parameters for integrating periodic functions of several variables a number theoretical method for numerical integration of periodic functions of several variables was developed some years ago this paper presents lists of numerical parameters to be used in implementing that method the parameters define quadrature formulas for functions of 2 3 8 variables error bounds for those formulas are also tabulated the derivation of the parameters and error bounds is described

temporal integration and multiple looks revisited weights as a function of time this study tests the hypothesis that temporal integration for detection of tone bursts with various durations can be explained by optimally combining multiple looks of brief signal segments whose contribution to detection increases over time detectability was measured for signals consisting of six consecutive 25 ms 1 khz tone pulses presented in a 50 hz wide masker or in maskers consisting of seven 50 hz wide noises one critical band apart with either coherent or incoherent envelopes the level of each signal pulse varied randomly around masked threshold according to a gaussian distribution the slopes of conditional psychometric functions plotted in terms of d 2 as a function of the squared signal pulse intensity for pulses in a particular temporal position yielded estimates of the contribution to detection provided by each pulse results for three normal listeners showed a small but significant effect of the temporal location of the pulse multiple looks predictions of temporal integration functio

on the state minimization of fuzzy automata this paper investigates the minimization problem of fuzzy automata aiming to obtain a procedure for finding a minimal state fuzzy automaton equivalent to a given one the decision version of the minimization problem is as follows given a fuzzy automaton cal a and a natural number k i e a pair langle cal a k rangle is there a k state fuzzy automaton equivalent to cal a we prove that the above problem is decidable for fuzzy automata over totally ordered lattices and then obtain a procedure for minimizing a given fuzzy automaton to this end we introduce the concept of systems of fuzzy polynomial equations present a procedure for finding solutions of these systems and finally reduce the above decision problem to finding a solution of a system of fuzzy polynomial equations it is worth pointing out that although some algorithms in the literature were claimed to be minimization algorithms the term minimization there did not mean state minimization in our sense since these algorithms did not aim at a minimal fuzzy automaton but found reasonably small fuzzy automata

optimal state reductions of automata with partially specified behaviors nondeterministic finite automata with don t care states namely states which neither accept nor reject are considered a characterization of deterministic automata compatible with such a device is obtained furthermore an optimal state bound for the smallest compatible deterministic automata is provided it is proved that the problem of minimizing deterministic don t care automata is np complete and pspace hard in the nondeterministic case the restriction to the unary case is also considered

quasi random methods for estimating integrals using relatively small samples much of the recent work dealing with quasi random methods has been aimed at establishing the best possible asymptotic rates of convergence to zero of the error resulting when a finite dimensional integral is replaced by a finite sum of integrand values in contrast with this perspective to concentrate on asymptotic convergence rates this paper emphasizes quasi random methods that are effective for all sample sizes throughout the paper the problem of estimating finite dimensional integrals is used to illustrate the major ideas although much of what is done applies equally to the problem of solving certain fredholm integral equations some new techniques based on error reducing transformations of the integrand are described that have been shown to be useful both in estimating high dimensional integrals and in solving integral equations these techniques illustrate the utility of carrying over to the quasi monte carlo method certain devices that have proven to be very valuable in statistical pseudoran

an algorithm to compute the t value of a digital net and of its projections abstract digital nets are among the most successful methods to construct low discrepancy point sets for quasi monte carlo integration their quality is traditionally assessed by a measure called the t value a refinement computes the t value of the projections over subsets of coordinates and takes a weighted average or some other function of these values it is also of interest to compute the t values of embedded nets obtained by taking subsets of the points in this paper we propose an efficient algorithm to compute such measures and we compare our approach with previously proposed methods both empirically and in terms of computational complexity

analytical expressions for the envelope correlation of certain narrow band stimuli analytical solutions are presented for the correlation between the envelopes of certain narrow band stimuli which are typically used in binaural research these stimuli are either the sum of an in phase masker and an out of phase signal or they are two partially correlated noises because an envelope has a nonzero mean the solutions differ depending on whether the envelope correlation is expressed as the normalized cross correlation or as the normalized cross covariance pearson product moment correlation the envelope correlation depends on the statistics of the masker and the signal whereas the waveform correlation depends on neither this influence only disappears for the normalized envelope cross correlation provided that the correlation is close to one in this case the normalized envelope cross correlation is equal to the square root of the waveform correlation the results for two partially correlated noise bands are also of relevance for experiments dealing with monaural envelope discrimination and comodulation masking release

