existential second order logic over graphs charting the tractability frontier fagin s theorem the first important result of descriptive complexity asserts that a property of graphs is in np if and only if it is definable by an existential second order formula in this article we study the complexity of evaluating existential second order formulas that belong to prefix classses of existential second order logic where a prefix class is the collection of all existential second order formulas in prenex normal form such that the second order and the first order quantifiers obey a certain quantifier pattern we completely characterize the computational complexity of prefix classes of existential second order logic in three different contexts 1 over directed graphs 2 over undirected graphs with self loops and 3 over undirected graphs without self loops our main result is that in each of these three contexts a dichotomy holds that is to say each prefix class of existential second order logic either contains sentences that can express np complete problems or each of its sentences expresses a polynomial time solvable problem although the boundary of the dichotomy coincides for the first two cases it changes as one moves to undirected graphs without self loops the key difference is that a certain prefix class based on the well known ackermann class of first order logic contains sentences that can express np complete problems over graphs of the first two types but becomes tractable over undirected graphs without self loops moreover establishing the dichotomy over undirected graphs without self loops turns out to be a technically challenging problem that requires the use of sophisticated machinery from graph theory and combinatorics including results about graphs of bounded tree width and ramsey s theorem

an algebraic theory of graph reduction we show how membership in classes of graphs definable in monadic second order logic and of bounded treewidth can be decided by finite sets of terminating reduction rules the method is constructive in the sense that we describe an algorithm which will produce from a formula in monadic second order logic and an integer k such that the class defined by the formula is of treewidth k a set of rewrite rules that reduces any member of the class to one of finitely many graphs in a number of steps bounded by the size of the graph this reduction system corresponds to an algorithm that runs in time linear in the size of the graph

probabilistic hyperedge replacement grammars abstract in a probabilistic graph grammar each production has a probability attached to it this induces a probability assigned to each derivation tree and to each derived graph conditions for this probability function to be a probabilistic measure are discussed the statistical properties of the generated language are investigated we show how to compute the average size of an inductive function and the probability of an inductive graph predicate a relationship can be established between production probabilities and some statistical information of the generated language this way probabilities can be assigned to productions so that the generated graphs satisfy some statistical conditions

a parametrized algorithm for matroid branch width branch width is a structural parameter very closely related to tree width but branch width has an immediate generalization from graphs to matroids we present an algorithm that for a given matroid m of bounded branch width t which is represented over a finite field finds a branch decomposition of m of width at most 3t in cubic time then we show that the branch width of m is a uniformly fixed parameter tractable problem other applications include recognition of matroid properties definable in the monadic second order logic for bounded branch width and s i oum approximating rank width and clique width quickly in proceedings of the 31st international workshop on graph theoretic concepts in computer science springer verlag heidelberg to appear a cubic time approximation algorithm for graph rank width and clique width

the monadic second order logic of graphs i recognizable sets of finite graphs abstract the notion of a recognizable set of finite graphs is introduced every set of finite graphs that is definable in monadic second order logic is recognizable but not vice versa the monadic second order theory of a context free set of graphs is decidable

a linear time algorithm for metric dimension of cactus block graphs an undirected graph g v e has metric dimension at most k if there is a vertex set u v such that u k and u v v u v there is a vertex w u such that d g w u d g w v where d g u v is the distance the length of a shortest path in an unweighted graph between u and v the metric dimension of g is the smallest integer k such that g has metric dimension at most k a cactus block graph is an undirected graph whose biconnected components are either cycles or complete graphs we present a linear time algorithm for computing the metric dimension of cactus block graphs

efficient parallel algorithms for parameterized problems abstract a parameterized problem is fixed parameter parallelizable fpp if it can be solved in o f k log n time using o g k n processors where n is the input size k is the parameter f and g are arbitrary computable functions and are constants independent of n and k we re examine the k vertex cover problem from a parameterized parallel complexity standpoint and present a parallel algorithm that outperforms the previous known algorithm using o m instead of o n 2 processors the running time improves from o k k to o k 3 log n 1 2738 k where n and m are the number of vertices and edges of the input graph respectively this is achieved by first showing that vertex cover kernelization that is based on crown decomposition is in fpp as well finally we consider the use of the recently introduced modular width parameter in particular we show that the weighted maximum clique problem is fpp when parameterized by this auxiliary parameter

the art of trellis decoding is fixed parameter tractable given n subspaces of a finite dimensional vector space over a fixed finite field mathbb f we wish to find a linear layout v 1 v 2 ldots v n of the subspaces such that dim v 1 v 2 cdots v i cap v i 1 cdots v n le k for all i such a linear layout is said to have width at most k when restricted to 1 dimensional subspaces this problem is equivalent to computing the trellis width or minimum trellis state complexity of a linear code in coding theory and computing the path width of an mathbb f represented matroid in matroid theory we present a fixed parameter tractable algorithm to construct a linear layout of width at most k if it exists for input subspaces of a finite dimensional vector space over mathbb f as corollaries we obtain a fixed parameter tractable algorithm to produce a path decomposition of width at most k for an input mathbb f represented matroid of path width at most k and a fixed parameter tractable algorithm to find a linear rank decomposition of width at most k for an input graph of linear rank width at most k in both corollaries no such algorithms were known previously our approach is based on dynamic programming combined with the idea developed by bodlaender and kloks 1996 for their work on path width and tree width of graphs it was previously known that a fixed parameter tractable algorithm exists for the decision version of the problem for matroid path width a theorem by geelen gerards and whittle 2002 implies that for each fixed finite field mathbb f there are finitely many forbidden mathbb f representable minors for the class of matroids of path width at most k an algorithm by hlin n 2006 can detect a minor in an input mathbb f represented matroid of bounded branch width however this indirect approach would not produce an actual path decomposition our algorithm is the first one to construct such a path decomposition and does not depend on the finiteness of forbidden minors

an exactly solvable nonlinear model constructive effects of correlations between gaussian noises abstract a system with two correlated gaussian white noises is analysed this system can describe both stochastic localization and long tails in the stationary distribution correlations between the noises can lead to a nonmonotonic behaviour of the variance as function of the intensity of one of the noises and to a stochastic resonance a method for improving the transmission of external periodic signal by tuning parameters of the system discussed in this paper is proposed

on the parameterized complexity of recognizing well covered r l graph an r ell partition of a graph g is a partition of its vertex set into r independent sets and ell cliques a graph is r ell if it admits an r ell partition a graph is well covered if every maximal independent set is also maximum a graph is r ell well covered if it is both r ell and well covered in this paper we consider two different decision problems in the r ell well covered graph problem r ell wcg for short we are given a graph g and the question is whether g is an r ell well covered graph in the well covered r ell graph problem wc r ell g for short we are given an r ell graph g together with an r ell partition of v g into r independent sets and ell cliques and the question is whether g is well covered we classify most of these problems into p conp complete np complete np hard or conp hard only the cases wc r 0 g for r ge 3 remain open in addition we consider the parameterized complexity of these problems for several choices of parameters such as the size alpha of a maximum independent set of the input graph its neighborhood diversity or the number ell of cliques in an r ell partition in particular we show that the parameterized problem of deciding whether a general graph is well covered parameterized by alpha can be reduced to the wc 0 ell g problem parameterized by ell and we prove that this latter problem is in xp but does not admit polynomial kernels unless mathsf conp subseteq mathsf np mathsf poly

