hit and run algorithms for the identification of nonredundant linear inequalities two probabilistic hit and run algorithms are presented to detect nonredundant constraints in a full dimensional system of linear inequalities the algorithms proceed by generating a random sequence of interior points whose limiting distribution is uniform and by searching for a nonredundant constraint in the direction of a random vector from each point in the sequence in the hypersphere directions algorithm the direction vector is drawn from a uniform distribution on a hypersphere in the computationally superior coordinate directions algorithm a search is carried out along one of the coordinate vectors the algorithms are terminated through the use of a bayesian stopping rule computational experience with the algorithms and the stopping rule will be reported

pure adaptive search in global optimization pure adaptive seach iteratively constructs a sequence of interior points uniformly distributed within the corresponding sequence of nested improving regions of the feasible space that is at any iteration the next point in the sequence is uniformly distributed over the region of feasible space containing all points that are strictly superior in value to the previous points in the sequence the complexity of this algorithm is measured by the expected number of iterations required to achieve a given accuracy of solution we show that for global mathematical programs satisfying the lipschitz condition its complexity increases at mostlinearly in the dimension of the problem

a soft approach for hard continuous optimization abstract this paper is to introduce a soft approach for solving continuous optimizations models where seeking an optimal solution is theoretically or practically impossible we first review methods for solving continuous optimization models and argue that only a few optimization models with some good structure are solved to solve a larger class of optimization problems we suggest a soft approach by softening the goal in solving a model and propose a two stage process for implementing the soft approach furthermore we offer an algorithm for solving optimization models with a convex feasible set and verify the validity of the soft approach with numerical experiments

tight binding approach to overdamped brownian motion on a multidimensional tilted periodic potential we present a theoretical treatment of overdamped brownian motion on a multidimensional tilted periodic potential that is analogous to the tight binding model of quantum mechanics in our approach we expand the continuous smoluchowski equation in the localized wannier states of the periodic potential to derive a discrete master equation this master equation can be interpreted in terms of hopping within and between bloch bands and for weak tilting and long times we show that a single band description is valid in the limit of deep potential wells we derive a simple functional dependence of the hopping rates and the lowest band eigenvalues on the tilt we also derive formal expressions for the drift and diffusion in terms of the lowest band eigenvalues

collective phase description of coupled oscillators with general network structure we develop a collective phase description for a population of nonidentical limit cycle oscillators with any network structure undergoing fully phase locked collective oscillations the whole network dynamics can be described by a single collective phase variable we derive a general formula for the collective phase sensitivity which quantifies the phase response of the whole network to weak external perturbations applied to the constituent oscillators moreover we consider weakly interacting multiple networks and develop an effective phase coupling description for them several examples are given to illustrate our theory

noise induced synchronization in small world networks of phase oscillators a small world sw network of similar phase oscillators interacting according to the kuramoto model is studied numerically it is shown that deterministic kuramoto dynamics on sw networks has various stable stationary states this can be attributed to the so called defect patterns in an sw network which it inherits from deformation of helical patterns in its regular parent turning on an uncorrelated random force causes vanishing of the defect patterns hence increasing the synchronization among oscillators for moderate noise intensities this phenomenon called stochastic synchronization is generally observed in some natural networks such as the brain neural network

computing behavior of finite fuzzy machines algorithm and its application to reduction and minimization we define finite fuzzy machines and investigate their behavior algorithm and software are proposed for computing behavior for establishing equivalence and redundancy of states and for solving reduction and minimization problems computational complexity of the algorithm is discussed testing examples are supplied the results are valid for finite max min min max and max product fuzzy machines

shake and bake algorithms for generating uniform points on the boundary of bounded polyhedra we present a class of shake and bake algorithms for generating asymptotically uniform points on the boundary of full dimensional bounded polyhedra we also report results of simulations for some elementary test problems

minimization of fuzzy finite automata abstract in this paper we show that a fuzzy finite automation m 1 has an equivalent minimal fuzzy finite automation m we also show that m can be chsen so that if m 2 is equivalent to m 1 then m is a homomorphic image of m 2

on fuzzy regular languages abstract we introduce the concept of a max min fuzzy language fl m and a min max fuzzy language fl m recognized by a type of fuzzy automaton m we show that if l1 and l2 are finite valued f regular languages then so are l1 l2 and l1 l2 we give a form of a fuzzified pumping lemma which we use to give a necessary and sufficient condition for fl m to be nonconstant

