algebraic methods for interactive proof systems a new algebraic technique for the construction of interactive proof systems is presented our technique is used to prove that every language in the polynomial time hierarchy has an interactive proof system this technique played a pivotal role in the recent proofs that ip pspace 28 and that mip nexp 4

estimation of the mean of a multivariate normal distribution estimation of the means of independent normal random variables is considered using sum of squared errors as loss an unbiased estimate of risk is obtained for an arbitrary estimate and certain special classes of estimates are then discussed the results are applied to smoothing by use of moving averages and to trimmed analogs of the james stein estimate a suggestion is made for calculating approximate confidence sets for the mean vector centered at an arbitrary estimate

optimized wavelet denoising for self similar alpha stable processes we investigate the performance of wavelet shrinkage methods for the denoising of symmetric alpha stable text s alpha text s self similar stochastic processes corrupted by additive white gaussian noise awgn where alpha is tied to the sparsity of the process the wavelet transform is assumed to be orthonormal and the shrinkage function minimizes the mean square approximation error mmse estimator we derive the corresponding formula for the expected value of the averaged estimation error we show that the predicted mmse is a monotone function of a simple criterion that depends on the wavelet and the statistical parameters of the process using the calculus of variations we then optimize this criterion to find the best performing wavelet within the extended family of meyer wavelets which are bandlimited these are compared with the daubechies wavelets which are compactly supported in time we find that the wavelets that are shorter in time in particular the haar basis are better suited to denoise the sparser processes say alpha while the bandlimited ones including the held and shannon wavelets offer the best performance for alpha 1 6 the limit corresponding to the gaussian case fbm with alpha 2

an unbiased risk estimator for image denoising in the presence of mixed poisson gaussian noise the behavior and performance of denoising algorithms are governed by one or several parameters whose optimal settings depend on the content of the processed image and the characteristics of the noise and are generally designed to minimize the mean squared error mse between the denoised image returned by the algorithm and a virtual ground truth in this paper we introduce a new poisson gaussian unbiased risk estimator pg ure of the mse applicable to a mixed poisson gaussian noise model that unifies the widely used gaussian and poisson noise models in fluorescence bioimaging applications we propose a stochastic methodology to evaluate this estimator in the case when little is known about the internal machinery of the considered denoising algorithm and we analyze both theoretically and empirically the characteristics of the pg ure estimator finally we evaluate the pg ure driven parametrization for three standard denoising algorithms with and without variance stabilizing transforms and different characteristics of the poisson gaussian noise mixture

random calibration with many measurements an application of stein estimation in the problem considered a vector of many imprecise measurements e g spectroscopic is used to linearly predict a quantity whose precise measurement is difficult or expensive the regression vector is estimated from a calibration experiment having both types of measurements for a random sample most previous approaches to this problem adjust for approximate multicollinearity which often results from the correlations among the imprecise measurements by inverting an approximation e g factor analytic to their covariance matrix in the approach here it is argued that the regression vector should lie in a lower dimensional suhspace determined by the principal components of the covariance matrix it is then estimated by applying a stein contraction of the least squares estimator to the principal components regression estimator examples using real data are presented in which the proposed estimator substantially improves on the ordinary least squares estimation

the extended stein procedure for simultaneous model selection and parameter estimation abstract a parameter truncation criterion developed in conjunction with stein s partitioned analog of the efron and morris limited translation estimator is used in an orthonormal linear statistical model setting as a basis for simultaneously selecting the relevant variables and estimating the unknown parameters using a squared error loss measure and making use of prior information concerning the coefficients of extraneous variables the sampling performance of the extended stein procedure esp is analyzed for two alternative structures of the parameter space and under normal and non normal errors

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

fuzzy homomorphisms of algebras in this paper we consider fuzzy relations compatible with algebraic operations which are called fuzzy relational morphisms in particular we aim our attention to those fuzzy relational morphisms which are uniform fuzzy relations called uniform fuzzy relational morphisms and those which are partially uniform f functions called fuzzy homomorphisms both uniform fuzzy relations and partially uniform f functions were introduced in a recent paper by us uniform fuzzy relational morphisms are especially interesting because they can be conceived as fuzzy congruences which relate elements of two possibly different algebras we give various characterizations and constructions of uniform fuzzy relational morphisms and fuzzy homomorphisms we establish certain relationships between them and fuzzy congruences and we prove homomorphism and isomorphism theorems concerning them we also point to some applications of uniform fuzzy relational morphisms

predicting multivariate responses in multiple linear regression we look at the problem of predicting several response variables from the same set of explanatory variables the question is how to take advantage of correlations between the response variables to improve predictive accuracy compared with the usual procedure of doing individual regressions of each response variable on the common set of predictor variables a new procedure is introduced called the curds and whey method its use can substantially reduce prediction errors when there are correlations between responses while maintaining accuracy even if the responses are uncorrelated in extensive simulations the new procedure is compared with several previously proposed methods for predicting multiple responses including partial least squares and exhibits superior accuracy one version can be easily implemented in the context of standard statistical packages

