sampling decomposable graphs using a markov chain on junction trees this paper makes two contributions to the computational geometry of decomposable graphs aimed primarily at facilitating statistical inference about such graphs where they arise as assumed conditional independence structures in stochastic models the rst of these provides sucient conditions under which it is possible to completely connect two disconnected cliques of vertices or perform the reverse procedure yet maintain decomposability of the graph the second is a new markov chain monte carlo sampler for arbitrary positive distributions on decomposable graphs taking a junction tree representing the graph as its state variable the resulting methodology is illustrated with two numerical experiments eld model determination

a generalized time quantifier approach to approximate reasoning abstract in this paper a rather expressive fuzzy temporal logic for linear time is introduced first this logic is a multivalued generalization lukasiewicz style of a two valued linear time temporal logic based on e g the until operator second it is obtained by introducing a generalized time quantifier a generalization of the partition operator investigated by shen applied to fuzzy time sets in this fuzzy temporal logic generalized compositional rules of inference suitable for approximate reasoning in a temporal setting are presented as valid formulas some medical examples illustrate our approach

an efficient algorithm for computing bisimulation equivalence we propose an efficient algorithmic solution to the problem of determining a bisimulation relation on a finite structure working both on the explicit and on the implicit symbolic representation as far as the explicit case is concerned starting from a set theoretic point of view we propose an algorithm that optimizes the solution to the relational coarsest partition problem given by paige and tarjan siam j comput 16 6 1987 973 its use in model checking packages is also discussed and tested for well structured graphs our algorithm reaches a linear worst case behaviour the proposed algorithm is then re elaborated to produce a symbolic version

fast bayes and the dynamic junction forest abstract it has been shown that junction tree algorithms can provide a quick and efficient method for propagating probabilities in complex multivariate problems when they can be described by a fixed conditional independence structure in this paper we formalise and illustrate with two practical examples how these probabilistic propagation algorithms can be applied to high dimensional processes whose conditional independence structure as well as their underlying distributions are augmented through the passage of time

approximation to a class of non autonomous systems by dynamic fuzzy inference marginal linearization method in this paper a dynamic fuzzy inference marginal linearization dfiml method is proposed for modeling nonlinear dynamic systems this method can transfer a group of input output data into a time variant fuzzy system with variable coefficients it is shown that solutions of time variant fuzzy systems generalized by dfiml method are universal approximators to solutions of a class of non autonomous systems also the analytical solutions of these time variant fuzzy systems can be obtained finally a simulation example is provided to illustrate the validity and potential of the developed techniques

fuzzy controls under various fuzzy reasoning methods abstract a fuzzy logic controller consists of linguistic control rules tied together by means of two concepts fuzzy implications and a compositional rule of inference most of the existing fuzzy logic controllers are based on the approximate reasoning method due to mamdani this paper introduces other fuzzy implications such as the arithmetic rule and maximin rule for linguistic control rules and compares control results for a plant model with first order delay under various approximate reasoning methods moreover control results are compared when the widths of fuzzy sets of linguistic control rules are changed

small schemes and varieties of minimal degree we prove that if x p r is any 2 regular scheme in the sense of castelnuovo mumford then x is small this means that if l is a linear space and y l x is finite then y is linearly independent in the sense that the dimension of the linear span of y is deg y 1 the converse is true and well known for finite schemes but false in general the main result of this paper is that the converse small implies 2 regular is also true for reduced schemes algebraic sets this is proven by means of a delicate geometric analysis leading to a complete classification we show that the components of a small algebraic set are varieties of minimal degree meeting in a particularly simple way from the classification one can show that if x p r is 2 regular then so is xred and so also is the projection of x from any point of x our results extend the del pezzo bertini classification of varieties of minimal degree the charac terization of these as the varieties of regularity 2 by eisenbud goto and the construction of 2 regular square free monomial ideals by froberg 0 introduction throughout this paper we will work with projective schemes x p r over an algebraically closed field k the castelnuovo mumford regularity of x p r is a basic homological measure of the complexity of x and its embedding in p r that gives a bound for the degrees of the generators of the defining ideal ix of x and for many other invariants the only schemes of regular ity 1 are the linear spaces but no classification is known for projective schemes of regularity 2 in this paper we prove a structure theorem for reduced 2 regular schemes showing that their irreducible components are varieties of minimal degree and characterizing how these components can meet we also show that the reduced structure on any 2 regular scheme is 2 regular and thus we obtain a complete description of the reduced structures on 2 regular schemes since a high veronese re embedding of any zero dimensional scheme is 2 regular one cannot hope to characterize the isomorphism types of all 2 regular nonreduced schemes before stating our results we review some basic notions for any subscheme x p r we write span x for the smallest linear subspace of p r containing x recall that every variety reduced irreducible scheme x p r satisfies the condition deg x 1 codim x span x

