contact processes on random graphs with power law degree distributions have critical value 0 if we consider the contact process with infection rate on a random graph on n vertices with power law degree distributions mean field calculations suggest that the critical value c of the infection rate is positive if the power 3 physicists seem to regard this as an established fact since the result has recently been generalized to bipartite graphs by gomez gardenes et al proc natl acad sci usa 105 2008 1399 1404 here we show that the critical value c is zero for any value of 3 and the contact process starting from all vertices infected with a probability tending to 1 as n maintains a positive density of infected sites for time at least exp n 1 for any 0 using the last result together with the contact process duality we can establish the existence of a quasi stationary distribution in which a randomly chosen vertex is occupied with probability it is expected that c as 0 here we show that 1 2 3 and so 2 for 3 thus even though the graph is locally tree like does not take the mean field critical value 1

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

the replica symmetric solution for potts models on d regular graphs we establish an explicit formula for the limiting free energy density log partition function divided by the number of vertices for ferromagnetic potts models on uniformly sparse graph sequences converging locally to the d regular tree for d even covering all temperature regimes this formula coincides with the bethe free energy functional evaluated at a suitable fixed point of the belief propagation recursion on the d regular tree the so called replica symmetric solution for uniformly random d regular graphs we further show that the replica symmetric bethe formula is an upper bound for the asymptotic free energy for any model with permissive interactions

robust event triggered mpc with guaranteed asymptotic bound and average sampling rate we propose a robust event triggered model predictive control mpc scheme for linear time invariant discrete time systems subject to bounded additive stochastic disturbances and hard constraints on the input and state for given probability distributions of the disturbances acting on the system we design event conditions such that the average frequency of communication between the controller and the actuator in the closed loop system attains a given value we employ tube mpc methods to guarantee robust constraint satisfaction and a robust asymptotic bound on the system state moreover we show that instead of a given periodically updated tube mpc scheme an appropriate event triggered mpc scheme can be applied with the same guarantees on constraints and region of attraction but with a reduced number of average communications

composite systems with uncertain couplings of fixed structure scaled riccati equations and the problem of quadratic stability we consider large scale systems consisting of a finite number of separate uncertain subsystems which interact via uncertain couplings of arbitrarily prescribed structure the couplings are viewed as structured perturbations of the block diagonal system representing the collection of the separate nominal subsystems the nominal system we define spectral value sets and stability radii for these time invariant structured perturbations and derive formulas for their computation scaled riccati equations are introduced to obtain explicit formulas for the stability radii with respect to time varying and possibly nonlinear perturbations of the given structure from these we derive necessary and sufficient conditions under which the stability radii with respect to time invariant and time varying perturbations are equal these results are obtained by constructing joint quadratic liapunov functions of optimal robustness with their help we prove necessary and sufficient conditions for quadratic stability and sufficient conditions for the validity of a generalized aizerman conjecture

switching stabilizability for continuous time uncertain switched linear systems this paper investigates the switching stabilizability problem for a class of continuous time switched linear systems with time variant parametric uncertainties first a necessary and sufficient condition for the asymptotic stabilizability of such uncertain switched linear system is derived under the assumption that the closed loop switched system does not generate sliding motions then an additional condition is introduced to exclude the possibility of unstable sliding motions finally a necessary and sufficient for the asymptotic stabilizability of such continuous time uncertain switched linear systems is presented this result improves upon conditions found in the literature which are either sufficient only or necessary only

recent developments on the stability of systems with aperiodic sampling an overview this article presents basic concepts and recent research directions about the stability of sampled data systems with aperiodic sampling we focus mainly on the stability problem for systems with arbitrary time varying sampling intervals which has been addressed in several areas of research in control theory systems with aperiodic sampling can be seen as time delay systems hybrid systems input output interconnections discrete time systems with time varying parameters etc the goal of the article is to provide a structural overview of the progress made on the stability analysis problem without being exhaustive which would be neither possible nor useful we try to bring together results from diverse communities and present them in a unified manner for each of the existing approaches the basic concepts fundamental results converse stability theorems when available and relations with the other approaches are discussed in detail results concerning extensions of lyapunov and frequency domain methods for systems with aperiodic sampling are recalled as they allow to derive constructive stability conditions furthermore numerical criteria are presented while indicating the sources of conservatism the problems that remain open and the possible directions of improvement at last some emerging research directions such as the design of stabilizing sampling sequences are briefly discussed

