minimal representation of directed hypergraphs in this paper the problem of minimal representations for particular classes of directed hypergraphs is analyzed various concepts of minimal representations of directed hypergraphs called minimal equivalent hypergraphs are introduced as extensions to the concepts of transitive reduction and minimum equivalent graph of directed graphs in particular we consider equivalent hypergraphs which are minimal with respect to all parameters which may be adopted to characterize a given hypergraph number of hyperarcs number of adjacency lists required for the representation length of the overall description etc the relationships among the various concepts of minimality are discussed and their computational properties are analyzed in order to derive such results a graph representation of hypergraphs is introduced

applications of field theoretic renormalization group methods to reaction diffusion problems we review the application of field theoretic renormalization group rg methods to the study of fluctuations in reaction diffusion problems we first investigate the physical origin of universality in these systems before comparing rg methods to other available analytic techniques including exact solutions and smoluchowski type approximations starting from the microscopic reaction diffusion master equation we then pedagogically detail the mapping to a field theory for the single species reaction ka a k we employ this particularly simple but non trivial system to introduce the field theoretic rg tools including the diagrammatic perturbation expansion renormalization and callan symanzik rg flow equation we demonstrate how these techniques permit the calculation of universal quantities such as density decay exponents and amplitudes via perturbative dc d expansions with respect to the upper critical dimension dc with these basics established we then provide an overview of more sophisticated applications to multiple species reactions disorder effects l evy flights persistence problems and the influence of spatial boundaries we also analyse field theoretic approaches to non equilibrium phase transitions separating active from absorbing states we focus particularly on the generic directed percolation universality class as well as on the most prominent exception to this class even offspring branching and annihilating random walks finally we summarize the state of the field and present our perspective on outstanding problems for the future

dynamic response optimization using an active set rqp algorithm a recently developed recursive quadratic programming rqp algorithm is applied to dynamic response design problems the algorithm incorporates updated hessians of the lagrange function and uses an active set strategy in which only a subset of the constraints is included in the direction finding qp subproblem hessian updating with dynamic response constraints presents some difficulties the primary difficulty is that the total number of constraints and the location of time points where they have to be imposed can change from iteration to iteration this can cause inconsistencies in hessian updating if proper numerical procedures are not used a numerical procedure to handle the situation is developed implemented and evaluated automatic restarting procedures are necessary for proper convergence of the algorithm the new algorithm is robust as well as more efficient than the purely linear algorithm the active set strategy plays an important role for application to dynamic response problems the rqp algorithms that do not use such a strategy are not applicable to this class of problems

finding the k best policies in a finite horizon markov decision process abstract directed hypergraphs represent a general modelling and algorithmic tool which have been successfully used in many different research areas such as artificial intelligence database systems fuzzy systems propositional logic and transportation networks however modelling markov decision processes using directed hypergraphs has not yet been considered in this paper we consider finite horizon markov decision processes mdps with finite state and action space and present an algorithm for finding the k best deterministic markov policies that is we are interested in ranking the first k deterministic markov policies in non decreasing order using an additive criterion of optimality the algorithm uses a directed hypergraph to model the finite horizon mdp it is shown that the problem of finding the optimal policy can be formulated as a minimum weight hyperpath problem and be solved in linear time with respect to the input data representing the mdp using different additive optimality criteria

epidemic models and percolation the authors argue that local epidemic models with immunisation are in the same universality class as percolation cluster growth models and show that the static exponents are equal to all orders in the epsilon expansion they calculate the dynamic exponent nu t 1 1 28 epsilon o epsilon 2 and relate this to other exponents involving the chemical distance

a hybrid formulation for treatment of point wise state variable constraints in dynamic response optimization abstract this paper presents methods of design sensitivity analysis and optimization of dynamic response of mechanical and structural systems the point wise state variable constraint function is divided into time sub domains such that each sub domain contains only one local maximum point then the original constraint is replaced by a number of equivalent functional constraints each functional constraint is the integration of the positive value of the original constraint over its own time sub domain a direct differentiation method and three adjoint variable methods of design sensitivity analysis are presented all of these methods are discussed and compared it turns out that two of the adjoint variable methods are more efficient than others a hybrid optimization algorithm based on these methods is proposed in detail two problems are solved for optimal design comparisons of results with those available in the literature are made numerical experience with the proposed method is discussed in detail it is concluded that the new formulation is extremely efficient and converges to either optimal or near optimal solutions without any difficulty

structural optimization using equivalent static loads at all time intervals a quasi static structural optimization for elastic structures under dynamic loads is presented an equivalent static load esl set is defined as a static load set which generates the same displacement field as that from a dynamic load at a certain time multiple esl sets calculated at all the time intervals are employed to represent the various states of the structure under the dynamic load they can cover all the critical states that might happen at arbitrary times the continuous characteristics of a dynamic load are considered by multiple static load sets the calculated sets of esls are utilized as a multiple loading condition in the optimization process a design cycle is defined as a circulated process between an analysis domain and a design domain the analysis domain gives the loading condition needed in the design domain the design domain gives a new updated design to be verified by the analysis domain in the next design cycle the design cycles are iterated until the design converges structural optimization with dynamic loads is tangible by the proposed method standard example problems are solved to verify the validity of the method