a generalized discrepancy and quadrature error bound an error bound for multidimensional quadrature is derived that includes the koksma hlawka inequality as a special case this error bound takes the form of a product of two terms one term which depends only on the integrand is defined as a generalized variation the other term which depends only on the quadrature rule is defined as a generalized discrepancy the generalized discrepancy is a figure of merit for quadrature rules and includes as special cases the l p star discrepancy and p that arises in the study of lattice rules

boundary sets of regular and context free languages we investigate the descriptional and computational complexity of boundary sets of regular and context free languages for a letter a the right left respectively a boundary set of a language l consists of the words in l whose a predecessor or a successor w r t the prefix suffix respectively relation is not in l for regular languages described by deterministic finite automata dfas we give tight bounds on the number of states for accepting boundary sets moreover the question whether the boundary sets of a regular language is finite is shown to be nl complete for dfas while it turns out to be pspace complete for nondeterministic devices boundary sets for context free languages are not necessarily context free anymore here we find a subtle difference of right and left a boundary sets while right a boundary sets of deterministic context free languages stay deterministic context free we give an example of a deterministic context free language whose a boundary set is already non context free in fact the finiteness problem for a boundary sets of context free languages becomes undecidable

the asymptotic efficiency of randomized nets for quadrature an l 2 type discrepancy arises in the average and worst case error analyses for multidimensional quadrature rules this discrepancy is uniquely defined by k x y which serves as the covariance kernel for the space of random functions in the average case analysis and a reproducing kernel for the space of functions in the worst case analysis this article investigates the asymptotic order of the root mean square discrepancy for randomized 0 m s nets in base b for moderately smooth k x y the discrepancy is o n 1 log n s 1 2 and for k x y with greater smoothness the discrepancy is o n 3 2 log n s 1 2 where n b m is the number of points in the net numerical experiments indicate that the t m s nets of faure niederreiter and sobol do not necessarily attain the higher order of decay for sufficiently smooth kernels however niederreiter nets may attain the higher order for kernels corresponding to spaces of periodic functions

further improvements of determinization methods for fuzzy finite automata in this paper we provide further improvements of determinization methods for fuzzy finite automata these methods perform better than all previous determinization methods for fuzzy finite automata developed by b lohlavek 3 li and pedrycz 38 ignjatovic et al 25 and jancic et al 33 in the sense that they produce smaller automata while require the same computation time the only exception is the brzozowski type determinization algorithm developed recently by jancic and iric 34 which produces a minimal crisp deterministic fuzzy automaton but the algorithms created here can also be used within the brzozowski type algorithm and improve its performance

on the computational complexity of problems related to distinguishability sets we study the computational complexity of problems related to distinguishability sets for regular languages roughly speaking the distinguishability set mathsf d l for a not necessarily regular language l consists of all words w that are a common suffix of a word xw in l and of a word yw that does not belong to l in particular we investigate the complexity of the representation problem i e deciding for given automata a and b whether b accepts the distinguishability set of l a it is shown that this problem and some of its variants are highly intractable namely pspace complete in fact determining the size of an automaton for mathsf d l a is already pspace complete on the other hand questions related to the hierarchy induced by iterated application of the mathsf d operator turn out to be much easier for instance the question whether for a given automaton a the accepted language is equal to its own distinguishability set i e whether l a mathsf d l a holds is shown to be nl complete as a byproduct of our investigations we found a compelling characterization of synchronizing automata namely that a minimal automaton a is synchronizing if and only if mathsf d l a mathsf d 2 l a

compression of finite state automata through failure transitions several linear time algorithms for automata based pattern matching rely on failure transitions for efficient back tracking like epsilon transitions failure transition do not consume input symbols but unlike them they may only be taken when no other transition is applicable at a semantic level this conveniently models catch all clauses and allows for compact language representation this work investigates the transition reduction problem for deterministic finite state automata dfa the input is a dfa a and an integer k the question is whether k or more transitions can be saved by replacing regular transitions with failure transitions we show that while the problem is np complete there are approximation techniques and heuristics that mitigate the computational complexity we conclude by demonstrating the computational difficulty of two related minimisation problems thereby cancelling the ongoing search for efficient algorithms

