geometry of sets of quantum maps a generic positive map acting on a high dimensional system is not completely positive we investigate the set a of positive trace preserving maps acting on density matrices of size n and a sequence of its nested subsets the sets of maps which are b decomposable c completely positive and d extended by identity impose positive partial transpose and e are superpositive working with the hilbert schmidt euclidean measure we derive tight explicit two sided bounds for the volumes of all five sets a sample consequence is the fact that as n increases a generic positive map becomes not decomposable and a fortiori not completely positive due to the jamiolkowski isomorphism the results obtained for quantum maps are closely connected to similar relations between the volume of the set of quantum states and the volumes of its subsets such as states with positive partial transpose or separable states or supersets our approach depends on the systematic use of duality to derive quantitative estimates and on various tools of classical convexity high dimensional probability and geometry of banach spaces some of which are not standard

a concise formula for generalized two qubit hilbert schmidt separability probabilities we report major advances in the research program initiated in moment based evidence for simple rational valued hilbert schmidt generic 2 2 separability probabilities slater and dunkl 2012 j phys a math theor 45 095305 a highly succinct separability probability function p is put forth yielding for generic nine dimensional two rebit systems 15 dimensional two qubit systems and 27 dimensional two quater nionic bit systems this particular form of p was obtained by qing hu hou by applying zeilberger s algorithm creative telescoping to a fully equivalent but considerably more complicated expression containing six 7f6 hypergeometric functions all with argument that hypergeometric form itself had been obtained using systematic high accuracy probability distribution reconstruction computations these employed 7501 determinantal moments of partially transposed 4 4 density matrices parameterized by from these computations exact rational valued separability probabilities were discernible the integral half integral sequences of 32 rational values then served as input to the mathematica findsequencefunction command from which the initially obtained hypergeometric form of p emerged

design of robust controllers for time delay systems the problem of stabilizing linear dynamical time delay systems subject to bounded uncertainties is investigated two memoryless feedback controllers are considered it is established that when the matching conditions are met and certain bounding relations are satisfied then the linear controller renders the zero response of the system asymptotically stable saturation type controllers are shown to guarantee that all system responses are uniformly ultimately bounded

on the structure of the body of states with positive partial transpose we show that the convex set of separable mixed states of the 2 2s ystem is a body of a constant height this fact is used to prove that the probability of finding a random state to be separable equals twice the probability of finding a random boundary state to be separable provided that the random states are generated uniformly with respect to the hilbert schmidt euclidean measure an analogous property holds for the set of positive partial transpose states for an arbitrary bipartite system

filtering on sampled data systems with parametric uncertainty the paper is concerned with the problem of robust h sub spl infin filtering for a class of systems with parametric uncertainties and unknown time delays under sampled measurements the parameter uncertainties considered are real time varying and norm bounded appearing in the state equation an approach has been proposed for the designing of h sub spl infin filters using sampled measurements which would guarantee a prescribed h sub spl infin performance in the continuous time context irrespective of the parameter uncertainties and unknown time delays both cases of finite and infinite horizon filtering are studied it has been shown that the above robust h sub spl infin filtering problem can be solved in terms of differential riccati inequalities with finite discrete jumps

a priori probabilities of separable quantum states zyczkowski horodecki sanpera and lewenstein zhsl recently proposed a natural measure on the n dimensional quantum systems but expressed surprise when it led them to conclude that for n 2 2 disentangled separable systems are more probable 0 632 0 002 in nature than entangled ones we contend however that zhsl s rejected intuition has in fact a sound theoretical basis and that the a priori probability of disentangled 2 2 systems should more properly be viewed as considerably less than 0 5 we arrive at this conclusion in two quite distinct ways the first based on classical and the second quantum considerations both approaches however replace in whole or part the zhsl product measure by ones based on the volume elements of monotone metrics which in the classical case amounts to adopting the jeffreys prior of bayesian theory only the quantum theoretic analysis which yields the smallest probabilities of disentanglement uses the minimum number of parameters possible that is n2 1 as opposed to n2 n 1 although this over parametrization as recently indicated by byrd should be avoidable however despite substantial computation we are not able to obtain precise estimates of these probabilities and the need for additional possibly supercomputer analyses is indicated particularly so for higher dimensional quantum systems such as the 2 3 ones which we also study here