uniform fuzzy relations and fuzzy functions in this paper we introduce and study the concepts of a uniform fuzzy relation and a partially uniform f function we give various characterizations and constructions of uniform fuzzy relations and uniform f functions we show that the usual composition of fuzzy relations is not convenient for f functions so we introduce another kind of composition and we establish a mutual correspondence between uniform f functions and fuzzy equivalences we also give some applications of uniform fuzzy relations in approximate reasoning especially in fuzzy control and we show that uniform fuzzy relations are closely related to the defuzzification problem

ridge regression estimation of the rotterdam model abstract the best guesses of unknown coefficients specified in theil s model of introspection are like predictions and not like de finetti s prevision and therefore not the values taken by random variables constrained least squares procedures can be formulated which are free of these difficulties the ridge estimator is a simple version of a constrained least squares estimator which can be made operational even when little prior information is available our operational ridge estimators are nearly minimax and are not less stable than least squares in the presence of high multicollinearity finally we have presented the ridge estimates for the rotterdam demand model

polynomial time algorithms for computing distances of fuzzy transition systems behaviour distances to measure the resemblance of two states in a nondeterministic fuzzy transition system have been proposed recently in literature such a distance defined as a pseudo ultrametric over the state space of the model provides a quantitative analogue of bisimilarity in this paper we focus on the problem of computing these distances we first extend the definition of the pseudo ultrametric by introducing discount such that the discounting factor being equal to 1 captures the original definition we then provide polynomial time algorithms to calculate the behavioural distances in both the non discounted and the discounted setting the algorithm is strongly polynomial in the former case

weak bisimulations for fuzzy automata abstract forward and backward bisimulations have been introduced recently by ciric et al 2012 9 as a means for modeling the equivalence between states of fuzzy automata and approximating the language equivalence as well as for use in the state reduction of fuzzy automata the main aim of the present paper is to introduce two new kinds of bisimulations weak forward and backward bisimulations which provide better approximations of the language equivalence than forward and backward bisimulations and when employed in the state reduction they provide better reductions we give procedures for deciding whether there exist weak forward and backward simulations and bisimulations and for computing the greatest ones whenever they exist using weak bisimulations in conjunction with the concept of a uniform fuzzy relation we determine necessary and sufficient conditions under which two fuzzy automata are weak bisimulation equivalent we also characterize uniform weak backward and forward bisimulations between two fuzzy automata in terms of isomorphisms between their nerode and reverse nerode automata

approximate bisimulations and state reduction of fuzzy automata under fuzzy similarity measures abstract for the purpose of reducing the number of states of fuzzy automata we study approximate bisimulations of fuzzy automata under fuzzy similarity measures which are induced by residuums of left continuous t norms for a real number 0 1 and a fuzzy similarity measure s we define approximate bisimulation under s between two fuzzy automata and prove that the degree of similarity between them is more than or equal to if there exists an approximate bisimulation between them furthermore we put forward the notion of surjective functional approximate bisimulations between two fuzzy automata under s using the notion of surjective functional approximate bisimulations under s the approximate bisimulations for a fuzzy automaton under s is defined as an equivalence relation with two additional properties according to an approximate bisimulation for a fuzzy automaton an aggregated fuzzy automaton has been constructed and the degree of similarity between them is also more than or equal to it is significant for us to find that there might not possess the greatest approximate bisimulation for a fuzzy automaton and we provide a polynomial time algorithm for computing all maximal approximate bisimulations finally we provide the conditions of the existence of the greatest approximate bisimulation

small confidence sets for the mean of a spherically symmetric distribution summary suppose that x has a k variate spherically symmetric distribution with mean vector 0 and identity covariance matrix wepresent two spherical confidence sets for 0 both centred at a positive part stein estimator t x in the first we obtain the radius by approximating the upper a point of the sampling disiribution of iits x 9112 by the first two non zero terms of its taylor series about the origin we can analyse some of the properties of this confidence set and see that it performs well in terms of coverage probability volume and conditional behaviour in the second method we find the radius by using a parametric bootstrap procedure here even greater improvement in terms of volume over the usual confidence set is possible at the expense of having a less explicit radius function a real data example is provided and extensions to the unknown covariance matrix and elliptically symmetric cases are discussed

nondeterministic automata equivalence bisimulations and uniform relations in this paper we study the equivalence of nondeterministic automata pairing the concept of a bisimulation with the recently introduced concept of a uniform relation in this symbiosis uniform relations serve as equivalence relations which relate states of two possibly different nondeterministic automata and bisimulations ensure compatibility with the transitions initial and terminal states of these automata we define six types of bisimulations but due to the duality we discuss three of them forward backward forward and weak forward bisimulations for each of these three types of bisimulations we provide a procedure which decides whether there is a bisimulation of this type between two automata and when it exists the same procedure computes the greatest one we also show that there is a uniform forward bisimulation between two automata if and only if the factor automata with respect to the greatest forward bisimulation equivalences on these automata are isomorphic we prove a similar theorem for weak forward bisimulations using the concept of a weak forward isomorphism instead of an isomorphism we also give examples that explain the relationships between the considered types of bisimulations