constructing embedded lattice rules for multivariate integration lattice rules are a family of equal weight cubature formulae for approximating high dimensional integrals by now it is well established that good generating vectors for lattice rules having n points can be constructed component by component for integrands belonging to certain weighted function spaces and that they can achieve the optimal rate of convergence although the lattice rules constructed this way are extensible in dimension they are not extensible in n thus when n is changed the generating vector needs to be constructed anew in this paper we introduce a new algorithm for constructing good generating vectors for embedded lattice rules which can be used for a range of n while still being extensible in dimension by using an adaptation of the fast component by component construction algorithm which makes use of fast fourier transforms we are able to obtain good generating vectors for thousands of dimensions and millions of points under both product weight and order dependent weight settings at the cost of calo d n log n 2 operations with a sufficiently large number of points and good overall quality these embedded lattice rules can be used for practical purposes in the same way as a low discrepancy sequence we show for a range of weight settings in an unanchored sobolev space that our embedded lattice rules achieve the same optimal rate of convergence calo n 1 delta delta 0 as those constructed for a fixed number of points and that the implied constant gains only a factor of 1 30 to 1 55

on the limits of the communication complexity technique for proving lower bounds on the size of minimal nfa s in contrast to the minimization of deterministic finite automata dfa s the task of constructing a minimal nondeterministic finite automaton nfa for a given nfa is pspace complete moreover there are no polynomial approximation algorithms with a constant approximation ratio for estimating the number of states of minimal nfa s since one is unable to efficiently estimate the size of a minimal nfa in an efficient way one should ask at least for developing mathematical proof methods that help to prove good lower bounds on the size of a minimal nfa for a given regular language here we consider the robust and most successful lower bound proof technique that is based on communication complexity in this paper it is proved that even a strong generalization of this method fails for some concrete regular languages to fail is considered here in a very strong sense there is an exponential gap between the size of a minimal nfa and the achievable lower bound for a specific sequence of regular languages the generalization of the concept of communication protocols is also strong here it is shown that cutting the input word into 2 o n 1 4 pieces for a size n of a minimal nondeterministic finite automaton and investigating the necessary communication transfer between these pieces as parties of a multiparty protocol does not suffice to get good lower bounds on the size of minimal nondeterministic automata it seems that for some regular languages one cannot really abstract from the automata model that cuts the input words into particular symbols of the alphabet and reads them one by one using its input head

complete statistical characterization of discrete time lqg and cumulant control as the performance index of the linear quadratic gaussian lqg problem is governed by the noncentral generalized chi square distribution solely controlling the expected value of the performance index as the traditional lqg theory aims at is insufficient to deliver a satisfactory solution in some situations while the risk sensitive control does control a specific weighting sum of various moments of the performance index the single degree of freedom in adjusting the weighting coefficients in this specific weighting sum of various moments of the performance index often prevents the risk sensitive control from generating a desired pattern of high order moment distribution we achieve in this note the complete statistical characterization of the performance index for the discrete time lqg formulation more specifically we derive a recursive relationship to obtain cumulants of various orders of the performance index successively parameterized in feedback gain the optimal feedback control law can be computed off line by solving a static polynomial optimization problem thus serving two design goals i to shape the probability density function pdf of the performance index to attain at least approximately a given desired pattern by regulating cumulants of various orders and ii to improve the performance measure of an incumbent solution generated by the risk sensitive control for example by adjusting the levels of cumulants of various orders

cost smoothing in discrete time linear quadratic control a smooth cost distribution can be a desirable feature in optimal control design when concerning even distribution of control energy and uniform resource allocation this consideration is formulated in this paper for discrete time linear systems where a square cost variation term is attached to a primal quadratic performance index in an additive form an analytical control law is obtained for the resulting non linear quadratic and nonseparable optimal control problem using a multilevel solution scheme investigating the trade off between minimizing the primal quadratic performance index and minimizing the square cost variation term offers some useful insights into multiobjective design of control systems