high dimensional gaussian graphical model selection walk summability and local separation criterion we consider the problem of high dimensional gaussian graphical model selection we identify a set of graphs for which an efficient estimation algorithm exists and this algorithm is based on thresholding of empirical conditional covariances under a set of transparent conditions we establish structural consistency or sparsistency for the proposed algorithm when the number of samples n jmin 2 log p where p is the number of variables and jmin is the minimum absolute edge potential of the graphical model the sufficient conditions for sparsistency are based on the notion of walk summability of the model and the presence of sparse local vertex separators in the underlying graph we also derive novel non asymptotic necessary conditions on the number of samples required for sparsistency

new approach to the stability of chemical reaction networks piecewise linear in rates lyapunov functions piecewise linear in rates pwlr lyapunov functions are introduced for a class of chemical reaction networks crns in addition to their simple structure these functions are robust with respect to arbitrary monotone reaction rates of which mass action is a special case the existence of such functions ensures the convergence of trajectories towards equilibria and can be used to establish their asymptotic stability with respect to the corresponding stoichiometric compatibility class we give the definition of these lyapunov functions prove their basic properties and provide algorithms for constructing them examples are provided relationship with consensus dynamics are discussed and future directions are elaborated

on the streamfunction vorticity formulation in sliding bi period frames application to bulk behavior for polymer blends the lees edwards description of bi periodic boundary conditions has been extended to the streamfunction and streamfunction vorticity formulation in sliding bi periodic frames the required compatibility conditions are formulated and uniqueness of the solution is shown the model has been implemented in a spectral element method context to describe bulk shear behavior far away from walls where no simple periodic boundary conditions can be used in the numerical model a lagrangian multiplier is introduced to couple the shearing boundaries the proposed method has been validated for a mathematical test problem convergence is shown and the influence of the order of approximation of the lagrangian multiplier is studied finally results are presented for drop coalescence across the boundaries of the bi periodic frame

polyhedral lyapunov functions structurally ensure global asymptotic stability of dynamical networks iff the jacobian is non singular for a vast class of dynamical networks including chemical reaction networks crns with monotonic reaction rates the existence of a polyhedral lyapunov function plf implies structural i e parameter free local stability global structural stability is ensured under the additional assumption that each of the variables chemical species concentrations in crns is subject to a spontaneous infinitesimal dissipation this paper solves the open problem of global structural stability in the absence of the infinitesimal dissipation showing that the existence of a plf structurally ensures global convergence if and only if the system jacobian passes a structural non singularity test it is also shown that if the jacobian is structurally non singular under positivity assumptions for the system partial derivatives the existence of an equilibrium is guaranteed for systems subject to positivity constraints it is shown that if the system admits a plf under structural non singularity assumptions global convergence within the positive orthant is structurally ensured while the existence of an equilibrium can be proven by means of a linear programming test and the computation of a piecewise linear in rate lyapunov function

ising models on power law random graphs we study a ferromagnetic ising model on random graphs with a power law degree distribution and compute the thermodynamic limit of the pressure when the mean degree is finite degree exponent 2 for which the random graph has a tree like structure for this we closely follow the analysis by dembo and montanari ann appl probab 20 2 565 592 2010 which assumes finite variance degrees 3 adapting it when necessary and also simplifying it when possible our results also apply in cases where the degree distribution does not obey a power law

a limit formula for joint spectral radius with p radius of probability distributions abstract in this paper we show a characterization of the joint spectral radius of a set of matrices as the limit of the p radius of an associated probability distribution when p tends to allowing the set to have infinitely many matrices the obtained formula extends the results in the literature based on the formula we then present a novel characterization of the stability of switched linear systems for an arbitrary switching signal via the existence of stochastic lyapunov functions of any higher degrees numerical examples are presented to illustrate the results

convergence in uncertain linear systems abstract state convergence is essential in many scientific areas e g multi agent consensus disagreement distributed optimization computational game theory multi agent learning over networks in this paper we study for the first time the state convergence problem in uncertain linear systems preliminarily we characterize state convergence in linear systems via equivalent linear matrix inequalities in the presence of uncertainty we complement the canonical definition of weak convergence with a stronger notion of convergence which requires the existence of a common kernel among the generator matrices of the difference differential inclusion strong convergence we investigate under which conditions the two definitions are equivalent then we characterize strong and weak convergence via lyapunov arguments linear matrix inequalities and separability of the eigenvalues of the generator matrices finally we show that unlike asymptotic stability state convergence lacks of duality

