universal truth tables and normal forms turksen s 1995 1986 fuzzy normal forms and kandel et al s 1995 and schwede and kandel s 1977 fuzzy maps are unified to establish universal truth tables and normal forms after an introduction to the topic we start out with a discussion on linguistic assertions next we develop a new universal truth table construction in order to generate normal forms for both the 16 main concepts of two variables as well as the subconcepts that can be generated from them it is shown how fuzzy propositional and fuzzy predicate expressions can be generated with the universal truth table construction furthermore it is shown that the laws of conservation hold in a general way on the fuzzified laws of exclude middle and contradiction generated by the class of t norms and their dual t conorms

locating a changed segment in a sequence of bernoulli variables the theory underlying inferences about a single change point in a sequence of independent bernoulli variables is extended to the two change points problem where the distance between the two change points is known namely a changed segment both null and nonnull distributions of the log likelihood ratio for testing the hypothesis that there is no changed segment against the alternative that there is one of specified length are derived using recurrence equations the distribution of the maximum likelihood estimator of the location of the changed segment is derived

power of the scan statistic in detecting a changed segment in a bernoulli sequence summary fu curnow 1990 derive recursive equations to find the level of significance and power of a likelihood ratio test for a changed segment of specified length based on the scan statistic the maximum number of successes within the specified length their method is computationally feasible for segment lengths of 20 or less we present and evaluate highly accurate approximations as well as bounds for the power function of this test that are computationally feasible even for very large segment lengths we also evaluate power when the duration of the increased length used in the test statistic does not correspond to the actual length scientists dealing with data sequences modelled by independent bernoulli trials frequently seek criteria to detect changes in the underlying process certain criteria have been developed to be sensitive to situations in which the probability of success on an individual trial changes at a point in the sequence fu curnow 1990 consider a version of a two change point problem with known distance m between the change points and with the trial probability of success at the two ends being equal they give recurrence relations for the probability of type i error and the power computational difficulties arise on even large computers when the number of trials is large in the present paper we derive highly accurate approximations that allow computation of power for all segment lengths consider a sequence of n independent 0 1 random variables x1 x2 xn let 1 denote success with pr x 1 i t we wish to test the null hypothesis of a constant probability of success ho i t i t 1 n against the alternative that some contiguous sequence of m events starting at an unknown trial z has a higher probability of success fu curnow 1990 note that the generalized likelihood ratio test for this alternative rejects ho for large values of the scan statistic

interpretations of various uncertainty theories using models of modal logic a summary abstract this paper summarizes our efforts to establish the usual semantics of propositional modal logic as a unifying framework for various uncertainty theories interpretations for fuzzy set theory dempster shafer theory probability theory and possibility theory are discussed some properties of these interpretations are also presented as well as directions for future research

granular neural networks with evolutionary interval learning to deal with different membership functions of the same linguistic term a new interval reasoning method using new granular sets is proposed based on yin yang methodology to make interval valued granular reasoning efficiently and optimize interval membership functions based on training data effectively a granular neural network gnn with a new high speed evolutionary interval learning is designed simulation results in nonlinear function approximation and bioinformatics have shown that the gnn with the evolutionary interval learning is able to extract interval valued granular rules effectively and efficiently from training data by using the new evolutionary interval learning algorithm

approximate p values for local sequence alignments assume that two sequences from a finite alphabet are optimally aligned according to a scoring system that rewards similarities according to a general scoring scheme and penalizes gaps insertions and deletions under the assumption that the letters in each sequence are independent and identically distributed and the two sequences are also independent approximate p values are obtained for the optimal local alignment when either i there are at most a fixed number of gaps or ii the gap initiation cost is sufficiently large in the latter case the approximation can be written in the same form as the well known case of ungapped alignments

fuzzy normal forms abstract linguistic expressions of a natural language are transformed at least three times before they are expressed in computational formulas between the linguistic and the computational expressions there are the meta linguistic and propositional expressions under various interpretations and assumptions fuzzy normal forms are canonical expressions derived at the propositional level with particular assumptions the fuzzy normal forms can be generated from fuzzy truth tables with a normal form derivation algorithm and an orthodox interpretation of conjunction disjunction and complementation operations it is shown that these fuzzy normal forms display a unique structure for certain general classes of crisp operators over fuzzy sets the fuzzy normal forms generated by crisp operators over fuzzy sets that correspond to max min standard complement de morgan triple are shown to be equivalent to the classical normal forms of two valued logic i e disjunctive and conjunctive normal forms known as dnf and cnf with a particular property i e the crisp containment fdnf 3 fcnf 3 whereas the fuzzy normal forms generated by crisp operators that correspond to non idempotent t norms t conorms and standard complement de morgan triples do not have in general a similar crisp containment property i e fdnf 2 fcnf 2 neither do the fuzzy normal forms generated by crisp operators over fuzzy sets that correspond to non idempotent and non commutative and non associative conjunction disjunction and standard complement de morgan triples have a crisp containment property i e fdnf 1 fcnf 1 however they still provide bounds on the combination of concepts

