map estimation via agreement on trees message passing and linear programming we develop and analyze methods for computing provably optimal maximum a posteriori probability map configurations for a subclass of markov random fields defined on graphs with cycles by decomposing the original distribution into a convex combination of tree structured distributions we obtain an upper bound on the optimal value of the original problem i e the log probability of the map assignment in terms of the combined optimal values of the tree problems we prove that this upper bound is tight if and only if all the tree distributions share an optimal configuration in common an important implication is that any such shared configuration must also be a map configuration for the original distribution next we develop two approaches to attempting to obtain tight upper bounds a a tree relaxed linear program lp which is derived from the lagrangian dual of the upper bounds and b a tree reweighted max product message passing algorithm that is related to but distinct from the max product algorithm in this way we establish a connection between a certain lp relaxation of the mode finding problem and a reweighted form of the max product min sum message passing algorithm

simultaneous exact controllability and some applications we study the exact controllability of two systems by means of a common finite dimensional input function a property called simultaneous exact controllability most of the time we consider one system to be infinite dimensional and the other finite dimensional in this case we show that if both systems are exactly controllable in time t 0 and the generators have no common eigenvalues then they are simultaneously exactly controllable in any time t t0 moreover we show that similar results hold for approximate controllability for exactly controllable systems we characterize the reachable subspaces corresponding to input functions of class h1 and h2 we apply our results to prove the exact controllability of a coupled system composed of a string with a mass at one end finally we consider an example of two infinite dimensional systems we characterize the simultaneously reachable subspace for two strings controlled from a common end the result is obtained using a recent generalization of a classical inequality of ingham

marginal consistency upper bounding partition functions over commutative semirings many inference tasks in pattern recognition and artificial intelligence lead to partition functions in which addition and multiplication are abstract binary operations forming a commutative semiring by generalizing max sum diffusion one of convergent message passing algorithms for approximate map inference in graphical models we propose an iterative algorithm to upper bound such partition functions over commutative semirings the iteration of the algorithm is remarkably simple change any two factors of the partition function such that their product remains the same and their overlapping marginals become equal in many commutative semirings repeating this iteration for different pairs of factors converges to a fixed point when the overlapping marginals of every pair of factors coincide we call this state marginal consistency during that an upper bound on the partition function monotonically decreases this abstract algorithm unifies several existing algorithms including max sum diffusion and basic costraint propagation or local consistency algorithms in constraint programming we further construct a hierarchy of marginal consistencies of increasingly higher levels and show than any such level can be enforced by adding identity factors of higher arity order finally we discuss instances of the framework for several semirings including the distributive lattice and the max sum and sum product semirings

control of wave processes with distributed controls supported on a subregion it is proved that solutions of one dimensional wave equations satisfying general boundary conditions at the ends of a bounded interval i can be exactly controlled to any finite energy state by means of distributed controls which vanish outside of any fixed nonempty subinterval of i an example is given which shows that no such general analogous result can hold in higher dimensions in this case for a spherical region those states are characterized which can be exactly controlled to zero by means of controls supported in an annulus within the region it is found that very strong controllability obtains when the controls are distributed near the boundary but that only rather weak controllability is possible with controls supported in an interior annulus applications of these results to boundary control problems in annular regions are also discussed

stabilization of hybrid stochastic differential equations by feedback control based on discrete time state observations recently mao 2013 discusses the mean square exponential stabilization of continuous time hybrid stochastic differential equations by feedback controls based on discrete time state observations mao 2013 also obtains an upper bound on the duration between two consecutive state observations however it is due to the general technique used there that the bound on is not very sharp in this paper we will consider a couple of important classes of hybrid sdes making full use of their special features we will be able to establish a better bound on our new theory enables us to observe the system state less frequently so costs less but still to be able to design the feedback control based on the discrete time state observations to stabilize the given hybrid sdes in the sense of mean square exponential stability

