interference alignment with finite extensions in partially connected networks in this paper we investigate the interference alignment ia for a class of partially connected multi input multi output heterogeneous networks which consist of l fully connected pico cells j partially connected pico cells and one macro cell in particular we investigate the feasibility of ia conditions with no channel extensions t independent channel extensions and t dependent channel extensions respectively for the single beam case we present three theorems to characterize some necessary conditions which l j t and the channel diversity order overline l must jointly satisfy when ia conditions are feasible these necessary conditions also implicitly impose the constraints on the upper bounds of achievable degrees of freedom with different channel extensions

on stabilization of bilinear uncertain time delay stochastic systems with markovian jumping parameters in this paper we investigate the stochastic stabilization problem for a class of bilinear continuous time delay uncertain systems with markovian jumping parameters specifically the stochastic bilinear jump system under study involves unknown state time delay parameter uncertainties and unknown nonlinear deterministic disturbances the jumping parameters considered here form a continuous time discrete state homogeneous markov process the whole system may be regarded as a stochastic bilinear hybrid system that includes both time evolving and event driven mechanisms our attention is focused on the design of a robust state feedback controller such that for all admissible uncertainties as well as nonlinear disturbances the closed loop system is stochastically exponentially stable in the mean square independent of the time delay sufficient conditions are established to guarantee the existence of desired robust controllers which are given in terms of the solutions to a set of either linear matrix inequalities lmis or coupled quadratic matrix inequalities the developed theory is illustrated by numerical simulation

decay rate dependent conditions for exponential stability of stochastic neutral systems with markovian jumping parameters abstract this note studies the problem of decay rate dependent exponential stability for neutral stochastic delay systems with markovian jumping parameters first by introducing an operator d x t i as well as a novel lyapunov krasovskii functional sufficient conditions for exponential stability of system with a decay rate are obtained second the results are extended to the robust exponential estimates for uncertain neutral stochastic delay systems with markovian jumping parameters finally numerical examples are provided to show the effectiveness of the proposed results

decentralized finite time h filtering for interconnected markovian jump system with interval mode dependent delays this paper concerns with the problem of finite time h filtering for a class of interconnected markovian jump system with mode dependent delays in the interconnection sufficient conditions guaranteeing the interconnected markovian jump systems to be finite time bounded are established by constructing an augmented lyapunov krasovskii functional the obtained conditions are delay range dependent and mode dependent based on the results the decentralized filter is proposed to guarantee the finite time bounded and h performance of the resulting augmented system for admissible disturbances the desired filter parameters can be obtained via solving a group of linear matrix inequalities lmis finally a numerical example is employed to illustrate the effectiveness of the proposed methods

dissipativity analysis for singular systems with time varying delays this paper is concerned with the dissipativity analysis problem for singular systems with time varying delays a delay dependent criterion is established to guarantee the dissipativity of the underlying systems using the delay partitioning technique all the results given in this paper are not only dependent upon the time delay but also dependent upon the number of delay partitions the effectiveness and the reduced conservatism of the derived results are demonstrated by two illustrative examples

dimer monomer model on the sierpinski gasket abstract we present the numbers of dimer monomers m d n on the sierpinski gasket s g d n at stage n with dimension d equal to two three and four the upper and lower bounds for the asymptotic growth constant defined as z s g d lim v ln m d n v where v is the number of vertices on s g d n are derived in terms of the results at a certain stage as the difference between these bounds converges quickly to zero as the calculated stage increases the numerical value of z s g d can be evaluated with more than a hundred significant figures accurate from the results for d 2 3 4 we conjecture the upper and lower bounds of z s g d for general dimension the corresponding results on the generalized sierpinski gasket s g d b n with d 2 and b 3 4 are also obtained

admissibility and dissipativity analysis for discrete time singular systems with mixed time varying delays abstract the problems of admissibility and dissipativity are studied for discrete time singular systems with mixed time varying delays the mixed time delays consist of both discrete and distributed delays by taking advantage of the delay partitioning technique a criterion that warrants the admissibility of the considered systems is established based on the criterion a dissipativity condition is also given all the results presented depend upon not only discrete delay and distributed delay but also depend upon the number of delay partitions some numerical examples are included to demonstrate the improvement and effectiveness of the proposed methods

