corrections to the equation of state above the upper critical dimension are discussed

finite time h filtering for a class of discrete time markovian jump systems with switching transition probabilities subject to average dwell time switching an extension of fixed transition probability markovian switching model to combine time varying transition probabilities has offered another set of useful regime switching models this paper investigated the problem of finite time h filtering for a class of discrete time markovian jump systems with switching transition probabilities subject to average dwell time switching based on the results of finite time boundness and average dwell time a novel sufficient condition for finite time bounded of h filtering is derived and the system trajectory stays within a prescribed bound finally an example is provided to illustrate the usefulness and effectiveness of the proposed method

statistical and systematic errors in monte carlo sampling we have studied the statistical and systematic errors which arise in monte carlo simulations and how the magnitude of these errors depends on the size of the system being examined when a fixed amount of computer time is used we find that depending on the degree of self averaging exhibited by the quantities measured the statistical errors can increase decrease or stay the same as the system size is increased the systematic underestimation of response functions due to the finite number of measurements made is also studied we develop a scaling formalism to describe the size dependence of these errors as well as their dependence on the bin length size of the statistical sample both at and away from a phase transition the formalism is tested using simulations of thed 3 ising model at the infinite lattice transition temperature we show that for a 96 96 96 system noticeable systematic errors systematic underestimation of response functions are still present for total run lengths of 106 monte carlo steps site mcs with measurements taken at regular intervals of 10 mcs

multiple impulse solutions to mckean s caricature of the nerve equation i existence mckean s caricature of the nerve equation is considered the h in 1 is the heaviside function we prove the existence of multiple impulse solutions consisting of any finite number of pulses these solutions are referred to as n ple impulse solutions where n is an arbitrary positive integer

social paradoxes of majority rule voting and renormalization group real space renormalization group ideas are used to study a voting problem in political science a model to construct self directed pyramidal structures from bottom up to the top is presented using majority rules it is shown that a minority and even a majority can be systematically self eliminated from top leadership provided the hierarchy has a minimal number of levels in some cases 70 of the population is found to have zero representation after six hierarchical levels results are discussed with respect to the internal operation of political organizations

the stable manifold of the standing wave of the nagumo equation on considere l equation de nagumo u t u xx u 1 u u a on montre que si u 0 h 1 est positive et paire et uc x t est la solution partant a cu 0 x alors il y a des multiplicateurs c c tels que u c x t decroit vers zero si 0 c c

further results on h control for discrete time markovian jump time delay systems abstractthis paper studies the problem of h control for a class of discrete time markovian jump systems with time delay the purpose is to improve the existing results on h controller design for markovian jump systems a novel summation inequality is presented and an improved stability criterion for the system is derived by utilising the new inequality which is proved to be less conservative than most results in the literature then the state feedback controller is designed which guarantees the stochastic stability of the closed loop system with a given disturbance attenuation numerical examples are provided to illustrate the effectiveness and advantages of the proposed techniques

l2 l filter design for discrete time singular markovian jump systems with time varying delays the problem of l 2 l filter design for discrete time singular systems with markovian jump and time varying delays is investigated in this paper by using the delay partitioning technique a delay dependent condition is established to guarantee the filtering error systems to be stochastically admissible and achieve a prescribed l 2 l performance index based on the derived condition the full order and reduced order filters with mode independent characterization are designed in a unified framework the corresponding filter parameters can be obtained by solving a set of linear matrix inequalities the reported results not only depend upon the delay but also depend upon the partitioning which aims at reducing the conservatism two numerical examples are provided to illustrate the effectiveness of the proposed methods

mean square stochastic stability of linear time delay system with markovian jumping parameters this paper deals with the mean square stochastic stability of the class of linear time delay systems with markovian jumping parameters a delay independent sufficient condition for checking the stochastic stability of this class of systems is established a numerical example is given to show the usefulness of the proposed theoretical results