interpreting and extracting fuzzy decision rules from fuzzy information systems and their inference information systems which contain only crisp data precise and unique attribute values for all objects have been widely investigated due to the fact that in realworld applications imprecise data are abundant uncertainty is inherent in real information systems in this paper information systems are called fuzzy information systems and formalized by objects attributes f in which f is a fuzzy set and expresses some uncertainty between an object and its attribute values to interpret and extract fuzzy decision rules from fuzzy information systems the meta theory based on modal logic proposed by resconi et al is modified the modified meta theory not only expresses uncertainty between objects and their attributes but also uncertainty in the process of recognizing fuzzy information systems in addition according to perception computing proposed by zadeh granules of fuzzy information systems can be represented by fuzzy decision rules so that fuzzy inference methods can be used to obtain the decision attribute of a new object finally a novel way of combining evidences based on the modified meta theory is introduced which extends the concept of combining evidences based on dempster shafer theory

an extreme value theory for long head runs for an infinite sequence of independent coin tosses withp heads p 0 1 the longest run of consecutive heads in the firstn tosses is a natural object of study we show that the probabilistic behavior of the length of the longest pure head run is closely approximated by that of the greatest integer function of the maximum ofn 1 p i i d exponential random variables these results are extended to the case of the longest head run interrupted byk tails the mean length of this run is shown to be log n klog n k 1 log 1 p log k k 1 2 r1 n o 1 where log log1 p 0 577 is the euler mascheroni constant ln 1 p andr1 n is small the variance is 2 6 2 1 12 r2 n o 1 wherer2 n is again small upper and lower class results for these run lengths are also obtained and extensions discussed

a model for the measurement of membership and the consequences of its empirical implementation representation and uniqueness theorems are presented for the fundamental measurement of the membership of a fuzzy set when the domain of discourse is order dense the conclusion that membership is on an interval scale is justified by the inapplicability of extensive measurement to fuzziness and the lack of a natural origin for membership some descriptive statistics are also presented from an empirical study currently in progress to construct membership functions they suggest that subjects differ in their perception of fuzziness and that the models in the literature for certain linguistic operators such as not very and antonym are not sufficiently general to account for the range of individual perceptions of vague attributes a more general mathematical model is proposed the question of the meaningfulness of statements about membership functions is also discussed in the light of the assertion that membership can be fundamentally measured at best on an interval scale some of the difficulties which arise in fuzzy set theory due to this property are illustrated and a solution is suggested involving the use of a function which is derived from membership but is on an absolute scale

a new wavelet multigrid method the standard multigrid procedure performs poorly or may break down when used to solve certain problems such as elliptic problems with discontinuous or highly oscillatory coefficients the method discussed in this paper solves this problem by using a wavelet transform and schur complements to obtain the necessary coarse grid interpolation and restriction operators a factorized sparse approximate inverse is used to improve the efficiency of the resulting method numerical examples are presented to demonstrate the versatility of the method

knowledge representation by conjunctive normal forms and disjunctive normal forms based on n variable m dimensional fundamental clauses and phrases abstract in this paper the n variable m dimensional fundamental phrases and clauses are used to completely build the universal basis for the general cnf and dnf furthermore the general n variable m dimensional cnf and dnf are also defined in order to construct the generally standard expressions of different axiom based cnfs and dnfs such as 11 axiom based boolean cnf and boolean dnf 9 axiom based fuzzy cnf and fuzzy dnf and 5 axiom based t norm t conorm cnf and t norm t conorm dnf especially the general algorithm to construct the general n variable m dimensional cnf dnf from any given dnf cnf is proposed in general the intrinsic relations among the axioms the space of the fundamental phrases clauses and the general cnf and dnf are briefly studied additionally some interesting applications of knowledge representation by using the axiom based cnf and dnf are also discussed finally some new conclusions are drawn based on the new algorithm and the applications