on the minimax solution of multiple linear quadratic problems multiple linear quadratic problems are studied a set of coupling riccati equations is derived for vector valued cost to go a minimax solution of multiobjective convex problems is proven to be an equalizer strategy this permits the development of a new algorithm for finding the minimax solution for multiple linear quadratic problems

quadrature error bounds with applications to lattice rules reproducing kernel hilbert spaces are used to derive error bounds and worst case integrands for a large family of quadrature rules in the case of lattice rules applied to periodic integrands these error bounds resemble those previously derived in the literature however the theory developed here does not require periodicity and is not restricted to lattice rules an analysis of variance anova decomposition is employed in defining the inner product it is shown that imbedded rules are superior when integrating functions with large high order anova effects

descriptional and computational complexity of finite automata a survey finite automata are probably best known for being equivalent to right linear context free grammars and thus for capturing the lowest level of the chomsky hierarchy the family of regular languages over the last half century a vast literature documenting the importance of deterministic nondeterministic and alternating finite automata as an enormously valuable concept has been developed in the present paper we tour a fragment of this literature mostly we discuss developments relevant to finite automata related problems like for example i simulation of and by several types of finite automata ii standard automata problems such as fixed and general membership emptiness universality equivalence and related problems and iii minimization and approximation we thus come across descriptional and computational complexity issues of finite automata we do not prove these results but we merely draw attention to the big picture and some of the main ideas involved

the construction of good extensible rank 1 lattices it has been shown by hickernell and niederreiter that there exist generating vectors for integration lattices which yield small integration errors for n p p 2 for all integers p 2 this paper provides algorithms for the construction of generating vectors which are finitely extensible for n p p 2 for all integers p 2 the proofs which show that our algorithms yield good extensible rank 1 lattices are based on a sieve principle particularly fast algorithms are obtained by using the fast component by component construction of nuyens and cools analogous results are presented for generating vectors with small weighted star discrepancy

on size reduction techniques for multitape automata we present a method for size reduction of two way multitape automata our algorithm applies local transformations that change the order in which transitions concerning different tapes occur in the automaton graph and merge suitable states into a single state our work is motivated by implementation of a language for string manipulation in database systems where string predicates are compiled into two way multitape automata additionally we present a one tape nfa reduction algorithm that is based on a method proposed for dfa minimization by kameda and weiner and apply this algorithm combined with the multitape automata reduction algorithm on our multitape automata empirical results on the performance of our method when applied on some multitape automata originating from string predicates are reported

extensible lattice sequences for quasi monte carlo quadrature integration lattices are one of the main types of low discrepancy sets used in quasi monte carlo methods however they have the disadvantage of being of fixed size this article describes the construction of an infinite sequence of points the first bm of which forms a lattice for any nonnegative integer m thus if the quadrature error using an initial lattice is too large the lattice can be extended without discarding the original points generating vectors for extensible lattices are found by minimizing a loss function based on some measure of discrepancy or nonuniformity of the lattice the spectral test used for finding pseudorandom number generators is one important example of such a discrepancy the performance of the extensible lattices proposed here is compared to that of other methods for some practical quadrature problems

average case complexity of multivariate integration we study the average case complexity of multivariate integration for the class of continuous functions of d variables equipped with the classical wiener sheet measure to derive the average case complexity one needs to obtain optimal sample points we prove that optimal design is closely related to discrepancy theory which has been extensively studied for many years this relation enables us to show that optimal sample points can be derived from hammersley points extending the result of roth and using the recent result of wasilkowski we conclude that the average case complexity is e 1 lne 1 d 1 2

efficient implementation of regular languages using reversed alternating finite automata alternating finite automata afa provide a natural and succinct way to denote regular languages we introduce a bit wise representation of reversed afa r afa transition functions and describe an efficient implementation method for r afa and their operations using this representation experiments have shown that this implementation is much more efficient than for instance the grail dfa implementation in both space and time