moment based evidence for simple rational valued hilbert schmidt generic 2 2 separability probabilities employing the hilbert schmidt measure we explicitly compute and analyze a number of determinantal product bivariate moments k pt n k n 0 1 2 3 with pt denoting the partial transpose for both generic 9 dimensional two rebit and generic 15 dimensional two qubit 1 density matrices the results are then incorporated into a general formula parameterized by k n and with the case 2 presumptively corresponding to generic 27 dimensional quaternionic systems holding the dyson index like parameter fixed the induced univariate moments pt n and pt n are inputted into a legendre polynomial based least squares probability distribution reconstruction algorithm of provost 2005 mathematica j 9 727 yielding specific separability probability estimates since as the number of inputted moments grows estimates based on the variable pt strongly decrease while ones employing pt strongly increase and converge faster the gaps between upper and lower estimates diminish yielding sharper and sharper bounds remarkably for 2 with the use of 2325 moments a separability probability lower bound 0 999 999 987 as large as is found for 1 based on 2415 moments a lower bound results that is 0 999 997 066 times as large as a simpler still fractional value that had previously been conjectured slater 2007 j phys a math theor 40 14279 furthermore for employing 3310 moments the lower bound is 0 999 955 times as large as a rational value previously considered slater 2010 j phys a math theor 43 195302

lasalle type theorems for stochastic differential delay equations the main aim of this paper is to establish the lasalle type asymptotic convergence theorems for the solutions of stochastic differential delay equations these stochastic versions are then applied to establish sufficient criteria for the stochastically asymptotic stability of the delay equations several examples are also given for illustration

quantized output feedback control for networked control systems this paper addresses the problem of output feedback control for networked control systems ncss with limited communication capacity firstly we propose a new model to describe the non ideal network conditions and the input output state quantization of the ncss in a unified framework secondly based on our newly proposed model and an improved separation lemma the observer based controller is developed for the asymptotical stabilization of the ncss which are shown in terms of nonlinear matrices inequalities the nonlinear problems can be computed through solving a convex optimization problems and the observed and controller gains could be derived by solving a set of linear matrix inequalities thirdly two simulation examples are given to demonstrate the effectiveness of the proposed method

optimum performance levels for minimax filters predictors and smoothers abstract for both discrete and continuous time linear time varying systems we obtain the achievable performance levels for minimax filters predictors and smoothers in terms of the finite escape times of some related discrete and continuous time riccati equations our game theoretic approach also yields an alternative derivation for the corresponding minimax estimators which were first obtained in 1 they are all bayes estimators with respect to particular gaussian distributions and admit recursive structures

stability analysis of neutral type systems in hilbert space the asymtoptic stability properties of neutral type systems are studied mainly in the critical case when the exponential stability is not possible we consider an operator model of the system in hilbert space and use recent results on the existence of a riesz basis of invariant finite dimensional subspaces in order to verify its dissipativity the main results concern the conditions of asymptotic non exponential stability we show that the property of asymptotic stability is not determinated only by the spectrum of the system but essentially depends on the geometric spectral characteristic of its main neutral term moreover we present an example of two systems of neutral type which have both the same spectrum in the open left half plane and the main neutral term but one of them is asymptotically stable while the other is unstable

observer with evolutionary programming based optimal digital tracker for analog neutral multiple time delay systems abstract in this paper the finite time optimal hybrid tracking control problem for analog neutral systems with multiple discrete and distributed time delays is formulated and studied a novel approach that combining the evolutionary programming ep algorithm and the high gain property for analog neutral multiple time delay systems is proposed to achieve the best tracking performance for the first time first the newton center interpolation formula and the linear interpolation formula together with a modified rectangular rule and an augmented state vector are utilized to construct the equivalent digital linear models next according to the separation principle the control gains of the digital tracker and the digital observer are designed separately by the discrete time optimal control theory and prediction based digital redesign method and then combined together to form an observer based optimal time varying digital tracker eventually the process is to combine the high gain property with ep algorithm to search the optimal weighting matrices in the performance index to form an observer with ep based low gain digital tracker to achieve the objective of optimal tracking control an example is given for illustrating the effectiveness of the new tracker design method