grid structures and undecidable constraint theories abstract we prove three new undecidability results for computational mechanisms over finite trees there is a linear ultra shallow noetherian and strongly confluent rewrite system r such that the fragment of the first order theory of one step rewriting by r is undecidable the emptiness problem for tree automata with equality tests between cousins is undecidable and the fragment of the first order theory of set constraints with the union operator is undecidable the common feature of these three computational mechanisms is that they allow us to describe the set of first order terms that represent grids we extend our representation of grids by terms to a representation of linear two dimensional patterns by linear terms which allows us to transfer classical techniques on the grid to terms and thus to obtain our undecidability results

the monadic second order logic of graphs ix machines and their behaviours abstract we establish that every monadic second order property of the behaviour of a machine transition systems and tree automata are typical examples of machines is a monadic second order property of the machine itself in this way we clarify the distinction between dynamic properties of machines i e properties of their behaviours and their static properties i e properties of the graphs or relational structures representing them it is important for program verification that the dynamic properties that one wants to verify can be formulated statically in the simplest possible way as a corollary of our main result we also obtain that the monadic theory of an algebraic tree is decidable

parameterized and approximation complexity of partial vc dimension abstract we introduce the problem partial vc dimension that asks given a hypergraph h x e and integers k and l whether one can select a set c x of k vertices of h such that the set e c e e of distinct hyperedge intersections with c has size at least l the sets e c define equivalence classes over e partial vc dimension is a generalization of vc dimension which corresponds to the case l 2 k and of distinguishing transversal which corresponds to the case l e the latter is also known as test cover in the dual hypergraph we also introduce the associated fixed cardinality maximization problem max partial vc dimension that aims at maximizing the number of equivalence classes induced by a solution set of k vertices we study the algorithmic complexity of partial vc dimension and max partial vc dimension both on general hypergraphs and on more restricted instances in particular neighborhood hypergraphs of graphs

computations by fly automata beyond monadic second order logic parameterized algorithms based on automata infinite automata computing their transitions problems described in monadic second order logic counting and other problems not expressible in monadic second order logic the validity of a monadic second order ms expressible property can be checked in linear time on graphs of bounded tree width or clique width given with appropriate decompositions this result is proved by constructing from the ms sentence expressing the property and an integer that bounds the tree width or clique width of the input graph a finite automaton intended to run bottom up on the algebraic term representing a decomposition of the input graph as we cannot construct practically the transition tables of these automata because they are huge we use fly automata whose states and transitions are computed on the fly only when needed for a particular input furthermore we allow infinite sets of states and we equip automata with output functions thus they can check properties that are not ms expressible and compute values for example the number of p colorings of a graph we obtain xp and fpt graph algorithms parameterized by tree width or clique width we show how to construct easily such algorithms by combining predefined automata for basic functions and properties these combinations reflect the structure of the ms formula that specifies the property to check or the function to compute

gain in stochastic resonance precise numerics versus linear response theory beyond the two mode approximation in the context of the phenomenon of stochastic resonance sr we study the correlation function the signal to noise ratio snr and the ratio of output over input snr i e the gain which is associated to the nonlinear response of a bistable system driven by time periodic forces and white gaussian noise these quantifiers for sr are evaluated using the techniques of linear response theory lrt beyond the usually employed two mode approximation scheme we analytically demonstrate within such an extended lrt description that the gain can indeed not exceed unity we implement an efficient algorithm based on work by greenside and helfand detailed in the appendix to integrate the driven langevin equation over a wide range of parameter values the predictions of lrt are carefully tested against the results obtained from numerical solutions of the corresponding langevin equation over a wide range of parameter values we further present an accurate procedure to evaluate the distinct contributions of the coherent and incoherent parts of the correlation function to the snr and the gain as a main result we show for subthreshold driving that both the correlation function and the snr can deviate substantially from the predictions of lrt and yet the gain can be either larger or smaller than unity in particular we find that the gain can exceed unity in the strongly nonlinear regime which is characterized by weak noise and very slow multifrequency subthreshold input signals with a small duty cycle this latter result is in agreement with recent analog simulation results by gingl et al icnf 2001 edited by g bosman world scientific singapore 2002 pp 545 548 fluct noise lett 1 l181 2001

induced packing of odd cycles in planar graphs an induced packing of odd cycles in a graph is a packing such that there is no edge in the graph between any two odd cycles in the packing we prove that an induced packing of k odd cycles in an n vertex graph can be found if it exists in time 2 o k 3 2 n 2 e for any constant e 0 when the input graph is planar we also show that deciding if a graph has an induced packing of two odd induced cycles is np complete

algorithms for vertex partitioning problems on graphs with fixed clique width many vertex partitioning problems can be expressed within a general framework introduced by telle and proskurowski they showed that optimization problems in this framework can be solved in polynomial time on classes of graphs with bounded tree width in this paper we consider a very similar framework in relationship with more general classes of graphs we propose a polynomial time algorithm on classes of graphs with bounded clique width for all the optimization problems in our framework these classes of graphs are more general than the classes of graphs with bounded tree width in the sense that classes of graphs with bounded tree width have also bounded clique width but not necessarily the inverse our framework includes problems such as independent dominating set p dominating set induced bounded degree subgraph induced p regular subgraph perfect matching cut graph k coloring and graph list k coloring with cardinality constraints fixed k this paper thus provides a second distinct framework within which the optimization problems can be solved in polynomial time on classes of graphs with bounded clique width after a first framework called ms1 due to the work of courcelle makowsky and rotics for which they obtained a linear time algorithm

identification location domination and metric dimension on interval and permutation graphs i bounds we consider the problems of finding optimal identifying codes open locating dominating sets and resolving sets of an interval or a permutation graph in these problems one asks to find a subset of vertices normally called a solution set using which all vertices of the graph are distinguished the identification can be done by considering the neighborhood within the solution set or by employing the distances to the solution vertices normally the goal is to minimize the size of the solution set then here we study the case of interval graphs unit interval graphs bipartite permutation graphs and cographs for these classes of graphs we give tight lower bounds for the size of such solution sets depending on the order of the input graph while such lower bounds for the general class of graphs are in logarithmic order the improved bounds in these special classes are of the order of either quadratic root or linear in terms of number of vertices moreover the results for cographs lead to linear time algorithms to solve the considered problems on inputs that are cographs

basic notions of universal algebra for language theory and graph grammars abstract this paper reviews the basic properties of the equational and recognizable subsets of general algebras these sets can be seen as generalizations of the context free and regular languages respectively this approach based on universal algebra facilitates the development of the theory of formal languages so as to include the description of sets of finite trees finite graphs finite hypergraphs tuples of words partially commutative words also called traces and other similar finite objects