brief paper nonlinear control design for linear differential inclusions via convex hull of quadratics this paper presents a nonlinear control design method for robust stabilization and robust performance of linear differential inclusions ldis a recently introduced non quadratic lyapunov function the convex hull of quadratics will be used for the construction of nonlinear state feedback laws design objectives include stabilization with maximal convergence rate disturbance rejection with minimal reachable set and least l 2 gain conditions for stabilization and performances are derived in terms of bilinear matrix inequalities bmis which cover the existing linear matrix inequality lmi conditions as special cases numerical examples demonstrate the advantages of using nonlinear feedback control over linear feedback control for ldis it is also observed through numerical computation that nonlinear control strategies help to reduce control effort substantially

direct simulation of particle suspensions in sliding bi periodic frames we present a new finite element scheme for direct simulations of inertialess particle suspensions in simple shear flows of a newtonian fluid the sliding bi periodic domain concept of lees and edwards j phys c 5 1972 1921 has been combined with a standard velocity pressure formulation of a fictitious domain finite element method by introducing sliding bi periodic frame constraints and it has been implemented with mortar element methods force free torque free rigid body motions of particles are described through rigid ring constraints and implemented by lagrangian multipliers only on the particle boundary which allows easy treatment of boundary crossing particles in our formulation the bulk stress is obtained by simple boundary integrals of lagrangian multipliers concentrating on two dimensional circular disk particles we discuss numerical examples of single two and many particle problems in sliding bi periodic frames which can represent an infinite number of such systems because of the bi periodicity the accuracy and convergence have been verified via comparison with a boundary fitted mesh problem for velocities pressures and velocity gradients the present formulation is quite well suited for suspensions of micro nano particles in simple shear flows and can be easily extended to viscoelastic flow problems

global asymptotic stability for a class of nonlinear chemical equations we consider a class of nonlinear differential equations that arises in the study of chemical reaction systems known to be locally asymptotically stable and prove that they are in fact globally asymptotically stable more specifically we will consider chemical reaction systems that are weakly reversible have a deficiency of zero and are equipped with mass action kinetics we show that if for each c in mathbb r 0 m the intersection of the stoichiometric compatibility class c s with the subsets on the boundary that could potentially contain equilibria l w are at most discrete then global asymptotic stability follows previous global stability results for the systems considered in this paper required c s cap l w emptyset for each c in mathbb r m 0

the deficiency zero theorem and global asymptotic stability for a class of chemical reaction networks with arbitrary time delays abstract the deficiency zero theorem dzt is extended to be applied to chemical reaction networks crns with time delays the time evolution of concentrations of species in which networks is described by delay differential equations ddes the extended dzt provides a sufficient condition for a positive equilibrium point of ddes to exist and be locally asymptotically stable furthermore it is proven that the absence of boundary equilibria is a sufficient condition for the positive equilibrium point to be globally asymptotically stable these results are natural analogues of theorems proven for crns without time delays

antiferromagnetic potts model on the erdős renyi random graph we study the antiferromagnetic potts model on the poissonian erd s renyi random graph by identifying a suitable interpolation structure and an extended variational principle together with a positive temperature second moment analysis we prove the existence of a phase transition at a positive critical temperature upper and lower bounds on the temperature critical value are obtained from the stability analysis of the replica symmetric solution recovered in the framework of derrida ruelle probability cascades and from an entropy positivity argument

ising critical exponents on random trees and graphs we study the critical behavior of the ferromagnetic ising model on random trees as well as so called locally tree like random graphs we pay special attention to trees and graphs with a power law offspring or degree distribution whose tail behavior is characterized by its power law exponent 2 we show that the critical inverse temperature of the ising model equals the hyperbolic arctangent of the reciprocal of the mean offspring or mean forward degree distribution in particular the critical inverse temperature equals zero when tau in 2 3 where this mean equals infinity

on anti bounce back boundary condition for lattice boltzmann schemes in this contribution we recall the derivation of the anti bounce back boundary condition for the d2q9 lattice boltzmann scheme we recall various elements of the state of the art for anti bounce back applied to linear heat and acoustics equations and in particular the possibility to take into account curved boundaries we present an asymptotic analysis that allows an expansion of all the fields in the boundary cells this analysis based on the taylor expansion method confirms the well known behaviour of anti bounce back boundary for the heat equation the analysis puts also in evidence a hidden differential boundary condition in the case of linear acoustics indeed we observe discrepancies in the first layers near the boundary to reduce these discrepancies we propose a new boundary condition mixing bounce back for the oblique links and anti bounce back for the normal link this boundary condition is able to enforce both pressure and tangential velocity on the boundary numerical tests for the poiseuille flow illustrate our theoretical analysis and show improvements in the quality of the flow