on stabilization by state feedback for neutral differential difference equations in this paper we consider a class of feedback operators for a linear differential difference equation of the neutral type we show that if a system has unstable neutral root chains any stabilizing feedback operator in this class must contain a derivative of the delayed state component under the assumption of exact controllability we construct a stabilizing feedback operator

approximating the set of separable states using the positive partial transpose test the positive partial transpose test is one of the main criteria for detecting entanglement and the set of states with positive partial transpose is considered as an approximation of the set of separable states however we do not know to what extent this criterion as well as the approximation is efficient in this paper we show that the positive partial transpose test gives no bound on the distance of a density matrix from separable states more precisely we prove that as the dimension of the space tends to infinity the maximum trace distance of a positive partial transpose state from separable states tends to 1 using similar techniques we show that the same result holds for other well known separability criteria such as reduction criterion majorization criterion and symmetric extension criterion we also bring in evidence that the sets of positive partial transpose states and separable states have totally different shapes

multivariate ornstein uhlenbeck processes with mean field dependent coefficients application to postural sway we study the transient and stationary behavior of many particle systems in terms of multivariate ornstein uhlenbeck processes with friction and diffusion coefficients that depend nonlinearly on process mean fields mean field approximations of this kind of system are derived in terms of fokker planck equations in such systems multiple stationary solutions as well as bifurcations of stationary solutions may occur in addition strictly monotonically decreasing steady state autocorrelation functions that decay faster than exponential functions are found which are used to describe the erratic motion of the center of pressure during quiet standing

robust observers for neutral jumping systems with uncertain information in this paper the problem of designing observer for a class of uncertain neutral systems the uncertainties are parametric and norm bounded both robust observation and robust h observation methods are developed by using linear state delayed observers in case of robust observation sufficient conditions are established for asymptotic stability of the system which is independent of time delay the results are then extended to robust h observation which renders the augmented system asymptotically stable independent of delay with a guaranteed performance measure furthermore a memoryless state estimate feedback is designed to stabilize the closed loop neutral system in all cases the gain matrices are determined by linear matrix inequality approach two numerical examples are presented to illustrate the validity of the theoretical results

chaos from nonlinear markov processes why the whole is different from the sum of its parts abstract nonlinear markov processes have been frequently used to address bifurcations and multistability in equilibrium and non equilibrium many body systems however our understanding of the range of phenomena produced by nonlinear markov processes is still in its infancy we demonstrate that in addition to bifurcations and multistability nonlinear markov processes can exhibit another key phenomena well known in the realm of nonlinear physics chaos it is argued that chaotically evolving process probabilities are a generic feature of many body systems exhibiting nonlinear markov processes even if the isolated subsystems do not exhibit chaos that is when considering a nonlinear markov process as an entity of its own type then the nonlinear markov process in general is qualitatively different from its constituent subprocesses which reflects that the many body system as a whole is different from the sum of its parts

brief filtering on nonlinear time delay stochastic systems in this paper we address the filtering problem for a general class of nonlinear time delay stochastic systems the purpose of this problem is to design a full order filter such that the dynamics of the estimation error is guaranteed to be stochastically exponentially ultimately bounded in the mean square both filter analysis and synthesis problems are considered sufficient conditions are proposed for the existence of desired exponential filters which are expressed in terms of the solutions to algebraic riccati inequalities involving scalar parameters the explicit characterization of the desired filters is also derived a simulation example is given to illustrate the design procedures and performances of the proposed method

steady state kalman filtering with an h error bound abstract an estimator design problem is considered which involves both l 2 least squares and h worst case frequency domain aspects specifically the goal of the problem is to minimize an l 2 state estimation error criterion subject to a prespecified h constraint on the state estimation error the h estimation error constraint is embedded within the optimization process by replacing the covariance lyapunov equation by a riccati equation whose solution leads to an upper bound on the l 2 state estimation error the principal result is a sufficient condition for characterizing fixed order i e full and reduced order estimators with bounded l 2 and h estimation error the sufficient condition involves a system of modified riccati equations coupled by an oblique projection i e idempotent matrix when the h constraint is absent the sufficient condition specializes to the l 2 state estimation result given in 2