set measure directed multi source information fusion our concern here is with the multi source fusion problem two important aspects of this problem are the representation of information provided by the sources and the formulation of the instructions on how to fuse the information provided which we refer to as the fusion imperative we investigate the use of a monotonic set measure as a means of representing the fusion imperative we look at the fusion of various different types of information precise data uncertain information such as probabilistic and possibilistic we also consider the case of imprecise uncertain information such as that represented by a dempster shafer belief structure

meta linguistic axioms as a foundation for computing with words abstract meta linguistic axioms are proposed in analogy to the axioms of classical theory as a foundation for computing with words consequences of these meta linguistic expressions are explored in the light of interval valued type 2 fuzzy sets the mapping of meta linguistic axioms to fuzzy disjunctive and conjunctive canonical forms generate two set theoretic axioms for each meta linguistic axiom that is composed of two elements such as commutativity and four set theoretic axioms for each meta linguistic axiom that is composed of three elements such as associativity as opposed to one axiom that is generated in the classical theory the set theoretic axioms double or quadruple because the basic equivalences of the classical theory break down in fuzzy theory in this setting we become aware that first these new axioms hold as a matter of degree and secondly there is an upper and lower limit with which they hold as a matter of degree

multiple changepoint fitting via quasilikelihood with application to dna sequence segmentation summary we consider situations where a step function with a variable number of steps provides an adequate model for a regression relationship while the variance of the observations depends on their mean this model provides for discontinuous jumps at changepoints and for constant means and error variances in between changepoints the basic statistical problem consists of identification of the number of changepoints their locations and the levels the function assumes in between we embed this problem into a quasilikelihood formulation and utilise the minimum deviance criterion to fit the model for the choice of the number of changepoints we discuss a modified schwarz criterion a dynamic programming algorithm makes the segmentation feasible for sequences of moderate length the performance of the segmentation method is demonstrated in an application to the segmentation of the bacteriophage l sequence

a fast wavelet multigrid method to solve elliptic partial differential equations abstract in this paper we present a wavelet based multigrid approach to solve elliptic boundary value problems encountered in mathematical physics the system of equations arising from finite difference discretization is represented in wavelet basis these equations are solved using multiresolution properties of wavelets characterized by sparse matrices having condition number o 1 together with a multigrid strategy for accelerating convergence the filter coefficients of d 2 k k 2 3 4 from daubechies family of wavelets are used to demonstrate the effectiveness and efficiency of the method the distinguishing feature of the method is it works as both solver and preconditioner as a consequence it avoids instability minimizes error and speeds up convergence compared to the classical multigrid method this approach requires substantially shorter computation time at the same time meeting accuracy requirements it is found that just one cycle is enough for the convergence of wavelet multigrid scheme whereas normally 7 8 cycles are required in classical multigrid schemes to meet the same accuracy numerical examples show that the scheme offers a fast and robust technique for elliptic pde s

a context model for fuzzy concept analysis based upon modal logic in this paper we present interesting relationships between the context model modal logic and fuzzy concept analysis it has been shown that the context model proposed by gebhardt and kruse int j approx reason 9 1993 283 can be semantically extended and considered as a data model for fuzzy concept analysis within the framework of the meta theory developed by resconi el al in 1990s consequently the context model provides a practical framework for constructing membership functions of fuzzy concepts and gives the basis for a theoretical justification of suitably use of well known t norm based connectives such as min max and product sum rules in applications furthermore an interpretation of mass assignments of fuzzy concepts within the context model is also established

longest runs in a sequence of m dependent random variables let x i i 1 be a sequence of random 0 s and 1 s we define the lengthr n of the longest head run as follows r n max left k leqq n mathop max limits 0 leqq i leqq n k 1 x i 1 cdots x i k 1 1 right the limit law for the distribution ofr n asn was found in 1943 the rate of convergence in that limit theorem remained unknown until recently even for bernoulli independent trials supposing that x i i 1 is a stationary sequence ofm dependent r v s we given an estimate on the rate of convergence in that limit theorem this estimate provides the unimprovable raten 1 lnn for the independent case a result of lim inf type is obtained too