nonperturbative spectrum of anomalous scaling exponents in the anisotropic sectors of passively advected magnetic fields we address the scaling behavior of the covariance of the magnetic field in the three dimensional kinematic dynamo problem when the boundary conditions and or the external forcing are not isotropic the velocity field is gaussian and delta correlated in time and its structure function scales with a positive exponent xi the covariance of the magnetic field is naturally computed as a sum of contributions proportional to the irreducible representations of the so 3 symmetry group the amplitudes are non universal determined by boundary conditions the scaling exponents are universal forming a discrete strictly increasing spectrum indexed by the sectors of the symmetry group when the initial mean magnetic field is zero no dynamo effect is found irrespective of the anisotropy of the forcing the rate of isotropization with decreasing scales is fully understood from these results

brief paper feedback and invariance under uncertainty via set iterates we examine discrete time control systems under non parametric disturbances sets which a given control feedback makes invariant under the disturbance are analyzed via lifting the feedback operation to the space of sets properties of being an attractor of the disturbed dynamics and being a minimal invariant set are derived from the corresponding notions of the set dynamics yielding in turn useful characterizations and error estimates for numerical algorithms which detect the minimal invariant sets concrete numerics for some examples of practical feedback rules are offered

a lagrange duality characterisation for stability under arbitrary switching in switched positive linear systems abstractthe present communication is concerned with uniform exponential stability under arbitrary switching in discrete time switched positive linear systems lagrange duality is used in order to obtain a new characterisation for uniform exponential stability which is in terms of sets of inequalities involving each of the matrices that represent the modes of the system these sets of inequalities are shown to generalise the classical linear lyapunov inequality that characterises in positive matrices the property of being schur each solution to these sets of inequalities is shown to provide a representation in terms of a number of linear functionals for a common lyapunov function for the switched positive linear system a result is further presented which conveys to a conservative upper bound on the minimum required number of linear functionals in the above mentioned representation and also to a method for computing them our proof for the aforementioned characterisation is based on another equ

robust minkowski lyapunov functions abstract a necessary and sufficient condition for solvability of the lyapunov inequality for polytopic linear inclusions over the space of minkowski functions of nonempty compact and convex sets that contain the origin as an interior point is derived it is demonstrated that the introduced framework results in a nonconservative stability analysis of polytopic linear inclusions

graph lyapunov function for switching stabilization and distributed computation abstract this paper studies stabilization of discrete time switched linear systems slss using the notion of graph control lyapunov functions gclfs a gclf is a set of lyapunov functions defined on a weighted digraph where each lyapunov function is represented by a node in the digraph and there is a lyapunov inequality associated with each subgraph consisting of a node and its out neighbors the weight of a directed edge indicates the decay or growth rate of the lyapunov functions it is proved that an sls is switching stabilizable if and only if there exists a gclf the main benefits of gclfs are reduced computational cost and conservatism for stabilizability tests besides we show that the proposed gclf framework unifies several control lyapunov functions and the related stabilization theorems moreover we propose a distributed algorithm to evaluate the stabilizability with reduced computational costs by taking benefits of the graph structure of gclfs several examples are given to demonstrate the efficiency of the algorithm

stabilization of switched systems via composite quadratic functions this paper investigates stabilization of switched systems by using a lyapunov function composed of a family of continuously differentiable functions switching laws are constructed by using the directional derivatives along the trajectories of the subsystems conditions for stabilization are established with careful consideration of sliding modes and directional derivatives along sliding modes three types of composite quadratic lyapunov functions the max of quadratics the min of quadratics and the convex hull of quadratics are used for deriving matrix conditions of stabilization and for constructing switching laws dual stabilization results are established with respect to the pair of conjugate lyapunov functions the max of quadratics and the convex hull of quadratics conditions of stabilization are derived as bilinear matrix inequalities and solved with lmi based numerical tools relationship between the newly derived conditions and some existing conditions are investigated it is observed that the min of quadratics which is nondifferentiable and nonconvex may be a more convenient tool than the other two types of functions which are convex and or differentiable numerical examples are used to demonstrate the synthesis results and the advantage of the composite quadratic functions over existing multiple lyapunov functions in particular better results have been obtained when the number of quadratic functions is greater than the number of subsystems