hilbert schmidt volume of the set of mixed quantum states we compute the volume of the convex n2 1 dimensional set n of density matrices of size n with respect to the hilbert schmidt measure the hyper area of the boundary of this set is also found and its ratio to the volume provides information about the structure of n similar investigations are also performed for the smaller set of all real density matrices as an intermediate step we analyse volumes of the unitary and orthogonal groups and of the flag manifolds

on robust stabilizability of linear differential difference systems with unstable d operator the robustness of linear delayed neutral type control systems with the unstable difference operator is considered the robustness analysis is stipulated by the impossibility of implementing precisely derivative feedback different approximations of stabilizing controls and their influence on the stability of the closed loop system are considered

periodic output feedback stabilization of neutral systems a new feedback control technique called periodic output feedback is investigated in the context of infinite dimensional linear systems modeled by neutral functional differential equations in this method discrete output samples are multiplied by a periodic gain function to generate a continuous feedback control this work focuses on stabilization of neutral systems with delayed control modeled in the state space w sub 2 sup 1 r 0 r sup n spl times l sup 2 r 0 r sup p where w sub 2 sup 1 r 0 r sup n denotes the sobolev space of r sup n valued absolutely continuous functions with square integrable derivatives on r 0 we show that a class of these systems can be stabilized by periodic output feedback even though their input operators are unbounded we overcome this difficulty by representing the system state using an abstract integral variation of constants formula an algorithm is presented at the end of this paper to construct a periodic output feedback gain function an example is provided to illustrate the construction of the gain function

stability analysis of stationary states of mean field models described by fokker planck equations abstract so far the stability of stationary solutions of mean field models described by fokker planck equations has only been determined analytically in some special cases following two earlier studies j korean phys soc 40 2002 1037 prog theoret phys suppl 150 2003 48 we discuss a stability analysis for a large class of mean field models based on fokker planck equations to this end we use linear stability analysis in addition to the well known approaches by means of transcendent equations and lyapunov s direct method we demonstrate that all three methods yield consistent results for systems that exhibit free energy functionals e g equilibrium systems we show that the simple transcendent equation analysis fails for systems that do not exhibit free energy functionals e g nonequilibrium systems and show how to solve this problem by means of a more sophisticated transcendent equation analysis furthermore we propose a norm for the perturbations of stationary states and illustrate some of our results by a model that exhibits a reentrant noise induced phase transition

input to state stable nonlinear filtering for a class of continuous time delayed nonlinear systems this paper investigates the input to state stable iss nonlinear filtering problem for a class of continuous time delayed nonlinear systems with external disturbance a new delay dependent nonlinear iss filter is established through available measurements to estimate the states of delayed nonlinear systems such that the filtering error system is both exponentially and input to state stable for any bounded external disturbance the design of the nonlinear iss filter for these nonlinear systems is achieved by solving a linear matrix inequality lmi which can be easily facilitated by using standard numerical packages an illustrative example is given to demonstrate the effectiveness of the proposed filter

entanglement thresholds for random induced states for a random quantum state on h c d otimes c d obtained by partial tracing a random pure state on h otimes c s we consider the whether it is typically separable or typically entangled for this problem we show the existence of a sharp threshold s 0 s 0 d of order roughly d 3 more precisely for any a 0 and for d large enough such a random state is entangled with very large probability when s 1 a s 0 one consequence of this result is as follows for a system of n identical particles in a random pure state there is a threshold k 0 k 0 n sim n 5 such that two subsystems of k particles each typically share entanglement if k k 0 and typically do not share entanglement if k k 0 our methods work also for multipartite systems and for unbalanced systems such as c d otimes c d d neq d the arguments rely on random matrices classical convexity high dimensional probability and geometry of banach spaces some of the auxiliary results may be of reference value a high level non technical overview of the results of this paper and of a related article arxiv 1011 0275 can be found in arxiv 1112 4582