monte carlo investigations of phase transitions status and perspectives abstract using the concept of finite size scaling monte carlo calculations of various models have become a very useful tool for the study of critical phenomena with the system linear dimension as a variable as an example several recent studies of ising models are discussed as well as the extension to models of polymer mixtures and solutions it is shown that using appropriate cluster algorithms even the scaling functions describing the crossover from the ising universality class to the mean field behavior with increasing interaction range can be described additionally the issue of finite size scaling in ising models above the marginal dimension d 4 is discussed

brief on robust stabilization of markovian jump systems with uncertain switching probabilities this brief paper is concerned with the robust stabilization problem for a class of markovian jump linear systems with uncertain switching probabilities the uncertain markovian jump system under consideration involves parameter uncertainties both in the system matrices and in the mode transition rate matrix first a new criterion for testing the robust stability of such systems is established in terms of linear matrix inequalities then a sufficient condition is proposed for the design of robust state feedback controllers a globally convergent algorithm involving convex optimization is also presented to help construct such controllers effectively finally a numerical simulation is used to illustrate the developed theory

phase transition in an optimal clusterization model abstract an optimal clusterization model resembling the infinite range potts glass type model with j bonds and unrestricted number of states p n is introduced and studied as a function of the q probability of j bonds it is found that the r relative size of the largest cluster or coalition shows a percolation like transition at q 1 2 by a simple renormalization approach and several optimization methods we investigate the r q curves for finite system sizes non trivial consequences for social percolation problems are discussed

mean field theory of modified voter model for opinions abstract we present a mean field theory for the modified three state voter model we obtain analytical results in asymptotic states for a general transition matrix numerical simulations can be well described within the proposed formulations distributions for both central plateau and boundary layer can be written explicitly the central plateau is determined solely by the ratio between the internal noise and the external pressure in the bulk these two factors substantially compete with each other near the boundary regions both the factors work together to introduce the exponential distribution of transit layer with the scaling simulations on a large lattice can be mapped into a small lattice the required computer time is hence reduced significantly

control of markovian jump discrete time systems with norm bounded uncertainty and unknown delay this paper studies the problem of control for discrete time delay linear systems with markovian jump parameters the system under consideration is subjected to both time varying norm bounded parameter uncertainty and unknown time delay in the state and markovian jump parameters in all system matrices we address the problem of robust state feedback control in which both robust stochastic stability and a prescribed h sub spl infin performance are required to be achieved irrespective of the uncertainty and time delay it is shown that the above problem can be solved if a set of coupled linear matrix inequalities has a solution

on the static and dynamical transition in the mean field potts glass we study the static as well as the glassy or dynamical transition in the mean field p state potts glass by numerical solution of the saddle point equations we investigate the static and dynamical transitions for all values of p in the non perturbative regime p 4 the static and dynamical edwards anderson parameter increase with p logarithmically this makes the glassy transition temperature lie very close to the static one we compare the main predictions of the theory with numerical simulations

finite size scaling in the p state mean field potts glass exact statistical mechanics for small samples the mean field potts glass with bimodal bond distribution is studied for p 3 and p 6 potts states via exact summation of the partition function of systems of up to n 15 sites averages over the disorder realizations are also done exactly up to n 8 while random bond configurations are generated for the larger systems our enumeration method is described in some detail and the applicability of finite size scaling fss for our very small systems is discussed for p 3 second order transition the data agree reasonably with the fss relations given by parisi et al for the p 2 ising case for p 6 no clear signs of the predicted first order behaviour could be observed this case is even more affected by finite size effects since the necessary antiferromagnetic bias of the bond distribution introduces an additional correction in the free energy for both p the data are compatible with a vanishing ground state entropy

kinetic models of opinion formation in the presence of personal conviction we consider a nonlinear kinetic equation of boltzmann type which takes into account the influence of conviction during the formation of opinion in a system of agents which interact through the binary exchanges introduced by toscani g toscani commun math sci 4 481 2006 the original exchange mechanism which is based on the human tendency to compromise and change of opinion through self thinking is here modified in the parameters of the compromise and diffusion terms which now are assumed to depend on the personal degree of conviction the numerical simulations show that the presence of conviction has the potential to break symmetry and to produce clusters of opinions the model is partially inspired by the recent work l pareschi and g toscani phil trans r soc a 372 20130396 2014 in which the role of knowledge in the formation of wealth distribution has been investigated