analytical expressions for the envelope correlation of narrow band stimuli used in cmr and bmld research analytical solutions are presented for the correlation between the envelopes of certain narrow band stimuli that are typically used in experiments on binaural unmasking and on comodulation masking release cmr these stimuli consist of two maskers with identical envelopes and a signal that is added to one of the maskers if the two maskers have the same center frequency and are presented to the right and left ear the stimulus resembles a binaural mosm condition if the two maskers have different center frequencies we have a cmr condition with one flanking band the solutions for the envelope correlation differ depending on whether the envelope correlation is expressed as normalized cross correlation or as normalized cross covariance pearson product moment correlation the envelope correlation depends on the statistics of the masker and the signal whereas the waveform correlation depends on neither this influence only disappears for the normalized envelope cross correlation provided that the masker level is much higher than the signal level in this case the envelope cross correlation is approximately equal to the square root of the waveform correlation it is argued that the different properties of both types of envelope correlation are of relevance for cmr research

on stochastic formalisms in transition state theory abstract the simulation of elementary gas phase reactions in a concentrated bath may be accomplished by a markoff chain model the concept of the state of secular equilibrium a necessary condition for the existence of rate coefficients local in time demands that the markoffian process be modelled using an inhomogeneous poisson process such a poisson process will possess microcanonical rates which are functions of time its simulation can be accomplished by quasi monte carlo schemes based on low discrepancy sequences which are also argued here for the computation of the flux integrals over the configurational space within the framework of variational microcanonical transition state theory

alternative sampling methods for estimating multivariate normal probabilities we study the performance of alternative sampling methods for estimating multivariate normal probabilities through the ghk simulator the sampling methods are randomized versions of some quasi monte carlo samples halton niederreiter niederreiter xing sequences and lattice points and some samples based on orthogonal arrays latin hypercube orthogonal array and orthogonal array based latin hypercube samples in general these samples turn out to have a better performance than monte carlo and antithetic monte carlo samples improvements over these are large for low dimensional 4 and 10 cases and still significant for dimensions as large as 50

quasi monte carlo integration the standard monte carlo approach to evaluating multidimensional integrals using pseudo random integration nodes is frequently used when quadrature methods are too difficult or expensive to implement as an alternative to the random methods it has been suggested that lower error and improved convergence may be obtained by replacing the pseudo random sequences with more uniformly distributed sequences known as quasi random in this paper quasi random halton sobol and faure and pseudo random sequences are compared in computational experiments designed to determine the effects on convergence of certain properties of the integrand including variance variation smoothness and dimension the results show that variation which plays an important role in the theoretical upper bound given by the koksma hlawka inequality does not affect convergence while variance the determining factor in random monte carlo is shown to provide a rough upper bound but does not accurately predict performance in general quasi monte carlo methods are superior to random monte carlo but the advantage may be slight particularly in high dimensions or for integrands that are not smooth for discontinuous integrands we derive a bound which shows that the exponent for algebraic decay of the integration error from quasi monte carlo is only slightly larger than 1 2 in high dimensions more 21 refs 6 figs 5 tabs less

successive method for general multiple linear quadratic control problem in discrete time a successive method is proposed for the general multiple linear quadratic control problem in discrete time a family of auxiliary parametric linear quadratic control problems is constructed such that its solution sequence converges to the optimal solution of the original problem theoretical analysis for the computational procedure and global convergence of the successive method is provided the successive method utilizes the special structure of the problem thus being computationally efficient and being able to furnish a closed loop optimal control law

generating quasi random paths for stochastic processes the need to simulate stochastic processes numerically arises in many fields frequently this is done by discretizing the process into small time steps and applying pseudorandom sequences to simulate the randomness this paper addresses the question of how to use quasi monte carlo methods to improve this simulation special techniques must be applied to avoid the problem of high dimensionality which arises when a large number of time steps is required two such techniques the generalized brownian bridge and particle reordering are described here these methods are applied to a problem from finance the valuation of a 30 year bond with monthly coupon payments assuming a mean reverting stochastic interest rate when expressed as an integral this problem is nominally 360 dimensional the analysis of the integrand presented here explains the effectiveness of the quasi random sequences on this high dimensional problem and suggests methods of variance reduction which can be used in conjunction with the quasi random sequences