non fragile observer based sliding mode control for markovian jump systems with mixed mode dependent time delays and input nonlinearity this paper is concerned with the state estimation and the sliding mode control smc for a class of markovian jump systems with mixed mode dependent time delays and input nonlinearity a non fragile observer is designed to estimate the system states and an observer based smc is synthesized to ensure the reachability of the sliding surfaces in the state estimation space by constructing a novel mode dependent lyapunov krasovskii functional some new criteria are established for the existence and the solvability of the desired observer based sliding mode controller finally numerical examples are presented to illustrate the effectiveness and less conservativeness of the proposed theoretical results

boundary field induced first order transition in the 2d ising model exact study we present in this paper an exact study of a first order transition induced by an inhomogeneous boundary magnetic field in the 2d ising model from a previous analysis of the interfacial free energy in the discrete case clusel and fortin 2005 j phys a math gen 38 2849 we identify using an asymptotic expansion in the thermodynamic limit the line of transition that separates the regime where the interface is localized near the boundary from the one where it is propagating inside the bulk in particular the transition line has a strong dependence on the aspect ratio of the lattice

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

monomer dimer problem on random planar honeycomb lattice we consider the monomer dimer md problem on a random planar honeycomb lattice model namely the random multiple chain this is a lattice system with non periodic boundary condition whose generating process is inspired by the growth of single walled zigzag carbon nanotubes by applying algebraic and combinatorial techniques we establish a calculating expression of the md partition function for bipartite graphs which corresponds to the permanent of a matrix further by using the transfer matrix argument we show that the computing problem of the permanent of high order matrix can be converted into some lower order matrices for this family of lattices based on which we derive an explicit recurrence formula for evaluating the md partition function of multiple chains and random multiple chains finally we analyze the expectation of the number of monomer dimer arrangements on a random multiple chain and the asymptotic behavior of the annealed md entropy when the multiple chain becomes infinite in width and length respectively

packing dimers on 2p 1 x 2q 1 lattices we use computational method to investigate the number of ways to pack dimers on m x n lattices where both m and n are odd in this case there is always a single vacancy in the lattices we show that the dimer configuration numbers on 2k 1 x 2k 1 odd square lattices have some remarkable number theoretical properties in parallel to those of close packed dimers on 2k x 2k even square lattices for which an exact solution exists furthermore we demonstrate that there is an unambiguous logarithmic term in the finite size correction of free energy of odd by odd lattice strips with any width n or 1 this logarithmic term determines the distinct behavior of the free energy of odd square lattices these findings reveal a deep and previously unexplored connection between statistical physics models and number theory and indicate the possibility that the monomer dimer problem might be solvable

a quadratic identity for the number of perfect matchings of plane graphs we present a quadratic identity on the number of perfect matchings of plane graphs by the method of graphical condensation which generalizes the results found by propp j propp generalized domino shuffling theoret comput sci 303 2003 267 301 kuo e h kuo applications of graphical condensation for enumerating matchings and tilings theoret comput sci 319 2004 29 57 and yan yeh and zhang w g yan y n yeh f j zhang graphical condensation of plane graphs a combinatorial approach theoret comput sci 349 2005 452 461

output feedback robust h sup spl infin control of uncertain fuzzy dynamic systems with time varying delay this paper presents an output feedback robust h sup spl infin control problem for a class of uncertain fuzzy dynamic systems with time varying delayed state the takagi sugeno fuzzy model is employed to represent an uncertain nonlinear systems with time varying delayed state using a single quadratic lyapunov function the globally exponential stability and disturbance attenuation of the closed loop fuzzy control system are discussed sufficient conditions for the existence of robust h sup spl infin controllers are given in terms of matrix inequalities constructive algorithm for design of robust h sup spl infin controller is also developed the resulting controller is nonlinear and automatically tuned based on fuzzy operation

stability analysis for continuous systems with two additive time varying delay components this paper presents a new result of stability analysis for continuous systems with two additive time varying delay components which represent a general class of delay systems with strong application background in network based control systems this criterion is expressed as a set of linear matrix inequalities which can be readily tested by using standard numerical software a numerical example is provided to show the effectiveness and advantage of the proposed stability condition