modeling of the financial market using the two dimensional anisotropic ising model we have used the two dimensional classical anisotropic ising model in an external field and with an ion single anisotropy term as a mathematical model for the price dynamics of the financial market the model presented allows us to test within the same framework the comparative explanatory power of rational agents versus irrational agents with respect to the facts of financial markets we have obtained the mean price in terms of the strong of the site anisotropy term which reinforces the sensitivity of the agent s sentiment to external news

voter model on networks and the multivariate beta distribution in elections the vote shares or turnout rates show a strong spatial correlation the logarithmic decay with distance suggests that a two dimensional 2d noisy diffusive equation describes the system based on the study of u s presidential elections data it was determined that the fluctuations of vote shares also exhibit a strong and long range spatial correlation previously it was considered difficult to induce strong and long range spatial correlation of the vote shares without breaking the empirically observed narrow distribution we demonstrate that a voter model on networks shows such a behavior in the model there are many voters in a node who are affected by the agents in the node and by the agents in the linked nodes a multivariate wright fisher diffusion equation for the joint probability density of the vote shares is derived the stationary distribution is a multivariate generalization of the beta distribution in addition we also estimate the equilibrium values and the covariance matrix of the vote shares and obtain a correspondence with a multivariate normal distribution this approach largely simplifies the calibration of the parameters in the modeling of elections

brief paper stability and stabilization of markovian jump linear systems with partly unknown transition probabilities in this paper the stability and stabilization problems of a class of continuous time and discrete time markovian jump linear system mjls with partly unknown transition probabilities are investigated the system under consideration is more general which covers the systems with completely known and completely unknown transition probabilities as two special cases the latter is hereby the switched linear systems under arbitrary switching moreover in contrast with the uncertain transition probabilities studied recently the concept of partly unknown transition probabilities proposed in this paper does not require any knowledge of the unknown elements the sufficient conditions for stochastic stability and stabilization of the underlying systems are derived via lmis formulation and the relation between the stability criteria currently obtained for the usual mjls and switched linear systems under arbitrary switching are exposed by the proposed class of hybrid systems two numerical examples are given to show the validity and potential of the developed results

initiation of propagation in a one dimensional excitable medium abstract this study examines the initiation of propagation in a one dimensional fiber by local stimulation with a small electrode the membrane dynamics is based on the generic fitzhugh nagumo model reduced in a singular limit to a nonlinear heat equation a steady state solution of this nonlinear heat equation defines the critical nucleus a time independent distribution of potential that acts as a threshold for propagating wavefronts the criterion for initiation of propagation from the initial conditions on potential is obtained by re writing the nonlinear heat equation as a gradient flow of an energy and projecting this gradient flow onto an approximate solution space assuming that the evolving potential has a shape of a gaussian pulse the solution space consists of the amplitude of the pulse a and the inverse of its width k the evolution of the potential is visualized on the a k phase plane in which the rest state is a stable node and the critical nucleus solution is a saddle point the criterion for initiating propagation takes the form of a pair of separatrices that bisect all possible pulse widths for a specific pulse width the separatrices determine the minimum amplitude necessary to start propagation infinitely broad pulses space clamped fiber require amplitude equal to the membrane excitation threshold as the width of the pulse decreases the requirement on the amplitude grows in a limit of very narrow pulses the pulse width and the amplitude are related by a linear relationship corresponding to a constant charge delivered by the pulse

nature s way of optimizing we propose a general purpose method for finding high quality solutions to hard optimization problems inspired by self organizing processes often found in nature the method called extremal optimization successively eliminates extremely undesirable components of sub optimal solutions drawing upon models used to simulate far from equilibrium dynamics it complements approximation methods inspired by equilibrium statistical physics such as simulated annealing with only one adjustable parameter its performance proves competitive with and often superior to more elaborate stochastic optimization procedures we demonstrate it here on two classic hard optimization problems graph partitioning and the traveling salesman problem 2000 elsevier science b v all rights reserved