model free plant tuning given a static plant described by a differentiable input output function which is completely unknown but whose jacobian takes values in a known polytope in the matrix space this paper considers the problem of tuning i e driving to a desired value the output by suitably choosing the input it is shown that if the polytope is robustly nonsingular or has full rank in the nonsquare case then a suitable tuning scheme drives the output to the desired point the proof exploits a lyapunov like function and applies a well known game theoretic result concerning the existence of a saddle point for a min max zero sum game when the plant output is represented in an implicit form it is shown that the same result can be obtained resorting to a different lyapunov like function the case in which proper input or output constraints must be enforced during the transient is considered as well some application examples are proposed to show the effectiveness of the approach

on convergence for piecewise affine models of gene regulatory networks via a lyapunov approach in this paper we analyse convergence and stability properties for piecewise affine models of gene regulatory networks by means of piecewise quadratic lyapunov functions in the first part we present the piecewise affine model of a gene regulatory network then after proving a result on the existence of a minimal attractive and positively invariant box we describe a linear matrix inequalitie framework to construct a lyapunov function for the system in the second part of the work after a characterization of the system solutions when considering also isolated zeno behavior of the trajectories a monotonicity property of the so found lyapunov function is formally proved together with a result on the convergence of the trajectories in the sense of measure finally we present two examples showing the applicability and utility of the main theoretical results previously explained

universality of the mean field for the potts model we consider the potts model with q colors on a sequence of weighted graphs with adjacency matrices a n allowing for both positive and negative weights under a mild regularity condition on a n we show that the mean field prediction for the log partition function is asymptotically correct whenever mathrm tr a n 2 o n in particular our results are applicable for the ising and the potts models on any sequence of graphs with average degree going to infty using this we establish the universality of the limiting log partition function of the ferromagnetic potts model for a sequence of asymptotically regular graphs and that of the ising model for bi regular bipartite graphs in both ferromagnetic and anti ferromagnetic domain we also derive a large deviation principle for the empirical measure of the colors for the potts model on asymptotically regular graphs

direct numerical simulations of droplet emulsions in sliding bi periodic frames using the level set method we present a direct numerical simulation technique for droplet emulsions of newtonian newtonian system in simple shear flow the lees edwards type boundary condition has been incorporated with the sliding bi periodic frame of hwang et al w r hwang m a hulsen h e h meijer direct simulation of particle suspensions in sliding bi periodic frames j comput phys 194 2004 742 for the continuous flow field problem and the level set method with the continuous surface stress css formulation has been used for accurate description of the sharp interfaces based on the standard velocity pressure formulation of the finite element method we use the mortar element method for the implementation of the sliding periodicity and employ the discontinuous galerkin dg method for the stabilization of the interface advection equation we present numerical results on the morphological development for a single two and multiple drops in sliding bi periodic frames for the demonstration of the feasibility of the present method in investigation of the relationship between the morphology and the bulk material responses such as the shear viscosity and the first normal stress difference

piecewise linear lyapunov functions for structural stability of biochemical networks we consider the problem of assessing structural stability of biochemical reaction networks with monotone reaction rates namely of establishing if all the networks with a certain structure are stable regardless of specific parameter values we investigate stability by absorbing the network equations in a linear differential inclusion and seeking for a polyhedral lyapunov function proper to the considered network structure a numerical recursive procedure is devised to test stability for a wide class of mono and bimolecular reaction networks which we name unitary the procedure is shown to be very efficient since due to the particular structure of the problem it requires iterations in the space of integer valued matrices we also consider a similar less conservative procedure that allows us to test even when the lyapunov function cannot be found whether the system evolution is structurally bounded in this case we absorb the equations in a positive linear differential inclusion to show the effectiveness of the proposed procedure we report the outcomes of both a stability and a boundedness test for many non trivial biochemical reaction networks and we analyze well established models in the literature

a new method to impose no slip boundary conditions in dissipative particle dynamics dissipative particle dynamics dpd is a potentially very effective approach in simulating mesoscale hydrodynamics however because of the soft potentials employed the simple no slip boundary conditions are difficult to impose in this work we first identify some of these difficulties and subsequently we propose a new method based on an equivalent force between wall and dpd particles to impose boundary conditions we demonstrate the validity of this approach for steady problems poiseuille flow lid driven cavity as well as for the unsteady oscillating flow over a flat plate

counting in two spin models on d regular graphs supported in part by alfred p sloan research fellowship supported in part by department of defense ndseg fellowships

