Search results for "ALGORITHM"

Fast Matrix Multiplication

2015

Until a few years ago, the fastest known matrix multiplication algorithm, due to Coppersmith and Winograd (1990), ran in time O(n2.3755). Recently, a surge of activity by Stothers, Vassilevska-Williams, and Le~Gall has led to an improved algorithm running in time O(n2.3729). These algorithms are obtained by analyzing higher and higher tensor powers of a certain identity of Coppersmith and Winograd. We show that this exact approach cannot result in an algorithm with running time O(n2.3725), and identify a wide class of variants of this approach which cannot result in an algorithm with running time $O(n^{2.3078}); in particular, this approach cannot prove the conjecture that for every e > 0, …

Noise-tolerant efficient inductive synthesis of regular expressions from good examples

1997

We present an almost linear time method of inductive synthesis restoring simple regular expressions from one representative (good) example. In particular, we consider synthesis of expressions of star-height one, where we allow one union operation under each iteration, and synthesis of expressions without union operations from examples that may contain mistakes. In both cases we provide sufficient conditions defining precisely the class of target expressions and the notion of good examples under which the synthesis algorithm works correctly, and present the proof of correctness. In the case of expressions with unions the proof is based on novel results in the combinatorics of words. A genera…

THE TOPOLOGY OF BASIN BOUNDARIES IN A CLASS OF THREE-DIMENSIONAL DYNAMICAL SYSTEMS

1996

We will develop new methods to determine the topology of the basin boundary in a class of three-dimensional dynamical systems. One approach is to approximate the basin boundary by backward integration. Unfortunately, there are dynamical systems where it is hard to approximate the basin boundary by a numerical backward integration algorithm. We will introduce topological methods which will provide new information about the structure of the basin boundary. The topological invariants which we will use can be numerically computed.

Impact of chaotic dynamics on the performance of metaheuristic optimization algorithms : An experimental analysis

2022

Random mechanisms including mutations are an internal part of evolutionary algorithms, which are based on the fundamental ideas of Darwin's theory of evolution as well as Mendel's theory of genetic heritage. In this paper, we debate whether pseudo-random processes are needed for evolutionary algorithms or whether deterministic chaos, which is not a random process, can be suitably used instead. Specifically, we compare the performance of 10 evolutionary algorithms driven by chaotic dynamics and pseudo-random number generators using chaotic processes as a comparative study. In this study, the logistic equation is employed for generating periodical sequences of different lengths, which are use…

Pattern classification using a new border identification paradigm: The nearest border technique

2015

Abstract There are many paradigms for pattern classification such as the optimal Bayesian, kernel-based methods, inter-class border identification schemes, nearest neighbor methods, nearest centroid methods, among others. As opposed to these, this paper pioneers a new paradigm, which we shall refer to as the nearest border (NB) paradigm. The philosophy for developing such a NB strategy is as follows: given the training data set for each class, we shall attempt to create borders for each individual class. However, unlike the traditional border identification (BI) methods, we do not undertake this by using inter-class criteria; rather, we attempt to obtain the border for a specific class in t…

Efficient learning of regular expressions from good examples

1994

We consider the problem of restoring regular expressions from expressive examples. We define the class of unambiguous regular expressions, the notion of the union number of an expression showing how many union operations can occur directly under any single iteration, and the notion of an expressive example. We present a polynomial time algorithm which tries to restore an unambiguous regular expression from one expressive example. We prove that if the union number of the expression is 0 or 1 and the example is long enough, then the algorithm correctly restores the original expression from one good example. The proof relies on original investigations in theory of covering symbol sequences (wo…

A new paradigm for pattern classification: Nearest Border Techniques

2013

Published version of a chapter in the book: AI 2013: Advances in Artificial Intelligence. Also available from the publisher at: http://dx.doi.org/10.1007/978-3-319-03680-9_44 There are many paradigms for pattern classification. As opposed to these, this paper introduces a paradigm that has not been reported in the literature earlier, which we shall refer to as the Nearest Border (NB) paradigm. The philosophy for developing such a NB strategy is as follows: Given the training data set for each class, we shall first attempt to create borders for each individual class. After that, we advocate that testing is accomplished by assigning the test sample to the class whose border it lies closest to…

On the zeros of Jacobi polynomials

1994

Variability of Classification Results in Data with High Dimensionality and Small Sample Size

2021

The study focuses on the analysis of biological data containing information on the number of genome sequences of intestinal microbiome bacteria before and after antibiotic use. The data have high dimensionality (bacterial taxa) and a small number of records, which is typical of bioinformatics data. Classification models induced on data sets like this usually are not stable and the accuracy metrics have high variance. The aim of the study is to create a preprocessing workflow and a classification model that can perform the most accurate classification of the microbiome into groups before and after the use of antibiotics and lessen the variability of accuracy measures of the classifier. To ev…

Integrated fuzzy classification

2003