an improved algorithm for determinization of weighted and fuzzy automata for a given weighted finite automaton over a strong bimonoid we construct its reduced nerode automaton which is crisp deterministic and equivalent to the original weighted automaton with respect to the initial algebra semantics we show that the reduced nerode automaton is even smaller than the nerode automaton which was previously used in determinization related to this semantics we determine necessary and sufficient conditions under which the reduced nerode automaton is finite and provide an efficient algorithm which computes the reduced nerode automaton whenever it is finite in determinization of weighted finite automata over semirings and fuzzy finite automata over lattice ordered monoids this algorithm gives smaller crisp deterministic automata than any other known determinization algorithm

determinization of fuzzy automata with membership values in complete residuated lattices in this paper we introduce a new method for determinization of fuzzy finite automata with membership values in complete residuated lattices in comparison with the previous methods developed by belohlavek r belohlavek determinism and fuzzy automata information sciences 143 2002 205 209 and li and pedrycz y m li w pedrycz fuzzy finite automata and fuzzy regular expressions with membership values in lattice ordered monoids fuzzy sets and systems 156 2005 68 92 our method always gives a smaller automaton and in some cases when the previous methods result in infinite automata our method can result in a finite one we also show that determinization of fuzzy automata is closely related to fuzzy right congruences on a free monoid and fuzzy automata associated with them and in particular to the concept of the nerode s fuzzy right congruence of a fuzzy automaton which we introduce and study here

frequency domain analysis of a family of minimax signal estimators a minimax estimator of the mean of x approximately n theta r sub n is evaluated where r sub n is toeplitz the problem can be viewed as estimating a signal theta that has been corrupted by additive wide sense stationary noise the evaluation is carried out using a frequency domain approach that yields advantages in design and analysis in particular counterintuitive performance of an entire class of minimax forms is discovered when r sub n is not diagonal a numerical example is presented to demonstrate the performance

backward and forward bisimulation minimization of tree automata we improve on an existing p a abdulla j hogberg l kaati bisimulation minimization of tree automata international journal of foundations of computer science 18 4 2007 699 713 bisimulation minimization algorithm for finite state tree automata by introducing backward and forward bisimulation and developing minimization algorithms for them minimization via forward bisimulation is also effective on deterministic tree automata faster than the previous algorithm and yields the minimal equivalent deterministic tree automaton minimization via backward bisimulation generalizes the previous algorithm and can yield smaller automata but is just as fast we demonstrate implementations of these algorithms on a typical task in natural language processing

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

bootstrapping improved estimators for linear regression models abstract since stein 1955 proved that the least squares ls estimator for the linear regression model is inadmissible and james and stein 1961 demonstrated a superior estimator under squared error loss a number of better estimators have been proposed one reason these estimators have not been used in empirical work is that it is difficult to derive their sampling distributions this study shows that nonparametric bootstrapping provides good estimates of the sampling distribution of mundlak s 1981 restricted principal components estimator and a new stein rule estimator which shrinks mundlak s towards ls a monte carlo study of the bootstrap is performed for a range of increasingly collinear designs with 100 observations and 10 regressors using a squared error loss function the stein rule estimator performed much better than ls over most of the designs the nonparametric bootstrap generated reasonable estimates of the estimator s risk as well as standard errors of the individual components

simple extractors for all min entropies and a new pseudorandom generator a randomness extractor is an algorithm that given a sample from a distribution with sufficiently high min entropy and a short random seed produces an output that is statistically indistinguishable from uniform min entropy is a measure of the amount of randomness in a distribution we present a simple self contained extractor construction that produces good extractors for all min entropies our construction is algebraic and builds on a new polynomial based approach introduced by ta shma et al 2001b using our improvements we obtain for example an extractor with output length m k log n o 1 and seed length 1 p log n for an arbitrary 0 1 where n is the input length and k is the min entropy of the input distribution a pseudorandom generator is an algorithm that given a short random seed produces a long output that is computationally indistinguishable from uniform our technique also gives a new way to construct pseudorandom generators from functions that require large circuits our pseudorandom generator construction is not based on the nisan wigderson generator nisan and wigderson 1994 and turns worst case hardness directly into pseudorandomness the parameters of our generator match those in impagliazzo and wigderson 1997 and sudan et al 2001 and in particular are strong enough to obtain a new proof that p bpp if e requires exponential size circuits our construction also gives the following improvements over previous work we construct an optimal hitting set generator that stretches o log n random bits into s 1 pseudorandom bits when given a function on log n bits that requires circuits of size s this yields a quantitatively optimal hardness versus randomness tradeoff for both rp and bpp and solves an open problem raised in impagliazzo et al 1999 we give the first construction of pseudorandom generators that fool nondeterministic circuits when given a function that requires large nondeterministic circuits this technique also give a quantitatively optimal hardness versus randomness tradeoff for am and the first hardness amplification result for nondeterministic circuits

automata theory based on complete residuated lattice valued logic reduction and minimization automata theory based on complete residuated lattice valued logic called l valued finite automata l vfas has been established by qiu recently in this paper we define a kind of mealy type of l vfas mlfas a generalization of l vfas two kinds of statewise equivalence relations are introduced and a minimal form is defined we study the existence of the minimal form of an mlfa then we show that any two states can be distinguished by some word with finite length also a minimization algorithm of the mlfas is presented in addition we obtain a minimization algorithm for l vfas as well finally we define l valued languages l vls and l valued regular languages l vrls recognized by l vfas and provide some properties of l vrls