hit and run mixes fast it is shown that the hit and run algorithm for sampling from a convex body k introduced by r l smith mixes in time o n2r2 r2 where r and r are the radii of the inscribed and circumscribed balls of k thus after appropriate preprocessing hit and run produces an approximately uniformly distributed sample point in time o n3 which matches the best known bound for other sampling algorithms we show that the bound is best possible in terms of r r and n

equivalence reduction and minimization of finite fuzzy automata abstract a new algebraic approach to the problem of equivalence reduction and minimization of some kinds of fuzzy automata is given a system of necessary and sufficient conditions for equivalence of weakly initial fuzzy automata is formulated some algorithms considering the equivalence for two fuzzy automata are constructed

constraint classification in mathematical programming consider a set of algebraic inequality constraints defining either an empty or a nonempty feasible region it is known that each constraint can be classified as either absolutely strongly redundant relatively strongly redundant absolutely weakly redundant relatively weakly redundant or necessary we show that is is worth making a distinction between weakly necessary constraints and strongly necessary constraints we also present afeasible set cover method which can detect both weakly and strongly necessary constraints the main interest in constraint classification is due to the advantages gained by the removal of redundant constraints since classification errors are likely to occur we examine how the removal of a single constraint can affect the classification of the remaining constraints

influence of noise on the synchronization of the stochastic kuramoto model we consider the kuramoto model of globally coupled phase oscillators subject to ornstein uhlenbeck and non gaussian colored noise and investigate the influence of noise on the order parameter of the synchronization process we use numerical methods to study the dependence of the threshold as well as the maximum degree of synchronization on the correlation time and the strength of the noise and find that the threshold of synchronization strongly depends on the nature of the noise it is found to be lower for both the ornstein uhlenbeck and non gaussian processes compared to the case of white noise a finite correlation time also favors the achievement of the full synchronization of the system in contract to the white noise process which does not allow that finally we discuss possible applications of the stochastic kuramoto model to oscillations taking place in biochemical systems

finite l fuzzy machines abstract for finite l fuzzy machines we develop behaviour reduction and minimization theory here l stands for l 0 1 where l is a totally ordered set with universal bounds 0 and 1 and the operations are join and meet the most essential results include investigating behaviour equivalence reduction and minimization problems and their algorithmical decidability

equivalence reduction and minimization of finite automata over semirings abstract a new unified approach to equivalence reduction and minimization of finite automata over semirings based on free semimodules is presented it includes as special cases deterministic nondeterministic stochastic and fuzzy automata a necessary and sufficient condition for the existence of a finite behaviour matrix for a given automaton is proved different algorithmical decidability properties for equivalence reduction and minimization are connected to a noetherian property in the category s mod c of the semimodules over the semiring c

on closure properties of l valued linear languages abstract in 2001 and 2002 daowen qiu has established a new theory of l valued automata which is based on complete residuated lattices moreover besides the finite automata several other classes of machines grammars and languages have been generalized using the ideas introduced by qiu this paper generalizes the concept of linear grammars and linear languages in this context moreover it presents some operations for l valued languages and some closure properties for the l valued linear languages

equivalence in automata theory based on complete residuated lattice valued logic automata theory based on complete residuated lattice valued logic called l valued finite automata abbr l vfas was introduced by the second author in 2001 in this paper we deal with the problems of equivalence between l valued sequential machines abbr l vsms and l vfas we define l vsms and particularly present a method for deciding the equivalence between l vsms as well an algorithm procedure for deciding the equivalence between l vsms is constructed we analyze the complexity and efficiency of the algorithm procedure and obtain the relative results to l vfas moreover the definitions of l valued languages abbr l vls and l valued regular languages abbr l vrls recognized by l vfas are given and some related properties are also discussed we show an equivalent relation between l vrls and conventional regular languages by using l valued pumping lemma we get a necessary and sufficient condition for an l vl to be nonconstant