on line algorithms for satisfiability problems with uncertainty in this paper the problem of the on line satisfiability of a horn formula with uncertainty is addressed we show how to represent a significant class of formulae by weighted directed hypergraphs and we present two algorithms that solve the on line sat problem and find a minimal interpretation for the formula working on the dynamic hypergraph representation these algorithms make increasing assumptions on the formula and we will find that the second one solves the on line sat problem with a total time linear in the size of the formula matching the optimal result for boolean horn formulae

crossover scaling functions and an extended minimal subtraction scheme abstract a field theoretic renormalization group method is presented which is capable of dealing with crossover problems associated with a change in the upper critical dimension the method leads to flow functions for the parameters and coupling constants of the model which depend on the set of parameters that characterize the fixed point landscape of the underlying problem similar to nelson s trajectory integral method any vertex function can be expressed as a line integral along a renormalization group trajectory which in the field theoretic formulation are given by the characteristics of the corresponding callan symanzik equation the field theoretic renormalization automatically leads to a separation of the regular and singular parts of all crossover scaling functions the method is exemplified for the crossover problem in magnetic phase transitions percolation problems and quantum phase transitions the broad applicability of the method is emphasized

design sensitivity analysis and optimization of dynamic response abstract the paper presents methods of design sensitivity analysis and optimization of dynamic response of mechanical and structural systems a key feature of the paper is the development of procedures to handle point wise state variable constraints difficulties with a previous treatment where such constraints were transformed to equivalent integral constraints are noted and explained from theoretical as well as engineering standpoints an alternate treatment of such constraints is proposed developed and evaluated in this treatment each point wise state variable constraint is replaced by several constraints that are imposed at all the local max points for the original constraint function the differential equations of motion are formulated in the first order form so as to handle more general problems the direct differentiation and adjoint variable methods of design sensitivity analysis to deal with the point wise constraints are presented with the adjoint variable methods there are two ways of calculating design sensitivity coefficients the first approach uses an impulse load and the second approach uses a step load for the corresponding adjoint equation since the adjoint variable methods are better for a large class of problems an efficient computational algorithm with these methods is presented in detail optimum results for several problems are obtained and compared with those available in the literature the new formulation works extremely well as precise optimum designs are obtained

an on line edge deletion problem there is given an undirected graph g v e from which edges are deleted one at a time and about which questions of the type are the vertices u and v in the same connected component have to be answered on line there is presented an algorithm which maintains a data structure in which each question is answered in constant time and for which the total time involved in answering q questions and maintaining the data structure is o q i vi led

dynamic maintenance of directed hypergraphs abstract in this paper we are concerned with the on line maintenance of directed hypergraphs a generalization of directed graphs previously introduced in the literature in particular we show how to maintain efficiently information about hyperpaths while new hyperarcs are inserted we present a data structure which allows us to check whether there exists a hyperpath between an arbitrarily given pair of nodes in constant time and to return such a hyperpath in a time which is linear in its size the total time required to maintain the data structure during the insertion of new hyperarcs is o mn where m is the total size of the description of the hyperarcs and n is the number of nodes this generalizes a previous result known for directed graphs and has applications in several areas of computer science such as rewriting systems database schemes logic programming and problem solving an extension of these results to hyperpaths between sets of nodes is also presented

amortized efficiency of a path retrieval data structure a data structure is presented for the problem of maintaining a digraph under an arbitrary sequence of two kinds of operations an add operation that inserts an arc in the digraph and a searchpath operation that checks the presence of a path between a pair of nodes our data structure supports both operations in o n amortized time and requires o n2 space where n is the number of nodes in the digraph

max horn sat and the minimum cut problem in directed hypergraphs in this paper we consider the maximum horn satisfiability problem which is reduced to the problem of finding a minimum cardinality cut on a directed hypergraph for the latter problem we propose different ip formulations related to three different definitions of hyperpath weight we investigate the properties of their linear relaxations showing that they define a hierarchy the weakest relaxation is shown to be equivalent to the relaxation of a well known ip formulation of max horn sat and to a max flow problem on hypergraphs the tightest relaxation which is a disjunctive programming problem is shown to have integer optimum the intermediate relaxation consists in a set covering problem with a possible exponential number of constraints this latter relaxation provides an approximation of the convex hull of the integer solutions which as proven by the experimental results given is much tighter than the one known in the literature 1998 the mathematical programming society inc published by elsevier science b v