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

robust kalman filtering for continuous time lag systems the linear continuous time kalman filter for a class of time lag systems with norm bounded uncertain parameters is considered we investigate the conditions for linear delayless state estimator such that the estimation error covariance is guaranteed to lie within a prescribed bound for all admissible uncertainties it is proven that a robust kalman filter algorithm can be determined in terms of two riccati equations involving scalar parameters the developed theory is illustrated by numerical simulation

robust kalman filtering for uncertain systems abstract this paper studies the problem of kalman filter design for uncertain systems the system under consideration is subjected to time varying norm bounded parameter uncertainties in both the state and measurement matrices the problem we address is the design of a state estimator such that the covariance of the estimation error is guaranteed to be within a certain bound for all admissible uncertainties a riccati equation approach is proposed to solve the above problem furthermore a suboptimal covariance upper bound can be computed by a convex optimization

filtering for a class of nonlinear mimo uncertain time delay stochastic systems in this article a high gain nonlinear observer based approach is proposed for filtering of nonlinear stochastic systems with time delays the system under consideration contains parameter uncertainties stochastic disturbances time delays as well as lipschitz like nonlinearities the objective is to design a robust filter such that the dynamics of the estimation error is guaranteed to be stochastically exponentially ultimately bounded in a sense of mean square a new high gain filter idea is introduced to solve the stochastic filtering problem by using the lyapunov method and stochastic analysis techniques the design of the proposed filter does not necessitate the resolution of any dynamics systems and its expression is explicitly given i e its calibration is achieved through the choice of a single parameter and does not rely on solving any matrix inequalities by numerical computation a simulation example is given to illustrate the performance of the proposed filter

spatiotemporal bounded noises and transitions induced by them in solutions of the real ginzburg landau model in this work we introduce two spatiotemporal colored bounded noises based on the zero dimensional cai lin and tsallis borland noises then we study and characterize the dependence of the defined stochastic processes on both a temporal correlation parameter ensuremath tau and a spatial coupling parameter ensuremath lambda in particular we found that varying ensuremath lambda may induce a transition of the distribution of the noise from bimodality to unimodality with the aim of investigating the role played by bounded noises in nonlinear dynamical systems we analyze the behavior of the real ginzburg landau time varying model additively perturbed by such noises the observed phase transition phenomenology is quite different from that observed when the perturbations are unbounded in particular we observed an inverse order to disorder transition and a reentrant transition with dependence on the specific type of bounded noise

ratios of maximal concurrence parameterized separability functions and generalized peres horodecki conditions the probability that a generic real complex or quaternionic two qubit state is separable can be considered to be the sum of three contributions one is from those states that are absolutely separable that is those which can not be entangled by unitary transformations for which the maximal concurrence over spectral orbits cmax is zero the other two contributions are from the states for which and for which we have previously arxiv 0805 0267 found exact formulas for the absolutely separable contributions in terms of the hilbert schmidt metric over the quantum states and here advance hypotheses as to the exact contributions for a crucial element in understanding the two contributions for cmax 0 is the nature of the ratio r of the cmax parameterized separability function for the complex states to the square of the comparable function for the real states both such functions having clearly displayed jump discontinuities at for the ratio r appears to be of the form 1 kcmax except near while for there is strong numerical evidence that it equals 2 thus according to the dyson index pattern of random matrix theory related phenomena also occur for the minimally degenerate two qubit states and the qubit qutrit states our results have immediate application to the computation of separability probabilities in terms of other metrics such as the bures minimal monotone metric the paper begins with continuous embeddings of the separability probability question in terms of four metrics of interest using generalized peres horodecki conditions

a note on stability and stabilizability of neutral systems this note presents frequency domain characterizations of exponential stability and stabilizability of neutral systems based on transfer function matrices and the existence of nice solutions of certain bezout equations it turns out that the existence of h sup spl infin solutions is not sufficient for exponential stabilizability but that they have to satisfy an additional growth assumption as well whilst the proofs of the authors results are based on an abstract infinite dimensional representation of the neutral system they emphasize that the results are expressed in terms of the original parameters of the neutral equation and do not require a reformulation of the system in an abstract state space form the sufficiency parts of the results hold even when the delay operator acting on the derivative contains a singular part

on the function space controllability of linear neutral systems a criterion is derived for approximate controllability of linear autonomous neutral functional differential equations in the sobolev space w 2 1 h 0 mathbb e n controllability conditions are based on an abstract evolution equation representation of the system an abstract criterion applicable to a general class of neutral systems is obtained and for the special case of matrix systems of the form frac d dt left x t a 1 x t h right e 0 x t e 1 x t h bu t this abstract criterion leads to an algebraic criterion

