on the lifetime behavior of a discrete time shock model in this article we study a shock model in which the shocks occur according to a binomial process i e the interarrival times between successive shocks follow a geometric distribution with mean 1 p according to the model the system fails when the time between two consecutive shocks is less than a prespecified level this is the discrete time version of the so called d shock model which has been previously studied for the continuous case we obtain the probability mass function and probability generating function of the system s lifetime we also present an extension of the results to the case where the shock occurrences are dependent in a markovian fashion

runs in superpositions of renewal processes with applications to discrimination wald and wolfowitz ann math statist 11 1940 147 162 introduced the run test for testing whether two samples of i i d random variables follow the same distribution here a run means a consecutive subsequence of maximal length from only one of the two samples in this paper we contribute to the problem of runs and resulting test procedures for the superposition of independent renewal processes which may be interpreted as arrival processes of customers from two different input channels at the same service station to be more precise let sn n 1 and tn n 1 be the arrival processes for channel 1 and channel 2 respectively and wn n 1 their be superposition with counting process n t def sup n 1 wn t let further rn be the number of runs in w1 wn and rt rn t the number of runs observed up to time t we study the asymptotic behavior of rn and rt first for the case where sn n 1 and tn n 1 have exponentially distributed increments with parameters 1 and 2 and then for the more difficult situation when these increments have an absolutely continuous distribution these results are used to design asymptotic level tests for testing 1 2 against 1 2 in the first case and for testing for equal scale parameters in the second

duhamel hollmann like discrete fourier transform algorithm with the smallest multiplicative complexity over a finite field the new method for the discrete fourier transform computation over a finite field is introduced this method is a nontrivial generalization of the duhamel hollmann algorithm with replacement of the toeplitz convolution calculation by the normalized cyclic convolution calculation both algorithms have the smallest multiplicative complexity

assessment of a generalized discrete time mixed δ shock model for the multi state systems abstract in this paper the life behavior of a shock model is studied when the external shocks occur according to a binomial process whose interarrival times between successive shocks follow a geometric distribution the system transits into a lower partially working state upon the occurrence of each interarrival time between two successive shocks less than a critical threshold say the system fails when k out of interarrival times between two successive shocks are less than or the magnitude of the shock is larger than the other critical level say such a model creates a multi state system having a number of different states the probability mass functions of system s life time the time spent by the system in a perfectly functioning state and the total time spent by the system in partially working states are derived for the proposed model the corresponding probability generating functions are also derived the case of markov shock occurrences is also studied to illustrate the model studied in this paper some numerical examples are also considered finally an application in insurance is also provided

a unified framework for the fractional fourier transform the paper investigates the possibility for giving a general definition of the fractional fourier transform frt for all signal classes one dimensional 1 d and multidimensional continuous and discrete periodic and aperiodic since the definition is based on the eigenfunctions of the ordinary fourier transform ft the preliminary conditions is that the signal domain periodicity be the same as the ft domain periodicity within these classes a general frt definition is formulated and the frt properties are established in addition the multiplicity which is intrinsic in a fractional operator is clearly developed the general definition is checked in the case in which the frt is presently available and moreover to establish the frt in new classes of signals

ordering conjunctive queries abstract conjunctive problems are pervasive in artificial intelligence and database applications in general such problems cannot be solved without carefully ordering the set of conjuncts for the problem solving system in this paper the problem of determining the best ordering for a set of conjuncts is addressed we first show how simple information about set sizes can be used to estimate the cost of solving a conjunctive problem assuming the availability of this information methods for ordering conjuncts are developed based on several theorems and corollaries about ordering we also consider two well known heuristic ordering rules and discuss their advantages and disadvantages finally the overall efficiency of including conjunct ordering in a problem solver is considered to help reduce the overhead we present an approach of monitoring problem solving cost at run time in this way conjunct ordering is limited to difficult problems where the cost of ordering is less significant we also consider several issues involved in extending conjunct ordering to problems involving inference and planning problems

avoiding cartesian products for multiple joins computing the natural join of a set of relations is an important operation in relational database systems the ordering of joins determines to a large extent the computation time of the join since the number of possible orderings could be very large query optimizers first reduce the search space by using various heuristics and then try to select an optimal ordering of joins avoiding cartesian products is a common heuristic for reducing the search space but it cannot guarantee optimal ordering in its search space because the cheapest cartesian product free cpf for short ordering could be significantly worse than an optimal non cpf ordering by a factor of an arbitrarily large number in this paper we use programs consisting of joins semijoins and projections for computing the join of some relations and we introduce a novel algorithm that derives programs from cpf orderings of joins we show that there exists a cpf ordering from which our algorithm derives a program whose cost is within a constant factor of the cost of an optimal ordering thus our result demonstrates the effectiveness of avoiding cartesian products as a heuristic for restricting the search space of orderings of joins