network based heuristics for constraint satisfaction problems abstract many ai tasks can be formulated as constraint satisfaction problems csp i e the assignment of values to variables subject to a set of constraints while some csps are hard those that are easy can often be mapped into sparse networks of constraints which in the extreme case are trees this paper identifies classes of problems that lend themselves to easy solutions and develops algorithms that solve these problems optimally the paper then presents a method of generating heuristic advice to guide the order of value assignments based on both the sparseness found in the constraint network and the simplicity of tree structured csps the advice is generated by simplifying the pending subproblems into trees counting the number of consistent solutions in each simplified subproblem and comparing these counts to decide among the choices pending in the original problem

counting and exploring sizes of markov equivalence classes of directed acyclic graphs when learning a directed acyclic graph dag model via observational data one generally cannot identify the underlying dag but can potentially obtain a markov equivalence class the size the number of dags of a markov equivalence class is crucial to infer causal effects or to learn the exact causal dag via further interventions given a set of markov equivalence classes the distribution of their sizes is a key consideration in developing learning methods however counting the size of an equivalence class with many vertices is usually computationally infeasible and the existing literature reports the size distributions only for equivalence classes with ten or fewer vertices in this paper we develop a method to compute the size of a markov equivalence class we first show that there are five types of markov equivalence classes whose sizes can be formulated as five functions of the number of vertices respectively then we introduce a new concept of a rooted sub class the graph representations of rooted subclasses of a markov equivalence class are used to partition this class recursively until the sizes of all rooted subclasses can be computed via the five functions the proposed size counting is efficient for markov equivalence classes of sparse dags with hundreds of vertices finally we explore the size and edge distributions of markov equivalence classes and find experimentally that in general 1 most markov equivalence classes are half completed and their average sizes are small and 2 the sizes of sparse classes grow approximately exponentially with the numbers of vertices

a structural markov property for decomposable graph laws that allows control of clique intersections summary we present a new kind of structural markov property for probabilistic laws on decomposable graphs which allows the explicit control of interactions between cliques and so is capable of encoding some interesting structure we prove the equivalence of this property to an exponential family assumption and discuss identifiability modelling inferential and computational implications

rough data deduction based on the upper approximation this paper describes how to construct a structure called a rough deduction space it is an extension of an approximation space and incorporates a deduction relation related to data connections in the rough deduction space a notion of data deduction is introduced and is referred to as rough data deduction based on integrated information of both the upper approximation and the deduction relation rough data deduction accomplishes deductions from data to data which is different from any logical deduction in mathematical logic research on rough data deduction covers two activities the rough data deduction with respect to an equivalence relation and rough data deductions with respect to different equivalence relations the activities also concern the relationship between rough data deduction and rough relations that are rough representations of the deduction relation this leads to properties involving approximate features implied by rough data deduction and reflecting the characteristic that rough data deduction can describe rough data connections in particular since the research correlates closely to granules it may offer an avenue of research on granular computing as an example a specific problem is modeled by a rough deduction space the rough data connections in the problem are described by use of rough data deduction

approximate reasoning with time abstract the need to make time dependent assumptions is frequently encountered in many systems especially in dynamical systems this paper presents a theoretical study of the representation and manipulation of some vague concepts in the temporally changing world our approach to the modeling is based on zadeh s theory of possibility we introduce a concept of similarity index in reasoning with time we present two different types of widely used models one rule based and another resolution based for reasoning with time we consider simply yet concrete examples to illustrate the usefulness of the proposed models

simple linear time algorithms to test chordality of graphs test acyclicity of hypergraphs and selectively reduce acyclic hypergraphs chordal graphs arise naturally in the study of gaussian elimination on sparse symmetric matrices acyclic hypergraphs arise in the study of relational data bases rose tarjan and lueker siam j c

rough set based logics for multicriteria decision analysis in this paper we propose some decision logic languages for rule representation in rough set based multicriteria analysis the semantic models of these logics are data tables each of which is comprised of a finite set of objects described by a finite set of criteria attributes the domains of the criteria may have ordinal properties expressing preference scales while the domains of the attributes may not the validity support and confidence of a rule are defined via its satisfaction in the data table

sequential and parallel triangulating algorithms for elimination game and new insights on minimum degree elimination game is a well known algorithm that simulates gaussian elimination of matrices on graphs and it computes a triangulation of the input graph the number of fill edges in the computed triangulation is highly dependent on the order in which elimination game processes the vertices and in general the produced triangulations are neither minimum nor minimal in order to obtain a triangulation which is close to minimum the minimum degree heuristic is widely used in practice but until now little was known on the theoretical mechanisms involved in this paper we show some interesting properties of elimination game in particular that it is able to compute a partial minimal triangulation of the input graph regardless of the order in which the vertices are processed this results in a new algorithm to compute minimal triangulations that are sandwiched between the input graph and the triangulation resulting from elimination game one of the strengths of the new approach is that it is easily parallelizable and thus we are able to present the first parallel algorithm to compute such sandwiched minimal triangulations in addition the insight that we gain through elimination game is used to partly explain the good behavior of the minimum degree algorithm we also give a new algorithm for producing minimal triangulations that is able to use the minimum degree idea to a wider extent