measurement of membership functions and their acquisition abstract three basic views of the representation of membership functions are reviewed together with fundamental measurement of linguistic terms of linguistic variables the conclusion is that such measurements are either on an ordinal or an interval scale based on whether the appropriate axioms are validated by the empirical data with an allowance for stochastic variation the conjoint measurement is introduced for the case of multi dimensional linguistic variables whose linguistic terms are compositions of two or finitely many more component linguistic terms of distinct independent linguistic variables it is shown that any composition of distinct independent component linguistic terms of component linguistic variables by any t norm or s norm or any finite convext linear combination preserves the monotonic weak order property of the components in the composite once the scale properties of the measurement values of particular terms are validated composition procedures may be applied to the experimental data to obtain compound membership functions of fuzzy sets induced by meaningful representations of compositions of linguistic terms of linguistic variables finally four methods of membership acquisition and construction are reviewed from the perspective of fundamental measurement

normal forms and truth tables for fuzzy logics in this paper we examine and compare de morgan kleene and boolean disjunctive and conjunctive normal forms and consider their role in fuzzy settings in particular we show that there are normal forms and truth tables for classical fuzzy propositional logic and interval valued fuzzy propositional logic that are completely analogous to those for boolean propositional logic thus determining logical equivalence of two expressions in fuzzy propositional logic is a finite problem and similarly for the interval valued case turksen s work on interval valued fuzzy sets is examined in light of these results

on generalized successive overrelaxation methods for augmented linear systems for the augmented system of linear equations golub wu and yuan recently studied an sor like method bit 41 2001 71 85 by further accelerating it with another parameter in this paper we present a generalized sor gsor method for the augmented linear system we prove its convergence under suitable restrictions on the iteration parameters and determine its optimal iteration parameters and the corresponding optimal convergence factor theoretical analyses show that the gsor method has faster asymptotic convergence rate than the sor like method also numerical results show that the gsor method is more effective than the sor like method when they are applied to solve the augmented linear system this gsor method is further generalized to obtain a framework of the relaxed splitting iterative methods for solving both symmetric and nonsymmetric augmented linear systems by using the techniques of vector extrapolation matrix relaxation and inexact iteration besides we also demonstrate a complete version about the convergence theory of the sor like method

the erdos renyi strong law for pattern matching with a given proportion of mismatches 1 informal introduction the erdos bnyi law erdijs and r6nyi 1970 l for coin tossing is a strong law for the behavior of the length of long success rich runs for the length r of the longest run of pure heads in n tosses the result is that with probability l lin rjlog n 1 where p flheads 0 a more general result is quoted as formula 1 in section 2 for rz the longest head rich run in which the fraction of heads is at least a p note that r ri in many practical situations such as manufacturing or roulette observations are taken sequentially and each can be classified as success or failure for these cases it is possible to use the erdijs wnyi law to test the hypothesis that the success probability is p from another point of view the erdijs bnyi law can be used to recognize patterns of unusually long runs of succe88e8 or failures our interest is in the recognition of unusually long patterns or words common to two random sequences the patterns are unknown prior to an examination of the sequences the motivation for this work is the comparison of dna sequences which can be modeled as sequences of i i d or markov distributed letters evolution operates to conserve although imperfectly patterns important to biological function it is a task of biology to discover these patterns and their function in earlier work we generalized the erdiie bnyi law for pure head runs a 1 to exact matching patterns between two sequences in this paper we extend those results to include matchings of quality a between p and 1 the examples below illustrate the natural analogs of rz studied in this paper two words form a quality a matching if they have the same length and the

a measure of dna sequence dissimilarity based on mahalanobis distance between frequencies of words summary a number of algorithms exist for searching genetic databases for biologically significant similarities in dna sequences past research has shown that word based search tools are computationally efficient and can find similarities or dissimilarities invisible to other algorithms like fasta we characterize a family of word based dissimilarity measures that define distance between two sequences by simultaneously comparing the frequencies of all subsequences of n adjacent letters i e n words in the two sequences applications to real data demonstrate that currently used word based methods that rely on euclidean distance can be significantly improved by using mahalanobis distance which accounts for both variances and covariances between frequencies of n words furthermore in those cases where mahalanobis distance may be too difficult to compute using standardized euclidean distance which only corrects for the variances of frequencies of n words still gives better performance than the euclidean distance also a simple way of combining distances obtained at different n words is considered the goal is to obtain a single measure of dissimilarity between two dna sequences the performance ranking of the preceding three distances still holds for their combined counterparts all results obtained in this paper are applicable to amino acid sequences with minor modifications

