on the complexity of some colorful problems parameterized by treewidth in this paper we study the complexity of several coloring problems on graphs parameterized by the treewidth of the graph 1 the list coloring problem takes as input a graph g together with an assignment to each vertex v of a set of colors c v the problem is to determine whether it is possible to choose a color for vertex v from the set of permitted colors c v for each vertex so that the obtained coloring of g is proper we show that this problem is w 1 hard parameterized by the treewidth of g the closely related precoloring extension problem is also shown to be w 1 hard parameterized by treewidth 2 an equitable coloring of a graph g is a proper coloring of the vertices where the numbers of vertices having any two distinct colors differs by at most one we show that the problem is hard for w 1 parameterized by the treewidth plus the number of colors we also show that a list based variation list equitable coloring is w 1 hard for forests parameterized by the number of colors on the lists 3 the list chromatic number g l g of a graph g is defined to be the smallest positive integer r such that for every assignment to the vertices v of g of a list l v of colors where each list has length at least r there is a choice of one color from each vertex list l v yielding a proper coloring of g we show that the problem of determining whether g l g

bounded coloring of co comparability graphs and the pickup and delivery tour combination problem the double traveling salesman problem with multiple stacks is a vehicle routing problem in which pickups and deliveries must be performed in two independent networks the items are stored in stacks and repacking is not allowed given a pickup and a delivery tour the problem of checking if there exists a valid distribution of items into s stacks of size h that is consistent with the given tours is known as pickup and delivery tour combination pdtc problem in the paper we show that the pdtc problem can be solved in polynomial time when the number of stacks s is fixed but the size of each stack is not we build upon the equivalence between the pdtc problem and the bounded coloring bc problem on permutation graphs for the latter problem s is the number of colors and h is the number of vertices that can get a same color we show that the bc problem can be solved in polynomial time when s is a fixed constant on co comparability graphs a superclass of permutation graphs to the contrary the bc problem is known to be hard on permutation graphs when h 6 is a fixed constant but s is unbounded

weighted and locally bounded list colorings in split graphs cographs and partial k trees abstract for a fixed number of colors we show that in node weighted split graphs cographs and graphs of bounded tree width one can determine in polynomial time whether a proper list coloring of the vertices of a graph such that the total weight of vertices of each color equals a given value in each part of a fixed partition of the vertices exists we also show that this result is tight in some sense by providing hardness results for the cases where any one of the assumptions does not hold the edge coloring variant is also studied as well as special cases of cographs and split graphs

on the arithmetic and homology of algebras of linear type three modifications of the symmetric algebra of a module are introduced and their arithmetical and homological properties studied emphasis is placed on converting syzygetic properties of the modules into ideal theoretic properties of the algebras e g cohen macaulayness factoriality the main tools are certain fitting ideals of the module and an extension to modules of a complex of not necessarily free modules that we have used in studying blowing up rings

restrictions of graph partition problems let j be a set of n jobs all with job processing time or job length one and let m be a set of k machines incompatibilities between jobs are described by an undirected graph g j e with vertex set j if g contains an edge between two jobs j and j j j we demand that these two jobs can not be executed by the same machine an assignment of the jobs to the machines which satisfies the incompatibility relation is called a schedule the processing time of a machine is given by the number of assigned jobs since each job has processing time one

heights of ideals of minors we prove new height inequalities for determinantal ideals in a regular local ring or more generally in a local ring of given embedding codimension our theorems extend and sharpen results of faltings and bruns

parameterized complexity of coloring problems treewidth versus vertex cover we compare the fixed parameter complexity of various variants of coloring problems including list coloring precoloring extension equitable coloring l p 1 labeling and channel assignment when parameterized by treewidth and by vertex cover number in most but not all cases we conclude that parametrization by the vertex cover number provides a significant drop in the complexity of the problems

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

filtering cohomology and lifting vector bundles for a module m over a local cohen macaulay ring r we develop a finite sequence of presentations of m which facilitates the study of invariants arising from the cohomology modules of m as an application we use this data in case r is regular and m represents a vector bundle on the punctured spectrum of r with a vanishing cohomology module to obtain bounds on how far m can be lifted as a vector bundle in an earlier article 5 we used the dual of a filtration of auslander and bridger 1 to obtain some results for nontrivial kth syzygies of rank k in this article we establish a different method for filtering a module over a local cohen macaulay ring or more precisely a method for filtering a free presentation of a module see discussion following theorem 1 8 this filtration is accomplished through a finite sequence of presentations to be specific let r be a local cohen macaulay ring and let m be a finitely generated r module such that depth ext m r i for all i less than or equal to the dimension of r in theorem 1 2 we establish an exact sequence which we term a q th presentation of m

on the support of local cohomology we examine the question of whether the support of an arbitrary local coho mology module of a finitely generated module over a noetherian ring with support in a given ideal must be closed in the zariski topology several results giving an armative answer to this question are given in particular we show that the support is closed when the given ideal has cohomological dimension at most two or the ambient ring is local of dimension at most four