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

on feasibility of interference alignment in mimo interference networks we explore the feasibility of interference alignment in signal vector space based only on beamforming for k user mimo interference channels our main contribution is to relate the feasibility issue to the problem of determining the solvability of a multivariate polynomial system which is considered extensively in algebraic geometry it is well known e g from bezout s theorem that generic polynomial systems are solvable if and only if the number of equations does not exceed the number of variables following this intuition we classify signal space interference alignment problems as either proper or improper based on the number of equations and variables rigorous connections between feasible and proper systems are made through bernshtein s theorem for the case where each transmitter uses only one beamforming vector the multibeam case introduces dependencies among the coefficients of a polynomial system so that the system is no longer generic in the sense required by both theorems in this case we show that the connection between feasible and proper systems can be further strengthened since the equivalency between feasible and proper systems does not always hold by including standard information theoretic outer bounds in the feasibility analysis

graphs determined by polynomial invariants many polynomials have been defined associated to graphs like the characteristic matchings chromatic and tutte polynomials besides their intrinsic interest they encode useful combinatorial information about the given graph it is natural then to ask to what extent any of these polynomials determines a graph and in particular whether one can find graphs that can be uniquely determined by a given polynomial in this paper we survey known results in this area and at the same time we present some new results

fa yueh wu s contributions in physics abstract we sketch a subset of professor f y wu s contributions in lattice statistical mechanics solid state physics graph theory enumerative combinatorics and other domains of physics and mathematics we will recall some of f y wu s most important and well known classic results and we will also sketch some of his most recent researches dedicated to the connections of lattice statistical mechanical models with deep problems in pure mathematics

enumeration of spanning trees in planar unclustered networks abstract among a variety of subgraphs spanning trees are one of the most important and fundamental categories they are relevant to diverse aspects of networks including reliability transport self organized criticality loop erased random walks and so on in this paper we introduce a family of modular self similar planar networks with zero clustering relevant properties of this family are comparable to those networks associated with technological systems having low clustering like power grids some electronic circuits the internet and some biological systems so it is very significant to research on spanning trees of planar networks however for a large network evaluating the relevant determinant is intractable in this paper we propose a fairly generic linear algorithm for counting the number of spanning trees of a planar network using the algorithm we derive analytically the exact numbers of spanning trees in planar networks our result shows that the computational complexity is o t which is better than that of the matrix tree theorem with o m 2 t 2 where t is the number of steps and m is the girth of the planar network we also obtain the entropy for the spanning trees of a given planar network we find that the entropy of spanning trees in the studied network is small which is in sharp contrast to the previous result for planar networks with the same average degree we also determine an upper bound and a lower bound for the numbers of spanning trees in the family of planar networks by the algorithm as another application of the algorithm we give a formula for the number of spanning trees in an outerplanar network with small world features

grassmannian representation of the two dimensional monomer dimer model we present an application of the grassmann algebra to the problem of the monomer dimer statistics on a two dimensional square lattice the exact partition function or total number of possible configurations of a system of dimers with a finite set of n monomers at fixed positions can be expressed via a quadratic fermionic theory we give an answer in terms of a product of two pfaffians and the solution is closely related to the kasteleyn result of the pure dimer problem correlation functions are in agreement with previous results both for monomers on the boundary where a simple exact expression is available in the discrete and continuous case and in the bulk where the expression is evaluated numerically

on the interference management for k user partially connected fading interference channels the multiplexing gain muxg of the k user interference channel ic with partially connected interfering links is analyzed the motivation for the partially connected ic comes from the fact that not all interferences are equally strong in practice we introduce the idea of the graphical representation of interference alignment ia condition we show that for a k user partially connected mimo ic with m antennas at each transmitter and receiver the transmit beamforming matrices achieving the muxg of km 2 can be generated sequentially almost surely if the interference channel has a graphical representation which follows certain criteria we also present a novel scheme where we use the idea of partially connected ic to obtain improvements in conventional distributed interference alignment algorithm for fully connected ic the improvements are obtained in terms of greater average sum rate and faster convergence