correlation clustering on networks random networks with co existing positive and negative links are studied from the viewpoint of the np hard correlation clustering problem the task is to produce a clustering of the vertices which maximizes the number of positive edges within clusters and the number of negative edges between clusters simulated annealing monte carlo renormalization and molecular dynamics optimization are used to find the optimal cluster structure recently this problem was studied for globally coupled systems and an interesting phase transition like phenomenon was predicted in the thermodynamic limit the relative size of the largest cluster r exhibits a step like behavior as a function of the density of positive links q r 0 if q 1 2 here we prove that when considering random networks with a constant bond density the same phase transition is expected a totally different result emerges however when networks with a fixed average number of connections per node are considered in such cases a nontrivial spin glass type behavior is found where the location of the critical point shifts toward q 1 2 values the results also suggest that instead of the simple step like behavior the r q curve has a more complex shape which depends on the specific topology of the considered network

multiple impulse solutions to mckean s caricature of the nerve equation ii stability we study mckean s caricature of a nerve conduction equation where h is the heaviside function it is proved that an n ple impulse solution resembling the superposition of n unstable solitary impulses has at most 2n 1 and at least n unstable modes exactly n unstable modes corresponding to the amplitudes and the rest of them corresponding to the spacings the n amplitude modes always exist we prove also that for an n ple impulse solution resembling the superposition of n stable solitary impulses there are at most n 1 unstable modes and all of them are of spacing type

opinion formation model with strong leader and external impact a mean field approach abstract we study a model of opinion formation based on the theory of social impact and the concept of cellular automata the case is considered when two strong agents influence the group a strong leader and an external social impact acting uniformly on every individual there are two basic stationary states of the system cluster of the leader s adherents and unification of opinions in the deterministic limit the variation of parameters like the leader s strength or external impact can change the size of the cluster or when they reach some critical values make the system jump to another phase for a certain range of parameters multistability and hysteresis phenomena are observed in the presence of noise social temperature the rapid changes can be regarded as the first order phase transitions when both agents are in a kind of balance a second order transition and critical behaviour can be observed another kind of noise induced transitions are the inverses flips of the unified group opinion due to random flips of the leader s opinion analytical results obtained within a mean field approximation are well reproduced in computer simulations

on designing of sliding mode control for stochastic jump systems in this note we consider the problems of stochastic stability and sliding mode control for a class of linear continuous time systems with stochastic jumps in which the jumping parameters are modeled as a continuous time discrete state homogeneous markov process with right continuous trajectories taking values in a finite set by using linear matrix inequalities lmis approach sufficient conditions are proposed to guarantee the stochastic stability of the underlying system then a reaching motion controller is designed such that the resulting closed loop system can be driven onto the desired sliding surface in a limited time it has been shown that the sliding mode control problem for the markovian jump systems is solvable if a set of coupled lmis have solutions a numerical example is given to show the potential of the proposed techniques

mixed h sub 2 h sub spl infin control of discrete time markovian jump linear systems in this paper we consider the mixed h sub 2 h sub spl infin control problem for the class of discrete time linear systems with parameters subject to markovian jump linear systems it is assumed that both the state variable and the jump variable are available to the controller the transition probability matrix may not be exactly known but belongs to an appropriate convex set for this controlled discrete time markovian jump linear system the problem of interest can be stated in the following way find a robust with respect to the uncertainty on the transition markov probability matrix mean square stabilizing state and jump feedback controller that minimizes an upper bound for the h sub spl infin norm under the restriction that the h sub spl infin norm is less than a prespecified value spl delta the problem of the determination of the smallest h sub spl infin norm is also addressed we present an approximate version of these problems via linear matrix inequality optimization