on success runs of a fixed length in bernoulli sequences exact and asymptotic results consider a sequence of n bernoulli success failure or 1 0 trials the exact and limiting distribution of the random variable e n k denoting the number of success runs of a fixed length k email protected email protected n is derived along with its mean and variance an associated waiting time is examined as well the exact distribution is given in terms of binomial coefficients and an extension of it covering exchangeable sequences is also discussed limiting distributions of e n k are obtained using poisson and normal approximations the exact mean and variance of e n k which are given in explicit forms are also used to derive bounds and an additional approximation of the distribution of e n k numbers associated with e n k and related random variables counting binary strings and runs of 1 s useful in applications of computer science are provided the overall study is illustrated by an extensive numerical experimentation

high speed vlsi multiplication algorithm with a redundant binary addition tree a high speed vlsi multiplication algorithm internally using redundant binary representation is proposed in n bit binary integer multiplication n partial products are first generated and then added up pairwise by means of a binary tree of redundant binary adders since parallel addition of two n digit redundant binary numbers can be performed in a constant time independent of n without carry propagation n bit multiplication can be performed in a time proportional to log2 n the computation time is almost the same as that by a multiplier with a wallace tree in which three partial products will be converted into two in contrast to our two to one conversion and is much shorter than that by an array multiplier for longer operands the number of computation elements of an n bit multiplier based on the algorithm is proportional to n2 it is almost the same as those of conventional ones furthermore since the multiplier has a regular cellular array structure similar to an array multiplier it is suitable for vlsi implementation thus the multiplier is excellent in both computation speed and regularity in layout it can be implemented on a vlsi chip with an area proportional to n2 log2 n the algorithm can be directly applied to both unsigned and 2 s complement binary integer multiplication

implementation of split radix fft algorithms for complex real and real symmetric data a new algorithm is presented for the fast computation of the discrete fourier transform this algorithm belongs to that class of recently proposed 2n fft s which present the same arithmetic complexity the lowest among any previously published one moreover this algorithm has the advantage of being performed in place by repetitive use of a butterfly type structure without any data reordering inside the algorithm furthermore it can easily be applied to real and real symmetric data with reduced arithmetic complexity by removing all redundancy in the algorithm

distribution theory of runs a markov chain approach abstract the statistics of the number of success runs in a sequence of bernoulli trials have been used in many statistical areas for almost a century even in the simplest case of independent and identically distributed bernoulli trials the exact distributions of many run statistics still remain unknown departing from the traditional combinatorial approach in this article we present a simple unified approach for the distribution theory of runs based on a finite markov chain imbedding technique our results cover not only the identical bernoulli trials but also the nonidentical bernoulli trials as a byproduct our results also yield the exact distribution of the waiting time for the mth occurrence of a specific run

the fractional discrete cosine transform the extension of the fourier transform operator to a fractional power has received much attention in signal theory and is finding attractive applications the paper introduces and develops the fractional discrete cosine transform dct on the same lines discussing multiplicity and computational aspects similarities and differences with respect to the fractional fourier transform are pointed out

finding optimal derivation in redundant knowledge bases abstract a backward chaining process uses a collection of rules to reduce a given goal to a sequence of database retrievals a derivation strategy is an ordering on these steps specifying when to use each rule and when to perform each retrieval given the costs of reductions and retrievals and the a priori likelihood that each particular retrieval will succeed one can compute the expected cost of any strategy for answering a specific query from a given knowledge base smith 19 presents an algorithm that finds the minimal cost strategy in time essentially linear in the number of rules for any disjunctive irredundant knowledge base this paper proves that the addition of redundancies renders this task np hard many explanation based learning systems work by adding in redundancies this shows the complexities inherent in their task

on runlength codes several results on binary d k codes are given first a novel derivation for the capacity of these codes based on information theoretic principles is given based on this result the spectrum of a d k code is computed finally the problem of computing the capacity of the binary symmetric channel under the condition that the input sequences satisfy the d k constraint is considered lower bounds on the capacity of such a channel are derived

a logic for default reasoning the need to make default assumptions is frequently encountered in reasoning about incompletely specified worlds inferences sanctioned by default are best viewed as beliefs which may well be modified or rejected by subsequent observations it is this property which leads to the non monotonicity of any logic of defaults in this paper we propose a logic for default reasoning we then specialize our treatment to a very large class of commonly occuring defaults for this class we develop a complete proof theory and show how to interface it with a top down resolution theorem prover finally we provide criteria under which the revision of derived beliefs must be effected