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

stochastic stability properties of jump linear systems jump linear systems are defined as a family of linear systems with randomly jumping parameters usually governed by a markov jump process and are used to model systems subject to failures or changes in structure the authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties it is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability and a testable necessary and sufficient condition for second moment stability is derived the lyapunov exponent method for the study of almost sure sample stability is discussed and a theorem which characterizes the lyapunov exponents of jump linear systems is presented finally for one dimensional jump linear system it is proved that the region for delta moment stability is monotonically converging to the region for almost sure stability at delta down arrow 0 sup

degrees of freedom of the k user m times n mimo interference channel we provide inner bound and outer bound for the total number of degrees of freedom of the k user multiple input multiple output mimo gaussian interference channel with m antennas at each transmitter and n antennas at each receiver if the channel coefficients are time varying and drawn from a continuous distribution the bounds are tight when the ratio max m n min m n r is equal to an integer for this case we show that the total number of degrees of freedom is equal to min m n k if k r and min m n r r 1 k if k r achievability is based on interference alignment we also provide examples where using interference alignment combined with zero forcing can achieve more degrees of freedom than merely zero forcing for some mimo interference channels with constant channel coefficients

constrained average cost markov control processes in borel spaces this paper considers constrained markov control processes in borel spaces with unbounded costs the criterion to be minimized is a long run expected average cost and the constraints can be imposed on similar average costs or on average rewards or discounted costs or rewards we give conditions under which the constrained problem cp is solvable and equivalent to an equality constrained ec linear program furthermore we show that there is no duality gap between ec and the dual program ec and that in fact the strong duality condition holds finally we introduce an explicit procedure to solve cp in some cases which is illustrated with a detailed example

h control of switched delayed systems with average dwell time this paper considers the problems of stability analysis and h controller design of time delay switched systems with average dwell time in order to obtain less conservative results than what is seen in the literature a tighter bound for the state delay term is estimated based on the scaled small gain theorem and the model transformation method an improved exponential stability criterion for time delay switched systems with average dwell time is formulated in the form of convex matrix inequalities the aim of the proposed approach is to reduce the minimal average dwell time of the systems which is made possible by a new lyapunov krasovskii functional combined with the scaled small gain theorem it is shown that this approach is able to tolerate a smaller dwell time or a larger admissible delay bound for the given conditions than most of the approaches seen in the literature moreover the exponential h controller can be constructed by solving a set of conditions which is developed on the basis of th

event based h_ infty filter design for a class of nonlinear time varying systems with fading channels and multiplicative noises in this paper a general event triggered framework is developed to deal with the finite horizon h infty filtering problem for discrete time varying systems with fading channels randomly occurring nonlinearities and multiplicative noises an event indicator variable is constructed and the corresponding event triggered scheme is proposed such a scheme is based on the relative error with respect to the measurement signal in order to determine whether the measurement output should be transmitted to the filter or not the fading channels are described by modified stochastic rice fading models some uncorrelated random variables are introduced respectively to govern the phenomena of state multiplicative noises randomly occurring nonlinearities as well as fading measurements the purpose of the addressed problem is to design a set of time varying filter such that the influence from the exogenous disturbances onto the filtering errors is attenuated at the given level quantified by a h infty norm in the mean square sense by utilizing stochastic analysis techniques sufficient conditions are established to ensure that the dynamic system under consideration satisfies the h infty filtering performance constraint and then a recursive linear matrix inequality rlmi approach is employed to design the desired filter gains simulation results demonstrate the effectiveness of the developed filter design scheme

exponential stabilization of a class of stochastic system with markovian jump parameters and mode dependent mixed time delays in this technical note the globally exponential stabilization problem is investigated for a general class of stochastic systems with both markovian jumping parameters and mixed time delays the mixed mode dependent time delays consist of both discrete and distributed delays we aim to design a memoryless state feedback controller such that the closed loop system is stochastically exponentially stable in the mean square sense first by introducing a new lyapunov krasovskii functional that accounts for the mode dependent mixed delays stochastic analysis is conducted in order to derive a criterion for the exponential stabilizability problem then a variation of such a criterion is developed to facilitate the controller design by using the linear matrix inequality lmi approach finally it is shown that the desired state feedback controller can be characterized explicitly in terms of the solution to a set of lmis numerical simulation is carried out to demonstrate the effectiveness of the proposed methods

