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The longest common subsequence is a well known and popular method for measuring similarity between sequences. It advocates the use of information contained in the longest common subsequence as an indication of similarity. In this paper we consider the count of all common subsequences as a measure of sequence similarity with the view that all common information is captured. This measure is inspired and derived from a generic similarity measure, neighborhood counting metric. The close connection of the neighborhood counting metric with probability and the Bayes classifier helps gain an insight from the probabilistic perspective into the all-common subsequences measure. We design algorithms to calculate this measure and we also carry out an experiment in the framework of k-nearest neighbors on a gene sequence classification task. The experiment shows that the all-common subsequences measure and the longest common subsequence measure have little difference for small k values, but differ significantly for large k values. The performance of the all-common subsequences measure remains steady as k gets larger, but the performance of the longest common subsequence measure drops sharply as k gets larger. Such a property may be useful for those tasks where we are interested not only in the nearest neighbor, but also in the first k nearest neighbors. The main contribution of this paper is a suite of algorithms for finding all common subsequences. [ABSTRACT FROM AUTHOR]

Many of the tools of dynamical systems and control theory have gone largely unused for fluids, because the governing equations are so dynamically complex, both high-dimensional and nonlinear. Model reduction involves finding low-dimensional models that approximate the full high-dimensional dynamics. This paper compares three different methods of model reduction: proper orthogonal decomposition (POD), balanced truncation, and a method called balanced POD. Balanced truncation produces better reduced-order models than POD, but is not computationally tractable for very large systems. Balanced POD is a tractable method for computing approximate balanced truncations, that has computational cost similar to that of POD. The method presented here is a variation of existing methods using empirical Gramians, and the main contributions of the present paper are a version of the method of snapshots that allows one to compute balancing transformations directly, without separate reduction of the Gramians; and an output projection method, which allows tractable computation even when the number of outputs is large. The output projection method requires minimal additional computation, and has a priori error bounds that can guide the choice of rank of the projection. Connections between POD and balanced truncation are also illuminated: in particular, balanced truncation may be viewed as POD of a particular dataset, using the observability Gramian as an inner product. The three methods are illustrated on a numerical example, the linearized flow in a plane channel. [ABSTRACT FROM AUTHOR]

This paper considers a renewal process in which the interarrival times and rewards are characterized as fuzzy variables. A fuzzy elementary renewal theorem shows that the expected number of renewals per unit time is just the expected reciprocal of the interarrival time. Furthermore, the expected reward per unit time is provided by a fuzzy renewal reward theorem. Finally, a numerical example is presented for illustrating the theorems introduced in the paper. [ABSTRACT FROM AUTHOR]

Feature selection is an important task in pattern recognition. Support Vector Machine (SVM) and Minimax Probability Machine (MPM) have been successfully used as the classification framework for feature selection. However, these paradigms cannot automatically control the balance between prediction accuracy and the number of selected features. In addition, the selected feature subsets are also not stable in different data partitions. Minimum Error Minimax Probability Machine (MEMPM) has been proposed for classification recently. In this paper, we outline MEMPM to select the optimal feature subset with good stability and automatic balance between prediction accuracy and the size of feature subset. The experiments against feature selection with SVM and MPM show the advantages of the proposed MEMPM formulation in stability and automatic balance between the feature subset size and the prediction accuracy. [ABSTRACT FROM AUTHOR]

In this paper, the reasons for the shortcoming of Zadeh's fuzzy set theory — it cannot correctly reflect different kinds of fuzzy phenomenon in the natural world — are discussed. In addition, the proof of the error of Zadeh's fuzzy set theory — it incorrectly defined the set complement that cannot exist in Zadeh's fuzzy set theory — is proposed. This error of Zadeh's fuzzy set theory causes confusion in thinking, logic and conception. It causes the seriously mistaken belief that logics of fuzzy sets necessarily go against classical and normal thinking, logic and conception. Two new fuzzy set theories, C-fuzzy set theory and probability-like fuzzy set theory, the N-fuzzy set theory, are proposed. The two are equivalent, and both overcome the error and shortcoming of Zadeh's fuzzy set theory, and they are consistent with normal, natural and classical thinking, logic and concepts. The similarities of N-fuzzy set theory with probability theory are also examined. [ABSTRACT FROM AUTHOR]