dynamical fuzzy reasoning and its application to system modeling abstract many fuzzy reasoning methods do not consider temporal information even though time delays are an inherent part of many kinds of information exchange we propose therefore a method of dynamical fuzzy reasoning that has a time delay between premise and consequent in fuzzy rule base knowledge in this paper we consider this reasoning method qualitatively and show how to apply it to system models whose basis is system dynamics

three partition refinement algorithms we present improved partition refinement algorithms for three problems lexicographic sorting relational coarsest partition and double lexical ordering our double lexical ordering algorithm uses a new efficient method for unmerging two sorted sets

a note on minimal d separation trees for structural learning structural learning of a bayesian network is often decomposed into problems related to its subgraphs although many approaches without decomposition were proposed in 2006 xie geng and zhao proposed using a d separation tree to improve the power of conditional independence tests and the efficiency of structural learning in our research note we study a minimal d separation tree under a partial ordering by which the maximal efficiency can be obtained our results demonstrate that a minimal d separation tree of a directed acyclic graph dag can be constructed by searching for the clique tree of a minimal triangulation of the moral graph for the dag

fuzzy reasoning as a control problem different from the dominant view of treating fuzzy reasoning as generalization of classical logical inference in this paper fuzzy reasoning is treated as a control problem a new fuzzy reasoning method is proposed that employs an explicit feedback mechanism to improve the robustness of fuzzy reasoning the fuzzy rule base given a priori serves as a controlled object and the fuzzy reasoning method serves as the corresponding controller the fuzzy rule base and the fuzzy reasoning method constitute a control system that may be open loop or closed loop depending on the underlying reasoning goals constraints the fuzzy rule base the fuzzy reasoning method and the corresponding reasoning goals constraints define the three distinct ingredients of fuzzy reasoning while various existing fuzzy reasoning methods are essentially a static mapping from the universe of single fuzzy premises to the universe of single fuzzy consequences the new fuzzy reasoning method maps sequences of fuzzy premises to sequences of fuzzy consequences and is a function of the underlying reasoning goals constraints the monte carlo simulation shows that the new fuzzy reasoning method is much more robust than the optimal fuzzy reasoning method proposed in our previous work the explicit feedback mechanism embedded in the fuzzy reasoning method does significantly improve the robustness of fuzzy reasoning which is concerned with the effects of perturbations associated with given fuzzy rule bases and or fuzzy premises on fuzzy consequences the work presented in this paper sets a new starting point for various principles of feedback control and optimization to be applied in fuzzy reasoning or logical inference and to explore new forms of reasoning including robust reasoning and adaptive reasoning it can be also expected that the new fuzzy reasoning method presented in this paper can be used for modeling and control of complex systems and for decision making under complex environments

rough sets theory for multicriteria decision analysis the original rough set approach proved to be very useful in dealing with inconsistency problems following from information granulation it operates on a data table composed of a set u of objects actions described by a set q of attributes its basic notions are indiscernibility relation on u lower and upper approximation of either a subset or a partition of u dependence and reduction of attributes from q and decision rules derived from lower approximations and boundaries of subsets identified with decision classes the original rough set idea is failing however when preference orders of attribute domains criteria are to be taken into account precisely it cannot handle inconsistencies following from violation of the dominance principle this inconsistency is characteristic for preferential information used in multicriteria decision analysis mcda problems like sorting choice or ranking in order to deal with this kind of inconsistency a number of methodological changes to the original rough sets theory is necessary the main change is the substitution of the indiscernibility relation by a dominance relation which permits approximation of ordered sets in multicriteria sorting to approximate preference relations in multicriteria choice and ranking problems another change is necessary substitution of the data table by a pairwise comparison table where each row corresponds to a pair of objects described by binary relations on particular criteria in all those mcda problems the new rough set approach ends with a set of decision rules playing the role of a comprehensive preference model it is more general than the classical functional or relational model and it is more understandable for the users because of its natural syntax in order to workout a recommendation in one of the mcda problems we propose exploitation procedures of the set of decision rules finally some other recently obtained results are given rough approximations by means of similarity relations rough set handling of missing data comparison of the rough set model with sugeno and choquet integrals and results on equivalence of a decision rule preference model and a conjoint measurement model which is neither additive nor transitive