admissibility of unbounded control operators for linear systems described by dot x t ax t bu t where a generates a semigroup on the state space x and b is an unbounded operator some necessary as well as some sufficient conditions are given for b to be admissible i e for any t the state x t should be in x and should depend continuously on the input u in l p this approach begins with an axiomatic description of such a system in terms of a functional equation the results are applied to the wave equation on a bounded interval

uniform controllability of semidiscrete approximations of parabolic control systems controlling an approximation model of a controllable infinite dimensional linear control system does not necessarily yield a good approximation of the control needed for the continuous model in the present paper under the main assumptions that the discretized semigroup is uniformly analytic and that the control operator is mildly unbounded we prove that the semidiscrete approximation models are uniformly controllable moreover we provide a computationally efficient way to compute the approximation controls an example of application is implemented for the one and two dimensional heat equation with neumann boundary control

on the cut polytope the cut polytopep c g of a graphg v e is the convex hull of the incidence vectors of all edge sets of cuts ofg we show some classes of facet defining inequalities ofp c g we describe three methods with which new facet defining inequalities ofp c g can be constructed from known ones in particular we show that inequalities associated with chordless cycles define facets of this polytope moreover for these inequalities a polynomial algorithm to solve the separation problem is presented we characterize the facet defining inequalities ofp c g ifg is not contractible tok 5 we give a simple characterization of adjacency inp c g and prove that for complete graphs this polytope has diameter one and thatp c g has the hirsch property a relationship betweenp c g and the convex hull of incidence vectors of balancing edge sets of a signed graph is studied

minimal time for the null controllability of parabolic systems the effect of the condensation index of complex sequences let a d a be a diagonalizable generator of a c0 semigroup of contractions on a complex hilbert space x b l c y y being some suitable extrapolation space of x and u l2 0 t c under some assumptions on the sequence of eigenvalues k k 1 c of a d a we prove the existence of a minimal time t0 0 depending on bernstein s condensation index of and on b such that y ay bu is null controllable at any time t t0 and not null controllable for t t0 as a consequence we solve controllability problems of various systems of coupled parabolic equations in particular new results on the boundary controllability of one dimensional parabolic systems are derived these seem to be difficult to achieve using other classical tools

discrete carleman estimates for elliptic operators in arbitrary dimension and applications in arbitrary dimension we consider the semidiscrete elliptic operator partial t 2 mathcal a scriptscriptstyle mathfrak m where mathcal a scriptscriptstyle mathfrak m is a finite difference approximation of the operator nabla x gamma x nabla x for this operator we derive a global carleman estimate in which the usual large parameter is connected to the discretization step size we address discretizations on some families of smoothly varying meshes we present consequences of this estimate such as a partial spectral inequality of the form of that proven by g lebeau and l robbiano for mathcal a scriptscriptstyle mathfrak m and a null controllability result for the parabolic operator partial t mathcal a scriptscriptstyle mathfrak m for the lower part of the spectrum of mathcal a scriptscriptstyle mathfrak m with the control function that we construct whose norm is uniformly bounded we prove that the l 2 norm of the final state converges to zero exponentially as the step size of the discretization goes to zero a relaxed observability estimate is then deduced

roof duality complementation and persistency in quadratic 0 1 optimization the paper is concerned with the primal problem of maximizing a given quadratic pseudo boolean function four equivalent problems are discussed the primal the complementation the discrete rhys lp and the weighted stability problem of a sam graph each of them has a relaxation the roof dual the quadratic complementation the continuous rhys lp and the fractional weighted stability problem of a sam graph the main result is that the four gaps associated with the four relaxations are equal furthermore a solution to any of these problems leads at once to solutions of the other three equivalent ones the four relaxations can be solved in polynomial time by transforming them to a bipartite maximum flow problem the optimal solutions of the roof dual define best linear majorantsp x off having the following persistency property if theith coefficient inp is positive negative thenx i 1 0 in every optimum of the primal problem several characterizations are given for the case where these persistency results cannot be used to fix any variable of the primal on the other hand a class of gap free functions properly including the supermodular ones is exhibited