In this paper, a procedure for comparing the patterns of time series using wavelets is developed. Randomization tests based on the ratio of the sum of squared wavelet coefficients of pairs of time series at different scales are used. A simulation study using pairs of different types of time series using the Haar and Daubechies wavelets is carried out. The results reveal that the tests perform fairly well at scales where there are a sufficient number of wavelet coefficients. The tests are applied to a set of financial time series. [ABSTRACT FROM AUTHOR]

We consider a discrete-time multi-server queue for which the moments of the stationary queue length can be expressed in terms of series over the zeros in the closed unit disk of a queue-specific characteristic function. In many important cases these zeros can be considered to be located on a queue-specific curve, called generalized Szegö curve. By adopting a special parametrization of these Szegö curves, the relevant zeros occur as equidistant samples of a 2π-periodic function whose Fourier coefficients can be determined analytically. Thus the series occurring in the expressions for the moments can be written as Fourier aliasing series with terms given in analytic form. This gives rise to formulas for e.g. the mean and variance of the queue length that are reminiscent of Spitzer's identity for the moment generating function of the steady-state waiting time for a G/G/1 queue. Indeed, by considering the queue under investigation as a G/G/1 queue, the new formulas for the mean and variance also follow from Spitzer's identity. The approach in this paper can also be used to compute the probability distribution function of the queue length in analytic form. [ABSTRACT FROM AUTHOR]

Traditionally the beta distribution has been used due to its ease for computing the mean of tasks, times, cash-flows, etc. because, in this case, the expected value is a weighted average of optimistic, most likely and pessimistic values. One of the critiques of PERT has been the difficulty of introducing the level of confidence that the expert has in his own estimate of the modal value. The Belief in Fuzzy Probability Estimations of Time (BIFPET) model uses human judgement instead of stochastic assumptions to determine the duration of a project. Thus, each supervisor responsible of an activity specifies the three values with their respective probabilities. The manager accepts these probabilities or may extend them within a certain range, according to his belief in these likelihoods or the degree of control exercised by himself in achieving the lower bound of the expected value. However, this approach can be implemented in the PERT methodology. Thus, in this paper, we introduce the confidence that the manager has in the most likely value supplied by the supervisor in order to determine the specific beta distribution to model the variable, showing the advantages of this intuitive procedure which moreover can be easily implemented. [ABSTRACT FROM AUTHOR]

A new hierarchical uncertainty model for combining different evidence about a system of statistically independent random variable is studied in the paper. It is assumed that the first-order level of the model is represented by sets of lower and upper previsions (expectations) of random variables and the second-order level is represented by sets of lower and upper probabilities which can be viewed as confidence weights for interval-valued expectations of the first-order level. The model is rather general and allows us to compute probability bounds and "average" bounds for previsions of a function of random variables. A numerical example illustrates this model. [ABSTRACT FROM AUTHOR]

In this paper we study conditional independence structures arising from conditional probabilities and lower conditional probabilities. Such models are based on notions of stochastic independence apt to manage also those situations where zero evaluations on possible events are present: this is particularly crucial for lower probability. The "graphoid" properties of such models are investigated, and the representation problem of conditional independence structures is dealt with by generalizing the well-known classic separation criteria for undirected and directed acyclic graphs. Our graphical models describe the independence statements and the possible logical dependencies among the random variables. [ABSTRACT FROM AUTHOR]

In belief functions, there is a total measure of uncertainty that quantify the lack of knowledge and verifies a set of important properties. It is based on two measures: maximum of entropy and non-specificity. In this paper, we prove that the maximum of entropy verifies the same set of properties in a more general theory as credal sets and we present an algorithm that finds the probability distribution of maximum entropy for another interesting type of credal sets as probability intervals. [ABSTRACT FROM AUTHOR]

This section is maintained by Vladik Kreinovich. Please send your abstracts (or copies of papers that you want to see reviewed here) to vladik@utep.edu, or by regular mail to: V. Kreinovich, Department of Computer Science, University of Texas, El Paso, TX 79968, USA. [ABSTRACT FROM AUTHOR]