hitting minors on bounded treewidth graphs ii single exponential algorithms abstract for a finite collection of graphs f the f m deletion resp f tm deletion problem consists in given a graph g and an integer k decide whether there exists s v g with s k such that g s does not contain any of the graphs in f as a minor resp topological minor we are interested in the parameterized complexity of both problems when the parameter is the treewidth of g denoted by tw and specifically in the cases where f contains a single connected planar graph h we present algorithms running in time 2 o tw n o 1 called single exponential when h is either p 3 p 4 c 4 the paw the chair and the banner for both h m deletion and h tm deletion and when h k 1 i with i 1 for h tm deletion some of these algorithms use the rank based approach introduced by bodlaender et al 2015 7 this is the second of a series of articles on this topic and the results given here together with other ones allow us in particular to provide a tight dichotomy on the complexity of h m deletion in terms of h

parallel algorithms with optimal speedup for bounded treewidth we describe the first parallel algorithm with optimal speedup for constructing minimum width tree decompositions of graphs of bounded treewidth on n vertex input graphs the algorithm works in o log n 2 time using o n operations on the erew pram we also give faster parallel algorithms with optimal speedup for the problem of deciding whether the treewidth of an input graph is bounded by a given constant and for a variety of problems on graphs of bounded treewidth including all decision problems expressible in monadic second order logic on n vertex input graphs the algorithms use o n operations together with o log n log n time on the erew pram or o log n time on the crcw pram

compatibility of unrooted phylogenetic trees is fpt a collection of t1 t2 tk of unrooted leaf labelled phylogenetic trees all with different leaf sets is said to be compatible if there exists a tree t such that each tree ti can be obtained from t by deleting leaves and contracting edges determining compatibility is np hard and the fastest algorithm to date has worst case complexity of around nk time n being the number of leaves here we present an o nf k algorithm proving that compatibility of unrooted phylogenetic trees is fixed parameter tractable fpt with respect to the number k of trees

the monadic second order logic of graphs xiv uniformly sparse graphs and edge set quantifications we consider the class usk of uniformly k sparse simple graphs i e the class of finite or countable simple graphs every finite subgraph of which has a number of edges bounded by k times the number of vertices we prove that for each k every monadic second order formula intended to express a graph property that uses variables denoting sets of edges can be effectively translated into a monadic second order formula where all set variables denote sets of vertices and that expresses the same property of the graphs in usk this result extends to the class of uniformly k sparse simple hypergraphs of rank at most m for any k and m it follows that every subclass of usk consisting of finite graphs of bounded clique width has bounded tree width clique width is a graph complexity measure similar to tree width and relevant to the construction of polynomial algorithms for np complete problems on special classes of graphs

trees grids and mso decidability from graphs to matroids monadic second order mso logic has proved to be a useful tool in many areas of application reaching flom decidability and complexity to picture processing correctness of programs and parallel processes to characterize the structural borderline between decidability and undecidability is a classical research problem here this problem is related to questions in computational complexity especially to the model checking problem for which many tools developed in the area of decidability have proved to be useful for more than two decades it was conjectured in d seese the structure of the models of decidable monadic theories of graphs ann pure appl logic 53 1991 169 195 that decidability of monadic theories of countable structures implies that the theory can be reduced via interpretability to a theory of trees it is one of the main goals of this article to prove a variant of this conjecture for matroids representable over a finite field matroids can be viewed as a wide generalization of graphs and they seem to capture some second order properties in a more suitable way than graphs themselves cf the recent development in matroid structure theory j f geelen a h m gerards g p whittle branch width and well quasi ordering in matroids and graphs j combin theory ser b 84 2002 270 290 j f geelen a h m gerards n robertson g p whittle excluding a planar graph from a gf q representable matroid manuscript 2003 more exactly we prove for every finite field f that any class of f representable matroids with a decidable mso theory must have uniformly bounded branch width moreover we show that bounding the branch width of all matroids in general is not sufficient to obtain a decidable mso theory our paper gives a rather detailed introduction to these different subjects and shows that a blend of ideas and methods from logic together with structural matroid theory can lead to new tools and algorithms and can shed light on some old open problems

uniform and nonuniform recognizability deterministic and nondeterministic finite state recognizability over finite structures are introduced in an algebraic setting avoiding detailed computational conventions as needed in the definition of finite state acceptors for deterministic recognizability the classical approach is adopted using a uniform homomorphism from the input domain consisting of terms into a finite algebra for the nondeterministic case we refer to relational input structures and to an acceptance via relational homomorphisms which are applied nonuniformly since they depend on the input structures we show how this approach encompasses known models of nondeterministic automata over finite words trees pictures and graphs and present some elementary metaresults connecting uniform recognizability nonuniform recognizability and monadic second order logic

on degenerations and extensions of finite dimensional modules abstract we derive a cancellation theorem for degenerations of modules that says in particular that projective or injective common direct summands can always be neglected combining the cancellation result with the existence of almost split sequences we characterize the orbit closure of a module living on preprojective components by the fact that the dimension of the homomorphism space to any other module does not decrease for representation directed algebras whence in particular for path algebras of dynkin quivers we provide an alternative proof which shows in addition that any minimal degenerationnofmcomes from an exact sequence with middle termmwhose end terms add up ton by a careful examination the same is true for degenerations of matrix pencils having used so far the existence of certain extensions to obtain degenerations we then turn the tables and use degenerations to produce a lot of interesting short exact sequences in particular we show that any non simple indecomposable over a tame quiver is an extension of an indecomposable and a simple

the monadic second order logic of graphs x linear orderings graphs are finite and handled as relational structures we give some answers to the following general questions 1 1 for which classes of graphs c is it possible to specify a linear ordering of the set of vertices of each graph of c by fixed monadic second order formulas 2 2 for which classes of graphs c does there exist an extension l of monadic second order logic such that a subclass l of c is recognizable if and only if it is the class of graphs in c that satisfy a formula of l in this paper recognizability is understood in an algebraic sense relative to a finite set of graph operations and basic graphs that generate all graphs of c 3 3 for which classes of graphs c is it possible to construct in every graph of the class and by fixed formulas of a suitable extension of monadic second order logic its hierarchichal structure i e a finite term written with the operations and basic graphs of 2 that defines the considered graph applications concern dependency graphs of partially commutative words partial k paths cographs and graphs the modular decomposition of which uses prime graphs of bounded size

equivalences and transformations of regular systems applications to recursive program schemes and grammars abstract this work presents a unified theory of recursive program schemes context free grammars grammars on arbitrary algebraic structures and in fact recursive definitions of all kind by means of regular systems the equivalences of regular systems associated with either all their solutions or their least solutions in all domains of appropriate type satisfying a set of algebraic laws expressed by equations are systematically investigated and characterized in some cases in terms of system transformations by folding unfolding and rewriting according to the equational algebraic laws grammars are better characterized in terms of polynomial systems which are regular systems involving the operation of set union and the same questions are raised for them we also examine conditions insuring the uniqueness of the solution of a regular or of a polynomial system this theory applies to grammars of many kinds which generate trees graphs etc we formulate some classical transformations of context free grammars in terms of correct transformations which only use folding unfolding and algebraic laws and we immediately obtain their correctness