a note on the run length function for intermittent maps abstract we study the run length function for intermittent maps in particular we show that the longest consecutive zero digits resp one digits having a time window of polynomial resp logarithmic length our proof is relatively elementary in the sense that it only relies on the classical borel cantelli lemma and the polynomial decay of intermittent maps our results are compensational to the erd s renyi law obtained by denker and nicol in 8

on convergence properties of pocket algorithm the problem of finding optimal weights for a single threshold neuron starting from a general training set is considered among the variety of possible learning techniques the pocket algorithm has a proper convergence theorem which asserts its optimality however the original proof ensures the asymptotic achievement of an optimal weight vector only if the inputs in the training set are integer or rational this limitation is overcome in this paper by introducing a different approach that leads to the general result furthermore a modified version of the learning method considered called pocket algorithm with ratchet is shown to obtain an optimal configuration within a finite number of iterations independently of the given training set

non specificity and interval valued fuzzy sets abstract non specificity is a characteristic of interval valued fuzzy sets vagueness is represented by fuzzy sets which capture the meaning representation of linguistic terms or linguistic variables this is type i semantic uncertainty combinations of two or more vague linguistic terms with vague linguistic operators generate semantic uncertainty when disjunctive and conjunctive combinations of concepts are formed in particular disjunctive and conjunctive normal form expressions of combined concepts generate an interval of uncertainty this is type ii semantic uncertainty the size i e the cardinality of this interval provides a foundation for the fuzzy measure theoretical investigation of the combination of vagueness associated with two or more linguistic concepts and the operators that combine them in particular the length of the interval provides the non specificity measure for interval valued fuzzy sets thus non specificity generated by interval valued fuzzy sets forms an essential linkage for the development of evidence theory with fuzzy sets

fast wavelet transforms and numerical algorithms i a class of algorithms is introduced for the rapid numerical application of a class of linear operators to arbitrary vectors previously published schemes of this type utilize detailed analytical information about the operators being applied and are specific to extremely narrow classes of matrices in contrast the methods presented here are based on the recently developed theory of wavelets and are applicable to all calderon zygmund and pseudo differential operators the algorithms of this paper require order o n or o n log n operations to apply an n n matrix to a vector depending on the particular operator and the version of the algorithm being used and our numerical experiments indicate that many previously intractable problems become manageable with the techniques presented here

critical phenomena for sequence matching with scoring consider two independent sequences x 1 x n and y 1 y n suppose that x 1 x n are i i d x and y 1 y n are i i d y where x and y are distributions on finite alphabets x and y respectively a score f x x y r is assigned to each pair x i y j and the maximal nonaligned segment score is m n max 0 i j n 0 l 1 f x i l y j l our result is that m n log n x y a s with determined by a tractable variational formula moreover the pair empirical measure of x i l y j l during the segment where m n is achieved converges to a probability measure which is accessible by the same formula these results generalize to x i y j taking values in any polish space to intrasequence scores under shifts to long quality segments and to more than two sequences

learning in feedforward layered networks the tiling algorithm the authors propose a new algorithm which builds a feedforward layered network in order to learn any boolean function of n boolean units the number of layers and the number of hidden units in each layer are not prescribed in advance they are outputs of the algorithm it is an algorithm for growth of the network which adds layers and units inside a layer at will until convergence the convergence is guaranteed and numerical tests of this strategy look promising

convergence of a multigrid method for elliptic equations with highly oscillatory coefficients standard multigrid methods are not so effective for equations with highly oscillatory coefficients new coarse grid operators based on homogenized operators are introduced to restore the fast convergence rate of multigrid methods finite difference approximations are used for the discretization of the equations convergence analysis is based on the homogenization theory proofs are given for a two level multigrid method with the homogenized coarse grid operator for two classes of two dimensional elliptic equations with dirichlet boundary conditions

variants of algebraic wavelet based multigrid methods application to shifted linear systems abstract in this paper we describe some new variants and applications of the wavelet algebraic multigrid method this method combines the algebraic multigrid method a well known family of multilevel techniques for solving linear systems without use of knowledge of the underlying problem and the discrete wavelet transform these two techniques can be combined in several ways obtaining different methods for solution of linear systems these can be used alone or as preconditioners for krylov iterative methods these methods can be applied for solution of linear systems with shifted matrices of the form a hi whose efficient solution is very important for implicit ode methods unsteady pdes computation of eigenvalues of large sparse matrices and other important problems