theta duality on prym varieties and a torelli theorem let c c be an unramified double covering of irreducible smooth curves and let p be the attached prym variety we prove the schemetheoretic theta dual equalities in the prym variety t c v 2 and t v 2 c where v 2 is the brill noether locus of p associated to considered by welters as an application we prove a torelli theorem analogous to the fact that the symmetric product d g of a curve d of genus g determines the curve

linearization of expectation based inequality conditions in control for discrete time linear systems represented with random polytopes abstract a technique of linearizing what we call expectation based inequality conditions is proposed for control of discrete time linear systems with stochastic dynamics in particular the coefficient random matrices of the systems are assumed to be represented with random polytopes and the linearization technique is discussed so as to appropriately deal with associated uncertainties our expectation based inequality is an inequality that involves decision variables contained in the expectation operation and has a unique difficulty in direct linearization in general hence two key lemmas are provided so that the decision variables can be taken out from the expectation operation the combinational use of such lemmas and the conventional linear matrix inequality lmi techniques which is nothing but our linearization technique is expected to be useful for transforming various kinds of expectation based nonlinear inequality into numerically solvable standard lmis as a demonstration new robust stability conditions are derived with the technique whose effectiveness is confirmed numerically

on linear complete intersections or some of its localizations becomes a complete intersection is a major factor in section 1 we describe a jacobian formulation of serre s normality criterion for symmetric algebras it is used to provide several classes of examples of normal and non normal rees algebras of prime ideals in regular domains adding to the catalog of cohen macaulay domains that are symmetric algebras we examine almost complete intersections these bear a close relationship to certain height three ideals of

stability and stabilization of discrete time switched systems this paper addresses two strategies for stabilization of discrete time linear switched systems the first one is of open loop nature trajectory independent and is based on the determination of an upper bound of the minimum dwell time by means of a family of quadratic lyapunov functions the relevant point on dwell time calculation is that the proposed stability condition does not require the lyapunov function be uniformly decreasing at every switching time the second one is of closed loop nature trajectory dependent and is designed from the solution of what we call lyapunov metzler inequalities from which the stability condition is expressed being non convex a more conservative but simpler to solve version of the lyapunov metzler inequalities is provided the theoretical results are illustrated by means of examples

equivalent stability notions lyapunov inequality and its application in discrete time linear systems with stochastic dynamics determined by an i i d process this paper is concerned with stability analysis and synthesis for discrete time linear systems with stochastic dynamics equivalence is first proved for three stability notions under some key assumptions on the randomness behind the systems in particular we use the assumption that the stochastic process determining the system dynamics is independent and identically distributed with respect to the discrete time then a lyapunov inequality condition is derived for stability in a necessary and sufficient sense although our lyapunov inequality will involve decision variables contained in the expectation operation an idea is provided to solve it as a standard linear matrix inequality the idea also plays an important role in state feedback synthesis based on the lyapunov inequality motivating numerical examples are further discussed as an application of our approach

a linear time algorithm for finding tree decompositions of small treewidth in this paper we give for constant k a linear time algorithm that given a graph g v e determines whether the treewidth of g is at most k and if so finds a tree decomposition of g with treewidth at most k a consequence is that every minor closed class of graphs that does not contain all planar graphs has a linear time recognition algorithm another consequence is that a similar result holds when we look instead for path decompositions with pathwidth at most some constant k

derivative complex bgg correspondence and numerical inequalities for compact kahler manifolds given an irregular compact kahler manifold x one can form the derivative complex of x which governs the deformation theory of the groups h i x as varies over pic x together with its variants it plays a central role in a body of work involving generic vanishing theorems the purpose of this paper is to present two new applications of this complex first we show that it fits neatly into the setting of the so called bernstein gel fand gel fand bgg correspondence between modules over an exterior algebra and linear complexes over a symmetric algebra cf bgg efs eis co what comes out here is that some natural cohomology modules associated to x have a surprisingly simple algebraic structure and that conversely one can read off from these modules some basic geometric invariants associated to the albanese mapping of x secondly under an additional hypothesis the derivative complex determines a vector bundle on the projectivized tangent space to pic x at the origin we show that this bundle which encodes the infinitesimal behavior of the hilbert scheme of paracanonical divisors along the canonical linear series can be used to generate inequalities among numerical invariants of x

robust stability analysis and state feedback synthesis for discrete time systems characterized by random polytopes this paper deals with discrete time linear systems whose state transition is determined by a sequence of random matrices having uncertain distributions in representing random matrices with uncertain distributions we use random polytopes whose vertices are random matrices with given fixed distributions for such systems characterized by random polytopes we first tackle a problem of analyzing robust second moment exponential stability in particular we show a linear matrix inequality based robust stability condition that can be solved through sample based evaluation of the associated expectations the confidence level for such sample based analysis is ensured by the central limit theorem then we extend the results about analysis toward robust stabilization state feedback synthesis in such a way that the confidence level arguments can be facilitated we also provide numerical examples illustrating our analysis and synthesis framework