the complexity of acyclic conjunctive queries this paper deals with the evaluation of acyclic booleanconjunctive queries in relational databases by well known resultsof yannakakis 1981 this problem is solvable in polynomial time its precise complexity however has not been pinpointed so far weshow that the problem of evaluating acyclic boolean conjunctivequeries is complete for logcfl the class of decision problems thatare logspace reducible to a context free language since logcfl iscontained in ac1 and nc2 the evaluation problem of acyclic booleanconjunctive queries is highly parallelizable we present a paralleldatabase algorithm solving this problem with alogarithmic number ofparallel join operations the algorithm is generalized to computingthe output of relevant classes of non boolean queries we also showthat the acyclic versions of the following well known database andai problems are all logcfl complete the query output tuple problemfor conjunctive queries conjunctive query containment clausesubsumption and constraint satisfaction the logcfl completenessresult is extended to the class of queries of bounded tree widthand to other relevant query classes which are more general than theacyclic queries

analysis and design of time variant fuzzy systems based on dynamic fuzzy inference in this paper a class of time variant fuzzy systems is designed and analyzed firstly a novel model of dynamic fuzzy inference dfi is proposed and the corresponding dfi method is obtained then the response abilities of time variant fuzzy systems constructed by the dfi method are analyzed some sufficient conditions for time variant fuzzy systems as step functions fitted functions and interpolation functions are derived furthermore a sufficient and necessary condition for time variant fuzzy systems as interpolation functions is also deduced in addition the approximation problem of time variant fuzzy systems is discussed it is proved that time variant fuzzy systems constructed by the dfi method are universal approximators to a class of nonlinear systems in addition the approximation accuracy of the corresponding time variant fuzzy systems is investigated finally a simulation experiment is provided to demonstrate how to design a time variant fuzzy system in order to approximate a given nonlinear system to a desired accuracy

connections in acyclic hypergraphs abstract we demonstrate a sense in which the equivalence between blocks subgraphs without articulation points and biconnected components subgraphs in which there are two edge disjoint paths between any pair of nodes that holds in ordinary graph theory can be generalized to hypergraphs the result has an interpretation for relational databases that the universal relations described by acyclic join dependencies are exactly those for which the connections among attributes are defined uniquely we also exhibit a relationship between the process of graham reduction graham 1979 of hypergraphs and the process of tableau reduction aho sagiv and ullman 1979 that holds only for acyclic hypergraphs

fuzzy reasoning method by optimizing the similarity of truth tables this paper presents a new fuzzy reasoning method by optimizing the similarity of truth tables os method for short its basic idea is to find a fuzzy set such that the truth tables generated by the antecedent rule and the consequent rule are as similar as possible based on this idea the principle of os method and the fuzzy reasoning with os method are given and discussed and then the os methods with certain similarity measure and several fuzzy implications are investigated finally numerical examples are analyzed to compare the proposed method with compositional rule of inference cri method

a fuzzy temporal rule based velocity controller for mobile robotics this paper describes a velocity controller implemented on a nomad 200 mobile robot the controller has been developed for wall following behaviour and its design is modularized into two blocks angular and linear velocity control a simple design and implementation was made for the former with the aim of focusing the design efforts on the linear velocity control block in order to remark the usefulness of this task the latter has been implemented using an explicit model for knowledge representation and reasoning called fuzzy temporal rules ftrs this model enables to explicitly incorporate time as a variable due to which the evolution of variables in a temporal reference can be described using this mechanism we obtain linear velocity values that are adapted to each different circumstance and thus a higher average velocity as well as smoother and more robust behaviours are achieved

on the desirability of acyclic database schemes a class of database schemes called acychc was recently introduced it is shown that this class has a number of desirable properties in particular several desirable properties that have been studied by other researchers m very different terms are all shown to be eqmvalent to acydicity in addition several equivalent charactenzauons of the class m terms of graphs and hypergraphs are given and a smaple algorithm for determining acychclty is presented also given are several eqmvalent characterizations of those sets m of multivalued dependencies such that m is the set of murlvalued dependencies that are the consequences of a given join dependency several characterizations for a conflict free in the sense of lien set of muluvalued dependencies are provided

rough set analysis of relational structures in classical rough set theory objects are partitioned into equivalence classes based on their attribute values which essentially represent the functional information associated with the objects therefore rough set theory can be viewed as a theory of functional granulation in contrast relational information systems riss specify the relationships between objects instead of their properties this study presents a rough set analysis of relational structures which are more general than functional information systems fiss and riss unlike classical rough set theory in which the attribute values of objects fully determine the indiscernibility relation the rough set analysis of relational structures must account for the relationships between objects this study considers three important concepts of indiscernibility with respect to relational structures congruence bisimulation and exact equivalence using these indiscernibility relations we investigate rough approximations and knowledge reduction this study extends the application scope of rough set analysis from table style information systems to relational structures this extension is important because relational structures play a crucial role in the processing of complex data such as graph mining or social network analysis