computation of the greatest right and left invariant fuzzy quasi orders and fuzzy equivalences abstract right invariant fuzzy quasi orders for fuzzy automata are broadly studied in the recent literature as they arise as solutions to particular systems of fuzzy relation equations and inequalities some of their applications include determinization and state reduction procedures as well as simulations and bisimulations for fuzzy automata in this paper we provide a procedure for computing the greatest right invariant fuzzy quasi order for a given fuzzy automaton over a complete residuated lattice the proposed procedure terminates in a finite number of steps whenever the underlying structure of the fuzzy automaton is locally finite when the previous condition is not satisfied we show that the greatest right invariant fuzzy quasi order can be obtained by taking the limit value of the convergent array of fuzzy quasi orders for fuzzy automata over bl algebras on the real unit interval 0 1 analogous procedures for computing the greatest left invariant fuzzy quasi order as well as the greatest right and left invariant fuzzy equivalences for a fuzzy automaton are also presented in addition the faster algorithm for computing the greatest right invariant equivalence on a nondeterministic automaton is also presented

pumping lemma in context free grammar theory based on complete residuated lattice valued logic residuated lattices are important algebras and have close links with various important algebras automata theory based on complete residuated lattice valued logic called l valued automata has been established by the second author in 2001 and 2002 as a continuation of automata theory based on complete residuated lattice valued logic in this paper we mainly deal with the problem concerning pumping lemma in l valued context free languages l cfls as a generalization of the notion in the theory of formal grammars the definition of l valued context free grammars l cfgs is introduced we also discuss a special case of l cfgs l right or left linear grammars and show the equivalence between l linear grammars and l regular grammars this result shows that we generalize the pumping lemma in l valued regular languages l rls more recently established by the second author

epsilon bisimulation relations for fuzzy automata this paper investigates the approximate bisimulation relations for fuzzy automata in order to study the approximate minimization problem of fuzzy automata for a small positive real number epsilon we introduce the notion of epsilon bisimulation relations between two fuzzy automata and prove that the behavior of a fuzzy automaton a differs by epsilon from the behavior of a fuzzy automaton b under a epsilon bisimulation relation between them also the notion of surjective functional epsilon bisimulation relations between two fuzzy automata is defined according to surjective functional epsilon bisimulation relations we discuss epsilon bisimulation relations for a fuzzy automaton a construction of aggregated fuzzy automaton by the given epsilon bisimulation for a fuzzy automaton is given furthermore we find that there might not exist the greatest epsilon bisimulation relation for a fuzzy automaton and we novelly give an effective algorithm to construct all maximal epsilon bisimulation relations for the given fuzzy automaton finally we point out that bisimulation relations for a fuzzy automaton are also epsilon bisimulation relations the conditions for the real number epsilon to ensure the existence of the greatest epsilon bisimulation are also discussed

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

a note on trillas chc models trillas et al e trillas s cubillo e castineira on conjectures in orthocomplemented lattices artificial intelligence 117 2000 255 275 recently proposed a mathematical model for conjectures hypotheses and consequences abbr chcs and with this model we can execute certain mathematical reasoning and reformulate some important theorems in classical logic we demonstrate that the orthomodular condition is not necessary for holding watanabe s structure theorem of hypotheses and indeed in some orthocomplemented but not orthomodular lattices this theorem is still valid we use the chc operators to describe the theorem of deduction the theorem of contradiction and the lindenbaum theorem of classical logic and clarify their existence in the chc models a number of examples is presented and we re define the chc operators in residuated lattices and particularly reveal the essential differences between the chc operators in orthocomplemented lattices and residuated lattices

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

automata theory based on complete residuated lattice valued logic pushdown automata automata theory based on complete residuated lattice valued logic called l valued automata has been proposed by qiu automata theory based on complete residuated latticed valued logic sci china ser f 44 6 2001 419 429 automata theory based on complete residuated latticed valued logic ii sci china ser f 45 6 2002 442 452 in this paper we discuss some properties of l valued context free grammars languages and pushdown automata we show that for such grammars chomsky and greibach normal forms can be equivalently constructed and we also prove that the languages accepted by final states and by empty stack in l valued pushdown automata are equivalent in particular we prove the equivalence between l valued context free grammars and l valued pushdown automata

graph nonisomorphism has subexponential size proofs unless the polynomial time hierarchy collapses traditional hardness versus randomness results focus on time efficient randomized decision procedures we generalize these trade offs to a much wider class of randomized processes we work out various applications most notably to derandomizing arthur merlin games we show that every language with a bounded round arthur merlin game has subexponential size membership proofs for infinitely many input lengths unless exponential time coincides with the third level of the polynomial time hierarchy and hence the polynomial time hierarchy collapses since the graph nonisomorphism problem has a bounded round arthur merlin game this provides the first strong evidence that graph nonisomorphism has subexponential size proofs we also establish hardness versus randomness trade offs for space bounded computation