evans functions and bifurcations of nonlinear waves of some nonlinear reaction diffusion equations abstract the main purposes of this paper are to accomplish the existence stability instability and bifurcation of the nonlinear waves of the nonlinear system of reaction diffusion equations u t u x x h u u w w t e u w and to establish the existence stability instability and bifurcation of the nonlinear waves of the nonlinear scalar reaction diffusion equation u t u x x h u u under different conditions on the model constants to establish the bifurcation for the system we will study the existence and instability of a standing pulse solution if 0 2 1 the existence and stability of two standing wave fronts if 2 1 and 2 e 1 the existence and instability of two standing wave fronts if 2 1 and 0 2 e 1 the existence and instability of an upside down standing pulse solution if 0 1 2 1 to establish the bifurcation for the scalar equation we will study the existence and stability of a traveling wave front as well as the existence and instability of a standing pulse solution if 0 2 the existence and stability of two standing wave fronts if 2 the existence and stability of a traveling wave front as well as the existence and instability of an upside down standing pulse solution if 0 2 by the way we will also study the existence and stability of a traveling wave back of the nonlinear scalar reaction diffusion equation u t u x x h u u w 0 where w 0 2 0 is a positive constant if 0 2 to achieve the main goals we will make complete use of the special structures of the model equations and we will construct evans functions and apply them to study the eigenvalues and eigenfunctions of several eigenvalue problems associated with several linear differential operators it turns out that a complex number 0 is an eigenvalue of the linear differential operator if and only if 0 is a zero of the evans function the stability instability and bifurcations of the nonlinear waves follow from the zeros of the evans functions a very important motivation to study the existence stability instability and bifurcations of the nonlinear waves is to study the existence and stability instability of infinitely many fast slow multiple traveling pulse solutions of the nonlinear system of reaction diffusion equations the existence and stability of infinitely many fast multiple traveling pulse solutions are of great interests in mathematical neuroscience

robust h sub spl infin control of discrete time markovian jump linear systems with mode dependent time delays considers the class of discrete time markovian jump linear system with norm bounded uncertainties and time delay which is dependent on the system mode linear matrix inequality lmi based sufficient conditions for the stability stabilization and h sub spl infin control are developed a numerical example is worked out to show the usefulness of the theoretical results

technical communique robust h2 control of continuous time markov jump linear systems this paper is concerned with the problem of designing robust h 2 state feedback controllers for continuous time markov jump linear systems subject to polytopic type parameter uncertainty based on the parameter dependent lyapunov function approach a new method for designing robust h 2 controllers is presented in terms of solutions to a set of linear matrix inequalities a numerical example is given to illustrate the effectiveness of the proposed design method

controllability stabilizability and continuous time markovian jump linear quadratic control consideration is given to the control of continuous time linear systems that possess randomly jumping parameters which can be described by finite state markov processes the relationship between appropriately defined controllability stabilizability properties and the solution of the infinite time jump linear quadratic jlq optimal control problems is also examined although the solution of the continuous time markov jlq problem with finite or infinite time horizons is known only sufficient conditions for the existence of finite cost constant stabilizing controls for the infinite time problem appear in the literature in this paper necessary and sufficient conditions are established these conditions are based on new definitions of controllability observability stabilizability and detectability that are appropriate for continuous time markovian jump linear systems these definitions play the same role for the jlq problem as the deterministic properties do for the linear quadratic regulator lqr problem

on weak solutions of parabolic initial value problems with discontinuous nonlinearities abstract we deal with parabolic initial value problems with discontinuous nonlinearities and obtain the existence uniqueness and non uniqueness of its weak solution moreover we study the asymptotic behavior of maximal and minimal weak solutions when they are different

stability of discrete time systems with time varying delays via a novel summation inequality this technical note is concerned with the stability analysis of discrete linear systems with time varying delays the novelty of the technical note comes from the consideration of a new inequality which is less conservative than the celebrated jensen inequality employed in the context of discrete time delay systems this inequality is a discrete time counterpart of the wirtinger based integral inequality that was recently employed for the improved analysis of continuous tine systems with delays however differently from the continuous time case the proof of the new inequality is not based on the wirtinger inequality the method is also combined with an efficient representation of the improved reciprocally convex combination inequality in order to reduce the conservatism induced by the lmis optimization setup the effectiveness of the proposed result is illustrated by some classical examples from the literature