graph algorithms for functional dependency manipulation abstract a graph theoretic approach for the representation of functional dependenoes in relauonal databases is introduced and applied in the construction of algorithms for manipulating dependencies this approach allows a homogeneous treatment of several problems closure minimization etc which leads to simpler proofs and m some cases more efficient algorithms than in the current literature categories and subject descriptors f 2 2 analysis of algorithms and problem complexity nonnumencal algorithms and problems computations on d screte structures g 2 2 diserete mathematics graph theory graph algorithms h 2 1 database management logical design normal forms schema and subschema general terms algorithms design management theory additional key words and phrases closure computational complexity functional dependency fd graph minimal coverings relational database 1 introduction

structural shape optimization using equivalent static loads transformed from dynamic loads in structural optimization static loads are generally utilized although real external forces are dynamic dynamic loads have been considered only in small scale problems recently an algorithm for dynamic response optimization using transformation of dynamic loads into equivalent static loads has been proposed the transformation is conducted to match the displacement fields from dynamic and static analyses this algorithm can be applied to large scale problems however the application has been limited to size optimization the present study applies the algorithm to shape optimization because the number of degrees of freedom of finite element models is usually very large in shape optimization it is difficult to conduct dynamic response optimization with conventional methods that directly treat dynamic response in the time domain the optimization process is carried out by interfacing an optimization system and an analysis system for structural dynamics various examples are solved to verify the algorithm the results are compared to the results from static loads it is found that the algorithm using static loads transformed from dynamic loads based on displacement is valid for very large scale shape optimization problems copyright 2005 john wiley sons ltd

on the range of validity of the 6 e expansion for percolation in 6 epsilon dimensions the critical properties of percolation can be computed starting from a phi 3 theory having the same symmetry of the one state potts model the authors argue that this fixed point must be unstable with respect to a phi 4 interaction in two dimensions therefore a phi 4 perturbation is relevant this suggestion is confirmed by an explicit two loops computation

auction algorithms for shortest hyperpath problems the auction reduction algorithm is a strongly polynomial version of the auction method for the shortest path problem in this paper we extend the auction reduction algorithm to different types of shortest hyperpath problems in directed hypergraphs the results of preliminary computational experiences show that the auction reduction method is comparable to other known methods for specific classes of hypergraphs

directed hypergraphs just as ordinary hypergraphs are a generalization of graphs directed hypergraphs dh are a natural generalization of digraphs a dh consists of a set of vertices v and a set of hyperarcs h where a hyperarc is a pair s v s non empty subset of v and v v dhs have a variety of applications they have been used to represent functional dependency in databases horn formulae in propositional logic and or graphs context free grammars etc in the paper after providing a brief historical introduction on the notion of dh and some relevant applications various problems regarding dhs are surveyed and analyzed in particular we consider the complexity of the reachability problem together with its application in the related satisfiability problem for horn cnf formulae and the computation of transitive closure and transitive reduction of directed hypergraphs together with its application to the computation of minimum coverings for a set of functional dependencies finally a short introduction to the problem of computing shortest hyperpaths in directed hypergraphs is provided

a hyperscaling relation in site bond correlated percolation a novel approach is used to construct a field theoretical model of site bond percolation the exponents nu and eta are calculated in an epsilon 6 d expansion for both ising and percolation fields and the scaling relation nu p 2 d 2 is demonstrated to hold to order one loop for d 4 using the equations of motion the scaling relation nu p 2 d 2 eta 1 is shown to hold to all orders extending below four dimensions although this scaling relation is shown to fail for d 1 epsilon it is argued that it is still valid for d or 3

linear time analysis of properties of conflict free and general petri nets we introduce the notion of a t path within petri nets and propose to adopt the model of directed hypergraphs in order to determine properties of nets in particular we study the relationships between t paths and firable sequences of transitions let us consider a petri net p and the set of places with a positive marking in m 0 i e p 0 p m 0 p 0 if we regard the net as a directed graph the existence of a simple path from any place in p 0 to a transition t is of course a necessary condition for the potential firability of t this is sufficient only if the net is a state machine where t t 1 for all t t in this paper we show that the existence of a t path from any subset of p 0 to a transition t is a more restrictive condition and is again a necessary condition for the potential firability of t but in this case a if p is a conflict free petri net this is also a sufficient condition b if p is a general petri net t is potentially firable by increasing the number of tokens inp 0 for conflict free nets cfpn we consider the following problems a determining the set of firable transitions b determining the set of coverable places c determining the set of live transitions d deciding the boundedness of the net for all these problems we provide algorithms requiring linear space and time i e o p t a for a net p previous results for this class of networks are given by howell et al 1987 20 providing algorithms for solving problems in conflict free nets in o p x t time and space given a petri net and a marking m the well known coverability problem consists in finding a reachable marking m such that m m this problem is known to be expspace hard rackoff 1978 33 for general petri nets we provide a partial answer to this problem m is coverable by augmentation if it is coverable from an augmented markingm 0 of the initial marking m 0 m 0 m 0 and for all p p m 0 p 0 if m 0 p 0 we solve this problem in linear time the algorithms for computing t paths are incremental it is possible to modify the network adding new places transitions arcs tokens and update the set of potentially firable transitions and coverable places without recomputing them from scratch this feature is meaningful when used during the interactive design of a system