geometry of quantum systems density states and entanglement various problems concerning the geometry of the space of hermitian operators on a hilbert space are addressed in particular we study the canonical poisson and riemann jordan tensors and the corresponding foliations into k hler submanifolds it is also shown that the space of density states on an n dimensional hilbert space is naturally a manifold stratified space with the stratification induced by the the rank of the state thus the space of rank k states k 1 n is a smooth manifold of real dimension 2nk k2 1 and this stratification is maximal in the sense that every smooth curve in viewed as a subset of the dual to the lie algebra of the unitary group at every point must be tangent to the strata it crosses for a quantum composite system i e for a hilbert space decomposition an abstract criterion of entanglement is proved

kalman filtering for continuous time uncertain systems with markovian jumping parameters studies the problem of kalman filtering for a class of uncertain linear continuous time systems with markovian jumping parameters the system under consideration is subjected to time varying norm bounded parameter uncertainties in the state and measurement equations stochastic quadratic stability of the above system is analyzed a state estimator is designed such that the covariance of the estimation error is guaranteed to be within a certain bound for all admissible uncertainties which is in terms of solutions of two sets of coupled algebraic riccati equations

computing stochastic traveling waves the aim of this paper is to investigate new numerical methods for computing traveling wave solutions and new ways for estimating characteristic properties such as wave speed for stochastically forced partial differential equations as a particular example we consider the nagumo equation with multiplicative noise which we mainly consider in the stratonovich sense a standard approach for determining the position and hence speed of a wave is to compute the evolution of a level set we compare this approach against an alternative where the wave position is found by minimizing the l 2 norm against a fixed reference profile this approach can be used to freeze or stop the wave and obtain a stochastic partial differential algebraic equation that we then discretize and solve although attractive because it leads to a smaller domain size it can be numerically unstable due to large convection terms we compare numerically the different approaches for estimating the wave speed we use these techniques to investigate the effect of both ito and stratonovich noise on the nagumo equation as correlation length and noise intensity increase

stabilization in probability and mean square of controlled stochastic dynamical system with state delay abstract although stochastic dynamical systems have received a great deal of attention in terms of stabilization studies so far there are few works on controlled stochastic dynamical systems with state delay in this paper a controlled stochastic dynamical system represented by a stochastic differential equation with state delay is considered condition under which the system is exponentially stable in mean square and in probability is examined

advances in delimiting the hilbert schmidt separability probability of real two qubit systems we seek to derive the probability expressed in terms of the hilbert schmidt euclidean or flat metric that a generic nine dimensional real two qubit system is separable by implementing the well known peres horodecki test on the partial transposes pts of the associated 4 4 density matrices but the full implementation of the test requiring that the determinant of the pt be nonnegative for separability to hold appears to be at least presently computationally intractable so we have previously implemented using the auxiliary concept of a diagonal entry parameterized separability function desf the weaker implied test of nonnegativity of the six 2 2 principal minors of the pt this yielded an exact upper bound on the separability probability of here we piece together reflection symmetric results obtained by requiring that each of the four 3 3 principal minors of the pt in turn be nonnegative giving an improved reduced upper bound of then we conclude that a still further improved upper bound of can be found by similarly piecing together the reflection symmetric results of enforcing the simultaneous nonnegativity of certain pairs of the four 3 3 principal minors numerical simulations as opposed to exact symbolic calculations indicate on the other hand that the true probability is certainly less than our analyses lead us to suggest a possible form for the true desf yielding a separability probability of while the absolute separability probability of provides the best exact lower bound established so far in deriving our improved upper bounds we rely repeatedly upon the use of certain integrals over cubes that arise finally we apply an independence assumption to a pair of desfs that comes close to reproducing our numerical estimate of the true separability function

h and bibo stabilization of delay systems of neutral type frequency domain tests for the h and bibo stability of large classes of delay systems of neutral type are derived the results are applied to discuss the stabilizability of such systems by finite dimensional controllers