brief paper new results on stabilization of markovian jump systems with time delay this paper studies the problem of stochastic stabilization for a class of markovian jump systems with time delay a new delay dependent stochastic stability criterion on the stochastic stability of the system is derived based on a novel lyapunov krasovskii functional lkf approach the equivalence and superiority to existing results are demonstrated then a state feedback controller which guarantees the stochastic stability of the closed loop system is designed illustrative examples are provided to show the reduced conservatism and effectiveness of the proposed techniques

brief paper mode dependent h filtering for discrete time markovian jump linear systems with partly unknown transition probabilities in this paper the problem of h filtering for a class of discrete time markovian jump linear systems mjls with partly unknown transition probabilities is investigated the considered systems are more general which cover the mjls with completely known and completely unknown transition probabilities as two special cases a mode dependent full order filter is constructed and the bounded real lemma brl for the resulting filtering error system is derived via lmi formulation then an improved version of the brl is further given by introducing additional slack matrix variables to eliminate the cross coupling between system matrices and lyapunov matrices among different operation modes finally the existence criterion of the desired filter is obtained such that the corresponding filtering error system is stochastically stable with a guaranteed h performance index a numerical example is presented to illustrate the effectiveness and potential of the developed theoretical results

robust stability criterion for discrete time uncertain markovian jumping neural networks with defective statistics of modes transitions this brief is concerned with the robust stability problem for a class of discrete time uncertain markovian jumping neural networks with defective statistics of modes transitions the parameter uncertainties are considered to be norm bounded and the stochastic perturbations are described in terms of brownian motion defective statistics means that the transition probabilities of the multimode neural networks are not exactly known as assumed usually the scenario is more practical and such defective transition probabilities comprise three types known uncertain and unknown by invoking the property of the transition probability matrix and the convexity of uncertain domains a sufficient stability criterion for the underlying system is derived furthermore a monotonicity is observed concerning the maximum value of a given scalar which bounds the stochastic perturbation that the system can tolerate as the level of the defectiveness varies numerical examples are given to verify the effectiveness of the developed results

stability of the travelling wave solution of the fitzhugh nagumo system on demontre la stabilite relative au systeme complet d equations aux derivees partielles de ces ondes de propagation

generalized solutions of parabolic initial value problems with discontinuous nonlinearities we proved recently that parabolic initial value problems with discontinuous nonlinearities have no unique weak solution in general but have a unique generalized solution in the sense of colombeau in this paper we study the relationship between generalized solutions and weak solutions

non fragile h control for markovian jump fuzzy systems with time varying delays abstract this paper focuses on the non fragile h control of markovian jump fuzzy systems with time varying delays in order to obtain less conservatism an improved delay partitioning method is introduced which divides the delay interval into multiple segments with a geometric sequence a modified lyapunov krasovskii functional is constructed and some less conservative delay dependent stability criteria are derived by using linear matrix inequalities technique then a non fragile controller is designed finally two numerical examples are given to show the effectiveness of the obtained results

obtaining critical point and shift exponent for the anisotropic two layer ising and potts models cellular automata approach abstract using probabilistic cellular automata with the glauber algorithm we have precisely calculated the critical points for the anisotropic two layer ising and potts models k x k y k z of the square lattice where k x and k y are the nearest neighbor interactions within each layer in the x and y directions respectively and k z is the inter layer coupling a general equation is obtained as a function of the inter and intra layer interactions for both the two layer ising and potts models separately where k z k x and k y k x furthermore the shift exponent for the two layer ising and potts models is calculated it was demonstrated that in the case of 1 for the two layer ising model the value of 1 756 0 0078 supports the scaling theories prediction that however for the unequal intra layer couplings for the two layer ising model and also in the case of both equal and unequal intra layer interactions for the two layer potts model our results are different from those obtained from the scaling theories finally an equation is obtained for the shift exponent as a function of intra layer couplings for the two layer ising and potts models