alternating sign matrices related 0 1 matrices and the smith normal form abstract we investigate the smith normal form snf of alternating sign matrices asms and related matrices of 0 s and 1 s 0 1 matrices we identify certain classes of asms and 0 1 matrices whose snfs are 0 1 matrices we relate some of our work to various ranks in particular the 0 1 rank of a 0 1 matrix that is the bipartite partition number of a bipartite graph

deterministic generalized automata a generalized automaton ga is a finite automaton where the single transitions are defined on words rather than on single letters generalized automata were considered by k hashiguchi who proved that the problem of calculating the size of a minimal ga is decidable

multiple objective optimal control of linear systems the quadratic norm case control of a linear system to meet requirements embodied in multiple performance criteria is recognized as the typical design problem the authors study the design of control when every criterion of interest takes the form of an h sub 2 norm defined over certain exogenous inputs and controlled outputs of the system the objective is to find all stabilizing controllers that are noninferior with respect to the defined objectives that is to find the set of pareto optimal controllers the novel feature is the use of the youla parametrization to represent the admissible controllers this representation enables the authors to show that each criterion and hence their weighted sum is convex over the class of admissible controllers since the set of admissible controllers is itself convex the pareto optimal controllers can be determined by the standard scalarization technique it is concluded that in general the controller order is higher than the order of the plant

on general multiple linear quadratic control problems general multiple linear quadratic control problems are studied where the overall objective is a nonlinear function of multiple quadratic performance indices a multilevel solution procedure is proposed to obtain an analytical linear control law for this nonseparable control problem the auxiliary lagrangian problem formulated at the lower level is of a parametric linear quadratic structure in which the weighting vector is adjusted by the upper level until a derived optimal condition is met

obtaining shorter regular expressions from finite state automata we consider the use of state elimination to construct shorter regular expressions from finite state automata fas although state elimination is an intuitive method for computing regular expressions from fas the resulting regular expressions are often very long and complicated we examine the minimization of fas to obtain shorter expressions first then we introduce vertical chopping based on bridge states and horizontal chopping based on the structural properties of given fas we prove that we should not eliminate bridge states until we eliminate all non bridge states to obtain shorter regular expressions in addition we suggest heuristics for state elimination that leads to shorter regular expressions based on vertical chopping and horizontal chopping

the construction of extensible polynomial lattice rules with small weighted star discrepancy in this paper we introduce a construction algorithm for extensible polynomial lattice rules and we prove that the construction algorithm yields generating vectors of polynomials which are optimal for a range of moduli chosen in advance the construction algorithm uses a sieve where the generating vectors are extended by one coefficient in each component at each step and where one keeps a certain number of good ones and discards the rest we also show that the construction can be done component by component

improved methods for calculating vectors of short length in a lattice including a complexity analysis the standard methods for calculating vectors of short length in a lattice use a reduction procedure followed by enumerating all vectors of z in a suitable box however it suffices to consider those x e z which lie in a suitable ellipsoid having a much smaller volume than the box we show in this paper that searching through that ellipsoid is in many cases much more efficient if combined with an appropriate reduction procedure our method allows to do computations in lattices of much higher dimensions several randomly constructed numerical examples illustrate the superiority of our new method over the known ones

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

global optimization with polynomials and the problem of moments we consider the problem of finding the unconstrained global minimum of a real valued polynomial p x mathbb r n to mathbb r as well as the global minimum of p x in a compact set k defined by polynomial inequalities it is shown that this problem reduces to solving an often finite sequence of convex linear matrix inequality lmi problems a notion of karush kuhn tucker polynomials is introduced in a global optimality condition some illustrative examples are provided

lattice methods for multiple integration theory error analysis and examples this paper is concerned with numerical integration over the unit cube in s dimensions of functions that have reasonably smooth periodic extensions in each dimension the concept of a lattice rule is introduced and error bounds are developed in terms of the dual lattice examples of lattice rules discussed in the paper are the rectangle rule the number theoretic good lattice methods of korobov and others the body centred cubic rule and a generalization of the latter to a family w nr the w nr rules appear to have interesting extrapolation properties both for fixed r and for r n