solution of the schrodinger equation by a spectral method abstract a new computational method for determining the eigenvalues and eigenfunctions of the schrodinger equation is described conventional methods for solving this problem rely on diagonalization of a hamiltonian matrix or iterative numerical solutions of a time independent wave equation the new method in contrast is based on the spectral properties of solutions to the time dependent schrodinger equation the method requires the computation of a correlation function r 0 r t from a numerical solution r t fourier analysis of this correlation function reveals a set of resonant peaks that correspond to the stationary states of the system analysis of the location of these peaks reveals the eigenvalues with high accuracy additional fourier transforms of r t with respect to time generate the eigenfunctions the effectiveness of the method is demonstrated for a one dimensional asymmetric double well potential and for the two dimensional henon heiles potential

new limits of treewidth based tractability in optimization sparse structures are frequently sought when pursuing tractability in optimization problems they are exploited from both theoretical and computational perspectives to handle complex problems that become manageable when sparsity is present an example of this type of structure is given by treewidth a graph theoretical parameter that measures how tree like a graph is this parameter has been used for decades for analyzing the complexity of various optimization problems and for obtaining tractable algorithms for problems where this parameter is bounded the goal of this work is to contribute to the understanding of the limits of the treewidth based tractability in optimization our results are as follows first we prove that in a certain sense the already known positive results on extension complexity based on low treewidth are the best possible secondly under mild assumptions we prove that treewidth is the only graph theoretical parameter that yields tractability for a wide class of optimization problems a fact well known in graphical models in machine learning and in constraint satisfaction problems which here we extend to an approximation setting in optimization

kernel bounds for path and cycle problems connectivity problems like k path and k disjoint paths relate to many important milestones in parameterized complexity namely the graph minors project color coding and the recent development of techniques for obtaining kernelization lower bounds this work explores the existence of polynomial kernels for various path and cycle problems by considering nonstandard parameterizations we show polynomial kernels when the parameters are a given vertex cover a modulator to a cluster graph or a promised max leaf number we obtain lower bounds via cross composition e g for hamiltonian cycle and related problems when parameterized by a modulator to an outerplanar graph

stochastic resonance of collective variables in finite sets of interacting identical subsystems we explore stochastic resonance effects in the response of a complex stochastic system formed by a finite number of interacting identical subunits driven by a time periodic force the driving force alone cannot induce sustained oscillations between the different attractors of the dynamics in the absence of noise we focus on a global stochastic variable defined as the arithmetic mean of the relevant stochastic variable of each subunit we construct numerical approximations to its first two long time cumulant moments and its long time correlation function we also compute the output signal to noise ratio and the stochastic resonance gain for a wide range of parameter values and several types of driving forces the coupling between the subsystems leads within adequate ranges of the parameter values to global outputs with very large signal to noise ratios we have also observed gains larger than unity in the global response to subthreshold sinusoidal driving forces

theory of stochastic resonance in signal transmission by static nonlinear systems a deterministic periodic signal plus a stationary random noise is applied to a static nonlinearity taking the form of a monovariable arbitrary function on real numbers the property of noise enhanced signal transmission through stochastic resonance is studied for this class of static nonlinear systems a theory is developed that provides expressions for the output autocorrelation function power spectral density signal to noise ratio and input output phase shift in the presence of a periodic input a noise distribution and a static nonlinearity all three being arbitrary both white and colored input noises are successively considered for white input noise exact expressions are derived in a discrete time framework directly confrontable to simulations or experiments the theory is applied to describe stochastic resonance in various examples of static nonlinear systems for instance a diode nonlinearity in addition confrontations with experiments and simulations are given that support the theory in particular interesting effects are reported such as a signal to noise ratio larger at the output than at the input or stochastic resonance at zero frequency finally the validity of the theory is extended to dynamic nonlinear systems that can be decomposed into a static nonlinearity followed by an arbitrary dynamic linear system s1063 651x 97 12002 5

testing first order properties for subclasses of sparse graphs we present a linear time algorithm for deciding first order fo properties in classes of graphs with bounded expansion a notion recently introduced by neset il and ossona de mendez this generalizes several results from the literature because many natural classes of graphs have bounded expansion graphs of bounded tree width all proper minor closed classes of graphs graphs of bounded degree graphs with no subgraph isomorphic to a subdivision of a fixed graph and graphs that can be drawn in a fixed surface in such a way that each edge crosses at most a constant number of other edges we deduce that there is an almost linear time algorithm for deciding fo properties in classes of graphs with locally bounded expansion more generally we design a dynamic data structure for graphs belonging to a fixed class of graphs of bounded expansion after a linear time initialization the data structure allows us to test an fo property in constant time and the data structure can be updated in constant time after addition deletion of an edge provided the list of possible edges to be added is known in advance and their simultaneous addition results in a graph in the class all our results also hold for relational structures and are based on the seminal result of neset il and ossona de mendez on the existence of low tree depth colorings

linear transmitter with correlated noises abstract a linear transmitter with correlated gaussian white additive and multiplicative noises and a periodic signal coupled either additively or multiplicatively is considered the correlations have a weak destructive effect in case of the additive signal and a strong constructive effect in case of the multiplicative one analytical results for the linear transmitter with the additive signal agree with those obtained previously by a different approach we also show how to analytically calculate certain expectation values involving exponentials of gaussian processes

obtaining planarity by contracting few edges the planar contraction problem is to test whether a given graph can be made planar by using at most k edge contractions this problem is known to be np complete we show that it is fixed parameter tractable when parameterized by k

finite tame and wild actions of parabolic subgroups in gl v on certain unipotent subgroups abstract let p be a parabolic subgroup of some general linear group gl v where v is a finite dimensional vector space over an infinite field the group p acts by conjugation on its unipotent radical pu and via the adjoint action on p u the lie algebra of pu more generally we consider the action of p on the lth member of the descending central series of p u denoted by p l u let l p u denote the nilpotency class of pu in our main result we show that p acts on p l u with a finite number of orbits precisely when l p u 4 for l 0 or l p u 5 2l for l 1 moreover in case the field is algebraically closed we consider the modality mod p p l u of the action of p on p l u we show that mod p p l u grows linearly in the minimal cases which admit infinitely many orbits i e l p u 5 for l 0 or l p u 6 2l for l 1 whereas the corresponding modality grows quadratically in all other infinite cases these results are obtained by interpreting the orbits of p on p l u as isomorphism classes of good modules over certain quasi hereditary algebras and by a detailed inspection of the representation types of these algebras