the linear regulator problem for parabolic systems we present an approximation framework for computation in finite dimensional spaces of riccati operators that can be guaranteed to converge to the riccati operator in feedback controls for abstract evolution systems in a hilbert space it is shown how these results may be used in the linear optimal regulator problem for a large class of parabolic systems

propagation observation and control of waves approximated by finite difference methods this paper surveys several topics related to the observation and control of wave propagation phenomena modeled by finite difference methods the main focus is on the property of observability corresponding to the question of whether the total energy of solutions can be estimated from partial measurements on a subregion of the domain or boundary the mathematically equivalent property of controllability corresponds to the question of whether wave propagation behavior can be controlled using forcing terms on that subregion as is often desired in engineering applications observability controllability of the continuous wave equation is well understood for the scalar linear constant coefficient case that is the focus of this paper however when the wave equation is discretized by finite difference methods the control for the discretized model does not necessarily yield a good approximation to the control for the original continuous problem in other words the classical convergence consistency stability property of a numerical scheme does not suffice to guarantee its suitability for providing good approximations to the controls that might be needed in applications observability controllability may be lost under numerical discretization as the mesh size tends to zero due to the existence of high frequency spurious solutions for which the group velocity vanishes this phenomenon is analyzed and several remedies are suggested including filtering tychonoff regularization multigrid methods and mixed finite element methods we also briefly discuss these issues for the heat beam and schrodinger equations to illustrate that diffusive and dispersive effects may help to retain the observability controllability properties at the discrete level we conclude with a list of open problems and future subjects for research

rounding based moves for semi metric labeling semi metric labeling is a special case of energy minimization for pairwise markov random fields the energy function consists of arbitrary unary potentials and pairwise potentials that are proportional to a given semi metric distance function over the label set popular methods for solving semi metric labeling include i move making algorithms which iteratively solve a minimum st cut problem and ii the linear programming lp relaxation based approach in order to convert the fractional solution of the lp relaxation to an integer solution several randomized rounding procedures have been developed in the literature we consider a large class of parallel rounding procedures and design move making algorithms that closely mimic them we prove that the multiplicative bound of a move making algorithm exactly matches the approximation factor of the corresponding rounding procedure for any arbitrary distance function our analysis includes all known results for move making algorithms as special cases

exact controllability stabilization and perturbations for distributed systems exact controllability is studied for distributed systems of hyperbolic type or for petrowsky systems like plate equations the control is a boundary control or a local distributed control exact controllability consists in trying to drive the system to rest in a given finite time the solution of the problems depends on the function spaces where the initial data are taken and also depends on the function space where the control can be chosen a systematic method named hum for hilbert uniqueness method is introduced as the terminology indicates it is based on uniqueness results classical or new and on hilbert spaces constructed in infinitely many ways by using uniqueness a number of applications are indicated having a general method for exact controllability implies having a general method for stabilization this leads to new and complicated nonlinear riccati s type pdes to be compared with direct methods when available in the last part of the paper we consider how all this behaves fo

necessary conditions for exact controllability with a finite dimensional input space we derive necessary conditions for exact controllability of infinite dimensional systems described by x ax bu where the generator a has a riesz basis of eigenvectors and the input space is finite dimensional these conditions are in terms of the eigenvalues of a and the degree of unboundedness of b but no further information about b is needed our results easily imply lack of exact controllability for a wide range of distributed parameter systems it is known from partial differential equation pde examples that the addition of damping into an exactly controllable second order system can destroy exact controllability we discuss the effect of damping on such systems using our general conditions we also give simple new proofs for results about the lack of exact controllability of hyperbolic systems in more than one space dimension

the complexity of soft constraint satisfaction over the past few years there has been considerable progress in methods to systematically analyse the complexity of constraint satisfaction problems with specified constraint types one very powerful theoretical development in this area links the complexity of a set of constraints to a corresponding set of algebraic operations known as polymorphisms in this paper we extend the analysis of complexity to the more general framework of combinatorial optimisation problems expressed using various forms of soft constraints we launch a systematic investigation of the complexity of these problems by extending the notion of a polymorphism to a more general algebraic operation which we call a multimorphism we show that many tractable sets of soft constraints both established and novel can be characterised by the presence of particular multimorphisms we also show that a simple set of np hard constraints has very restricted multimorphisms finally we use the notion of multimorphism to give a complete classification of complexity for the boolean case which extends several earlier classification results for particular special cases