an accurate and versatile lattice closure scheme for lattice boltzmann equation fluids under external forces we derive and demonstrate a practical analytic versatile and accurate algorithm designed to impose dirichlet boundary conditions specified boundary velocity on the edge nodes of a lattice boltzmann fluid simulation space valid for situations in which the fluid at the boundary is subject to a force the current algorithm models the lattice fluid on boundary and bulk nodes to the same accuracy and in a demonstrably equivalent manner whilst the new method presented here applies to rectangular geometries it adds to our previous method i halliday l a hammond c m care a stevens j phys a math gen 35 2002 157 i the condition of mass conservation ii the ability to subject boundary fluid to a force and iii the ability to treat a range of complicated geometries with unimpaired accuracy

multiple equilibria in complex chemical reaction networks ii the species reaction graph for mass action kinetics the capacity for multiple equilibria in an isothermal homogeneous continuous flow stirred tank reactor is determined by the structure of the underlying network of chemical reactions we suggest a new graph theoretical method for discriminating between complex reaction networks that can admit multiple equilibria and those that cannot in particular we associate with each network a species reaction graph which is similar to reaction network representations drawn by biochemists and we show that if the graph satisfies certain weak conditions the differential equations corresponding to the network cannot admit multiple equilibria em no matter what values the rate constants take because these conditions are very mild they amount to powerful and quite delicate necessary conditions that a network must satisfy if it is to have the capacity to engender multiple equilibria broad qualitative results of this kind are especially apt for individual reaction rate constants are rare

criteria of asymptotic stability of differential and difference inclusions encountered in control theory abstract for a class of differential inclusions to which many of the practically important control systems can be reduced necessary and sufficient conditions for asymptotic stability of the zero solution are established by the method of lyapunov functions similar results are obtained for the corresponding class of difference inclusions

robust stability of linear time varying delta operator formulated discrete time systems some earlier results on robust stability of continuous time and discrete time control systems are extended to a class of linear time varying delta operator formulated discrete time systems

ising model on networks with an arbitrary distribution of connections we find the exact critical temperature t c of the nearest neighbor ferromagnetic ising model on an equilibrium random graph with an arbitrary degree distribution p k we observe an anomalous behavior of the magnetization magnetic susceptibility and specific heat when p k is fat tailed or loosely speaking when the fourth moment of the distribution diverges in infinite networks when the second moment becomes divergent t c approaches infinity the phase transition is of infinite order and size effect is anomalously strong

diffeomorphisms with banach space domains so f is a local diffeomorphism at every point by the inverse function theorem the aim of this paper is to find a sufficient condition for f to be injective and so a global diffeomorphism x f x theorem 2 l and a sufficient condition for f to be bijective and so a global diffeomorphism onto y theorem 3 1 this last condition is also necessary in the particular case x y r in these theorems the key role is played by nonnegative auxiliary scalar coercive functions that is continuous mappings k x r with k x a as llxll a as far as we know the use of such auxiliary functions in these questions is new first we find some corollaries to the aforementioned theorems the author hopes that suitable auxiliary functions adapted to particular problems may lead to new consequences in order to briefly discuss the results and some of their relations with the literature let us consider the case where x is a hilbert space with scalar product and k e c this simplifies the formulas a little however our results will be formulated and proved for banach spaces where we will ask for k to be locally lipschitz continuous and to have the right directional derivatives only these last assumptions are not made to quibble about this matter but are related to the nondifferentiability of the map x y ix in general banach spaces in this paper we use the hypothesis that the operator norm 11 f i x 11 is bounded on bounded sets i e sup iif ii vr o r w 1 2 il4 5 r

common lyapunov functions and gradient algorithms this note is concerned with the problem of finding a quadratic common lyapunov function for a large family of stable linear systems we present gradient iteration algorithms which give deterministic convergence for finite system families and probabilistic convergence for infinite families

correction to structure and stability of certain chemical networks and applications to the kinetic proofreading model of t cell receptor signal transduction deals with the theory of structure stability robustness and stabilization for an appealing class of nonlinear systems which arises in the analysis of chemical networks the results given here extend but are also heavily based upon certain previous work by feinberg 1977 1979 1987 1995 and horn and jackson 1972 of which a self contained and streamlined exposition is included the theoretical conclusions are illustrated through an application to the kinetic proofreading model proposed by mckeithan 1995 for t cell receptor signal transduction

on pade approximations quadratic stability and discretization of switched linear systems in this note we consider the stability preserving propertie s of diagonal pade approximations to the matrix exponential we show that while diagonal pade approximations preserve quadratic stability when going from continuous time to discrete time the converse is not true we discuss the implications of this result for discretizing switched linear systems we also show that for continuous time switched systems which are exponentially stable but not quadratically stable a pade approximation may not preserve stability