counting modulo quantifiers on finite structures we give a combinatorial method for proving elementary equivalence in first order logic fo with counting modulo n quantifiers dn inexpressibility results for fo dn with built in linear order are also considered for instance the class of linear orders of length divisible by n 1 cannot be expressed in fo dn using this result we prove that comparing cardinalities or connectivity of ordered graphs are not definable in fo dn we also show that the height of complete n ary trees cannot be expressed in fo dn with linear order interpreting the predicate y nx as a complete n ary tree we show that the predicate y px cannot be defined in fo dn with linear order whenever p has a prime factor that does not divide n this solves the problem raised by niwi ski and stolboushkin lics 93 we also discuss a connection between our results and the well known open problem in circuit complexity theory whether acc nc1

the recognizability of sets of graphs is a robust property once the set of finite graphs is equipped with an algebra structure arising from the definition of operations that generalize the concatenation of words one can define the notion of a recognizable set of graphs in terms of finite congruences applications to the construction of efficient algorithms and to the theory of context free sets of graphs follow naturally the class of recognizable sets depends on the signature of graph operations we consider three signatures related respectively to hyperedge replacement hr context free graph grammars to vertex replacement vr context free graph grammars and to modular decompositions of graphs we compare the corresponding classes of recognizable sets we show that they are robust in the sense that many variants of each signature where in particular operations are defined by quantifier free formulas a quite flexible framework yield the same notions of recognizability we prove that for graphs without large complete bipartite subgraphs hr recognizability and vr recognizability coincide the same combinatorial condition equates hr context free and vr context free sets of graphs inasmuch as possible results are formulated in the more general framework of relational structures

algorithms for decision problems in argument systems under preferred semantics for dung s model of abstract argumentation under preferred semantics argumentation frameworks may have several distinct preferred extensions i e in informal terms sets of acceptable arguments thus the acceptance problem for a specific argument can consider deciding whether an argument is in at least one such extensions credulously accepted or in all such extensions skeptically accepted we start by presenting a new algorithm that enumerates all preferred extensions following this we build algorithms that decide the acceptance problem without requiring explicit enumeration of all extensions we analyze the performance of our algorithms by comparing these to existing ones and present experimental evidence that the new algorithms are more efficient with respect to the expected running time moreover we extend our techniques to solve decision problems in a widely studied development of dung s model namely value based argumentation frameworks vafs in this regard we examine analogous notions to the problem of enumerating preferred extensions and present algorithms that decide subjective respectively objective acceptance

on the path width of integer linear programming we consider the feasibility problem of integer linear programming ilp we show that solutions of any ilp instance can be naturally represented by an fo definable class of graphs for each solution there may be many graphs representing it however one of these graphs is of path width at most 2n where n is the number of variables in the instance since fo is decidable on graphs of bounded path width we obtain an alternative decidability result for ilp the technique we use underlines a common principle to prove decidability which has previously been employed for automata with auxiliary storage we also show how this new result links to automata theory and program verification

large induced subgraphs via triangulations and cmso we obtain an algorithmic metatheorem for the following optimization problem let varphi be a counting monadic second order logic cmso formula and t geq 0 be an integer for a given graph g v e the task is to maximize x subject to the following there is a set f subseteq v such that x subseteq f the subgraph g f induced by f is of treewidth at most t and the structure g f x models varphi i e g f x models varphi we give an algorithm solving this optimization problem on any n vertex graph g in time cal o pi g cdot n t 4 cdot f t varphi where pi g is the set of all potential maximal cliques in g and f is a function of t and varphi only pipelined with the known bounds on the number of potential maximal cliques in different graph classes there are a plethora of algorithmic consequences extending and subsuming many known results on polynomial time algorithms for graph classes we also show that all potential maximal cliques of g can be enumerated in time cal o 1 7347 n this implies the existence of an exact exponential algorithm of running time cal o 1 7347 n for many np hard problems related to finding maximum induced subgraphs with different properties

signal amplification factor in stochastic resonance an analytic non perturbative approach abstract the response of an overdamped bistable system driven by a gaussian white noise and perturbed by a weak monochromatic force signal is studied analytically in order to get amplitude dependent signal amplification factor a non perturbative scheme is put forward by taking into account all the terms of a perturbation series with amplitude of the signal as an expansion parameter an approximate analytic expression of the signal amplification factor is derived and compared with the numerical results the contributions of infinite number of relaxation modes of the stochastic dynamics to the response are also taken into account in the final expression the calculation of the response based on the derived expression requires only the knowledge of the first non trivial eigenvalue and the lowest eigenfunction of the unperturbed fokker planck operator

on the decidability of certain integer subgraph problems on context free graph languages we show the decidability of integer subgraph problems isps on context free sets of graphs l defined by hyperedge replacement systems hrss additionally we give a very general characterization of isps to be decidable on a set l an isp consists of a property s and a mapping f if j is a subgraph of a graph g then s g j is true or false and f g j is an integer we show the decidability of the following problem let 1 n be n isps that fulfill our characterization and let c be a set of conditions i o j that specify two isps i and j and a compare symbol o given a context free set of graphs l defined by a hrs is there a graph g l that has n subgraphs j1 j n such that s prod i g j holds true for i 1 n and s prod i g j i o s prod j g j j for each condition i o j

the recognition of series parallel digraphs we present a linear time algorithm to recognize the class of vertex series parallel vsp digraphs our method is based on the relationship between vsp digraphs and the class of edge series paralle

weakly noisy chaotic scattering received 30 april 2013 published 23 september 2013 the effect of a weak source of noise on the chaotic scattering is relevant to situations of physical interest we investigate how a weak source of additive uncorrelated gaussian noise affects both the dynamics and thetopology of a paradigmatic chaotic scattering problem as the one taking place in the open nonhyperbolic regimeof the h enon heiles hamiltonian system we have found long transients for the time escape distributions forcritical values of the noise intensity for which the particles escape slower as compared with the noiseless case an analysis of the survival probability of the scattering function versus the gaussian noise intensity shows asmooth curve with one local maximum and with one local minimum which are related to those long transientsand with the basin structure in phase space on the other hand the computation of the exit basins in phase spaceshows a quadratic curve for which the basin boundaries lose their fractal like structure as noise turned on doi 10 1103 physreve 88 032914 pacs number s 05

local search is a ptas for feedback vertex set in minor free graphs abstract we show that an extremely simple local search gives a ptas for the feedback vertex set fvs problem in minor free graphs it keeps exchanging a constant number of vertices to improve the current solution until a local optimum is reached the previous ptas by fomin lokshtanov raman and saurabh 1 despite theoretical efficiency is much more complicated in the sense that it combines many advanced algorithmic tools such as contraction decomposition framework by demaine and hajiaghayi 2 courcelle s theorem 3 and the robertson and seymour decomposition 4 our main technical contribution is to show that the local optimum only differs the global optimum by a 1 factor we do so by introducing steiner points those who are not in the local and optimal solutions to the standard analysis of local search we believe that our technique is of independent interest