factoring a band matrix over a semiring abstract matrix factorization problems over various semirings naturally arise in different contexts of modern pure and applied mathematics these problems are very hard in general and cause computational difficulties in applications we give a survey of what is known on the algorithmic complexity of boolean tropical nonnegative and positive semidefinite factorizations and we examine the behavior of the corresponding rank functions on matrices of bounded bandwidth we show that the boolean tropical and t norm versions of matrix factorization become polynomial time solvable when restricted to this class of matrices and we also show that the nonnegative rank of a tridiagonal matrix is easy to compute we recall several open problems from earlier papers on the topic and formulate a number of further questions

the mean square discrepancy of scrambled t s sequences the discrepancy arises in the worst case error analysis for quasi monte carlo quadrature rules low discrepancy sets yield good quadrature rules this article considers the mean square discrepancies for scrambled lam t m s nets and t s sequences in base b it is found that the mean square discrepancy for scrambled nets and sequences is never more than a constant multiple of that under simple monte carlo sampling if the reproducing kernel defining the discrepancy satisfies a lipschitz condition with respect to one of its variables separately then the asymptotic order of the root mean square discrepancy is o n 1 log n s 1 2 for scrambled nets if the reproducing kernel satisfies a lipschitz condition with respect to both of its variables then the asymptotic order of the root mean square discrepancy is o n 3 2 log n s 1 2 for scrambled nets for an arbitrary number of points taken from a t s sequence the root mean square discrepancy appears to be no better than o n 1 log n s 1 2 regardless of the smoothness of the reproducing kernel

reduction of fuzzy automata by means of fuzzy quasi orders abstract in our recent paper we have established close relationships between state reduction of a fuzzy automaton and resolution of a particular system of fuzzy relation equations in that paper we have also studied reductions by means of those solutions which are fuzzy equivalences in this paper we will see that in some cases better reductions can be obtained using the solutions of this system that are fuzzy quasi orders generally fuzzy quasi orders and fuzzy equivalences are equally good in the state reduction but we show that right and left invariant fuzzy quasi orders give better reductions than right and left invariant fuzzy equivalences we also show that alternate reductions by means of fuzzy quasi orders give better results than alternate reductions by means of fuzzy equivalences furthermore we study a more general type of fuzzy quasi orders weakly right and left invariant ones and we show that they are closely related to determinization of fuzzy automatons we also demonstrate some applications of weakly left invariant fuzzy quasi orders in conflict analysis of fuzzy discrete event systems

the efficiency of identifying timed automata and the power of clocks we develop theory on the efficiency of identifying learning timed automata in particular we show that i deterministic timed automata cannot be identified efficiently in the limit from labeled data and ii that one clock deterministic timed automata can be identified efficiently in the limit from labeled data we prove these results based on the distinguishability of these classes of timed automata more specifically we prove that the languages of deterministic timed automata cannot and that one clock deterministic timed automata can be distinguished from each other using strings in length bounded by a polynomial in addition we provide an algorithm that identifies one clock deterministic timed automata efficiently from labeled data our results have interesting consequences for the power of clocks that are interesting also out of the scope of the identification problem

an intractability result for multiple integration we prove that the problem of multiple integration in the korobov class e d is intractable since the number of function evaluations required to achieve a worst case error less than 1 is exponential in the dimension

variance reduction via lattice rules this is a review article on lattice methods for multiple integration over the unit hypercube with a variance reduction viewpoint it also contains some new results and ideas the aim is to examine the basic principles supporting these methods and how they can be used effectively for the simulation models that are typically encountered in the area of management science these models can usually be reformulated as integration problems over the unit hypercube with a large sometimes infinite number of dimensions we examine selection criteria for the lattice rules and suggest criteria which take into account the quality of the projections of the lattices over selected low dimensional subspaces the criteria are strongly related to those used for selecting linear congruential and multiple recursive random number generators numerical examples illustrate the effectiveness of the approach

bisimulation relations for weighted automata bisimulation is a well known equivalence relation for discrete event systems and has been extended to probabilistic and stochastic systems this paper introduces a general definition of bisimulation which can be applied to finite automata where weights and labels are assigned to transitions it is shown that this general view contains several known bisimulations as special cases and defines naturally equivalences for different classes of models apart from the well known forward bisimulation also backward bisimulation is introduced and it is shown that both types of bisimulation preserve different types of results furthermore it is shown that forward and backward bisimulation are congruences according to commonly known composition operations for automata