digital computation of the fractional fourier transform an algorithm for efficient and accurate computation of the fractional fourier transform is given for signals with time bandwidth product n the presented algorithm computes the fractional transform in o nlogn time a definition for the discrete fractional fourier transform that emerges from our analysis is also discussed

unified fractional fourier transform and sampling theorem the fractional fourier transform frt is an extension of the ordinary fourier transform ft applying the language of the unified ft we develop frt expressions for discrete and continuous signals introducing a particular form of periodicity chirp periodicity the frt sampling theorem is derived as an extension of its ordinary counterpart

q bernstein polynomials and bezier curves we define q bernstein polynomials which generalize the classical bernstein polynomials and show that the difference of two consecutive q bernstein polynomials of a function f can be expressed in terms of second order divided differences of f it is also shown that the approximation to a convex function by its q bernstein polynomials is one sided a parametric curve is represented using a generalized bernstein basis and the concept of total positivity is applied to investigate the shape properties of the curve we study the nature of degree elevation and degree reduction for this basis and show that degree elevation is variation diminishing as for the classical bernstein basis

discrete fractional fourier transform based on orthogonal projections the continuous fractional fourier transform frft performs a spectrum rotation of signal in the time frequency plane and it becomes an important tool for time varying signal analysis a discrete fractional fourier transform has been developed by santhanam and mcclellan see ibid vol 42 p 994 98 1996 but its results do not match those of the corresponding continuous fractional fourier transforms we propose a new discrete fractional fourier transform dfrft the new dfrft has dft hermite eigenvectors and retains the eigenvalue eigenfunction relation as a continous frft to obtain dft hermite eigenvectors two orthogonal projection methods are introduced thus the new dfrft will provide similar transform and rotational properties as those of continuous fractional fourier transforms moreover the relationship between frft and the proposed dfrft has been established in the same way as the conventional dft to continuous fourier transform

q geometric and q binomial distributions of order k abstract in this paper we generalize geometric and binomial distributions of order k to q geometric and q binomial distributions of order k using bernoulli trials with a geometrically varying success probability in particular we derive expressions for the probability mass functions of these distributions for q 1 these distributions reduce to geometric and binomial distributions of order k which have been extensively studied in the literature

the discrete fractional fourier transform we propose and consolidate a definition of the discrete fractional fourier transform that generalizes the discrete fourier transform dft in the same sense that the continuous fractional fourier transform generalizes the continuous ordinary fourier transform this definition is based on a particular set of eigenvectors of the dft matrix which constitutes the discrete counterpart of the set of hermite gaussian functions the definition is exactly unitary index additive and reduces to the dft for unit order the fact that this definition satisfies all the desirable properties expected of the discrete fractional fourier transform supports our confidence that it will be accepted as the definitive definition of this transform

a full likelihood procedure for analysing exchangeable binary data a full likelihood procedure is proposed for analyzing correlated binary data under the assumption of exchangeability the binomial and beta binomial models are shown to occur as special cases correspondingly respectively to the choice of degenerate and beta mixing distributions for a finite exchangeable binary sequence of random variables expressions for the joint distribution moments and correlations of all orders are derived maximum likelihood estimates of the moments of all orders are computed and used to estimate correlations and the distribution of the number of responses in a cluster in an application to developmental toxicology data analysis the procedure introduced is compared with a beta binomial and a generalized estimating equation procedure in which mean response and intralitter correlation are linked to dose

on the distribution of runs of ones in binary strings in this paper we derive the number of binary strings which contain for a given i k exactly i k runs of 1 s of length k in all possible binary strings of length n email protected email protected n such a knowledge about the distribution pattern of runs of 1 s in binary strings is useful in many engineering applications for example data compression bus encoding techniques to reduce crosstalk in vlsi chip design computer arithmetic using redundant binary number system and design of energy efficient communication schemes in wireless sensor networks by transformation of runs of 1 s into compressed information patterns among others we present here a generating function based approach to derive a solution to this counting problem our experimental results demonstrate that for most commonly used file formats the observed distributions of exactly i k runs of length k email protected email protected n closely follow the theoretically derived distributions for a given n for n 8 we find that the experimentally obtained values for most file formats agree within 5 of the theoretically obtained values for all i k runs of length k email protected email protected n also the root mean square rms values of these deviations across all file types studied in this paper are less than 5 for n 8 in view of these facts the results presented in this paper could be useful in various application domains like the ones mentioned above

on the mean and extreme distances between failures in markovian binary sequences this paper is concerned with the mean minimum and maximum distances between two successive failures in a binary sequence consisting of markov dependent elements these random variables are potentially useful for the analysis of the frequency of critical events occurring in certain stochastic processes exact distributions of these random variables are derived via combinatorial techniques and illustrative numerical results are presented