an axiomatic definition of context free rewriting and its application to nlc graph grammars abstract an abstract notion of context free grammar is introduced it deals with abstract objects that can be words trees graphs or other combinatorial objects it is applied to nlc graph grammars introduced by rozenberg and janssens the monadic second order theory of a context free nlc set of graphs is decidable

monadic second order evaluations on tree decomposable graphs abstract every graph generated by a hyperedge replacement graph grammar can be represented by a tree namely the derivation tree of the derivation sequence that produced it certain functions on graphs can be computed recursively on the derivation trees of these graphs by using monadic second order logic and semiring homomorphisms we describe in a single formalism a large class of such functions polynomial and even linear algorithms can be constructed for some of these functions we unify similar results obtained by takamizawa 1982 bern 1987 arnborg 1991 and habel 1989

stochastic resonance in biological nonlinear evolution models we investigate stochastic resonance in the nonlinear one dimensional fisher eigen model fem which represents an archetypal model for biological evolution based on a global coupling scheme in doing so we consider different periodically driven fitness functions which govern the evolution of a biological phenotype population for the case of a simple harmonic fitness function we are able to derive the exact analytic solution for the asymptotic probability density a distinct feature of this solution is a phase lag between the driving signal and the linear response of the system furthermore for more complex systems a general perturbation theory linear response approximation is put forward using the latter approach we investigate stochastic resonance in terms of the spectral amplification measure for a quadratic a quartic single peaked and for a bistable fitness function our analytical results are also compared with those of detailed numerical simulations our findings vindicate that stochastic resonance does occur in these nonlinear globally coupled biological systems

query evaluation via tree decompositions a number of efficient methods for evaluating first order and monadic second order queries on finite relational structures are based on tree decompositions of structures or queries we systematically study these methods in the first part of the article we consider arbitrary formulas on tree like structures we generalize a theorem of courcelle 1990 by showing that on structures of bounded tree width a monadic second order formula with free first and second order variables can be evaluated in time linear in the structure size plus the size of the output in the second part we study tree like formulas on arbitrary structures we generalize the notions of acyclicity and bounded tree width from conjunctive queries to arbitrary first order formulas in a straightforward way and analyze the complexity of evaluating formulas of these fragments moreover we show that the acyclic and bounded tree width fragments have the same expressive power as the well known guarded fragment and the finite variable fragments of first order logic respectively

stochastic resonance induced by bounded noise and periodic signal in an asymmetric bistable system abstract stochastic resonance sr induced by the bounded noise in an asymmetric bistable system is investigated based on stochastic simulation the signal power amplification s p a is derived for the case of the additive modulated signal the simulation results indicate that 1 the sr phenomenon is weakened by the asymmetry of the system 2 increasing the frequency restricts the sr of the system 3 there is an optimum value of amplitude a matching the strongest sr phenomenon

signal to noise ratio gain of a noisy neuron that transmits subthreshold periodic spike trains the transmission properties of an integrate and fire neuron model that transmits coherent subthreshold spike trains in a shot noise environment are investigated by numerical simulation for very weak coherent couplings it is shown that the input output signal to noise ratio snr gain is easier to exceed unity while for stronger coherent couplings it is difficult to observe the snr gain larger than unity at the optimal noise intensity these observations are different from those acquired in the case of continuous noise our analysis further suggests that the larger snr gain in the very weak coherent coupling case should be due to the noise induced resonance it is also shown that there is more possibility of the snr gain above unity for slower periodic spike trains transmitted by the model the results may be useful in understanding the performance of real noisy neurons acting as signal processing elements

towards fixed parameter tractable algorithms for abstract argumentation abstract argumentation frameworks have received a lot of interest in recent years most computational problems in this area are intractable but several tractable fragments have been identified in particular dunne showed that many problems can be solved in linear time for argumentation frameworks of bounded tree width however these tractability results which were obtained via courcelle s theorem do not directly lead to efficient algorithms the goal of this paper is to turn the theoretical tractability results into efficient algorithms and to explore the potential of directed notions of tree width for defining larger tractable fragments as a by product we will sharpen some known complexity results

counting h colorings of partial k trees the problem of counting all h colorings of a graph g with n vertices is considered while the problem is in general p complete we give linear time algorithms that solve the main variants of this problem when the input graph g is a k tree or in the case where g is directed when the underlying graph of g is a k tree our algorithms remain polynomial even in the case where k o logn or in the case where the size of h is o n our results are easy to implement and imply the existence of polynomial time algorithms for a series of problems on partial k trees such as core checking and chromatic polynomial computation

a comparison of compatible finite and inductive graph properties abstract in the theory of hyperedge replacement grammars and languages one encounters three types of graph properties that play an important role in proving decidability and structural results the three types are called compatible finite and inductive graph properties all three of them cover graph properties that are well behaved with respect to certain operations on hypergraphs in this paper we show that the three notions are essentially equivalent consequently three lines of investigation in the theory of hyperedge replacement so far separated merge into one

size and treewidth bounds for conjunctive queries this article provides new worst case bounds for the size and treewith of the result q d of a conjunctive query q applied to a database d we derive bounds for the result size q d in terms of structural properties of q both in the absence and in the presence of keys and functional dependencies these bounds are based on a novel coloring of the query variables that associates a coloring number c q to each query q intuitively each color used represents some possible entropy of that variable using this coloring number we derive tight bounds for the size of q d in case i no functional dependencies or keys are specified and ii simple functional dependencies keys are given these results generalize recent size bounds for join queries obtained by atserias et al 2008 in the case of arbitrary compound functional dependencies we use tools from information theory to provide lower and upper bounds establishing a close connection between size bounds and a basic question in information theory our new coloring scheme also allows us to precisely characterize both in the absence of keys and with simple keys the treewidth preserving queries the queries for which the treewidth of the output relation is bounded by a function of the treewidth of the input database finally we give some results on the computational complexity of determining the size bounds and of deciding whether the treewidth is preserved

bounded treewidth as a key to tractability of knowledge representation and reasoning several forms of reasoning in ai like abduction closed world reasoning circumscription and disjunctive logic programming are well known to be intractable in fact many of the relevant problems are on the second or third level of the polynomial hierarchy in this paper we show how the notion of treewidth can be fruitfully applied to this area in particular we show that all these problems become tractable actually even solvable in linear time if the treewidth of the involved formulae or programs is bounded by some constant clearly these theoretical tractability results as such do not immediately yield feasible algorithms however we have recently established a new method based on monadic datalog which allowed us to design an efficient algorithm for a related problem in the database area in this work we exploit the monadic datalog approach to construct new algorithms for logic based abduction