stabilization of regime switching processes by feedback control based on discrete time observations this work aims to extend x r mao s work automatica j ifac 49 2013 pp 3677 3681 on stabilization of hybrid stochastic differential equations by discrete time feedback control in x r mao s work the feedback control depends on discrete time observation of the state process but on continuous time observation of the switching process while in this work we study the feedback control depending on discrete time observations of the state process and the switching process our criteria depend explicitly on the regular conditions of the coefficients of the stochastic differential equation and on the stationary distribution of the switching process the sharpness of our criteria is shown through studying the stability of linear systems which also shows explicitly that the stability of hybrid stochastic differential equations depends essentially on the long time behavior of the switching process

robust stability and controllability of stochastic differential delay equations with markovian switching in this paper we investigate the almost surely asymptotic stability for the nonlinear stochastic differential delay equations with markovian switching some sufficient criteria on the controllability and robust stability are also established for linear stochastic differential delay equations with markovian switching

a linear programming approach to max sum problem a review the max sum labeling problem defined as maximizing a sum of binary i e pairwise functions of discrete variables is a general np hard optimization problem with many applications such as computing the map configuration of a markov random field we review a not widely known approach to the problem developed by ukrainian researchers schlesinger et al in 1976 and show how it contributes to recent results most importantly those on the convex combination of trees and tree reweighted max product in particular we review schlesinger et al s upper bound on the max sum criterion its minimization by equivalent transformations its relation to the constraint satisfaction problem the fact that this minimization is dual to a linear programming relaxation of the original problem and the three kinds of consistency necessary for optimality of the upper bound we revisit problems with boolean variables and supermodular problems we describe two algorithms for decreasing the upper bound we present an example application for structural image analysis

collective inference for extraction mrfs coupled with symmetric clique potentials many structured information extraction tasks employ collective graphical models that capture inter instance associativity by coupling them with various clique potentials we propose tractable families of such potentials that are invariant under permutations of their arguments and call them symmetric clique potentials we present three families of symmetric potentials max sum and majority we propose cluster message passing for collective inference with symmetric clique potentials and present message computation algorithms tailored to such potentials our first message computation algorithm called pass is sub quadratic in the clique size outputs exact messages for max and computes 13 15 approximate messages for potts a popular member of the sum family empirically it is upto two orders of magnitude faster than existing algorithms based on graph cuts or belief propagation our second algorithm based on lagrangian relaxation operates on majority potentials and provides close to exact solutions while being two orders of magnitude faster we show that the cluster message passing framework is more principled accurate and converges faster than competing approaches we extend our collective inference framework to exploit associativity of more general intra domain properties of instance labelings which opens up interesting applications in domain adaptation our approach leads to significant error reduction on unseen domains without incurring any overhead of model retraining

uniform exponential long time decay for the space semi discretization of a locally damped wave equation via an artificial numerical viscosity we consider the finite difference space semi discretization of a locally damped wave equation the damping being supported in a suitable subset of the domain under consideration so that the energy of solutions of the damped wave equation decays exponentially to zero as time goes to infinity the decay rate of the semi discrete systems turns out to depend on the mesh size h of the discretization and tends to zero as h goes to zero we prove that adding a suitable vanishing numerical viscosity term leads to a uniform with respect to the mesh size exponential decay of the energy of solutions this numerical viscosity term damps out the high frequency numerical spurious oscillations while the convergence of the scheme towards the original damped wave equation is kept we discuss this problem in 1d and 2d in the interval and the square respectively our method of proof relies on discrete multiplier techniques

new phenomena for the null controllability of parabolic systems minimal time and geometrical dependence abstract we consider the null controllability problem for two coupled parabolic equations with a space depending coupling term we analyze both boundary and distributed null controllability in each case we exhibit a minimal time of control that is to say a time t 0 0 such that the corresponding system is null controllable at any time t t 0 and is not if t t 0 in the distributed case this minimal time depends on the relative position of the control interval and the support of the coupling term we also prove that for a fixed control interval and a time 0 0 there exist coupling terms such that the associated minimal time is 0

stabilization of hybrid systems by feedback control based on discrete time state observations recently mao automatica j ifac 49 2013 pp 3677 3681 initiated the study the mean square exponential stabilization of continuous time hybrid stochastic differential equations by feedback controls based on discrete time state observations in the same paper mao also obtains an upper bound on the duration tau between two consecutive state observations however it is due to the general technique used there that the bound on tau is not very sharp in this paper we will be able to establish a better bound on tau making use of lyapunov functionals we will discuss the stabilization not only in the sense of exponential stability as mao does in automatica j ifac 49 2013 pp 3677 3681 but also in other sense that of h infty stability or asymptotic stability we will consider not only the mean square stability but also the almost sure stability

spectral analysis of discrete elliptic operators and applications in control theory in this paper we propose an analysis of discrete spectral properties for a finite difference discretization of quite general 1d second order self adjoint elliptic operators we particularly investigate some uniform in the discretization parameter qualitative behavior of eigenfunctions and eigenvalues with those estimates we manage to obtain new results for the construction of bounded families of controls for semi discrete parabolic pdes in particular for boundary controls of a coupled parabolic system with fewer controls than equations

uniform boundary controllability of a discrete 1 d wave equation a numerical scheme for the controlled discrete 1 d wave equation is considered we prove the convergence of the boundary controls of the discrete equations to a control of the continuous wave equation when the mesh size tends to zero when time and space steps coincide this positive result is in contrast with previous negative ones for space semi discretizations

an approximation theorem for the algebraic riccati equation for an infinite dimensional linear quadratic control problem in hilbert space approximation of the solution of the algebraic riccati operator equation in the strong operator topology is considered under conditions weaker than uniform exponential stability of the approximating systems as an application strong onvergence of the approximating riccati operators in case of a previously developed spline approximation scheme for delay systems is established finally convergence of the transfer functions of the approximating systems is investigated

stabilization of stochastic differential equations driven by g brownian motion with feedback control based on discrete time state observation abstract this paper mainly concerns the stability of the solutions for stochastic differential equations driven by g brownian motion g sdes via feedback control based on discrete time state observation more precisely the discrete time state feedback control is included in the drift coefficient of the g sdes by constructing an appropriate g lyapunov function a set of conditions is obtained for the h stability asymptotic stability and mean square exponential stability of the controlled systems finally an example with numerical simulation is presented to illustrate the effectiveness of the proposed control design technique

approximation of the controls for the wave equation with a potential this article deals with the approximation of the boundary controls of a 1 d linear wave equation with a variable potential by using a finite difference space semi discrete scheme due to the high frequency numerical spurious oscillations the semi discrete model is not uniformly controllable with respect to the mesh size and the convergence of the approximate controls cannot be guaranteed in this paper we analyze how do the initial data to be controlled and their discretization affect the approximation of the controls under certain conditions on the potential we prove that the convergence of the scheme is ensured if the highest frequencies of the discrete initial data have been previously filtered out several filtration procedures are proposed and analyzed moreover we identify a class of regular continuous initial data which can be controlled uniformly without any special treatment

iterative linear programming decoding of nonbinary ldpc codes with linear complexity the problem of low complexity linear programming lp decoding of nonbinary low density parity check ldpc codes is considered and an iterative lp decoding algorithm is presented results that were previously derived for binary ldpc codes are extended to the nonbinary case both simple and generalized nonbinary ldpc codes are considered it is shown how the algorithm can be implemented efficiently using a finite field fast fourier transform then the convergence rate of the algorithm is analyzed the complexity of the algorithm scales linearly in the block length and it can approximate up to an arbitrarily small relative error the objective function of the exact lp solution when applied to a typical code from an appropriate nonbinary ldpc code ensemble the algorithm can correct a constant fraction of errors in linear in the block length computational complexity computer experiments with the new iterative lp decoding algorithm show that in the error floor region it can have better performance compared to belief propagation decoding with similar computational requirements

null controllability of the heat equation using flatness we derive in a direct and rather straightforward way the null controllability of the n dimensional heat equation in a bounded cylinder with boundary control at one end of the cylinder we use the so called flatness approach which consists in parameterizing the solution and the control by the derivatives of a flat output this yields an explicit control law achieving the exact steering to zero replacing the involved series by partial sums we obtain a simple numerical scheme for which we give explicit error bounds numerical experiments demonstrate the relevance of the approach

optimal control of switching diffusions with application to flexible manufacturing systems a controlled switching diffusion model is developed to study the hierarchical control of flexible manufacturing systems the existence of a homogeneous markov nonrandomized optimal policy is established by a convex analytic method using the existence of such a policy the existence of a unique solution in a certain class to the associated hamilton jacobi bellman equations is established and the optimal policy is characterized as a minimizing selector of an appropriate hamiltonian

convergence estimates for semidiscrete approximations of nonselfadjoint parabolic equations semidiscrete galerkin approximations of the second order nonselfadjoint parabolic equations are considered l 2 error estimates for l 2 initial conditions are derived by use of semigroup methods and of analyticity of the underlined semigroup the scheme here presented can be also freely applied to nonconforming elements

revisiting the linear programming relaxation approach to gibbs energy minimization and weighted constraint satisfaction we present a number of contributions to the lp relaxation approach to weighted constraint satisfaction gibbs energy minimization we link this approach to many works from constraint programming which relation has so far been ignored in machine vision and learning while the approach has been mostly considered only for binary constraints we generalize it to n ary constraints in a simple and natural way this includes a simple algorithm to minimize the lp based upper bound n ary max sum diffusion however we consider using other bound optimizing algorithms as well the diffusion iteration is tractable for a certain class of high arity constraints represented as a black box which is analogical to propagators for global constraints csp diffusion exactly solves permuted n ary supermodular problems a hierarchy of gradually tighter lp relaxations is obtained simply by adding various zero constraints and coupling them in various ways to existing constraints zero constraints can be added incrementally which leads to a cutting plane algorithm the separation problem is formulated as finding an unsatisfiable subproblem of a csp

what is optimized in convex relaxations for multilabel problems connecting discrete and continuously inspired map inference in this work we present a unified view on markov random fields mrfs and recently proposed continuous tight convex relaxations for multilabel assignment in the image plane these relaxations are far less biased toward the grid geometry than markov random fields on grids it turns out that the continuous methods are nonlinear extensions of the well established local polytope mrf relaxation in view of this result a better understanding of these tight convex relaxations in the discrete setting is obtained further a wider range of optimization methods is now applicable to find a minimizer of the tight formulation we propose two methods to improve the efficiency of minimization one uses a weaker but more efficient continuously inspired approach as initialization and gradually refines the energy where it is necessary the other one reformulates the dual energy enabling smooth approximations to be used for efficient optimization we demonstrate the utility of our proposed minimization schemes in numerical experiments finally we generalize the underlying energy formulation from isotropic metric smoothness costs to arbitrary nonmetric and orientation dependent smoothness terms

boundary controllability of a linear semi discrete 1 d wave equation derived from a mixed finite element method in this article one discusses the controllability of a semi discrete system obtained by discretizing in space the linear 1 d wave equation with a boundary control at one extremity it is known that the semi discrete models obtained with finite difference or the classical finite element method are not uniformly controllable as the discretization parameter h goes to zero see 8 here we introduce a new semi discrete model based on a mixed finite element method with two different basis functions for the position and velocity we show that the controls obtained with these semi discrete systems can be chosen uniformly bounded in l 2 0 t and in such a way that they converge to the hum control of the continuous wave equation i e the minimal l 2 norm control we illustrate the mathematical results with several numerical experiments