construction of fuzzy automata from fuzzy regular expressions li and pedrycz have proved fundamental results that provide different equivalent ways to represent fuzzy languages with membership values in a lattice ordered monoid and generalize the well known results of the classical theory of formal languages in particular they have shown that a fuzzy language over an integral lattice ordered monoid can be represented by a fuzzy regular expression if and only if it can be recognized by a fuzzy finite automaton however they did not give any efficient method for constructing an equivalent fuzzy finite automaton from a given fuzzy regular expression in this paper we provide such an efficient method transforming scalars appearing in a fuzzy regular expression ainto letters of the new extended alphabet we convert the fuzzy regular expression ato an ordinary regular expression a r then starting from an arbitrary nondeterministic finite automaton a that recognizes the language a r represented by the regular expression a r we construct fuzzy finite automata a a and a a r with the same or even less number of states than the automaton a which recognize the fuzzy language a represented by the fuzzy regular expression a the starting nondeterministic finite automaton a can be obtained from a r using any of the well known constructions for converting regular expressions to nondeterministic finite automata such as glushkov mcnaughton yamada s position automaton brzozowski s derivative automaton antimirov s partial derivative automaton or ilie yu s follow automaton

estimating the prediction function and the number of unseen species in sampling with replacement abstract a sample of n units is taken from a population consisting of an unknown number of species we are interested in estimating the number of species and the prediction function for future sampling the prediction function is defined as the expected number of new species that will be found if an additional sample of size tn is taken for any positive real number t in this paper we point out that an estimator suggested by efron and thisted lacks some essential properties of the true prediction function for example the property of alternating copositivity as a result it cannot be used for large values of t we propose an alternative estimator that possesses the essential properties and is easily obtained we illustrate our estimator with two numerical examples and a simulation study

fisher information and criticality in the kuramoto model of nonidentical oscillators we use the fisher information to provide a lens on the transition to synchronization of the kuramoto model of nonidentical frequencies on a variety of undirected graphs we numerically solve the equations of motion for a n 400 complete graph and n 1000 small world scale free uniform random and random regular graphs for large but finite graphs of small average diameter the fisher information f as a function of coupling shows a peak closely coinciding with the critical point as determined by kuramoto s order parameter or synchronization measure r however for graphs of larger average diameter the position of the peak in f differs from the critical point determined by estimates of r on the one hand this is a finite size effect even at n 1000 however we show across a range of topologies that the fisher information peak points to a transition for smaller graphs that indicates structural changes in the numbers of locally phase synchronized clusters often directly from metastable to stable frequency synchronization solving explicitly for a two cluster ansatz subject to gaussian noise shows that the fisher infomation peaks at such a transition we discuss the implications for fisher information as an indicator for edge of chaos phenomena in finite coupled oscillator systems

on the best case performance of hit and run methods for detecting necessary constraints the hit and run methods are probabilistic algorithms that can be used to detect necessary nonredundant constraints in systems of linear constraints these methods construct random sequences of lines that pass through the feasible region these lines intersect the boundary of the region at twohit points each identifying a necessary constraint in order to study the statistical performance of such methods it is assumed that the probabilities of hitting particular constraints are the same for every iteration an indication of the best case performance of these methods can be determined by minimizing with respect to the hit probabilities the expected value of the number of iterations required to detect all necessary constraints we give a set of isolated strong local minimizers and prove that for two three and four necessary constraints the set of local minimizers is the complete set of global minimizers we conjecture that this is also the case for any number of necessary constraints the results in this paper also apply to sampling problems e g balls from an urn and to the coupon collector s problem

fuzzy language on free monoid in this paper we shall introduce the notion of fuzzy regular language adjunctive language and dense language and discuss their algebraic character and algebraic properties

efficient monte carlo procedures for generating points uniformly distributed over bounded regions we consider the monte carlo problem of generating points uniformly distributed within an arbitrary bounded measurable region the class of markovian methods considered generate points asymptotically uniformly distributed within the region computational experience suggests the methods are potentially superior to conventional rejection techniques for large dimensional regions

synchronization of two interacting populations of oscillators we analyze synchronization between two interacting populations of different phase oscillators for the important case of asymmetric coupling functions we find a much richer dynamical behavior compared to that of symmetrically coupled populations of identical oscillators it includes three types of bistabilities higher order entrainment and the existence of states with unusual stability properties all possible routes to synchronization of the populations are presented and some stability boundaries are obtained analytically the impact of these findings for neuroscience is discussed