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

robust extended dissipative control for sampled data markov jump systems this paper investigates the problem of the sampled data extended dissipative control for uncertain markov jump systems the systems considered are transformed into markov jump systems with polytopic uncertainties and sawtooth delays by using an input delay approach the focus is on the design of a mode independent sampled data controller such that the resulting closed loop system is mean square exponentially stable with a given decay rate and extended dissipative a novel exponential stability criterion and an extended dissipativty condition are established by proposing a new integral inequality the reduced conservatism of the criteria is demonstrated by two numerical examples furthermore a sufficient condition for the existence of a desired mode independent sampled data controller is obtained by solving a convex optimisation problem finally a resistance inductance and capacitance rlc series circuit is employed to illustrate the effectiveness of the proposed approach

a pfaffian formula for monomer dimer partition functions we consider the monomer dimer partition function on arbitrary finite planar graphs and arbitrary monomer and dimer weights with the restriction that the only non zero monomer weights are those on the boundary we prove a pfaffian formula for the corresponding partition function as a consequence of this result multipoint boundary monomer correlation functions at close packing are shown to satisfy fermionic statistics our proof is based on the celebrated kasteleyn theorem combined with a theorem on pfaffians proved by one of the authors and a careful labeling and directing procedure of the vertices and edges of the graph

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

interference alignment for partially connected mimo cellular networks in this paper we propose an iterative interference alignment ia algorithm for mimo cellular networks with partial connectivity which is induced by heterogeneous path losses and spatial correlation such systems impose several key technical challenges in the ia algorithm design namely the overlapping between the direct and interfering links due to the mimo cellular topology as well as how to exploit the partial connectivity we shall address these challenges and propose a three stage ia algorithm as illustration we analyze the achievable degree of freedom dof of the proposed algorithm for a symmetric partially connected mimo cellular network we show that there is significant dof gain compared with conventional ia algorithms due to partial connectivity the derived dof bound is also backward compatible with that achieved on fully connected k pair mimo interference channels

the complexity of counting in sparse regular and planar graphs we show that a number of graph theoretic counting problems remain cal np hard indeed cal p complete in very restricted classes of graphs in particular we prove that the problems of counting matchings vertex covers independent sets and extremal variants of these all remain hard when restricted to planar bipartite graphs of bounded degree or regular graphs of constant degree we obtain corollaries about counting cliques in restricted classes of graphs and counting satisfying assignments to restricted classes of monotone 2 cnf formulae to achieve these results a new interpolation based reduction technique which preserves properties such as constant degree is introduced

worst case control of uncertain jumping systems with multi state and input delay information in this paper the problem of worst case also called h control for a class of uncertain systems with markovian jump parameters and multiple delays in the state and input is investigated the jumping parameters are modelled as a continuous time discrete state markov process and the parametric uncertainties are assumed to be real time varying and norm bounded that appear in the state input and delayed state matrices the time delay factors are unknowns and time varying with known bounds complete results for instantaneous and delayed state feedback control designs are developed which guarantee the weak delay dependent stochastic stability with a prescribed h performance the solutions are provided in terms of a finite set of coupled linear matrix inequalities lmis application of the developed theory to a typical example has been presented

robust finite time stability and stabilization of uncertain markovian jump systems with time varying delay this paper deals with the robust finite time stability and stabilization problems of uncertain stochastic delayed jump systems where the uncertainty is in the form of additive perturbations and exists in the drift and diffusion sections simultaneously though perturbation time varying delay and brownian motion existing at the same time two conditions checking its robust finite time stability are proposed by a mode dependent parameter approach which are different from some existing methods based on the proposed results sufficient conditions for the existence of the state feedback controller are provided with lmis which could be solved directly it is seen that all the features of the underlying system such as time varying delay perturbation diffusion mode dependent parameters and uncertain transition rate matrix play important roles in the system analysis and synthesis of finite time stability finally numerical examples are used to demonstrate the effectiveness and superiority of the proposed methods