formal power series and regular operations on fuzzy languages in this paper we study formal power series over a quantale with coefficients in the algebra of all languages over a given alphabet and representation of fuzzy languages by these formal power series this representation generalizes the well known representation of fuzzy languages by their cut and kernel languages we show that regular operations on fuzzy languages can be represented by regular operations on power series which are defined by means of operations on ordinary languages we use power series in study of fuzzy languages which are recognized by fuzzy finite automata and deterministic finite automata and we study closure properties of the set of polynomials and the set of polynomials with regular coefficients under regular operations on power series

automata theory based on complete residuated lattice valued logic turing machines automata theory based on complete residuated lattice valued logic called l valued finite automata l vfas has been established by the second author in 2001 in view of the importance of turing machines in this paper we establish a theory of turing machines based on complete residuated lattice valued logic which is a continuation of l vfas first we give the definition of l valued nondeterministic turing machines l ntms and observe that the multitape l ntms have the same language recognizing power as the single tape l ntms we give some related properties of l valued turing machines and discuss computing with fuzzy letters via l valued turing machines second we introduce the concepts of l valued recursively enumerable languages and l valued recursive languages and obtain some equivalent relations some results concerning the characterization of n recursively enumerable sets are given and the super computing power of l valued turing machines is investigated we also prove that l valued deterministic turing machines and l ntms are not equivalent in the sense of recognizing or deciding languages finally we show that there is no universal l valued turing machine however a universal l valued turing machine exists if the membership degrees of l valued sets are restricted to a finite complete residuated lattice with universal bounds 0 and 1

how to generate cryptographically strong sequences of pseudo random bits we give a set of conditions that allow one to generate 50 50 unpredictable bits based on those conditions we present a general algorithmic scheme for constructing polynomial time deterministic algorithms that stretch a short secret random input into a long sequence of unpredictable pseudo random bits we give an implementation of our scheme and exhibit a pseudo random bit generator for which any efficient strategy for predicting the next output bit with better than 50 50 chance is easily transformable to an equally efficient algorithm for solving the discrete logarithm problem in particular if the discrete logarithm problem cannot be solved in probabilistic polynomial time no probabilistic polynomial time algorithm can guess the next output bit better than by flipping a coin if head guess 0 if tail guess 1

combining minimax shrinkage estimators abstract when one estimates a multivariate normal mean the use of stein estimation entails both the grouping of coordinates and the selection of a set of targets toward which to shrink each group in this article we propose new minimax multiple shrinkage estimators that allow for multiple specifications of these aspects we provide examples that are evaluated on real and simulated data including an estimator that adaptively resolves the issue of combining possibly related estimation problems and an adaptive clustering shrinkage estimator the construction and properties of these estimators are shown to follow from the application of the multiple shrinkage results of george 1986a to general partitioned shrinkage estimators

bisimulations for fuzzy transition systems there has been a long history of using fuzzy language equivalence to compare the behavior of fuzzy systems however the comparison at this level is too coarse recently a finer behavioral measure i e bisimulation has been introduced to fuzzy finite automata however the results obtained are applicable only to finite state systems in this paper we consider bisimulation for general fuzzy systems which may be infinite state or infinite event by modeling them as fuzzy transition systems ftss to help understand and check bisimulation we characterize it in three ways by enumerating whole transitions comparing individual transitions and using a monotonic function in addition we address composition operations subsystems quotients and homomorphisms of ftss and discuss their properties connected with bisimulation the results presented here are useful to compare the behavior of general fuzzy systems in particular this makes it possible to relate an infinite fuzzy system to a finite one which is easier to analyze with the same behavior

bayesian robustness and the stein effect abstract in simultaneous estimation of normal means it is shown that through use of the stein effect surprisingly large gains of a bayesian nature can be achieved at little or no cost if the prior information is misspecified this provides a justification in terms of robustness with respect to mis specification of the prior for employing the stein effect even when combining a priori independent problems i e problems in which no empirical bayes effects are obtainable to study this issue a class of minimax estimators that closely mimic the conjugate prior bayes estimators is introduced

an adaptive empirical bayes estimator of the multivariate normal mean under quadratic loss abstract for shrinkage estimators to achieve significant risk improvement over their traditional competitors one must identify the region or subspace where the unknown location vector lies or is thought likely to lie a priori when vague or conflicting priors suggest that a broad class of estimators may be effective under a squared error loss measure new minimax or near minimax empirical bayes estimators are proposed that make use of stein s unbiased estimator of the risk to identify the optimum risk effective shrinkage estimator

weak random sources hitting sets and bpp simulations we show how to simulate any bpp algorithm in polynomial time by using a weak random source of r bits and min entropy r gamma for any gamma 0 this follows from a more general result about sampling with weak random sources our result matches an information theoretic lower bound and solves a question that has been open for some years the previous best results were a polynomial time simulation of rp m saks a srinivasan and s zhou proc 27th acm symp on theory of computing 1995 pp 479 488 and a quasi polynomial time simulation of bpp a ta shma proc 28th acm symp on theory of computing 1996 pp 276 285 departing significantly from previous related works we do not use extractors instead we use the or disperser of saks srinivasan and zhou in combination with a tricky use of hitting sets borrowed from andreev clementi and rolim j acm 45 1998 pp 179 213