generating functions of switched linear systems analysis computation and stability applications in this paper a unified framework is proposed to study the exponential stability of discrete time switched linear systems and more generally the exponential growth rates of their trajectories under three types of switching rules arbitrary switching optimal switching and random switching it is shown that the maximum exponential growth rates of system trajectories over all initial states under these three switching rules are completely characterized by the radii of convergence of three suitably defined families of functions called the strong the weak and the mean generating functions respectively in particular necessary and sufficient conditions for the exponential stability of the switched linear systems are derived based on these radii of convergence various properties of the generating functions are established and their relations are discussed algorithms for computing the generating functions and their radii of convergence are also developed and illustrated through examples

stability and stabilizability of switched linear systems a survey of recent results during the past several years there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems this paper aims to briefly survey recent results in this field first the stability analysis for switched systems is reviewed we focus on the stability analysis for switched linear systems under arbitrary switching and we highlight necessary and sufficient conditions for asymptotic stability after a brief review of the stability analysis under restricted switching and the multiple lyapunov function theory the switching stabilization problem is studied and a variety of switching stabilization methods found in the literature are outlined then the switching stabilizability problem is investigated that is under what condition it is possible to stabilize a switched system by properly designing switching control laws note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature a necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here

universality for distances in power law random graphs we survey the recent work on phase transition and distances in various random graph models with general degree sequences we focus on inhomogeneous random graphs the configuration model and affine preferential attachment models and pay special attention to the setting where these random graphs have a power law degree sequence this means that the proportion of vertices with degree k in large graphs is approximately proportional to k for some 1 since many real networks have been empirically shown to have power law degree sequences these random graphs can be seen as more realistic models for real complex networks than classical random graphs such as the erd s renyi random graph it is often suggested that the behavior of random graphs should have a large amount of universality meaning in this case that random graphs with similar degree sequences share similar behavior we survey the available results on graph distances in power law random graphs that are consistent with this prediction

stability analysis of uncertain genetic sum regulatory networks this paper addresses the problem of establishing robust stability of uncertain genetic networks with sum regulatory functions specifically we first consider uncertain genetic networks where the regulation occurs at the transcriptional level and we derive a sufficient condition for robust stability by introducing a bounding set of the uncertain nonlinearity we hence show that this condition can be formulated as a convex optimization through polynomial lyapunov functions and polynomial descriptions of the bounding set by exploiting the square matricial representation smr of polynomials which allows to establish whether a polynomial is a sum of squares sos via a linear matrix inequality lmi then we propose a method for computing a family of bounding sets by means of convex optimizations it is worthwhile to remark that these results are derived in spite of the fact that the variable equilibrium point cannot be computed as being the solution of a system of parameter dependent nonlinear equations and is hence unknown lastly the proposed approach is extended to models where the regulation occurs at different levels and both mrna and protein dynamics are nonlinear

quenched central limit theorems for the ising model on random graphs the main goal of the paper is to prove central limit theorems for the magnetization rescaled by sqrt n for the ising model on random graphs with n vertices both random quenched and averaged quenched measures are considered we work in the uniqueness regime beta beta c or beta 0 and b ne 0 where beta is the inverse temperature beta c is the critical inverse temperature and b is the external magnetic field in the random quenched setting our results apply to general tree like random graphs as introduced by dembo montanari and further studied by dommers and the first and third author and our proof follows that of ellis in mathbb z d for the averaged quenched setting we specialize to two particular random graph models namely the 2 regular configuration model and the configuration model with degrees 1 and 2 in these cases our proofs are based on explicit computations relying on the solution of the one dimensional ising models

affine characterizations of minimal and mode dependent dwell times for uncertain linear switched systems an alternative approach for minimum and mode dependent dwell time characterization for switched systems is derived while minimum dwell time results require the subsystems to be asymptotically stable mode dependent dwell time results can consider unstable subsystems and dwell times within a possibly unbounded range of values the proposed approach is related to lyapunov looped functionals a new type of functionals leading to stability conditions affine in the system matrices unlike standard results for minimum dwell time these conditions are expressed as infinite dimensional lmis which can be solved using recent polynomial optimization techniques such as sum of squares the specific structure of the conditions is finally utilized in order to derive dwell time stability results for uncertain switched systems several examples illustrate the efficiency of the approach

the weak limit of ising models on locally tree like graphs we consider the ising model with inverse temperature and without external field on sequences of graphs g n which converge locally to the k regular tree we show that for such graphs the ising measure locally weakly converges to the symmetric mixture of the ising model with boundary conditions and the boundary conditions on the k regular tree with inverse temperature in the case where the graphs g n are expanders we derive a more detailed understanding by showing convergence of the ising measure conditional on positive magnetization sum of spins to the measure on the tree