robust h fuzzy control for uncertain nonlinear markovian jump systems with time varying delay this paper investigates the problem of robust h fuzzy control for a class of uncertain nonlinear markovian jump systems with time varying delay the class of systems under consideration is described by the takagi sugeno fuzzy model the goal of the paper is to design a mode dependent fuzzy state feedback controller such that the closed loop system is stochastically stable with a prescribed h performance of disturbance attenuation for all admissible parameter uncertainties in order to obtain a less conservative control design a new stochastic lyapunov krasovskii functional is first constructed by decomposing the delay interval into multiple equidistant subintervals then by employing this functional a delay decomposition approach to the design of robust h fuzzy controllers is developed in terms of linear matrix inequalities finally two examples are given to illustrate the merit and usability of the proposed design method

stability analysis of a class of hybrid stochastic retarded systems under asynchronous switching the stability of a class of hybrid stochastic retarded systems hsrss with an asynchronous switching controller is investigated in this model the controller design relies on the observed jumping parameters which are however delayed and thus can not be measured in real time precisely this delayed time interval referred to as the asynchronous switching interval is markovian and dependent on the actual switching signal the sufficient conditions under which the system is either stochastically asymptotic stable or input to state stable are obtained by applying the extended razumikhin type theorem to the asynchronous switching interval these results are less conservative as it is only required that the designed lyapunov function is non decreasing it is shown that the stability of the considered system can be guaranteed by a sufficiently small mode transition rate of the underlying markov process which is a conclusion similar to that in asynchronous deterministic switched systems the effectiveness and correctness of the obtained results are finally verified by a numerical example

dimers on a simple quartic net with a vacancy a seminal milestone in lattice statistics is the exact solution of the enumeration of dimers on a simple quartic net obtained by fisher kasteleyn and temperley fkt in 1961 an outstanding related and yet unsolved problem is the enumeration of dimers on a net with vacant sites here we consider this vacant site problem with a single vacancy occurring at certain specific sites on the boundary of a simple quartic net first using a bijection between dimer and spanning tree configurations due to temperley kenyon propp and wilson we establish that the dimer generating function is independent of the location of the vacancy and deduce a closed form expression for the generating function we next carry out finite size analyses of this solution as well as that of the fkt solution our analyses lead to a logarithmic correction term in the large size expansion for the vacancy problem with free boundary conditions a concrete example exhibiting this difference is given we also find the central charge c 2 in the language of conformal field theory for the vacancy problem as versus the value c 1 when there is no vacancy

pfaffian solution of a dimer monomer problem single monomer on the boundary we consider the dimer monomer problem for the rectangular lattice by mapping the problem into one of close packed dimers on an extended lattice we rederive the tzeng wu solution for a single monomer on the boundary by evaluating a pfaffian we also clarify the mathematical content of the tzeng wu solution by identifying it as the product of the nonzero eigenvalues of the kasteleyn matrix

two dimensional monomer dimer systems are computationally intractable the classic problem of counting monomer dimer arrangements on a two dimensional lattice is analyzed using techniques from theoretical computer science under a certain assumption made precise in the text it can be shown that the general problem is computationally intractable this negative result contrasts with the special case of a system with monomer density zero for which efficient solutions have been known for some time a second much easier result obtained under the same assumption is that the partition function of a three dimensional ising system is computationally intractable again the negative result contrasts with known efficient techniques for evaluating the partition function of a two dimensional system

long range properties of spanning trees we compute some large scale properties of the uniform spanning tree process on bounded regions in z2 in particular we compute the distribution of the meeting point of the branches of the tree issued from three boundary points we also compute the crossing probabilities of branches of the tree on rectangular and annular regions as well as the winding number of the branches of the tree

logarithmic corrections in the free energy of monomer dimer model on plane lattices with free boundaries using exact computations we study the classical hard core monomer dimer models on m x n plane lattice strips with free boundaries for an arbitrary number v of monomers or vacancies we found a logarithmic correction term in the finite size correction of the free energy per lattice site the coefficient of the logarithmic correction term depends on the number of monomers present v and the parity of the width n of the lattice strip the coefficient equals to v when n is odd and v 2 when n is even the results are generalizations of the previous results for a single monomer in an otherwise fully packed lattice of dimers we also study the finite size correction in the low dimer density limit where the number of dimers d is fixed in this case the coefficient of the logarithmic correction term equals to d for both odd and even n