weakly linear systems of fuzzy relation inequalities the heterogeneous case new types of systems of fuzzy relation inequalities and equations called weakly linear have been recently introduced in j ignjatovic et al on the greatest solutions to weakly linear systems of fuzzy relation inequalities and equations fuzzy sets syst 161 2010 3081 3113 the mentioned paper dealt with homogeneous weakly linear systems composed of fuzzy relations on a single set and a method for computing their greatest solutions has been provided this method is based on the computing of the greatest post fixed point contained in a given fuzzy relation of an isotone function on the lattice of fuzzy relations here we adapt this method for computing the greatest solutions of heterogeneous weakly linear systems where the unknown fuzzy relation relates two possibly different sets we also introduce and study quotient fuzzy relational systems and establish relationships between solutions to heterogeneous and homogeneous weakly linear systems besides we point out to applications of the obtained results in the state reduction of fuzzy automata and computing the greatest simulations and bisimulations between fuzzy automata as well as in the positional analysis of fuzzy social networks

on truncation of shrinkage estimators in simultaneous estimation of normal means abstract in estimating a multivariate normal mean 1 k t under sum of squares error loss it is well known that stein estimators improve upon the usual estimator in terms of expected loss if k 3 the improvement obtained is significant however only if the i are fairly close to the point towards which the stein estimator shrinks when extreme i are likely such as when the i are thought to arise from a possibly heavy tailed prior distribution the standard stein estimators may offer little improvement over the usual estimator stein 1981 proposed a limited translation stein estimator to correct this deficiency this estimator is analyzed herein for a number of heavy tailed prior distributions an adaptive version of the estimator is also discussed

differential geometric least angle regression a differential geometric approach to sparse generalized linear models sparsity is an essential feature of many contemporary data problems remote sensing various forms of automated screening and other high throughput measurement devices collect a large amount of information typically about few independent statistical subjects or units in certain cases it is reasonable to assume that the underlying process generating the data is itself sparse in the sense that only a few of the measured variables are involved in the process we propose an explicit method of monotonically decreasing sparsity for outcomes that can be modelled by an exponential family in our approach we generalize the equiangular condition in a generalized linear model although the geometry involves the fisher information in a way that is not obvious in the simple regression setting the equiangular condition turns out to be equivalent with an intuitive condition imposed on the rao score test statistics in certain special cases the method can be tweaked to obtain l1 penalized generalized linear model solution paths but the method itself defines sparsity more directly although the computation of the solution paths is not trivial the method compares favourably with other path following algorithms

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

low end uniform hardness versus randomness tradeoffs for am impagliazzo and wigderson proceedings of the 39th annual ieee symposium on foundations of computer science ieee computer society washington dc 1998 pp 734 743 proved a hardness versus randomness tradeoff for bpp in the uniform setting which was subsequently extended to give optimal tradeoffs for the full range of possible hardness assumptions in slightly weaker settings gutfreund shaltiel and ta shma comput complexity 12 2003 pp 85 130 proved a uniform hardness versus randomness tradeoff for am but that result worked only on the high end of possible hardness assumptions in this work we give uniform hardness versus randomness tradeoffs for am that are near optimal for the full range of possible hardness assumptions following gutfreund shaltiel and ta shma we do this by constructing a hitting set generator hsg for am with resilient reconstruction our construction is a recursive variant of the miltersen vinodchandran hsg comput complexity 14 2005 pp 256 279 the only known hsg construction with this required property the main new idea is to have the reconstruction procedure operate implicitly and locally on superpolynomially large objects using tools from pcps low degree testing self correction together with a novel use of extractors that are built from reed muller codes for a sort of locally computable error reduction as a consequence we obtain gap theorems for am and am cap coam that state roughly that either am or am cap coam protocols running in time t n can simulate all of exp arthur merlin games are powerful or else all of am or am cap coam can be simulated in nondeterministic time s n arthur merlin games can be derandomized for a near optimal relationship between t n and s n as in gutfreund shatiel and ta shma the case of am cap coam yields a particularly clean theorem that is of special interest due to the wide array of cryptographic and other problems that lie in this class

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

shrinkage estimation in the two way multivariate normal model a two way multivariate normal model is proposed and attention is focused on estimation of the mean values when the common variance of the observations is unknown a class of empirical bayes estimators is proposed and mean squared errors are given a lower bound on the mean squared error is found and related to risk asymptotics a jamesstein type estimator is derived and compared with its competitor a modal estimator that is obtained from a hierarchical prior for the unknown parameters

minimax multiple shrinkage estimation on presente des nouveaux estimateurs qui incorporent l information partielle a priori en utilisant les donnees comme emulation du comportement et du risque des estimateurs consideres les plus efficaces