from incoherence to synchronicity in the network kuramoto model we study the synchronization properties of the kuramoto model of coupled phase oscillators on a general network here we distinguish the ability of such a system to self synchronize from the stability of this behavior while self synchronization is a consequence of genuine nonperturbative dynamics the stability in dynamical systems is usually accessible by fluctuations about a fixed point here taken to be the phase synchronized solution we examine this problem in terms of modes of the graph laplacian by which the absolute lyapunov stability of the phase synchronized fixed point is readily demonstrated departures from stability are seen to arise at the next order in fluctuations where depending on a truncation in the number of time dependent laplacian modes the dynamical equations can be reduced to forms resembling those for species population models the logistic and the lotka volterra equations methods from these systems are exploited to analytically derive new critical couplings signaling deviation from classical stability we thereby analytically explain the existence of an intermediate regime of behavior between incoherence and synchronization where system wide periodic behaviors are exhibited and stable unstable and hyperbolic fixed points can be identified we discuss these results in light of numerical solutions of the equations of motion for various networks

fuzzy finite automata and fuzzy regular expressions with membership values in lattice ordered monoids we study fuzzy finite automata in which all fuzzy sets are defined by membership functions whose codomain forms a lattice ordered monoid l for these l fuzzy finite automata l ffa for short we provide necessary and sufficient conditions for the extendability of the state transition function it is shown that nondeterministic l ffa nl ffa for short are more powerful than deterministic l ffa dl ffa for short then we give necessary and sufficient conditions for the simulation of an nl ffa by an equivalent dl ffa next we turn to the closure properties of languages defined by l ffas we establish closure under the regular operations and provide conditions for closure under intersection and reversal in particular we show that the family of fuzzy languages accepted by dl ffas is not closed under kleene closure operation and the family of fuzzy languages accepted by nl ffas is not closed under complement operation furthermore we introduce the notions of l fuzzy regular expressions and give the kleene theorem for nl ffas the description of dl ffas by l fuzzy regular expressions is also given finally we investigate the level structures of l ffas our results provide some insight as to what extend properties of l ffas and their languages depend on the algebraic properties of l

discrete hit and run for sampling points from arbitrary distributions over subsets of integer hyperrectangles we consider the problem of sampling a point from an arbitrary distribution over an arbitrary subset s of an integer hyperrectangle neither the distribution nor the support set s are assumed to be available as explicit mathematical equations but may only be defined through oracles and in particular computer programs this problem commonly occurs in black box discrete optimization as well as counting and estimation problems the generality of this setting and high dimensionality of s precludes the application of conventional random variable generation methods as a result we turn to markov chain monte carlo mcmc sampling where we execute an ergodic markov chain that converges to so that the distribution of the point delivered after sufficiently many steps can be made arbitrarily close to unfortunately classical markov chains such as the nearest neighbor random walk or the coordinate direction random walk fail to converge to because they can get trapped in isolated regions of the support set to surmount this difficulty we propose discrete hit and run dhr a markov chain motivated by the hit and run algorithm known to be the most efficient method for sampling from log concave distributions over convex bodies in rn we prove that the limiting distribution of dhr is as desired thus enabling us to sample approximately from by delivering the last iterate of a sufficiently large number of iterations of dhr in addition to this asymptotic analysis we investigate finite time behavior of dhr and present a variety of examples where dhr exhibits polynomial performance

how to compute the volume in high dimension in some areas of theoretical computer science we feel that randomized algorithms are better and in some others we can prove that they are more efficient than the deterministic ones

computing and estimating the volume of the solution space of smt la constraints abstract the satisfiability modulo theories smt problem is a decision problem i e deciding the satisfiability of logical formulas with respect to combinations of background theories like reals integers arrays bit vectors in this paper we study the counting version of smt with respect to linear arithmetic smt la which generalizes both model counting and volume computation of convex polytopes we describe a method for estimating the volume of convex polytopes based on the multiphase monte carlo method it employs a new technique to reutilize random points so that the number of random points can be significantly reduced we prove that the reutilization technique has no side effect on the error we also investigate a simplified version of hit and run method the coordinate directions method based on volume estimation method for polytopes we present an approach to estimating the volume of the solution space of smt la formulas it employs a heuristic strategy to accelerate the volume estimation procedure in addition we devise some specific techniques for instances that arise from program analysis