the mutual exclusion scheduling problem for permutation and comparability graphs in this paper we consider the mutual exclusion scheduling problem for comparability graphs given an undirected graph g and a fixed constant m the problem is to find a minimum coloring of g such that each color is used at most m times the complexity of this problem for comparability graphs was mentioned as an open problem by mohring problem 9 10 in i rival ed graphs and orders reidel dordrecht 1985 p 583 and for permutation graphs a subclass of comparability graphs as an open problem by lonc on complexity of some chain and antichain partition problem in g schmidt r berghammer eds graph theoretical concepts in computer science wg 91 lecture notes in computer science vol 570 1999 pp 97 104 we prove that this problem is already np complete for permutation graphs and for each fixed constant m 6

sufficient and necessary criteria for existence of pullback attractors for non compact random dynamical systems abstract we study pullback attractors of non autonomous non compact dynamical systems generated by differential equations with non autonomous deterministic as well as stochastic forcing terms we first introduce the concepts of pullback attractors and asymptotic compactness for such systems we then prove a sufficient and necessary condition for existence of pullback attractors we also introduce the concept of complete orbits for this sort of systems and use these special solutions to characterize the structures of pullback attractors for random systems containing periodic deterministic forcing terms we show the pullback attractors are also periodic under certain conditions as an application of the abstract theory we prove the existence of a unique pullback attractor for reaction diffusion equations on r n with both deterministic and random external terms since sobolev embeddings are not compact on unbounded domains the uniform estimates on the tails of solutions are employed to establish the asymptotic compactness of solutions

mutual exclusion scheduling abstract mutual exclusion scheduling is the problem of scheduling unit time tasks non preemptively on m processors subject to constraints represented by a graph g such that tasks represented by adjacent vertices in g must run in disjoint time intervals this problem arises in load balancing the parallel solution of partial differential equations by domain decomposition minimizing the completion time is np hard even if either the number of processors or the completion time is fixed but greater than two however polynomial time is sufficient to produce optimal schedules for forests and simple heuristics perform well on certain classes of graphs for graphs derived from the two dimensional domain decomposition problem heuristics yield solutions within 4 c 7 time units of optimal where c is the maximal number of regions that touch each other at a single point in the domain decomposition these solutions are within a constant factor of optimal

restrictions of graph partition problems part i in this paper partition problems into k independent sets or cliques of bounded size k are analyzed for several classes of graphs we prove the computational complexity of both problems restricted to cographs split graphs bipartite graphs and interval graphs given general or constant k and k it is shown that the assignment problem for operations in a branching flow graph to processors each with a limit on the number of executable operations equals the first problem restricted to cographs in addition a job assignment problem given intervals for each job and k machines each executing at most k jobs equals the first problem restricted to interval graphs it is shown that both problem are np complete

depth for complexes and intersection theorems this paper introduces a new notion of depth for complexes it agrees with the classical definition for modules and coincides with earlier extensions to complexes whenever those are defined techniques are developed leading to a quick proof of an extension of the improved new intersection theorem this uses hochster s big cohen macaulay modules and also a generalization of the depth formula for tensor product of modules properties of depth for complexes are established extending the usual properties of depth for modules

equitable colorings of bounded treewidth graphs a proper coloring of a graph g is equitable if the sizes of any two color classes differ by at most one a proper coloring is l bounded when each color class has size at most l we consider the problems to determine for a given graph g and a given integer l whether g has an equitable l bounded k coloring we prove that both problems can be solved in polynomial time on graphs of bounded treewidth and show that a precolored version remains np complete on trees

stochastic stability of jump discrete time linear systems with markov chain in a general borel space necessary and sufficient conditions for stochastic stability ss of discrete time linear systems subject to markov jumps in the parameters are considered assuming that the markov chain takes values in a general borel space s it is shown that ss is equivalent to the spectrum radius of a bounded linear operator in a banach space being less than 1 or to the existence of a solution of a lyapunov type equation these results generalize several previous results in the literature which considered only the case of the markov chain taking values in a finite or infinite countable space

stability of model based networked control systems with time varying transmission times in model based networked control systems mb ncss an explicit model of the plant is used to produce an estimate of the plant state behavior between transmission times in this paper the stability of mb ncss is studied when the controller actuator is updated with the sensor information at nonconstant time intervals networked control systems with transmission times that are varying either within a time interval or are driven by a stochastic process with identically independently distributed and markov chain driven transmission times are studied sufficient conditions for lyapunov stability are derived for stochastically modeled transmission times almost sure stability and mean square sufficient conditions for stability are introduced

parameter dependent lyapunov functions for discrete time systems with time varying parametric uncertainties abstract in this paper we consider discrete time systems with polytopic time varying uncertainty we look for a class of parameter dependent lyapunov functions which are quadratic on the system state and depend in a polytopic way on the uncertain parameter we show that extending the new discrete time stability condition proposed by de oliveira et al systems control lett 36 1999 135 to the case of time varying uncertainty leads to a necessary and sufficient condition for the computation of such a lyapunov function this allows to check asymptotic stability of the system under study the obtained linear matrix inequalities condition can also be used to cope with the control synthesis problem