statics and dynamics of the ten state mean field potts glass model a monte carlo study we investigate by means of monte carlo simulations the fully connected p state potts model for different system sizes in order to see how the static and dynamic properties of a finite model compare with the exactly known behaviour of the system in the thermodynamic limit using p 10 we are able to study the equilibrium dynamics for system sizes as large as n 2560 we find that the static quantities such as the energy the entropy the spin glass susceptibility as well as the distribution of the order parameter p q show very strong finite size effects from p q we calculate the fourth order cumulant g4 n t and the guerra parameter g n t and show that these quantities cannot be used to locate the static transition temperature for the system sizes investigated also the spin autocorrelation function c t shows strong finite size effects in that it does not show a plateau even for temperatures around the dynamical critical temperature td we show that the dependence on n and t of the relaxation time can be understood by means of a dynamical finite size scaling ansatz c t does not obey the time temperature superposition principle for temperatures around td but does so for significantly lower t finally we study the relaxation dynamics of the individual spins and show that their dependence on time depends strongly on the chosen spin i e that the system is dynamically very heterogeneous which explains the non exponentiality of c t

four dimensional ising spin glass scaling within the spin glass phase we investigate the nature of the spin glass phase in the four dimensional king spin glass we study he probability dishibutions of overlaps of energy overlaps and ullrmetricity for several sizes we discover the existence of finite size scaling in the fails of the first and second of these this allows us to exmct mame exponents within the spin glass phase we also perform studies on quenched thermalization of large samples our results together with previous work favour the mean field picfure of the spin glass phase

generalized h2 fault detection for two dimensional markovian jump systems this paper is concerned with the generalized h 2 fault detection for two dimensional 2 d discrete time markovian jump systems the mathematical model of the 2 d system is established upon the well known roesser model and the measurement missing phenomenon which appears typically in a network environment is modeled by a stochastic variable satisfying the bernoulli random binary distribution in addition the transition probabilities of the markovian jump process are assumed to be partly accessed that is the transition probabilities are partly known our attention is focused on the design of a fault detection filter or a residual generation system which guarantees the fault detection system to be mean square asymptotically stable and to have a prescribed generalized h 2 performance sufficient conditions for the existence of a desired fault detection filter are established in terms of linear matrix inequalities lmis a numerical example is provided to illustrate the effectiveness of the proposed design method

brief paper robust exponential stabilization for markovian jump systems with mode dependent input delay this paper is concerned with the problem of exponential stabilization for uncertain linear systems with markovian jump parameters and mode dependent input delays sufficient stabilization conditions are developed in terms of matrix inequalities which can be solved by a proposed iterative algorithm based on the cone complementarity linearization ccl method memory controllers are also designed such that the closed loop system is exponentially mean square stable for all admissible uncertainties numerical examples are given to show that the developed method is efficient and less conservative

mean field theory and fluctuations in potts spin glasses ii for pt i see ibid vol 22 p 4971 1989 the fluctuations in the ordered phase around the mean field solution are incorporated in a renormalization group approach and it is found that for a small range of the parameters they restore scaling close to the upper critical dimension for the 3 state case it appears that fluctuations destroy the stability of the solution and cause the system to undergo a first order phase transition non universal fluctuation corrections to the equation of state above six dimensions are obtained

output feedback control of markov jump linear systems in continuous time this paper addresses the dynamic output feedback control problem of continuous time markovian jump linear systems the fundamental point in the analysis is an lmi characterization comprising all dynamical compensators that stabilize the closed loop system in the mean square sense the h sub 2 and h sub spl infin norm control problems are studied and the h sub 2 and h sub spl infin filtering problems are solved as a by product

optimal filter approximations in conditionally gaussian pairwise markov switching models we consider a general triplet markov gaussian linear system bf x bf r bf y where bf x is an hidden continuous random sequence bf r is an hidden discrete markov chain bf y is an observed continuous random sequence when the triplet bf x bf r bf y is a classical conditionally gaussian linear state space model cglssm the mean square error optimal filter is not workable with a reasonable complexity and different approximate methods e g based on particle filters are used we propose two contributions the first one is to extend the cglssm to a new more general model called the conditionally gaussian pairwise markov switching model cgpmsm in which bf x is not necessarily markov given bf r the second contribution is to consider a particular case of cgpmsm in which bf r bf y is markov and in which an exact filter optimal in the sense of mean square error can be performed with linear time complexity some experiments show that the proposed method and the suited particle filter have comparable efficiency while the second one is much faster