bayesian stopping rules for multistart global optimization methods by far the most efficient methods for global optimization are based on starting a local optimization routine from an appropriate subset of uniformly distributed starting points as the number of local optima is frequently unknown in advance it is a crucial problem when to stop the sequence of sampling and searching by viewing a set of observed minima as a sample from a generalized multinomial distribution whose cells correspond to the local optima of the objective function we obtain the posterior distribution of the number of local optima and of the relative size of their regions of attraction this information is used to construct sequential bayesian stopping rules which find the optimal trade off between reliability and computational effort

bisimulations for fuzzy automata bisimulations have been widely used in many areas of computer science to model equivalence between various systems and to reduce the number of states of these systems whereas uniform fuzzy relations have recently been introduced as a means to model the fuzzy equivalence between elements of two possible different sets here we use the conjunction of these two concepts as a powerful tool in the study of equivalence between fuzzy automata we prove that a uniform fuzzy relation between fuzzy automata a and b is a forward bisimulation if and only if its kernel and co kernel are forward bisimulation fuzzy equivalence relations on a and b and there is a special isomorphism between factor fuzzy automata with respect to these fuzzy equivalence relations as a consequence we get that fuzzy automata a and b are ufb equivalent i e there is a uniform forward bisimulation between them if and only if there is a special isomorphism between the factor fuzzy automata of a and b with respect to their greatest forward bisimulation fuzzy equivalence relations this result reduces the problem of testing ufb equivalence to the problem of testing isomorphism of fuzzy automata which is closely related to the well known graph isomorphism problem we prove some similar results for backward forward bisimulations and we point to fundamental differences because of the duality with the studied concepts backward and forward backward bisimulations are not considered separately finally we give a comprehensive overview of various concepts on deterministic nondeterministic fuzzy and weighted automata which are related to bisimulations

on accelerated random search a new variant of pure random search prs for function optimization is introduced the basic finite descent accelerated random search ars algorithm is simple the search is confined to shrinking neighborhoods of a previous record generating value with the search neighborhood reinitialized to the entire space when a new record is found local maxima are avoided by including an automatic restart feature which reinitializes the search neighborhood after some number of shrink steps have been performed one goal of this article is to provide rigorous mathematical comparisons of ars to prs it is shown that the sequence produced by the ars process converges with probability one to the maximum of a continuous objective function faster than that of the prs process by adjustably large multiples of the time step theorem regarding an infinite descent no automatic restart version of ars it is shown that if the objective function satisfies a local nonflatness condition then the right tails of the distributions of inter record times are exponentially smaller than those of prs theorem performance comparisons between ars prs and three quasi newton type optimization routines are reported in attempting to find extrema of i each of a small collection of standard test functions of two variables and ii d dimensional polynomials with random roots also reported is a three way performance comparison between ars prs and a simulated annealing algorithm in attempting to solve traveling salesman problems

constrained nonlinear optimization approaches to color signal separation separating a color signal into illumination and surface reflectance components is a fundamental issue in color reproduction and constancy this can be carried out by minimizing the error in the least squares ls fit of the product of the illumination and the surface spectral reflectance to the actual color signal when taking in account the physical realizability constraints on the surface reflectance and illumination the feasible solutions to the nonlinear ls problem should satisfy a number of linear inequalities four distinct novel optimization algorithms are presented to employ these constraints to minimize the nonlinear ls fitting error the first approach which is based on ritter s superlinear convergent method luengerger 1980 provides a computationally superior algorithm to find the minimum solution to the nonlinear ls error problem subject to linear inequality constraints unfortunately this gradient like algorithm may sometimes be trapped at a local minimum or become unstable when the parameters involved in the algorithm are not tuned properly the remaining three methods are based on the stable and promising global minimizer called simulated annealing the annealing algorithm can always find the global minimum solution with probability one but its convergence is slow to tackle this a cost effective variable separable formulation based on the concept of golub and pereyra 1973 is adopted to reduce the nonlinear ls problem to be a small scale nonlinear ls problem the computational efficiency can be further improved when the original boltzman generating distribution of the classical annealing is replaced by the cauchy distribution