a behavioral distance for fuzzy transition systems in contrast with the existing approaches to exact bisimulation for fuzzy systems we introduce a robust notion of behavioral distance to measure the behavioral similarity of nondeterministic fuzzy transition systems which are a generalization of fuzzy automata this behavioral distance provides a quantitative analogue of bisimilarity and is defined as the greatest fixed point of a suitable monotonic function the behavioral distance has the important property that two systems are at zero distance if and only if they are bisimilar moreover for any given threshold we find that systems with behavioral distances bounded by the threshold are equivalent in addition we show that two system combinators parallel composition and product are nonexpansive with respect to our behavioral distance which makes compositional verification possible the theory developed here is applicable to the quantitative verification approximate reduction and reliability analysis of fuzzy transition systems

fuzzy ϵ approximate regular languages and minimal deterministic fuzzy automata ϵ accepting them abstract in this paper for a real number 0 1 we put forward the notion of fuzzy approximate regular languages and study their properties especially the pumping lemma in the context of this kind of languages by comparing sets of fuzzy approximate regular languages under the order of set inclusion we get an infinite hierarchy of fuzzy languages the smallest is the set of fuzzy regular languages and the biggest is the set of fuzzy languages and the sets of approximate regular languages are different for different 0 1 2 we also investigate whether operations closed in the set of fuzzy regular languages are still closed in the set of fuzzy approximate regular languages furthermore for a fuzzy approximate regular language f approximate equivalence relations for f are characterized in order to construct deterministic fuzzy automata accepting f if a fuzzy approximate regular language f is also a fuzzy regular language and accepted by a given accessible deterministic fuzzy automaton a then we give a polynomial time algorithm to construct at least one minimal deterministic fuzzy automaton accepting f by means of a finally we point out that the number of states of minimal deterministic fuzzy automata accepting a fuzzy regular language is smaller than or equal to that of minimal deterministic fuzzy automata accepting this language

efficient shrinkage in parametric models this paper introduces shrinkage for general parametric models we show how to shrink maximum likelihood estimators towards parameter subspaces de ned by general nonlinear restrictions we derive the asymptotic distribution and risk of the generalized shrinkage estimator using a local asymptotic framework we show that if the shrinkage dimension exceeds two the asymptotic risk of the shrinkage estimator is strictly less than that of the mle this reduction holds globally in the parameter space we show that the reduction in asymptotic risk is substantial even for moderately large values of the parameters the formula simplify in a very convenient way in the context of high dimensional models we derive a simple bound for the asymptotic risk we also provide a new large sample minimax e ciency bound we use the concept of local asymptotic minimax bounds a generalization of the conventional asymptotic minimax bounds the

myhill nerode type theory for fuzzy languages and automata the myhill nerode theory is a branch of the algebraic theory of languages and automata in which formal languages and deterministic automata are studied through right congruences and congruences on a free monoid in this paper we develop a general myhill nerode type theory for fuzzy languages with membership values in an arbitrary set with two distinguished elements 0 and 1 which are needed to take crisp languages in consideration we establish connections between extensionality of fuzzy languages w r t right congruences and congruences on a free monoid and recognition of fuzzy languages by deterministic automata and monoids and we prove the myhill nerode type theorem for fuzzy languages we also prove that each fuzzy language possess a minimal deterministic automaton recognizing it we give a construction of this automaton using the concept of a derivative automaton of a fuzzy language and we give a method for minimization of deterministic fuzzy recognizers in the second part of the paper we introduce and study nerode s and myhill s automata assigned to a fuzzy automaton with membership values in a complete residuated lattice the obtained results establish nice relationships between fuzzy languages fuzzy automata and deterministic automata

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

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

simultaneous estimation in the multiparameter gamma distribution under weighted quadratic losses on obtient une nouvelle classe de solutions pour une inegalite differentielle souvent rencontree dans les problemes d estimation a plusieurs parametres

bayesian input in stein estimation and a new minimax empirical bayes estimator abstract the relationship between stein estimation of a multivariate normal mean and bayesian analysis is considered the necessity to involve prior information is discussed and the various methods of so doing are reviewed these include direct bayesian analyses ad hoc utilization of prior information restricted class bayesian and minimax analyses and type ii maximum likelihood empirical bayes methods a new empirical bayes stein type estimator is developed via the latter method for an interesting e contamination class of priors and is shown to be minimax under reasonable conditions the minimax proof contains some novel theoretical features

how much does stein estimation help in multiple linear regression the use of stein estimation in multiple linear regression is considered tables and graphs are presented that compare the prediction mean squared errors of positive part james stein preliminary test reduced and full model least squares estimates the appropriateness of using stein contraction on possibly extraneous variables is emphasized and a procedure is presented for evaluating the likely savings in using stein estimation on the problem at hand an example is given

computation of the greatest simulations and bisimulations between fuzzy automata recently two types of simulations forward and backward simulations and four types of bisimulations forward backward forward backward and backward forward bisimulations between fuzzy automata have been introduced if there is at least one simulation bisimulation of some of these types between the given fuzzy automata it has been proved that there is the greatest simulation bisimulation of this kind in the present paper for any of the above mentioned types of simulations bisimulations we provide an efficient algorithm for deciding whether there is a simulation bisimulation of this type between the given fuzzy automata and for computing the greatest one whenever it exists the algorithms are based on the method developed in ignjatovic et al on the greatest solutions to weakly linear systems of fuzzy relation inequalities and equations fuzzy sets syst 161 2010 3081 3113 which comes down to the computing of the greatest post fixed point contained in a given fuzzy relation of an isotone function on the lattice of fuzzy relations