an orthonormal class of exact and simple dft eigenvectors with a high degree of symmetry the paper presents a novel orthonormal class of eigenvectors of the discrete fourier transform dft whose order n is factored as n rm sup 2 the dft eigenvectors have the form e e spl alpha where spl alpha are eigenvectors of some spl lscr spl times spl lscr matrices given by or related to the dft matrix of order r with spl lscr r 2r or 4r and the matrix e expands spl alpha to the full dft size n rm sup 2 in particular when n is an arbitrarily large power of 2 r may be 1 or 2 the resulting eigenvectors are expressed exactly with simple exponential expressions have a considerable number of elements constrained to 0 and show a high degree of symmetry the derivation of such a class is based on a partition of the n dimensional linear space into subspaces of very small dimension r 2r or 4r

multiplicity of fractional fourier transforms and their relationships the multiplicity of the fractional fourier transform frt which is intrinsic in any fractional operator has been claimed by several authors but never systematically developed the paper starts with a general frt definition based on eigenfunctions and eigenvalues of the ordinary fourier transform which allows us to generate all possible definitions the multiplicity is due to different choices of both the eigenfunction and the eigenvalue classes a main result obtained by a generalized form of the sampling theorem gives explicit relationships between the different frts

a compound negative binomial distribution with mutative termination conditions based on a change point abstract in this paper an extended negative binomial distribution called nbm is proposed by considering mutative termination conditions based on a change point if the condition a is satisfied before the occurrence of the change point the trial is terminated according to condition a otherwise if the condition a does not happen and the change point is satisfied the termination condition of the trial changes from condition a to condition b we consider the conditions under which the resulting distribution can be degenerated to the existing negative binomial distributions and other new negative binomial distributions the finite markov chain imbedding approach is employed to derive the new negative binomial distribution nbm and to obtain the related probabilistic indexes furthermore we study the distribution of the compound negative binomial distribution with mutative termination conditions based on a change point cnbm by means of phase type representations

non monotonic logic i abstract non monotonic logical systems are logics in which the introduction of new axioms can invalidate old theorems such logics are very important in modeling the beliefs of active processes which acting in the presence of incomplete information must make and subsequently revise assumptions in light of new observations we present the motivation and history of such logics we develop model and proof theories a proof procedure and applications for one non monotonic logic in particular we prove the completeness of the non monotonic predicate calculus and the decidability of the non monotonic sentential calculus we also discuss characteristic properties of this logic and its relationship to stronger logics logics of incomplete information and truth maintenance systems

the discrete cosine transform each discrete cosine transform dct uses n real basis vectors whose components are cosines in the dct 4 for example the j th component of boldv k is cos j frac 1 2 k frac 1 2 frac pi n these basis vectors are orthogonal and the transform is extremely useful in image processing if the vector boldx gives the intensities along a row of pixels its cosine series sum c k boldv k has the coefficients c k boldx boldv k n they are quickly computed from a fast fourier transform but a direct proof of orthogonality by calculating inner products does not reveal how natural these cosine vectors are we prove orthogonality in a different way each dct basis contains the eigenvectors of a symmetric second difference matrix by varying the boundary conditions we get the established transforms dct 1 through dct 4 other combinations lead to four additional cosine transforms the type of boundary condition dirichlet or neumann centered at a meshpoint or a midpoint determines the applications that are appropriate for each transform the centering also determines the period n 1 or n in the established transforms n frac 1 2 or n frac 1 2 in the other four the key point is that all these eigenvectors of cosines come from simple and familiar matrices

on the equivalence of cost functions in the design of circuits by cost table in the cost table approach to logic design a function is realized as a combination of functions from a table the objective of the synthesis is to find the least cost realization where realization cost is the sum of the costs of the functions used plus the cost of combining them the costs of cost table functions are defined by a cost function which represents chip area speed power dissipation or a combination of these factors it is shown that there is an arbitrarily large set s of cost functions which yield the same cost table this implies for example that every minimal realization of any function over a cost function in s is independent of the actual cost function used with any cost function if the cost of combining functions from a cost table f is sufficiently large the realizations behave as if the cost function belonged to s that is any minimal realization of a function f using cost table f is one of the minimal realizations of f using f and a cost function in s the interpretation of these results is that there are not as many distinct cost tables as originally thought

efficient dft architectures based upon symmetries this paper presents an efficient discrete fourier transform dft approach based upon an eigenvalue decomposition method the work is based on some recent results on dft eigenvectors expressed exactly not numerically with simple exponential terms with a considerable number of elements constrained to 0 and with a high degree of symmetry the result provides a generalization of known fast fourier transform fft algorithms based upon a divide and conquer approach moreover it can have interesting applications in the context of fractional fourier transforms where it provides an efficient implementation