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

boundary monomers in the dimer model the correlation functions of an arbitrary number of boundary monomers in the system of close packed dimers on the square lattice are computed exactly in the scaling limit the equivalence of the 2n point correlation functions with those of a complex free fermion is proved thereby reinforcing the description of the monomer dimer model by a conformal free field theory with central charge c 1 comment 15 pages 2 figures

brief paper new delay dependent stability criteria for systems with interval delay this paper provides a new delay dependent stability criterion for systems with a delay varying in an interval with a different lyapunov functional defined a tight upper bound of its derivative is given the resulting criterion has advantages over some previous ones in that it involves fewer matrix variables but has less conservatism which is established theoretically examples are provided to demonstrate the advantage of the stability result

dynamic output feedback control for singular markovian jump system lmi approach for the dynamic output feedback stabilization of continuous time singular markovian jump systems this paper introduces the necessary and sufficient condition whereas the previous research works suggested the sufficient conditions a special choice of the block entries of lyapunov matrices leads to derive the necessary and sufficient condition in terms of linear matrix inequalities a numerical example shows the validity of the derived results

state estimation and sliding mode control for semi markovian jump systems with mismatched uncertainties this paper is concerned with the state estimation and sliding mode control problems for phase type semi markovian jump systems using a supplementary variable technique and a plant transformation a finite phase type semi markov process has been transformed into a finite markov chain which is called its associated markov chain as a result phase type semi markovian jump systems can be equivalently expressed as its associated markovian jump systems a sliding surface is then constructed and a sliding mode controller is synthesized to ensure that the associated markovian jump systems satisfy the reaching condition moreover an observer based sliding mode control problem is investigated sufficient conditions are established for the solvability of the desired observer two numerical examples are presented to show the effectiveness of the proposed design techniques

degrees of freedom of mimo x networks spatial scale invariance and one sided decomposability we show that an m n user mimo x network with a antennas at each node has a mn m n 1 degrees of freedom dof thus resolving in this case a discrepancy between the spatial scale invariance conjecture scaling the number of antennas at each node by a constant factor will scale the total dof by the same factor and a decomposability property of overconstrained wireless networks while the best previously known general dof outer bound is consistent with the spatial invariance conjecture the best previously known general dof inner bound inspired by the k user mimo interference channel was based on the decomposition of every transmitter and receiver into multiple single antenna nodes transforming the network into an am an user siso x network while such a decomposition is dof optimal for the k user mimo interference channel a gap remained between the best inner and outer bounds for the mimo x channel here we close this gap with the new insight that the mimo x network is only one sided decomposable i e either all the transmitters or all the receivers but not both can be decomposed by splitting multiple antenna nodes into multiple single antenna nodes without loss of dof the result is extended to simo and miso x networks as well and in each case the dof results satisfy the spatial scale invariance property

vacancy localization in the square dimer model we study the classical dimer model on a square lattice with a single vacancy by developing a graph theoretic classification of the set of all configurations which extends the spanning tree formulation of close packed dimers with this formalism we can address the question of the possible motion of the vacancy induced by dimer slidings we find a probability 57 4 ensuremath 10 sqrt 2 for the vacancy to be strictly jammed in an infinite system more generally the size distribution of the domain accessible to the vacancy is characterized by a power law decay with exponent 9 8 on a finite system the probability that a vacancy in the bulk can reach the boundary falls off as a power law of the system size with exponent 1 4 the resultant weak localization of vacancies still allows for unbounded diffusion characterized by a diffusion exponent that we relate to that of diffusion on spanning trees we also implement numerical simulations of the model with both free and periodic boundary conditions