gaussian noise and the two network frustrated kuramoto model abstract we examine analytically and numerically a variant of the stochastic kuramoto model for phase oscillators coupled on a general network two populations of phased oscillators are considered labelled blue and red each with their respective networks internal and external couplings natural frequencies and frustration parameters in the dynamical interactions of the phases we disentangle the different ways that additive gaussian noise may influence the dynamics by applying it separately on zero modes or normal modes corresponding to a laplacian decomposition for the sub graphs for blue and red under the linearisation ansatz that the oscillators of each respective network remain relatively phase synchronised centroids or clusters we are able to obtain simple closed form expressions using the fokker planck approach for the dynamics of the average angle of the two centroids in some cases this leads to subtle effects of metastability that we may analytically describe using the theory of ratchet potentials these considerations are extended to a regime where one of the populations has fragmented in two the analytic expressions we derive largely predict the dynamics of the non linear system seen in numerical simulation in particular we find that noise acting on a more tightly coupled population allows for improved synchronisation of the other population where deterministically it is fragmented

fixed points and stability in the two network frustrated kuramoto model we examine a modification of the kuramoto model for phase oscillators coupled on a network here two populations of oscillators are considered each with different network topologies internal and cross network couplings and frequencies additionally frustration parameters for the interactions of the cross network phases are introduced this may be regarded as a model of competing populations internal to any one network phase synchronisation is a target state while externally one or both populations seek to frequency synchronise to a phase in relation to the competitor we conduct fixed point analyses for two regimes one where internal phase synchronisation occurs for each population with the potential for instability in the phase of one population in relation to the other the second where one part of a population remains fixed in phase in relation to the other population but where instability may occur within the first population leading to fragmentation we compare analytic results to numerical solutions for the system at various critical thresholds

hit and run algorithms for generating multivariate distributions we introduce a general class of hit and run algorithms for generating essentially arbitrary absolutely continuous distributions on rd they include the hypersphere directions algorithm and the coordinate directions algorithm that have been proposed for identifying nonredundant linear constraints and for generating uniform distributions over subsets of rd given a bounded open set s in rd an absolutely continuous probability distribution on s the target distribution and an arbitrary probability distribution i on the boundary of the d dimensional unit sphere centered at the origin the direction distribution the i hit and run algorithm produces a sequence of iteration points as follows given the nth iteration point x choose a direction i according to the distribution i and then choose the n 1st iteration point according to the conditionalization of the distribution along the line defined by x and x i under mild conditions we show that this sequence of points is a harris recurrent reversible markov chain converging in total variation to the target distribution

a new approach to the analysis of random methods for detecting necessary linear inequality constraints a new approach is given for the analysis of random methods for detecting necessary constraints in systems of linear inequality constraints this new approach directly accounts for the fact that two constraints are detected as necessary hit at each iteration of a random method the significance of this two hit analysis is demonstrated by comparing it with the usual one hit analysis

direction choice for accelerated convergence in hit and run sampling hit and run algorithms are monte carlo procedures for generating points that are asymptotically distributed according to general absolutely continuous target distributions g over open bounded regions s applications include nonredundant constraint identification global optimization and monte carlo integration these algorithms are reversible random walks that commonly incorporate uniformly distributed step directions we investigate nonuniform direction choice and show that under regularity conditions on the region s and target distribution g there exists a unique direction choice distribution characterized by necessary and sufficient conditions depending on s and g which optimizes the doob bound on rate of convergence we include computational results demonstrating greatly accelerated convergence for this optimizing direction choice as well as for more easily implemented adaptive heuristic rules

pumping lemma in automata theory based on complete residuated lattice valued logic a note abstract automata theory based on complete residuated lattice valued logic called l valued automata was established in qiu automata theory based on completed residuated lattice valued logic i science in china f 44 6 2001 419 429 qiu automata theory based on completed residuated lattice valued logic ii science in china f 45 6 2002 442 452 in this note we deal with the pumping lemma in l valued automata theory after recalling some preliminaries related to complete residuated lattices and l valued automata we define a number of l valued accepting predicates in particular the pumping lemma for l valued automata theory is set up we show that if those related l valued predicates are defined by using connective instead of then the pumping lemma may not hold again furthermore we investigate the l valued automata with e transitions and present the equivalence between the l valued automata without e transitions and those with e transitions finally a number of related questions is addressed