quasi random sequences and their discrepancies quasi random also called low discrepancy sequences are a deterministic alternative to random sequences for use in monte carlo methods such as integration and particle simulations of transport processes the error in uniformity for such a sequence of n points in the s dimensional unit cube is measured by its discrepancy which is of size log n s n 1 for large n as opposed to discrepancy of size log log n 1 2 n 1 2 for a random sequence i e for almost any randomly chosen sequence several types of discrepancies one of which is new are defined and analyzed a critical discussion of the theoretical bounds on these discrepancies is presented computations of discrepancies are presented for a wide choice of dimension s number of points n and different quasi random sequences in particular for moderate or large s there is an intermediate regime in which the discrepancy of a quasi random sequence is almost exactly the same as that of a randomly chosen sequence a simplified p

some factors affecting the magnitude of comodulation masking release this paper examines some of the factors that can affect the magnitude of comodulation masking release cmr in experiment i psychometric functions were measured for the detection of a 1 khz sinusoidal signal in a multiplied narrow band noise centered at 1 khz reference condition and the same noise with two comodulated flanking bands added the functions were slightly steeper for the comodulated than for the reference masker thus cmrs measured at a high percent correct point were slightly 0 4 db larger than cmrs measured at a low percent correct point large individual differences were found for the reference masker but not for the comodulated masker experiment ii compared cmrs obtained with narrow band gaussian noise and multiplied noise using a single flanking band for a flanking band remote from the signal frequency the cmrs were smaller and more variable for the multiplied noise than for the gaussian noise this variability arose mainly from individual differences in the reference condition experiment iii compared growth of masking functions for a signal centered in gaussian noise and multiplied noise thresholds were lower for the multiplied than for the gaussian noise and the differences were greatest at high noise levels the results are consistent with the idea that for multiplied noise some subjects can detect a change in the distribution of the envelope of the stimulus when the signal is added to the masker such subjects have low thresholds in the reference condition and give small cmrs other subjects are relatively insensitive to this cue they have higher thresholds in the reference condition and give larger cmrs for gaussian noise thresholds for the reference condition are relatively stable across subjects and cmrs tend to be substantial even for flanking band frequencies remote from the signal frequency

performance first control for discrete time lqg problems performance first control for discrete time lqg is considered in this paper to minimize the probability that the performance index exceeds a preselected threshold via constructing a closed loop feedback control law this problem can be converted into a mean variance control problem which can be solved by developing a nested form of the variance and using polynomial optimization as a solution scheme

simulation of multivariate normal rectangle probabilities and their derivatives theoretical and computational results abstract an extensive literature in econometrics and in numerical analysis has considered the problem of evaluating the multiple integral p b a b n v dv e v 1 v b where v is a m dimensional normal vector with mean covariance matrix and density n v and 1 v b is an indicator for the event b v a a leading case of such an integral is the negative orthant probability where b v v the problem is computationally difficult except in very special cases the multinomial probit mnp model used in econometrics and biometrics has cell probabilities that are negative orthant probabilities with and depending on unknown parameters and in general on covariates estimation of this model requires for each trial parameter vector and each observation in a sample evaluation of p b and of its derivatives with respect to and this paper surveys monte carlo techniques that have been developed for approximations of p b and its linear and logarithmic derivatives that limit computation while possessing properties that facilitate their use in iterative calculations for statistical inference the crude frequency simulator cfs normal importance sampling nis a kernel smoothed frequency simulator kfs stern s decomposition simulator sds the geweke hajivassiliou keane simulator ghk a parabolic cylinder function simulator pcf deak s chi squared simulator dcs an acceptance rejection simulator ars the gibbs sampler simulator gss a sequentially unbiased simulator sus and an approximately unbiased simulator aus we also discuss gauss and fortran implementations of these algorithms and present our computational experience with them we find that ghk is overall the most reliable method

minimal nfa problems are hard finite automata fa s are of fundamental importance in theory and in applications the following basic minimization problem is studied given a dfa deterministic fa find a minimum equivalent no