optimal data compression algorithm abstract a practical source coding scheme based on approximate string matching is proposed it is an approximate fixed length string matching data compression combined with a block coder based on the empirical distribution a lemma on approximate string matching which is an extension of the kac lemma is proved it is shown based on the lemma that the deterministic algorithm converts the stationary and ergodic source u into an output process v and under the assumption that v is a stationary process after the scheme has run for an infinite time the optimal compression ratio r d is achieved this reduces the problem of the universal lossy coder to the proof of stationarity of the output process v in the proposed algorithm the main advantages of the proposed method are the asymptotic sequential behavior of the encoder and the simplicity of the decoder

approximations for distributions of scan statistics abstract certain statistical applications deal with the extremal distributions of the number of points in a moving interval or window of fixed length this article gives an approximation that is highly accurate for several of these distributions applications include the maximum cluster of points on a line or circle multiple coverage by subintervals or subarcs of fixed size the length of the longest success run in bernoulli trials and the generalized birthday problem

distribution of the length of the longest significance run on a bernoulli net and its applications we consider the length of the longest significance run in a two dimensional bernoulli net and derive its asymptotic limit distribution our results can be considered as generalizations of known theorems in significance runs we give three types of theoretical results 1 reliability style lower and upper bounds 2 erdos renyi law and 3 the asymptotic limit distribution to understand the rate of convergence to the asymptotic distributions we carry out numerical simulations the convergence rates in a variety of situations are presented to understand the relation between the length of the longest significance run s and the success probability p we propose a dynamic programming algorithm to implement simultaneous simulations insights from numerical studies are important for choosing the values of design parameters in a particular application which motivates this article the distribution of the length of the longest significance run in a bernoulli net is critical in applying a multiscale metho

canonical forms of fuzzy truthoods by meta theory based upon modal logic in this paper we redefine with the meta theory based on modal logic the operations between fuzzy sets of verity i e fuzzy sets of truthood with this new approach we can unify the different formulas for the operations and or and not between the fuzzy sets of verity i e truthood the operations between the fuzzy sets of verity become sensitive to the logic value true or false that agents persons sensors assign to the worlds contexts the operations are also sensitive to the difference of the worlds and time of synchronisation it should be pointed out that when we use the logic operations as and or and not we generally assume that the worlds are the same and change their truth value at the same time but it is known that there are cases where this synchronic situation and identity is not always valid that is there exist transformations that change one world for one proposition to another world for another proposition in conclusion the linguistic and or not operations become dependent on the particular truth value of a world on the synchronisation and on the worlds assigned to the two propositions via transformations thus all of these possible changes in the structure of the worlds in the modal logic cause the gradation of the linguistic operations e g and or and not an individual world person agent sensor assigns to an atomic sentence either a true or false value and uses the classical two value logic operations of and or not that is the crisp true or false responses assignments of worlds generate gradation of truthood value the uncertainty in a fuzzy set is represented with sets of worlds in a conflict situation i e the same proposition may be true in one world and false in another consonant or dissonant relations between sets of worlds that depends on the synchronisation and or transformation of worlds cause the generation of gradation by the linguistic operations and or and not that is the linguistic operations change for different concrete situations set of worlds caused by the generation of a representation in each world where the descriptive set membership assignment d may be two or infinite valued but the verity assignment v is two valued in a particular world representation whereas membership values of the fuzzy set of truth verifications associated with the set of worlds are in 0 1 furthermore the combination of fuzzy membership values generates a type ii fuzzy set that is captured by fdcf and fccf formulas in this paper we show that there exist a deeper connection between the set membership assignment and the verity assignment of truthood by modal logic with suitable extensions

local algorithms for pattern recognition and dependencies estimation in previous publications bottou and vapnik 1992 vapnik 1992 we described local learning algorithms which result in performance improvements for real problems we present here the theoretical framework on which these algorithms are based first we present a new statement of certain learning problems namely the local risk minimization we review the basic results of the uniform convergence theory of learning and extend these results to local risk minimization we also extend the structural risk minimization principle for both pattern recognition problems and regression problems this extended induction principle is the basis for a new class of algorithms

a fast wavelet block jacobi method abstract in this paper we develop a fast block jacobi method for linear systems based on discrete wavelet transform dwt traditional wavelet based methods for linear systems do not fully utilize the sparsity and the multi level block structure of the transformed matrix after dwt for the sake of numerical efficiency we truncate the transformed matrix to be a sparse matrix by letting the small values be zero to combine the advantages of the direct method and the iterative method we solve the sub systems appropriately based on the multi level block structure of the transformed matrix after dwt numerical examples show that the proposed method is very numerically effective