parameterized algorithms for conflict free colorings of graphs abstract in this paper we study the conflict free coloring of graphs induced by neighborhoods a coloring of a graph is conflict free if every vertex has a uniquely colored vertex in its neighborhood the conflict free coloring problem is to color the vertices of a graph using the minimum number of colors such that the coloring is conflict free we consider both closed neighborhoods where the neighborhood of a vertex includes itself and open neighborhoods where a vertex does not include in its neighborhood we study the parameterized complexity of conflict free closed neighborhood coloring and conflict free open neighborhood coloring problems we show that both problems are fixed parameter tractable fpt when parameterized by the cluster vertex deletion number of the input graph this generalizes the result of gargano and rescigno theoretical computer science 2015 that conflict free coloring is fpt parameterized by the vertex cover number also we show that both problems admit an additive constant approximation algorithm when parameterized by the distance to threshold graphs we also study the complexity of the problem on special graph classes for split graphs we give a polynomial time algorithm for closed neighborhood conflict free coloring problem whereas we show that open neighborhood conflict free coloring is np complete for cographs we show that conflict free closed neighborhood coloring can be solved in polynomial time and conflict free open neighborhood coloring need at most three colors we show that interval graphs can be conflict free colored using at most four colors

complexity of conflict free colorings of graphs we consider conflict free colorings of graph neighborhoods each vertex of the graph must be assigned a color so that for each vertex v there is at least one color appearing exactly once in the neighborhood of v the goal is to minimize the number of used colors we consider both the case of closed neighborhoods when the neighborhood of a node includes the node itself and the case of open neighborhoods when a node does not belong to its neighborhood in this paper we study complexity aspects of the problem we show that the problem of conflict free coloring of closed neighborhoods is np complete moreover we give non approximability results for the conflict free coloring of open neighborhoods from a positive point of view both problems become tractable if parameterized by the vertex cover number or the neighborhood diversity number of the graph we present simple algorithms which improve on existing results

role of fluctuations in the response of coupled bistable units to weak time periodic driving forces we analyze the stochastic response of a finite set of globally coupled noisy bistable units driven by rather weak time periodic forces we focus on the stochastic resonance and phase frequency synchronization of the collective variable defined as the arithmetic mean of the variable characterizing each element of the array for single unit systems stochastic resonance can be understood with the powerful tools of linear response theory proper noise induced phase frequency synchronization for a single unit system in this linear response regime does not exist for coupled arrays our numerical simulations indicate an enhancement of the stochastic resonance effects leading to gains larger than unity as well as genuine phase frequency synchronization the nonmonotonicity of the response with the strength of the coupling strength is investigated comparison with simplifying schemes proposed in the literature to describe the random response of the collective variable is carried out

increasing the minimum degree of a graph by contractions abstract the degree contractibility problem is to test whether a given graph g can be modified to a graph of minimum degree at least d by using at most k contractions we prove the following three results first degree contractibility is np complete even when d 14 second it is fixed parameter tractable when parameterized by k and d third it is w 1 hard when parameterized by k we also study its variant where the input graph is weighted i e has some edge weighting and the contractions preserve these weights the weighted degree contractibility problem is to test if a weighted graph g can be contracted to a weighted graph of minimum weighted degree at least d by using at most k weighted contractions we show that this problem is np complete and that it is fixed parameter tractable when parameterized by k in addition we pinpoint a relationship with the problem of finding a minimal edge cut of maximum size in a graph and study the parameterized complexity of this problem and its variants

complexity of path forming games abstract for a number of two player games where players alternately choose the next vertex of a simple or an elementary path in a graph we consider the problem to determine whether for a given game instance there is a winning strategy for the first player we show several of these problems to be pspace complete in some special cases we obtain polynomial time algorithms based on graph rewriting or an intricate form of dynamic programming e g we show generalized geography and some other pspace complete problems to be linear time solvable on graphs with constant bounded treewidth

intractability of clique width parameterizations we show that edge dominating set hamiltonian cycle and graph coloring are w 1 hard parameterized by clique width it was an open problem explicitly mentioned in several papers whether any of these problems is fixed parameter tractable when parameterized by the clique width that is solvable in time g k cdot n o 1 on n vertex graphs of clique width k where g is some function of k only our results imply that the running time o n f k of many clique width based algorithms is essentially the best we can hope for up to a widely believed assumption from parameterized complexity namely fpt neq w 1

all structured programs have small tree width and good register allocation the register allocation problem for an imperative program is often modelled as the coloring problem of the interference graph of the control flow graph of the program the interference graph of a flow graph g is the intersection graph of some connected subgraphs of g these connected subgraphs represent the lives or life times of variables so the coloring problem models that two variables with overlapping life times should be in different registers for general programs with unrestricted gotos the interference graph can be any graph and hence we cannot in general color within a factor o n from optimality unless np p

the role of planarity in connectivity problems parameterized by treewidth for some years it was believed that for connectivity problems such as hamiltonian cycle algorithms running in time 2 o tw n o 1 called single exponential existed only on planar and other topologically constrained graph classes where tw stands for the treewidth of the n vertex input graph this was recently disproved by cygan et al 3 focs 2011 bodlaender et al 1 icalp 2013 and fomin et al 11 soda 2014 who provided single exponential algorithms on general graphs for most connectivity problems that were known to be solvable in single exponential time on topologically constrained graphs in this article we further investigate the role of planarity in connectivity problems parameterized by treewidth and convey that several problems can indeed be distinguished according to their behavior on planar graphs known results from the literature imply that there exist problems like cycle packing that cannot be solved in time 2 o tw log tw n o 1 on general graphs but that can be solved in time 2 o tw n o 1 when restricted to planar graphs our main contribution is to show that there exist natural problems that can be solved in time 2 o tw log tw n o 1 on general graphs but that cannot be solved in time 2 o tw log tw n o 1 even when restricted to planar graphs furthermore we prove that planar cycle packing and planar disjoint pathscannot be solved in time 2 o tw n o 1 the mentioned negative results hold unless the eth fails we feel that our results constitute a first step in a subject that can be further exploited

the monadic second order logic of graphs vii graphs as relational structures abstract relational structures form a unique framework in which various types of graphs and hypergraphs can be formalized and studied we define operations on structures that are compatible with monadic second order logic and that are powerful enough to represent context free graph and hypergraph grammars of various types namely the so called hyperedge replacement c ednce and separated handle rewriting grammars several results concerning monadic second order properties of the generated sets are obtained in a uniform way we also give a logical characterization of the equational sets of structures that generalizes the ones obtained by engelfriet and courcelle for hyperedge replacement and c ednce sets of graphs

syntactic recognizability of graphs with fuzzy attributes abstract we present a syntactic recognition theory for graphs with fuzzy edges and fuzzy nodes by employing the algebraic structure of magmoids several examples are illustrated and it is proved that the cut of a recognizable set of fuzzy graphs is not always recognizable as a set of crisp graphs the described theory is then applied for the recognition of fuzzy cognitive maps and the recognizability of interesting examples of sets of fuzzy cognitive maps is examined

two state markovian theory of input output frequency and phase synchronization abstract a markovian dichotomic system driven by a deterministic time periodic force is analyzed in terms of the statistical properties of the switching events between the states the consideration of the counting process of the switching events leads us to define a discrete phase we obtain expressions for the instantaneous output frequency and phase diffusion associated to the dichotomic process as well as for their cycle averages these expressions are completely determined by the rates of escape from both states they are a convenient starting point for the study of the stochastic frequency and phase synchronization in a wide range of situations both classical and quantum in which two metastable states are involved