how often is a random quantum state k entangled the set of trace preserving positive maps acting on density matrices of size d forms a convex body we investigate its nested subsets consisting of kpositive maps where k 2 d working with the measure induced by the hilbert schmidt distance we derive asymptotically tight bounds for the volumes of these sets our results strongly suggest that the inner set of k 1 positive maps forms a small fraction of the outer set of k positive maps these results are related to analogous bounds for the relative volume of the sets of k entangled states describing a bipartite d d system

subnormalized states and trace nonincreasing maps we investigate the set of completely positive trace nonincreasing linear maps acting on the set mn of mixed quantum states of size n extremal point of this set of maps are characterized and its volume with respect to the hilbert schmidt hs euclidean measure is computed explicitly for an arbitrary n the spectra of partially reduced rescaled dynamical matrices associated with trace nonincreasing completely positive maps belong to the n cube inscribed in the set of subnormalized states of size n as a by product we derive the measure in mn induced by partial trace of mixed quantum states distributed uniformly with respect to the hs measure in mn2

dyson indices and hilbert schmidt separability functions and probabilities a confluence of numerical and theoretical results leads us to conjecture that the hilbert schmidt separability probabilities of the 15 and 9 dimensional convex sets of complex and real two

large time behaviour for functional differential equations with dominant eigenvalues of arbitrary order the spectral theory for linear autonomous neutral functional differential equations fde yields explicit formulas for the large time behaviour of solutions our results are based on resolvent computations and dunford calculus applied to establish explicit formulas for the large time behaviour of solutions of fde we investigate in detail a class of two dimensional systems of fde

bures volume of the set of mixed quantum states we compute the volume of the n2 1 dimensional set n of density matrices of size n with respect to the bures measure and show that it is equal to that of an n2 1 dimensional hyper hemisphere of radius 1 2 for n 2 we obtain the volume of the uhlmann hemisphere s3 4 we find also the area of the boundary of the set n and obtain analogous results for the smaller set of all real density matrices an explicit formula for the bures hall normalization constants is derived for an arbitrary n

stability results for discrete time linear systems with markovian jumping parameters stability results for discrete time linear systems subject to random jumps in the parameters are obtained first necessary and sufficient conditions for mean square stability mss including the case in which the system is driven by an independent wide sense stationary random sequence are derived it is shown that mss is equivalent to the spectral radius of an augmented matrix being less than one or to the existence of a solution of a certain lyapunov equation in addition it is shown that the lyapunov equation can be derived in four equivalent forms and as a by product each one gives risc to an easier to check sufficient condition these results give inter alia a unified and rather complete picture for mss of markovian jump linear systems next we derive sufficient conditions for almost sure stability of the noiseless ease finally we conclude by presenting an illustrative application to adaptive filtering where a mild condition for almost sure convergence is provided

an optimal stochastic production planning problem with randomly fluctuating dem and this paper considers an infinite horizon stochastic production planning problem with demand assumed to be a continuous time markov chain the problems with control production and state inventory constraints are treated it is shown that a unique optimal feedback solution exists after first showing that convex viscosity solutions to the associated dynamic programming equation are continuously differentiable

noise induced coupling and phase transition in initially homogeneous bistable system abstract we show that a colored spatial noise induces a heterogeneous behavior and coupling of initially uncoupled single bistable units a formal approximation reduces a non markovian stochastic process described by the initial set of equations into markovian process in terms of langevin equation for which a simple piecewise linear emulation was used to represent the nonlinear deterministic force it turned out that the coupling leads to a phase transition due to the noise induced diffusive term as an example a typical bistable noisy system with symmetric double well potential was studied

reentrant transition induced by multiplicative noise in the time dependent ginzburg landau model an effect of multiplicative noise in the time dependent ginzburg landau model is reported namely that noise at a relatively low intensity induces a phase transition towards an ordered state whereas strong noise plays a destructive role driving the system back to its disordered state through a reentrant phase transition the phase diagram is calculated analytically using a mean field theory and a more sophisticated approach and is compared with the results from extensive numerical simulations

technical communique robust h control of linear neutral systems this paper investigates the problems of robust stability and robust h control for a class of uncertain neutral systems the class describes linear state models with norm bounded uncertain system parameters and unknown constant state delay first we develop a sufficient condition for robust stability independent of delay then we provide sufficient conditions for designing a memoryless state feedback controller which stabilizes the uncertain neutral system under consideration and guarantees an h norm bound constraint on the disturbance attenuation for all admissible uncertainties and unknown state delay in both problems the results are expressed in the form of linear matrix inequalities it has been established that several earlier results are special cases of the developed theory

new filter design for linear time delay systems abstract this paper develops new robust delay dependent filter design for a class of linear systems with time varying delays and convex bounded parameter uncertainties the design procedure hinges upon the constructive use of an appropriate lyapunov functional plus a free weighting matrices in order to exhibit the delay dependent dynamics the developed approach utilizes smaller number of lmi decision variables thereby leading to less conservative solutions to the delay dependent stability and filtering problems subsequently linear matrix inequalities lmis based conditions are characterized such that the linear delay system is robustly asymptotically stable with an level l 2 gain all the developed results are tested on representative examples

delay dependent stability analysis and controller synthesis for markovian jump systems with state and input delays this paper focuses on the problem of delay dependent robust stochastic stability analysis and controller synthesis for markovian jump systems with state and input delays it is assumed that the delays are constant and unknown but their upper bounds are known by constructing a new lyapunov krasovskii functional and introducing some appropriate slack matrices new delay dependent stochastic stability and stabilization conditions are proposed by means of linear matrix inequalities lmis an important feature of the results proposed here is that all the robust stability and stabilization conditions are dependent on the upper bound of the delays memoryless state feedback controllers are designed such that the closed loop system is robustly stochastically stable some numerical examples are provided to illustrate the effectiveness of the proposed method

phase transitions induced by microscopic disorder a study based on the order parameter expansion based on the order parameter expansion we present an approximate method which allows us to reduce large systems of coupled differential equations with diverse parameters to three equations one for the global mean field variable and two which describe the fluctuations around this mean value the method is based on a systematic perturbation expansion and can be applied around the vicinity of the homogeneous state with this tool we analyze phase transitions induced by microscopic disorder in three prototypical models of phase transitions which have been studied previously in the presence of thermal noise we study how macroscopic order is induced or destroyed by time independent local disorder and analyze the limits of the approximation by comparing the results with the numerical solutions of the self consistency equation which arises from the property of self averaging finally we carry on a finite size analysis of the numerical results and calculate the corresponding critical exponents

a method for computing the interval of delay values for which a differential delay system is stable a test for determining the interval of delay values for which delay differential system is asymptotically stable is presented i e an explicit method is given for calculating h such that for 0

robust minimum variance filtering this paper deals with the robust minimum variance filtering problem for linear systems subject to norm bounded parameter uncertainty in both the state and the output matrices of the state space model the problem addressed is the design of linear filters having an error variance with a guaranteed upper bound for any allowed uncertainty two methods for designing robust filters are investigated the first one deals with constant parameter uncertainty and focuses on the design of steady state filters that yield an upper bound to the worst case asymptotic error variance this bound depends on an upper bound for the power spectrum density of a signal at a specific point in the system and it can be made tighter if a tight bound on the latter power spectrum can be obtained the second method allows for time varying parameter uncertainty and for general time varying systems and is more systematic we develop filters with an optimized upper bound for the error variance for both finite and infinite horizon filtering problems

robust filtering for a class of stochastic uncertain nonlinear time delay systems via exponential state estimation we investigate the robust filter design problem for a class of nonlinear time delay stochastic systems the system under study involves stochastics unknown state time delay parameter uncertainties and unknown nonlinear disturbances which are all often encountered in practice and the sources of instability the aim of this problem is to design a linear delayless uncertainty independent state estimator such that for all admissible uncertainties as well as nonlinear disturbances the dynamics of the estimation error is stochastically exponentially stable in the mean square independent of the time delay sufficient conditions are proposed to guarantee the existence of desired robust exponential filters which are derived in terms of the solutions to algebraic riccati inequalities the developed theory is illustrated by numerical simulation

a theorem on neutral delay systems abstract it is known that the stabilization of neutral delay differential tems requires first the stabilization of the difference operator or d operator in case all delays in the system are commensurable necessary and sufficient conditions for the existence of suitable derivative feedback for the stabilization of the d operator have been known for some time 14 in this note we derive a result in the case of noncommensurable delays analogous to the known results for the commensurable delay case