on the feasibility of linear interference alignment for mimo interference broadcast channels with constant coefficients in this paper we analyze the feasibility of linear interference alignment ia for multi input multi output mimo interference broadcast channel mimo ibc with constant coefficients we pose and prove the necessary conditions of linear ia feasibility for general mimo ibc except for the proper condition we find another necessary condition to ensure a kind of irreducible interference to be eliminated we then prove the necessary and sufficient conditions for a special class of mimo ibc where the numbers of antennas are divisible by the number of data streams per user since finding an invertible jacobian matrix is crucial for the sufficiency proof we first analyze the impact of sparse structure and repeated structure of the jacobian matrix considering that for the mimo ibc the sub matrices of the jacobian matrix corresponding to the transmit and receive matrices have different repeated structure we find an invertible jacobian matrix by constructing the two sub matrices separately we show that for the mimo ibc where each user has one desired data stream a proper system is feasible for symmetric mimo ibc we provide proper but infeasible region of antenna configurations by analyzing the difference between the necessary conditions and the sufficient conditions of linear ia feasibility

dimer coverings on the sierpinski gasket we present the number of dimer coverings nd n on the sierpinski gasket sgd n at stage n with dimension d equal to two three four or five when the number of vertices denoted as v n of the sierpinski gasket is an even number nd n is the number of close packed dimers when the number of vertices is an odd number no close packed configurations are possible and we allow one of the outmost vertices uncovered the entropy of absorption of diatomic molecules per site defined as s mathit sg d lim n to infty ln n d n v n is calculated to be ln 2 3 exactly for sg2 the numbers of dimers on the generalized sierpinski gasket sgd b n with d 2 and b 3 4 5 are also obtained exactly with entropies equal to ln 6 7 ln 28 12 ln 200 18 respectively the number of dimer coverings for sg3 is given by an exact product expression such that its entropy is given by an exact summation expression the upper and lower bounds for the entropy are derived in terms of the results at a certain stage for sgd n with d 3 4 5 as the difference between these bounds converges quickly to zero as the calculated stage increases the numerical value of s mathit sg d with d 3 4 5 can be evaluated with more than a hundred significant figures accurate

on the degrees of freedom achievable through interference alignment in a mimo interference channel consider a k user flat fading mimo interference channel where the kth transmitter or receiver is equipped with mk respectively nk antennas if an exponential in k number of generic channel extensions are used either across time or frequency cadambe and jafar 1 showed that the total achievable degrees of freedom dof can be maximized via interference alignment resulting in a total dof that grows linearly with a even if mk and nk are bounded in this work we consider the case where no channel extension is allowed and establish a general condition that must be satisfied by any degrees of freedom tuple d1 d2 dk achievable through linear interference alignment for a symmetric system with mk m nk n dk d for all k this condition implies that the total achievable dof cannot grow linearly with k and is in fact no more than k m n k 1 we also show that this bound is tight when the number of antennas at each transceiver is divisible by d the number of data streams per user

counting spanning trees in a small world farey graph the problem of spanning trees is closely related to various interesting problems in the area of statistical physics but determining the number of spanning trees in general networks is computationally intractable in this paper we perform a study on the enumeration of spanning trees in a specific small world network with an exponential distribution of vertex degrees which is called a farey graph since it is associated with the famous farey sequence according to the particular network structure we provide some recursive relations governing the laplacian characteristic polynomials of a farey graph and its subgraphs then making use of these relations obtained here we derive the exact number of spanning trees in the farey graph as well as an approximate numerical solution for the asymptotic growth constant characterizing the network finally we compare our results with those of different types of networks previously investigated

the feasibility conditions for interference alignment in mimo networks interference alignment ia has attracted great attention in the last few years for its breakthrough performance in interference networks however despite the numerous works dedicated to ia the feasibility conditions of ia remains unclear for most network topologies the ia feasibility analysis is challenging as the ia constraints are sets of high degree polynomials for which no systematic tool to analyze the solvability conditions exists in this work by developing a new mathematical framework that maps the solvability of sets of polynomial equations to the linear independence of their first order terms we propose a sufficient condition that applies to mimo interference networks with general configurations we have further proved that this sufficient condition coincides with the necessary conditions under a wide range of configurations these results further consolidate the theoretical basis of ia

erratum pfaffian solution of a dimer monomer problem single monomer on the boundary phys rev e74 020104 r 2006

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

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