decidability of the finiteness of ranges of tree transductions abstract the finiteness of ranges of tree transductions is shown to be decidable for tby the composition closure of macro tree transductions furthermore tby definable sets and tby computable relations are considered which are obtained by viewing a tree as an expression that denotes an element of a given algebra a sufficient condition on the considered algebra is formulated under which the finiteness problem is decidable for tby definable sets and for the ranges of tby computable relations the obtained result applies in particular to the class of string languages that can be defined by tby transductions via the yield mapping this is a large class which is proved to form a substitution closed full afl

listing all potential maximal cliques of a graph a potential maximal clique of a graph is a vertex set that induces a maximal clique in some minimal triangulation of that graph it is known that if these objects can be listed in polynomial time for a class of graphs the treewidth and the minimum fill in are polynomially tractable for these graphs we show here that the potential maximal cliques of a graph can be generated in polynomial time in the number of minimal separators of the graph thus the treewidth and the minimum fill in are polynomially tractable for all classes of graphs with a polynomial number of minimal separators

the bruhat chevalley order of parabolic group actions in general linear groups and degeneration for δ filtered modules abstract let k be an algebraically closed field and v a finite dimensional k space let gl v be the general linear group of v and p a parabolic subgroup of gl v now p acts on its unipotent radical p u and on p u lie p u the lie algebra of p u via the adjoint action more generally we consider the action of p on the l th member of the descending central series of p u denoted by p l u all instances when p acts on p l u for l 0 with a finite number of orbits are known in this note we give a complete combinatorial description of the closure relation on the set of p orbits on p l u i e the bruhat chevalley order for every finite case there is a canonical bijection between the set of p orbits on p l u and the set of isomorphism classes of filtered modules of a particular dimension vector e of a certain quasi hereditary algebra a t l these isomorphism classes in turn are given by the orbits of a reductive group g e on the variety r e of all a t l modules with filtration and dimension vector e the subcategory of a t l mod of all filtered a t l modules of dimension vector e is denoted by f e in our chief result theorem 1 1 we show that provided there is only a finite number of isomorphism classes of indecomposable modules in f the following three posets coincide 1 the bruhat chevalley order on the set of p orbits on p l u 2 the bruhat chevalley order on the set of g e orbits on r e 3 the poset opposite to the so called hom order on the set of isomorphism classes of f e the advantage of this hom order is that it is given purely by discrete invariants and that it can be computed explicitly for any given finite case theorem 1 1 then in turn allows us to explicitly determine the closure relations for the p orbits on p l u with the aid of this hom order we present some examples of hasse diagrams in an appendix

the monadic second order logic of graphs xii planar graphs and planar maps we prove that we can specify by formulas of monadic second order logic the unique planar embedding of a 3 connected planar graph if the planar graph is not 3 connected but given with a linear order of its set of edges we can also define a planar embedding by monadic second order formulas we cannot do so in general without the ordering even for 2 connected planar graphs the planar embedding of a graph can be specified by a relational structure called a map which is a graph enriched with a circular ordering of the edges incident with each vertex this circular ordering called a rotation system represents a planar embedding of the neighbourhood of each vertex for each connected map one can define a linear order on its vertices by formulas of monadic second order logic hence we have for planar graphs some kind of equivalence between linear orderings and planar embeddings

boundary classes for graph problems involving non local properties abstract we continue the study of boundary classes for np hard problems and focus on seven np hard graph problems involving non local properties hamiltonian cycle hamiltonian cycle through specified edge hamiltonian path feedback vertex set connected vertex cover connected dominating set and graph vc con dimension our main result is the determination of the first boundary class for feedback vertex set we also determine boundary classes for hamiltonian cycle through specified edge and hamiltonian path and give some insights on the structure of some boundary classes for the remaining problems

a partial k arboretum of graphs with bounded treewidth the notion of treewidth has seen to be a powerful vehicle for many graph algorithmic studies this survey paper wants to give an overview of many classes of graphs that can be seen to have a uniform upper bound on the treewidth of graphs in the class also some mutual relations between such classes are discussed

subthreshold stochastic resonance rectangular signals can cause anomalous large gains the main objective of this work is to explore aspects of stochastic resonance sr in noisy bistable symmetric systems driven by subthreshold periodic rectangular external signals possessing a large duty cycle of unity using a precise numerical solution of the langevin equation we carry out a detailed analysis of the behavior of the first two cumulant averages the correlation function and its coherent and incoherent parts we also depict the nonmonotonic behavior versus the noise strength of several sr quantifiers such as the average output amplitude i e the spectral amplification the signal to noise ratio and the sr gain in particular we find that with subthreshold amplitudes and for an appropriate duration of the pulses of the driving force the phenomenon of stochastic resonance is accompanied by sr gains exceeding unity this analysis thus sheds light on the interplay between nonlinearity and the nonlinear response which in turn yields nontrivial unexpected sr gains above unity

theory of frequency and phase synchronization in a rocked bistable stochastic system we investigate the role of noise in the phenomenon of stochastic synchronization of switching events in a rocked overdamped bistable potential driven by white gaussian noise the archetype description of stochastic resonance we present an approach to the stochastic counting process of noise induced switching events starting from the markovian dynamics of the nonstationary continuous particle dynamics one finds upon contraction onto two states a non markovian renewal dynamics a proper definition of an output discrete phase is given and the time rate of change of its noise average determines the corresponding output frequency the phenomenon of noise assisted phase synchronization is investigated in terms of an effective instantaneous phase diffusion the theory is applied to rectangular shaped rocking signals versus increasing input noise strengths in this case for an appropriate choice of the parameter values the system exhibits a noise induced frequency locking accompanied by a very pronounced suppression of the phase diffusion of the output signal precise numerical simulations corroborate very favorably our analytical results the novel theoretical findings are also compared with prior ones

stochastic resonance in a periodically driven linear system with multiplicative and periodically modulated additive white noises abstract the stochastic resonance sr of periodically driven linear system with multiplicative white noise and periodically modulated additive white noise is studied exact expressions of output signal to noise ratio are obtained the sr characteristics features are shown in two different situations the driven frequency is equal to the modulative frequency 1 and the driven frequency is not equal to the modulative frequency 1 the result was as follows the exact expression of output signal to noise ratio snr exhibits sr in three aspects in the case of 1 1 the curve of snr versus noise strength q exists a resonance peak this is a standard form of sr 2 a resonance peak exists in the snr vs curve in the region of 0 3 a maximum appears in the curve of snr as a function of the characteristic of signal itself the signal frequency it is of interest to examine the snr in the case of 1 from the exact expression of snr we see for 1 that the snr vs q curve exhibits a minimum firstly then a maximum that is to say it exhibits a suppression firstly resonance later and is very different from the case of 1