automata theory based on complete residuated lattice valued logic a categorical approach automata theory based on complete residuated lattice valued logic called l valued automata l vas has been primarily established by qiu in 2001 and 2002 in this paper we consider the l vas that have l valued initial and final states we study the categorical issue of l vas the main technical contributions include 1 we investigate the relationship between the category of l vas and the category of non deterministic automata ndas also we study the relationship between the category of generalized l vas and the category of ndas 2 we prove the existence of isomorphisms between the category of l vas and the subcategory of generalized l vas and between the category of l vas and the category of sets of ndas 3 finally we further investigate some specific relationships between the output l valued subsets of generalized l vas and the output l valued subsets of ndas

on minimax estimation of a sparse normal mean vector mallows has conjectured that among distributions which are gaussian but for occasional contamination by additive noise the one having least fisher information has two sided geometric contamination a very similar problem arises in estimation of a non negative vector parameter in gaussian white noise when it is known also that most i e 1i components are zero we provide a partial asymptotic expansion of the minimax risk as 0 while the conjecture seems unlikely to be exactly true for flnite we verify it asymptotically up to the accuracy of the expansion numerical work suggests the expansion is accurate for as large as 05 the best 1 estimation rule is flrst but not second order minimax the results bear on an earlier study of maximum entropy estimation and various questions in robustness and function estimation using wavelet bases

a theory of vague lattices based on many valued equivalence relations i general representation results the present work introduces a new and general theory of ordering relations and lattices based on many valued equivalence relations under the name vague ordering relations and vague lattices respectively representations and constructions of vague ordering relations and vague lattices are the main subjects of this paper and various desirable results in this direction are established furthermore algebraic characterizations of vague lattices are studied

group linear empirical bayes estimates for a heteroscedastic normal mean abstractthe problem of estimating the mean of a normal vector with known but unequal variances introduces substantial difficulties that impair the adequacy of traditional empirical bayes estimators by taking a different approach that treats the known variances as part of the random observations we restore symmetry and thus the effectiveness of such methods we suggest a group linear empirical bayes estimator which collects observations with similar variances and applies a spherically symmetric estimator to each group separately the proposed estimator is motivated by a new oracle rule which is stronger than the best linear rule and thus provides a more ambitious benchmark than that considered in the previous literature our estimator asymptotically achieves the new oracle risk under appropriate conditions and at the same time is minimax the group linear estimator is particularly advantageous in situations where the true means and observed variances are empirically dependent to demonstrate the meri

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

characterizations of fuzzy finite automata in this paper we establish some important concepts in fuzzy finite automata ffas with bifuzzy property and clarify their essential relationships first we present a number of basic definitions and properties in ffas we then define a bifuzzy family of subautomata bifuzzy source and successor operators as well as demonstrate the bifuzzy topological characterization of ffas also we clarify the relationships between our results and previous ones and thus derive a relation figure visualizing their connections afterwards we investigate further the bifuzzy separability retrievability and homomorphism fuzzy continuous mapping and open mapping are also incorporated in particular we prove a number of equivalent characterizations for these concepts and expound the relationships amongst them this also concludes that both the bifuzzy source and successor operators are fuzzy closure operators we discover that our investigation generalizes to some extent the algebraic fuzzy automata elaborated by malik mordeson and others finally the main results obtained are summarized the potential applications are indicated and a number of related problems for further study are addressed

designing programs that check their work a program correctness checker is an algorithm for checking the output of a computation that is given a program and an instance on which the program is run the checker certifies whether the output of the program on that instance is correct this paper defines the concept of a program checker it designs program checkers for a few specific and carefully chosen problems in the class fp of functions computable in polynomial time problems in fp for which checkers are presented in this paper include sorting matrix rank and gcd it also applies methods of modern cryptography especially the idea of a probabilistic interactive proof to the design of program checkers for group theoretic computations two structural theorems are proven here one is a characterization of problems that can be checked the other theorem establishes equivalence classes of problems such that whenever one problem in a class is checkable all problems in the class are checkable

on pseudorandomness and resource bounded measure abstract in this paper we extend a key result of nisan and wigderson j comput system sci 49 1994 149 167 to the nondeterministic setting for all 0 we show that if there is a language in e dtime 2 o n that is hard to approximate by nondeterministic circuits of size 2 n then there is a pseudorandom generator that can be used to derandomize bp np in symbols bp np np by applying this extension we are able to answer some open questions in lutz theory comput systems 30 1997 429 442 regarding the derandomization of the classes bp p k and bp p k under plausible measure theoretic assumptions as a consequence if p 2 does not have p measure 0 then am coam is low for p 2 thus in this case the graph isomorphism problem is low for p 2 by using the nisan wigderson design of a pseudorandom generator we unconditionally show the inclusion ma zpp np and that ma coma is low for zpp np