constructive necessary and sufficient condition for the stability of quasi periodic linear impulsive systems the technical note provides a computation oriented necessary and sufficient condition for the global exponential stability of linear impulsive systems whose impulsions are assumed to occur quasi periodically based on the set theoretic conditions for robust stability of uncertain linear systems the existence of polyhedral lyapunov functions is proved to be necessary and sufficient for global exponential stability of quasi periodic linear impulsive systems a constructive method is developed for testing the stability of the system and for computing set induced polyhedral lyapunov functions the method leads to an algorithm whose complexity is similar to the standard algorithm related to discrete time parametric uncertain systems with the state matrix belonging to a convex polytopic set

factor models on locally tree like graphs we consider homogeneous factor models on uniformly sparse graph sequences converging locally to a unimodular random tree t and study the existence of the free energy density the limit of the log partition function divided by the number of vertices n as n tends to infinity we provide a new interpolation scheme and use it to prove existence of and to explicitly compute the quantity subject to uniqueness of a relevant gibbs measure for the factor model on t by way of example we compute for the independent set or hard core model at low fugacity for the ferromagnetic ising model at all parameter values and for the ferromagnetic potts model with both weak enough and strong enough interactions even beyond uniqueness regimes our interpolation provides useful explicit bounds on in the regimes in which we establish existence of the limit we show that it coincides with the bethe free energy functional evaluated at a suitable fixed point of the belief propagation bethe recursions on t in the special case that t has a galton watson law this formula coincides with the nonrigorous bethe prediction obtained by statistical physicists using the replica or cavity methods thus our work is a rigorous generalization of these heuristic calculations to the broader class of sparse graph sequences converging locally to trees we also provide a variational characterization for the bethe prediction in this general setting which is of independent interest

sufficient and necessary lmi conditions for robust stability of rationally time varying uncertain systems this technical note addresses robust stability of uncertain systems with rational dependence on unknown time varying parameters constrained in a polytope first the technical note proves that a sufficient linear matrix inequality lmi condition that we previously proposed based on homogeneous polynomial lyapunov functions hplfs and on the introduction of an extended version of polya s theorem is also necessary second the technical note proposes a new sufficient and necessary lmi condition by exploiting properties of the simplex and sum of squares sos parameter dependent polynomials lastly the technical note investigates relationships among these conditions and conditions based on the linear fractional representation lfr it is worth remarking that sufficient and necessary lmi conditions for this problem have not been proposed yet in the literature

comprehensive lyapunov functions for linear switching systems abstract for a linear dynamical switching system we analyse maximal asymptotic growth of trajectories depending on the initial point both discrete and continuous time systems in r d are considered we prove the existence of a lyapunov norm in r d with the following property for every invariant linear subspace l r d of the system the restriction of the norm on l provides a tight upper bound for the growth of trajectories on l for this we introduce the concept of the spectral normal form of a family of matrices properties of the comprehensive lyapunov norms are analysed and methods of their construction are discussed

metastability of the ising model on random regular graphs at zero temperature we study the metastability of the ferromagnetic ising model on a random r regular graph in the zero temperature limit we prove that in the presence of a small positive external field the time that it takes to go from the all minus state to the all plus state behaves like exp beta r 2 mathcal o sqrt r n when the inverse temperature beta rightarrow infty and the number of vertices n is large enough but fixed the proof is based on the so called pathwise approach and bounds on the isoperimetric number of random regular graphs

lees edwards boundary conditions for lattice boltzmann lees edwards boundary conditions lebc for molecular dynamics simulations 1 are an extension of the well known periodic boundary conditions and allow the simulation of bulk systems in a simple shear flow we show how the idea of lebc can be implemented in isothermal lattice boltzmann simulations and how lebc can be used to overcome the problem of a maximum shear rate that is limited to less then 1 l y with l y the transverse system size in traditional lattice boltzmann implementations of shear flow the only previous lattice boltzmann implementation of lebc 2 requires a specific fourth order equilibrium distribution in this paper we show how lebc can be implemented with the usual quadratic equilibrium distributions

convex liftings based robust control design this paper presents a new approach for control design of constrained linear systems affected by bounded additive disturbances and polytopic uncertainties this method hinges on so called convex liftings which emulate control lyapunov function by providing a constructive framework for optimization based control implementation it will be shown that this method can guarantee the recursive feasibility and robust stability finally a numerical example will be presented to illustrate this method