a wavelet based algebraic multigrid preconditioner for sparse linear systems this work considers the use of discrete wavelet transform dwt based in filters in the construction of the hierarchy of matrices in the algebraic multigrid method amg the two dimensional dwt is applied to produce an approximation of the matrix in each level of the wavelets multiresolution decomposition process in this procedure an operator is created formed only by lowpass filters that is applied to the rows and columns of the matrix capturing this approximation this same operator is used as an intergrid transfer in the amg wavelet based algebraic multigrid method wamg was implemented with daubechies wavelets of orders 6 4 and 2 and used as a preconditioner for the generalized minimal residual method gmres numerical results are presented comparing this new approach with the standard algebraic multigrid as preconditioner for sparse linear systems

a suboptimal lossy data compression based on approximate pattern matching a practical suboptimal variable source coding algorithm for lossy data compression is presented this scheme is based on approximate string matching and it naturally extends the lossless lempel ziv 1977 data compression scheme among others we consider the typical length of an approximately repeated pattern within the first n positions of a stationary mixing sequence where d percent of mismatches is allowed we prove that there exists a constant r sub 0 d such that the length of such an approximately repeated pattern converges in probability to 1 r sub 0 d log n pr but it almost surely oscillates between 1 r sub spl infin d log n and 2 r sub 1 d log n where r sub spl infin d r sub 0 d r sub 1 d 2 are some constants these constants are natural generalizations of renyi entropies to the lossy environment more importantly we show that the compression ratio of a lossy data compression scheme based on such an approximate pattern matching is asymptotically equal to r sub 0 d we also establish the asymptotic behavior of the so called approximate waiting time n sub l which is defined as the time until a pattern of length c repeats approximately for the first time we prove that log n sub l l spl rarr r sub 0 d pr as l spl rarr spl infin in general r sub 0 d r d where r d is the rate distortion function thus for stationary mixing sequences we settle in the negative the problem investigated by steinberg and gutman by showing that a lossy extension of the wyner ziv 1989 scheme cannot be optimal

treating fuzziness in subjective evaluation data this paper proposes a technique to deal with fuzziness in subjective evaluation data and applies it to principal component analysis and correspondence analysis in the existing method or techniques developed directly from it fuzzy sets are defined from some standpoint on a data space and the fuzzy parameters of the statistical model are identified with linear programming or the method of least squares in this paper we try to map the variation in evaluation data into the parameter space while preserving information as much as possible and thereby define fuzzy sets in the parameter space clearly it is possible to use the obtained fuzzy model to derive things like the principal component scores from the extension principle however with a fuzzy model which uses the extension principle the possibility distribution spreads out as the explanatory variable values increase this does not necessarily make sense for subjective evaluations such as a 5 level evaluation for instance instead of doing so we propose a method for explicitly expressing the vagueness of evaluation using certain quantities related to the eigenvalues of a matrix which specifies the fuzzy parameter spread as a numerical example we present an analysis of subjective evaluation data on local environments

critical phenomena in sequence matching we give a generalization of the result of erdos and renyi on the length r n of the longest head run in the first n tosses of a coin consider two independent sequences x 1 x 2 cdots x m and y 1y 2 cdots y n suppose that x 1 x 2 cdots are i i d mu and y 1 y 2 cdots are i i d nu where mu and nu are possibly different distributions on a common finite alphabet s let p equiv p x 1 y 1 in 0 1 the length of the longest matching consecutive subsequence is m m n equiv max k x i r y j r for r 1 to k for some 0 leq i leq m k 0 leq j leq n k for m and n rightarrow infty with log m log mn rightarrow lambda in 0 1 our result is that there is a constant k equiv k mu nu lambda in 0 1 rbrack such that p lim m m n log 1 p mn k 1 the proof uses large deviation methods the constant k is determined from a variational formula involving the kullback liebler distance or relative entropy a simple necessary and sufficient condition for k 1 is given for the case m n lambda 1 2 and mu nu k 1 the set of mu nu lambda for which k 1 has nonempty interior the boundary of this set is the location of a phase transition the results generalize to more than two sequences and to markov chains a strong law of large numbers is given for the proportion of letters within the longest matching word the limiting proportion exhibits critical behavior similar to that of k

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed