event structures and trace monoids event structures are a poset based model for describing the behaviour of distributed systems they give rise to a well understood class of scott domains event structures are also related to petri nets in a fundamental way trace monoids are a string based formalism for describing the behaviour of distributed systems they have an independent theory rooted in the theory of formal languages here we obtain a representation of trace monoids in terms of a subclass of labelled event structures

prox penalization and splitting methods for constrained variational problems this paper is concerned with the study of a class of prox penalization methods for solving variational inequalities of the form ax n c x ni0 where mathcal h is a real hilbert space a mathcal h rightrightarrows mathcal h is a maximal monotone operator and n c is the outward normal cone to a closed convex set c subset mathcal h given psi mathcal h to mathbb r cup infty which acts as a penalization function with respect to the constraint x in c and a penalization parameter beta n we consider a diagonal proximal algorithm of the form x n i lambda n a beta n partial psi 1 x n 1 and an algorithm which alternates proximal steps with respect to a and penalization steps with respect to c and reads as x n i lambda n beta n partial psi 1 i lambda na 1 x n 1 we obtain weak ergodic convergence for a general maximal monotone operator a and weak convergence of the whole sequence x n when a is the subdifferential of a proper lower semicontinuous convex function mixing with passty s idea we can extend the ergodic convergence theorem thus obtaining the convergence of a prox penalization splitting algorithm for constrained variational inequalities governed by the sum of several maximal monotone operators our results are applied to an optimal control problem where the state variable and the control are coupled by an elliptic equation we also establish robustness and stability results that account for numerical approximation errors

asymptotic control and stabilization of nonlinear oscillators with non isolated equilibria let h r be a c1 function on a real hilbert space h and let 0 be a positive damping parameter for any control function e r r which tends to zero as t we study the asymptotic behavior of the trajectories of the damped nonlinear oscillator hbfc x t x t x t e t x t 0 we show that if e t does not tend to zero too rapidly as t then the term e t x t asymptotically acts as a tikhonov regularization which forces the trajectories to converge to a particular equilibrium indeed in the main result of this paper it is established that when is convex and s argmin under the key assumption that e is a slow control i e 0 e t dt then each trajectory of the hbfc system strongly converges as t to the element of minimal norm of the closed convex set s as an application we consider the damped wave equation with neumann boundary condition formula

on the decidability and complexity of diagnosability for labeled petri nets in this paper we investigate the decidability and complexity of the fault diagnosis problem in unbounded labeled petri nets first we show that checking diagnosability for unbounded petri nets is decidable we present a new necessary and sufficient condition for diagnosability which can be reduced to a model checking problem for unbounded petri nets then we show that checking diagnosability for unbounded petri nets is expspace complete this complexity result is further extended to various subclasses of petri nets to the best of our knowledge this is the first paper that establishes decidability and complexity results for diagnosability of unbounded petri nets

schemes for finding minimum norm solutions of variational inequalities abstract consider the variational inequality vi of finding a point x such that x f i x t and i s x x x 0 x f i x t where t s are nonexpansive self mappings of a closed convex subset c of a hilbert space and f i x t is the set of fixed points of t assume that the solution set of this vi is nonempty this paper introduces two schemes one implicit and one explicit that can be used to find the minimum norm solution of vi namely the unique solution x to the quadratic minimization problem x arg min x x 2

well behaved flow event structures for parallel composition and action refinement flow event structures were introduced as a model for giving semantics to process algebras however it turned out that certain restrictions have to be made to make them suitable for this purpose in this paper we investigate subclasses of flow event structures which are both suited for the process algebraic composition operators and for action refinement as a means of regarding processes on different levels of abstraction first suitable subclasses are characterised then two specific subclasses are proposed the larger class generalises the one from castellani and zhang theoret comput sci 179 1997 203 215 which is not suitable for action refinement the smaller one is still sufficiently expressive for dealing with all standard process algebras and action refinement

convergence of a hybrid projection proximal point algorithm coupled with approximation methods in convex optimization in order to minimize a closed convex function that is approximated by a sequence of better behaved functions we investigate the global convergence of a general hybrid iterative algorithm which consists of an inexact relaxed proximal point step followed by a suitable orthogonal projection onto a hyperplane the latter permits to consider a fixed relative error criterion for the proximal step we provide various sets of conditions ensuring the global convergence of this algorithm the analysis is valid for nonsmooth data in infinite dimensional hilbert spaces some examples are presented focusing on penalty barrier methods in convex programming we also show that some results can be adapted to the zero finding problem for a maximal monotone operator

a partial ordering semantics for ccs a new operational semantics for pure ccs is proposed that considers the parallel operator as a first class one and permits a description of the calculus in terms of partial orderings the new semantics also for unguarded agents is given in the sos style via the partial ordering derivation relation ccs agents are decomposed into sets of sequential subagents the new derivations relate sets of subagents and describe their actions and the casual dependencies among them the computations obtained by composing partial ordering derivations are observed either as interleaving or partial orderings of events interleavings coincide with milner s many step derivations and linearizations of partial orderings are all and only interleavings abstract semantics are obtained by introducing two relations of observational equivalence and congruence that preserve concurrency these relations are finer than milner s in that they distinguish interleaving of sequential nondeterministic agents from their concurrent execution

maximum likelihood parameter estimation of discrete homogeneous random fields with mixed spectral distributions this paper presents a maximum likelihood solution to the general problem of fitting a parametric model to observations from a single realization of a real valued 2 d homogeneous random field with mixed spectral distribution on the basis of a 2 d wold like decomposition the field is represented as a sum of mutually orthogonal components of three types purely indeterministic harmonic and evanescent the proposed algorithm provides a complete solution to the joint estimation problem of the random field components by introducing appropriate parameter transformations the highly nonlinear least squares problem that results from the maximization of the likelihood function is transformed into a separable least squares problem in this new problem the solution for the unknown spectral supports of the harmonic and evanescent components reduces the problem of solving for the transformed parameters of the field to linear least squares solution of the transformation equations provides a complete solution of the field model parameter estimation problem

determinism event structure isomorphism step sequence equivalence abstract a concurrent system s is called determinism if for all states s of s we have that whenever s can evolve from state s into states s and s by doing an action a it must be the case that s equals s it is well known that for deterministic concurrent systems most of the interleaved equivalences bisimulation failure trace equivalence coincide in this paper we prove in the setting of event structures that also most of the non interleaved equivalences coincide with each other on this domain in the last section of the paper we show that as a consequence of our result the causal structure of a deterministic concurrent system can be unravelled by observers who are capable of observing the beginning and termination of events

infinitesimal robustness for autoregressive processes we define the influence function and construct optimal robust estimators for autoregressive processes we show that the asymptotic bias caused by small contaminations of the marginals can be written as the integral of a certain function with respect to the contamination this function is called the influence function it is unique only up to an equivalence relation but there is a natural unique version which describes the limiting influence of an additional observation given the previous observations moreover with this version the asymptotic variance at the true model can be expressed in a simple form optimal robust estimators minimize this asymptotic variance under a constraint on the influence function as in the i i d case they are found by truncating a multiple of the influence function of the maximum likelihood estimator

proximal point algorithm controlled by a slowly vanishing term applications to hierarchical minimization let phi 0 mathbb r n to mathbb r cup infty be a closed convex function and phi 1 mathbb r n to mathbb r be a finite convex function that are bounded from below our goal is to build an algorithm which first minimizes the map phi 0 and secondly the map phi 1 over the set s 0 rm argmin phi 0 for that purpose we define the following proximal type algorithm x n 1 x n lambda n in partial eta n phi 0 varepsilon n phi 1 x n 1 leqno mathcal a 1 where lambda n is a positive step sequence eta n is a summable error sequence and varepsilon n is a control sequence tending toward 0 partial eta denotes the eta approximate subdifferential when varepsilon n is a slow control i e sum n 0 infty varepsilon n infty we prove that under adequate conditions the sequence x n defined by mathcal a 1 tends toward an element of s 1 rm argmin s 0 phi 1 more generally given finite convex functions phi 2 ldots phi n mathbb r n to mathbb r let us define the sets s i i in 1 ldots n by the recursive relation s i rm argmin s i 1 phi i we introduce an extension of algorithm mathcal a 1 to minimize hierarchically each function phi i on the set s i 1 for i in 1 ldots n

asymptotic behavior of coupled dynamical systems with multiscale aspects abstract we study the asymptotic behavior as time variable t goes to of nonautonomous dynamical systems involving multiscale features as a benchmark case given h a general hilbert space h r and h r two closed convex functions and a function of t which tends to as t goes to we consider the differential inclusion x t x t t x t 0 this system models the emergence of various collective behaviors in game theory as well as the asymptotic control of coupled systems we show several results ranging from weak ergodic to strong convergence of the trajectories as a key ingredient we assume that for every p belonging to the range of n c 0 t p t c p t d t where is the fenchel conjugate of c is the support function of c argmin and n c x is the normal cone to c at x as a by product we revisit the system x t t x t x t 0 where t tends to zero as t goes to and 0 t d t whose asymptotic behavior can be derived from the preceding one by time rescaling applications are given in game theory optimal control variational problems and pdes

a robust nonlinear filter for image restoration a class of nonlinear regression filters based on robust estimation theory is introduced the goal of the filtering is to recover a high quality image from degraded observations models for desired image structures and contaminating processes are employed but deviations from strict assumptions are allowed since the assumptions on signal and noise are typically only approximately true the robustness of filters is usually addressed only in a distributional sense i e the actual error distribution deviates from the nominal one in this paper the robustness is considered in a broad sense since the outliers may also be due to inappropriate signal model or there may be more than one statistical population present in the processing window causing biased estimates two filtering algorithms minimizing a least trimmed squares criterion are provided the design of the filters is simple since no scale parameters or context dependent threshold values are required experimental results using both real and simulated data are presented the filters effectively attenuate both impulsive and nonimpulsive noise while recovering the signal structure and preserving interesting details

asymptotic behavior of solutions to a class of nonlinear evolution equations on etudie les equations de la chaleur a controle de temperature a l interieur ou sur la frontiere du domaine pour cela on considere un type de problemes variationnels paraboliques avec obstacles

two dimensional harmonic retrieval and its time domain analysis technique the two dimensional harmonic retrieval is examined in theory by confirming that the 2 d sinusoids in white noise are modeled as a special 2 d autoregressive moving average arma process whose ar parameters are identical to the ma ones a new analysis technique for resolving 2 d sinusoids in white noise is proposed

petri nets are moniods abstract petri nets are widely used to model concurrent systems however their composition and abstraction mechanisms are inadequate we solve this problem in a satisfactory way we start by remarking that place transition petri nets can be viewed as ordinary directed graphs equipped with two algebraic operations corresponding to parallell and sequential composition of transitions a distributive law between the two operations captures a basic fact about concurrency new morphisms are defined mapping single atomic transitions into whole computations thus relating system descriptions at different levels of abstraction categories equipped with products and coproducts corresponding to parallel and nondeterministic compositions are introduced for petri nets with and without initial markings petri net duality is expressed as a duality functor and several new invariants are introduced a tensor product is defined on nets and their category is proved to be symmetric monoidal closed this construction is generalized to a large class of algebraic theories on graphs these results provide a formal basis for expressing the semantics of concurrent languages in terms of petri nets they also provide a new understanding of concurrency in terms of algebraic structures over graphs and categories that should apply to other models besides petri nets and thus contribute to the conceptual unification of concurrency

regularized and inertial algorithms for common fixed points of nonlinear operators this paper deals with a general fixed point iteration for computing a point in some nonempty closed and convex solution set included in the common fixed point set of a sequence of mappings on a real hilbert space the proposed method combines two strategies viscosity approximations regularization and inertial type extrapolation the first strategy is known to ensure the strong convergence of some successive approximation methods while the second one is intended to speed up the convergence process under classical conditions on the operators and the parameters we prove that the sequence of iterates generated by our scheme converges strongly to the element of minimal norm in the solution set this algorithm works for instance for approximating common fixed points of infinite families of demicontractive mappings including the classes of quasi nonexpansive operators and strictly pseudocontractive ones

regularized algorithms for hierarchical fixed point problems abstract let c be a nonempty closed convex subset of a real hilbert space h let s c c be a non expansive mapping and t i i 1 c c be an infinite family of non expansive mappings the purpose of this paper is to find the minimum norm solution of the following general hierarchical fixed point problem find x n 1 f i x t n such that x s x x x 0 x n 1 f i x t n we introduce an explicit regularized algorithm with strong convergence for finding the minimum norm solution of the above hierarchical fixed point problem

asymptotic control and stabilization of nonlinear oscillators with non isolated equilibria a note from l 1 to non l 1 in h attouch m o czarnecki asymptotic control and stabilization of non linear oscillators with non isolated equilibria j differential equations 179 2002 278 310 we exhibited a sharp condition ensuring the efficiency of the tikhonov like control term in the hbfc system precisely let h r be a c1 function on a real hilbert space h let 0 be a positive damping parameter and let r r be a control function which decreases to zero as t in order to select particular equilibria in the important case where has non isolated equilibria we introduced in h attouch m o czarnecki j differential equations 179 2002 278 310 the following damped nonlinear oscillator and studied its asymptotic behavior hbfc x t x t x t t x t 0 we established that when is convex and s argmin under the key assumption that is a slow control i e 0 t dt then each trajectory of the hbfc system strongly converges when t to the element of minimal norm of the closed convex set s the condition on the control term is sharp indeed when 0 t dt the trajectory weakly converges but it may not strongly converge and we have no information a priori on the weak limit in this note we give an answer to the following question when does an l1 control term becomes or behave non l1 precisely take a control term l1 let x be the solution of the corresponding hbfc system take n to be a non increasing truncation of n t t for t 0 n let x be the solution of the corresponding hbfc system we show that limn xn x 0 in particular the weak limits of the trajectories xn strongly converge when n to the strong limit of the trajectory x in other words there is no loss of the information gained by the slow behavior for t n

hybrid methods for a class of monotone variational inequalities abstract we use contractions to regularize a class of monotone variational inequalities where the monotone operators are complements of nonexpansive mappings and the solutions are sought in the set of fixed points of another nonexpansive mapping such variational inequalities include monotone inclusions and convex optimization problems to be solved over the fixed point sets of nonexpansive mappings both implicit and explicit schemes are shown to be strongly convergent an application in hierarchical minimization is included

asymptotic behavior of nonautonomous monotone and subgradient evolution equations in a hilbert setting h we study the asymptotic behavior of the trajectories of nonautonomous evolution equations dot x t a t x t ni 0 where for each t geq 0 a t h rightrightarrows h denotes a maximal monotone operator we provide general conditions guaranteeing the weak ergodic convergence of each trajectory x cdot to a zero of a limit maximal monotone operator a infty as the time variable t tends to infty the crucial point is to use the brezis haraux function or equivalently the fitzpatrick function to express at which rate the excess of mathrm gph a infty over mathrm gph a t tends to zero this approach gives a sharp and unifying view of this subject in the case of operators a t partial phi t which are subdifferentials of proper closed convex functions phi t we show convergence results for the trajectories then we specialize our results to multiscale evolution equations and obtain asymptotic properties of hierarchical minimization and selection of viscosity solutions illustrations are given in the field of coupled systems and partial differential equations

complexity results for 1 safe nets we study the complexity of several standard problems for 1 safe petri nets and some of its subclasses we prove that reachability liveness and deadlock are all pspace complete for 1 safe nets we also prove that deadlock is np complete for free choice nets and for 1 safe free choice nets finally we prove that for arbitrary petri nets deadlock is equivalent to reachability and liveness

zero safe nets comparing the collective and individual token approaches abstract the main feature of zero safe nets is a primitive notion of transition synchronization to this aim besides ordinary places called stable places zero safe nets are equipped with zero places which in an observable marking cannot contain any token this yields the notion of transaction a basic atomic computation which may use zero tokens as triggers but defines an evolution between observable markings only the abstract counterpart of a generic zero safe net b consists of an ordinary p t net whose places are the stable places of b and whose transitions represent the transactions of b the two nets offer the refined and the abstract models of the same system respectively where the former can be much smaller than the latter because of the transition synchronization mechanism depending on the chosen approach collective vs individual token philosophy two notions of transaction may be defined each leading to different operational and abstract models their comparison is fully discussed on the basis of a multicasting system example in the second part of the paper we make use of category theory to analyze and motivate our framework more precisely the two operational semantics of zero safe nets are characterized as adjunctions and the derivation of abstract p t nets as coreflections

unfolding semantics of graph transformation several attempts have been made of extending to graph grammars the unfolding semantics originally developed by winskel for safe petri nets but only partial results were obtained in this paper we fully extend winskel s approach to single pushout grammars providing them with a categorical concurrent semantics expressed as a coreflection between the category of semi weighted graph grammars and the category of prime algebraic domains which factorises through the category of occurrence grammars and the category of asymmetric event structures for general possibly nonsemi weighted single pushout grammars we define an analogous functorial concurrent semantics which however is not characterised as an adjunction similar results can be obtained for double pushout graph grammars under the assumptions that nodes are never deleted

coloured petri nets and the invariant method abstract in many systems a number of different processes have a similar structure and behaviour to shorten system description and system analysis it is desirable to be able to treat such similar processes in a uniform and succinct way in this paper it is shown how petri nets can be generalized to allow processes to be described by a common subnet without losing the ability to distinguish between them our generalization called coloured petri nets is heavily influenced by predicate transition nets introduced by h j genrich and k lautenbach moreover our paper shows how the invariant method introduced for petri nets by k lautenbach can be generalized to coloured petri nets

non interleaving semantics for mobile processes abstract this paper studies causality in the calculus our notion of causality combines the dependencies given by the syntactic structure of processes with those originated by passing names our studies show that two transitions not causally related may however occur in a fixed ordering in any computation i e the calculus may implicitly express a precedence between actions the same partial order of transitions is associated with all the computations that are obtained by shuffling transitions that are concurrent i e related neither by causality nor by precedence other non interleaving semantics are investigated and compared the presentation takes advantage of a parametric definition of process behaviour given in sos style that permits us to take almost for free the interleaving theory and tools finally we extend our approach to higher order calculus enriched with a spawn operation

on two dimensional markov spectral estimation we give systematic methods for two dimensional 2 d spectral estimation from raw data using gaussian markov random field mrf models the mrf models considered in this paper characterize the statistical dependence of the observation y s on its neighbors in all directions due to the modeling assumption the 2 d spectrum is an explicit function of the parameters of the mrf model thus the spectral estimation problem reduces to that of estimating the appropriate structure and the parameters of the mrf model a tractable algorithm for maximum likelihood ml estimation of parameters is obtained by using doubly periodic boundary conditions for the given data asymptotically consistent decision rules are used to choose the appropriate neighbor set of the mrf model the mrf spectral estimate obtained using the doubly periodic boundary conditions has the property that its inverse discrete fourier transforms are in perfect agreement with the periodic sample correlation values of the given observations over a symmetric window identical to the structure of the mrf model using this result and the fact that the 2 d maximum entropy spectral mes estimate has a structure similar to the mrf power spectrum we show that the mrf spectral estimate developed in this paper is a good approximation to the mes estimate this result provides a reasonable basis i e maximum likelihood on which to justify the use of the mes estimate with correlation estimates obtained from a finite piece of data samples

a robust approach for high resolution frequency estimation a robust estimation method for frequencies of received signals is considered the influence function of a robust estimate is derived for the sinusoidal signals the variance of the robust estimate is also derived using the influence function it is found that the robust estimate attains the cramer rao lower bound crlb for the contaminated gaussian distribution it is of order o n sup 3 and is close to the crlb for the perfect gaussian distribution the authors introduce some basic definitions for the high resolution frequency estimation method and prove that the robust estimate has the high resolution property this property is also confirmed by numerical simulations

two dimensional spectrum estimation using noncausal autoregressive models two dimensional 2 d spectrum estimation from raw data is of interest in signal and image processing a parametric technique for spectrum estimation using 2 d noncausal autoregressive ncar models is given the ncar models characterize the statistical dependency of the observation at location s on its neighbors in all directions this modeling assumption reduces the spectrum estimation problem to two subproblems the choice of appropriate structure of the ncar model and the estimation of parameters in ncar models by assuming that the true structure of the ncar model is known we first analyze the existence and uniqueness of gaussian maximum likelihood gml estimates of ncar model parameters due to the noncausal nature of the models the computation of gml estimates is burdensome by assuming specific boundary conditions computationally tractable expressions are obtained for the likelihood function expressions for the asymptotic covariance matrix of the gml estimates as well as the simultaneous confidence bands for the estimated spectrum using gml estimates are derived finally the usefulness of the method is illustrated by computer simulation results

weak pullback attractors of setvalued processes weak pullback attractors are defined for nonautonomous setvalued processes and their existence and upper semicontinuous convergence under perturbation is established unlike strong pullback attractors invariance and pullback attraction here are required only for at least one trajectory rather than all trajectories at each starting point the concept is useful in for example continuous time control systems and is related to that of viability

asymptotic control of pairs of oscillators coupled by a repulsion with nonisolated equilibria ii the singular case let phi h rightarrow mathbb r be a mathcal c 1 function on a real hilbert space h and let gamma 0 be a positive damping parameter for any singular repulsive potential v h setminus 0 to mathbb r i e such that lim z to 0 v z infty and any control function varepsilon mathbb r to mathbb r setminus 0 which tends to zero as t to infty we study the asymptotic behavior of the trajectories of the coupled dissipative system of nonlinear oscillators left begin array l ddot x gamma dot x nabla phi x varepsilon t nabla v x y 0 vspace 1mm ddot y gamma dot y nabla phi y varepsilon t nabla v x y 0 end array right leqno rm hbfc 2 sing this system is the singular version of the regular rm hbfc 2 reg system studied in a cabot and m o czarnecki siam j control optim 41 2002 pp 1254 1280 where the potential v is defined on the whole space h the purpose of this paper is to obtain whenever possible the same existence and convergence results in the singular case as in the regular case considered by a cabot and m o czarnecki this study is mainly motivated by a better convergence behavior of rm hbfc 2 sing with the same sharp condition on the control varepsilon exhibited in h attouch and m o czarnecki j differential equations 179 2002 pp 278 310 and by a cabot and m o czarnecki precisely when h mathbb r and if varepsilon is a slow control i e int 0 infty varepsilon t dt infty then the trajectories x and y converge to extremal points of the set s lambda in mathbb r nabla phi lambda 0 of the equilibria of phi the awkward case in a cabot and m o czarnecki where the trajectories may have the same limit disappears of importance from a physical point of view we thus can consider actual for example electromagnetic repulsive potentials

two dimensional robust spectrum estimation robust estimation is studied of two dimensional 2 d power spectra of signals which are adequately represented by gaussian random field models but for which there are imperfect observations two situations of particular interest occur when the contaminating noise is additive and when the contaminating noise appears in the innovations in these cases the observed data are not gaussian and conventional procedures are no longer efficient to estimate the parameters of the signal model from the contaminated data two procedures are described which were originally proposed for estimation of scale and location from independent data and adapted to one dimensional autoregression parameter estimation by previous researchers the first algorithm is a robustification of least squares and equivalent to an iterated weighted least squares problem where the weights are data dependent the second algorithm is an iterative procedure known as a filter cleaner experiments using the robust procedures with synthetic data are reported and the results compared to a conventional method of model based spectrum estimation

petri nets event structures and domains part i abstract the general aim of this paper is to find a theory of concurrency combining the approaches of petri and scott and others in part i we introduce our formalisms to connect the abstract ideas of events and domains of information we show how casual nets induce certain kinds of domains where the information points are certain sets of events this allows translations between the languages of net theory and domain theory following the idea that events of causal nets are occurrences we generalise causal nets to occurrence nets by adding forwards conflict just as infinite flow charts unfold finite ones so transition nets can be unfolded into occurrence nets next we extend the above connections between nets and domains to these new nets event structures which are intermediate between nets and domains play an important part in all our work finally as an example of how concepts translate from one formalism to the other we show how petri s notion of confusion ties up with kahn and plotkin s concrete domains in part ii we shall continue the job of connecting up notions within net theory and the theory of domains in particular we shall examine the idea of states of computations

on the expressiveness of higher dimensional automata in this paper i compare the expressive power of several models of concurrency based on their ability to represent causal dependence to this end i translate these models in behaviour preserving ways into the model of higher dimensional automata hda which is the most expressive model under investigation in particular i propose four different translations of petri nets corresponding to the four different computational interpretations of nets found in the literature i also extend various equivalence relations for concurrent systems to hda these include the history preserving bisimulation which is the coarsest equivalence that fully respects branching time causality and their interplay as well as the st bisimulation a branching time respecting equivalence that takes causality into account to the extent that it is expressible by actions overlapping in time through their embeddings in hda it is now well defined whether members of different models of concurrency are equivalent

bounds on the accuracy of estimating the parameters of discrete homogeneous random fields with mixed spectral distributions this paper considers the achievable accuracy in jointly estimating the parameters of a real valued two dimensional 2 d homogeneous random field with mixed spectral distribution from a single observed realization of it on the basis of a 2 d wold like decomposition the field is represented as a sum of mutually orthogonal components of three types purely indeterministic harmonic and evanescent an exact form of the cramer rao lower bound on the error variance in jointly estimating the parameters of the different components is derived it is shown that the estimation of the harmonic component is decoupled from that of the purely indeterministic and the evanescent components moreover the bound on the parameters of the purely indeterministic and the evanescent components is independent of the harmonic component numerical evaluation of the bounds provides some insight into the effects of various parameters on the achievable estimation accuracy

alternating proximal algorithms for linearly constrained variational inequalities application to domain decomposition for pde s abstract let x y z be real hilbert spaces let f x r g y r be closed convex functions and let a x z b y z be linear continuous operators let us consider the constrained minimization problem p min f x g y a x b y given a sequence n which tends toward 0 as n we study the following alternating proximal algorithm a x n 1 argmin n 1 f 1 2 a b y n z 2 2 x n x 2 x y n 1 argmin n 1 g 1 2 a x n 1 b z 2 2 y n y 2 y where and are positive parameters it is shown that if the sequence n tends moderately slowly toward 0 then the iterates of a weakly converge toward a solution of p the study is extended to the setting of maximal monotone operators for which a general ergodic convergence result is obtained applications are given in the area of domain decomposition for pde s

an event structure semantics for general petri nets abstract in this paper we address the following question what type of event structures are suitable for representing the behaviour of general petri nets as a partial answer to this question we define a new class of event structures called local event structures and identify a subclass called ul event structures we propose that ul event structures are appropriate for capturing the behaviour of general petri nets our answer is a partial one in that in the proposed event structure semantics auto concurrency is filtered out from the behaviour of petri nets it turns out that this limited event structure semantics for petri nets is nevertheless a non trivial and conservative extension of the prime event structure semantics of 1 safe petri nets provided in nielsen et al 1981 we also show that the strong relationship between prime event structures and 1 safe petri nets established in a categorical framework in winskel 1987 can be extended to the present setting provided we restrict our attention to the subclass of petri nets whose behaviours do not exhibit any auto concurrency finally we show that winskel s general and stable event structures can be smoothly related to local event structures and that similarly prime event structures can be related to ul event structures

texture synthesis using 2 d noncausal autoregressive models the purpose of this paper is to illustrate the usefulness of two dimensional noncausal autoregressive ncar models for the synthesis of textures these models characterize the gray level at a pixel as a linear combination of gray levels at nearby locations in all directions and an additive white noise variable we first show that the class of ncar models is capable of generating a wide variety of image patterns posessing the local replication attribute an essential ingredient of many natural textures it is also shown that the theoretical variograms of many ncar models possess an oscillatory behavior a characteristic of the variograms of many natural textures next we give experimental results of synthesis of 64 64 textures resembling several real textures in the brodatz album the synthetic textures generated by 16 parameter ncar models retain most the visual characteristics of the original textures the variograms of the original and synthetic textures are also similar

a convergence result for nonautonomous subgradient evolution equations and its application to the steepest descent exponential penalty trajectory in linear programming abstract we present a new result on the asymptotic behavior of nonautonomous subgradient evolution equations of the form u t t u t where t t 0 is a family of closed proper convex functions the result is used to study the flow generated by the family t x f x r t where f x r ctx r exp aix bi r is the exponential penalty approximation of the linear program min ctx ax b and r t is a positive function tending to 0 when t we prove that the trajectory u t converges to an optimal solution u of the linear program and we give conditions for the convergence of an associated dual trajectory t toward an optimal solution of the dual program

a trace semantics for petri nets a generalization of the notion of trace is proposed this enables us to associate with each petri net a single behavioural object namely a poset of generalized traces a characterization is given of the trace languages defined by petri nets we show that the general event structures of winskel and the stable event structures can also be characterized in terms of our trace languages one consequence is that in this framework stable event structures general event structures and petri nets constitute a strictly ascending chain in terms of expressive power

asymptotic behavior of gradient like dynamical systems involving inertia and multiscale aspects abstract in a hilbert space h we study the asymptotic behavior as time variable t goes to of nonautonomous gradient like dynamical systems involving inertia and multiscale features given h r and h r two convex differentiable functions a positive damping parameter and t a function of t which tends to zero as t goes to we consider the second order differential equation x t x t x t t x t 0 this system models the emergence of various collective behaviors in game theory as well as the asymptotic control of coupled nonlinear oscillators assuming that t tends to zero moderately slowly as t goes to infinity we show that the trajectories converge weakly in h the limiting equilibria are solutions of the hierarchical minimization problem which consists in minimizing over the set c of minimizers of as key assumptions we suppose that 0 t d t and that for every p belonging to a convex cone c depending on the data and 0 t p c t p d t where is the fenchel conjugate of and c is the support function of c an application is given to coupled oscillators

the gradient and heavy ball with friction dynamical systems the quasiconvex case we consider the gradient system dot x t nabla phi x t 0 and the so called heavy ball with friction dynamical system ddot x t lambda dot x t nabla phi x t 0 as well as an implicit discrete proximal version of it and study the asymptotic behavior of their solutions in the case of a smooth and quasiconvex objective function minimization properties of trajectories are obtained under various additional assumptions we finally show a minimizing property of the heavy ball method which is not shared by the gradient method the genericity of the convergence of each trajectory at least when is a morse function towards local minimum of

petr nets algebras morphisms and compositionality abstract it is shown how a category of petri nets can be viewed as a subcategory of two sorted algebras over multisets this casts petri nets in a familiar framework and provides a useful idea of morphism on nets different from the conventional definition the morphisms here respect the behaviour of nets the categorical constructions which result provide a useful way to synthesise nets and reason about nets in terms of their components for example various forms of parallel composition of petri nets arise naturally from the product in the category this abstract setting makes plain a useful functor from the category of petri nets to a category of spaces of invariants and provides insight into the generalisations of the basic definition of petri nets for instance the coloured and higher level nets of kurt jensen arise through a simple modification of the sorts of the algebras underlying nets further it provides a smooth formal relation with other models of concurrency such as milner s calculus of communicating systems ccs and hoare s communicating sequential processes csp though this is only indicated in this paper

vi constrained hemivariational inequalities distributed algorithms and power control in ad hoc networks we consider centralized and distributed algorithms for the numerical solution of a hemivariational inequality hvi where the feasible set is given by the intersection of a closed convex set with the solution set of a lower level monotone variational inequality vi the algorithms consist of a main loop wherein a sequence of one level strongly monotone hvis are solved that involve the penalization of the non vi constraint and a combination of proximal and tikhonov regularization to handle the lower level vi constraints minimization problems possibly with nonconvex objective functions over implicitly defined vi constraints are discussed in detail the methods developed in the paper are then used to successfully solve a new power control problem in ad hoc networks

a model based approach for estimation of two dimensional maximum entropy power spectra a stochastic model based approach is presented for estimation of the two dimensional maximum entropy power spectrum meps from given finite uniform array data the method consists of fitting an appropriate two dimensional noncausal gaussian markov random field gmrf model to the given data using the maximum likelihood ml technique for parameter estimation the nonlinear criterion function used for ml estimation is similar in structure to the function arising in the deterministic approach of lang and mcclellan the model based approach provides new insights into the two dimensional meps estimation problem for example using the asymptotic normality of ml estimates we derive simultaneous confidence bands for the estimated meps it turns out that when the true correlations are generated by a noncausal gmrf model the two dimensional meps can be obtained by solving linear equations this approach also suggests techniques for realizing two dimensional gmrf models from the given correlation data several numerical examples are given to illustrate the usefulness of the approach

calculi for synchrony and asynchrony abstract a calculus for distributed computation is studied based upon four combinators a central idea is an abelian group of actions which models the interfaces between components of a distributed computing agent using a notion of bisimulation congruence relations are defined over computing agents and thence an algebraic theory is derived the calculus models both synchronous and asynchronous computation in particular it is shown that the author s calculus of communicating systems 1980 which is an asynchronous model is derivable from the calculus presented here

a bundle method for a class of bilevel nonsmooth convex minimization problems we consider the bilevel problem of minimizing a nonsmooth convex function over the set of minimizers of another nonsmooth convex function standard convex constrained optimization is a particular case in this framework corresponding to taking the lower level function as a penalty of the feasible set we develop an explicit bundle type algorithm for solving the bilevel problem where each iteration consists of making one descent step for a weighted sum of the upper and lower level functions after which the weight can be updated immediately convergence is shown under very mild assumptions we note that in the case of standard constrained optimization the method does not require iterative solution of any penalization subproblems not even approximately and does not assume any regularity of constraints e g the slater condition we also present some computational experiments for minimizing a nonsmooth convex function over a set defined by linear complementarity constraints

real and complex monotone communication games noncooperative game theoretic tools have been increasingly used to study many important resource allocation problems in communications networking smart grids and portfolio optimization in this paper we consider a general class of convex nash equilibrium problems neps where each player aims at solving an arbitrary smooth convex optimization problem differently from most of current works we do not assume any specific structure for the players problems and we allow the optimization variables of the players to be matrices in the complex domain our main contribution is the design of a novel class of distributed asynchronous best response algorithms suitable for solving the proposed neps even in the presence of multiple solutions the new methods whose convergence analysis is based on variational inequality vi techniques can select among all the equilibria of a game those that optimize a given performance criterion at the cost of limited signaling among the players this is a major departure from existing best response algorithms whose convergence conditions imply the uniqueness of the ne some of our results hinge on the use of vi problems directly in the complex domain the study of these new kind of vis also represents a noteworthy innovative contribution we then apply the developed methods to solve some new generalizations of single input single output siso and multiple input multiple output mimo games in cognitive radio systems showing a considerable performance improvement over classical pure noncooperative schemes

estimation and choice of neighbors in spatial interaction models of images some aspects of statistical inference for a class of spatial interaction models for finite images are presented primarily the simultaneous autoregressive sar models and conditional markov cm models each of these models is characterized by a set of neighbors a set of coefficients and a noise sequence of specified characteristics we are concerned with two problems the estimation of the unknown parameters in both sar and cm models and the choice of an appropriate model from a class of such competing models assuming gaussian distributed variables we discuss maximum likelihood ml estimation methods in general the ml scheme leads to nonlinear optimization problems to avoid excessive computation an iterative scheme is given for sar models which gives approximate ml estimates in the gaussian case and reasonably good estimates in some non gaussian situations as well likewise for cm models an easily computable consistent estimate is given the asymptotic mean squared error mse of this estimate for a four neighbor cm model is shown tn be substantially less than the mse of the popular coding estimate asymptotically consistent decision rules are given for choosing an appropriate sar or cm model the usefulness of the estimation scheme and the decision rule for the choice of neighbors is illustrated by using synthetic patterns synthetic patterns obeying known sar and cm models are generated and the models corresponding to true and several competing neighbor sets are fitted the estimation scheme yields estimates close to the parameters of the true models and the decision rule for the choice of neighbors picks up the true model from the class of competing models

viscosity solutions of minimization problems viscosity methods for minimization problems are revisited from some modern perspectives in variational analysis variational convergences for sequences of functions epi convergence gamma convergence mosco convergence and for sequences of operators graph convergence provide a flexible tool for such questions it is proved in a rather large setting that the solutions of the approximate problems converge to a viscosity solution of the original problem that is a solution that is minimal among all the solutions with respect to some viscosity criteria various examples coming from mathematical programming calculus of variations semicoercive elliptic equations phase transition theory hamilton jacobi equations singular perturbations and optimal control theory are considered

process versus unfolding semantics for place transition petri nets in the last few years the semantics of petri nets has been investigated in several different ways apart from the classical token game one can model the behaviour of petri nets via non sequential processes via unfolding constructions which provide formal relationships between nets and domains and via algebraic models which view petri nets as essentially algebraic theories whose models are monoidal categories in this paper we show that these three points of view can be reconciled in our formal development a relevant role is played by cdecocc a category of occurrence nets appropriately decorated to take into account the history of tokens the structure of decorated occurrence nets at the same time provides natural unfoldings for place transition pt nets and suggests a new notion of processes the decorated processes which induce on petri nets the same semantics as that of unfolding in addition we prove that the decorated processes of a net can be axiomatized as the arrows of a symmetric monoidal category which therefore provides the aforesaid unification

functorial models for petri nets we show that although the algebraic semantics of place transition petri nets under the collective token philosophy can be fully explained in terms of strictly symmetric monoidal categories the analogous construction under the individual token philosophy is not completely satisfactory because it lacks universality and also functoriality we introduce the notion of pre nets to overcome this obtaining a fully satisfactory categorical treatment where the operational semantics of nets yields an adjunction this allows us to present a uniform logical description of net behaviors under both the collective and the individual token philosophies in terms of theories and theory morphisms in partial membership equational logic moreover since the universal property of adjunctions guarantees that colimit constructions on nets are preserved in our algebraic models the resulting semantic framework has good compositional properties

convergence of global and bounded solutions of the wave equation with linear dissipation and analytic nonlinearity abstract we prove convergence of global bounded and smooth solutions of the wave equation with linear dissipation and analytic nonlinearity a generalization and examples of applications are given at the end of the paper

true concurrency probabilistic models branching cells and distributed probabilities for event structures this paper is devoted to probabilistic models for concurrent systems under their true concurrency semantics here we address probabilistic event structures we consider a new class of event structures called locally finite that extend confusion free event structure in locally finite event structures maximal configurations can be tiled with branching cells branching cells are minimal and finite sub structures capturing the choices performed while scanning a maximal configuration the probabilistic event structures that we introduce have the property that concurrent processes are independent in the probabilistic sense

primal and dual convergence of a proximal point exponential penalty method for linear programming we consider the diagonal inexact proximal point iteration frac u k u k 1 lambda k in partial varepsilon k f u k r k nu k where f x r ctx r exp a i x b i r is the exponential penalty approximation of the linear program min ctx ax b we prove that under an appropriate choice of the sequences k e k and with some control on the residual k for every r k 0 the sequence u k converges towards an optimal point u of the linear program we also study the convergence of the associated dual sequence i k exp a i u k b i r k towards a dual optimal solution