Minimal Committee Problem for Inconsistent Systems of Linear Inequalities on the Plane

A representation of an arbitrary system of strict linear inequalities in R^n as a system of points is proposed. The representation is obtained by using a so-called polarity. Based on this representation an algorithm for constructing a committee solution of an inconsistent plane system of linear inequalities is given. A solution of two problems on minimal committee of a plane system is proposed. The obtained solutions to these problems can be found by means of the proposed algorithm.Comment: 29 pages, 2 figure

Discriminative power for ensembles of linear decision rules

A novel class of ensembles of linear decision rules is introduced which includes majority voting-based ensembles as a particular case. Based on this general framework, new results are given that state the ability of a subclass to discriminate between two infinite subsets A and B in R n, thus generalizing Mazurov's theorem for two finite sets. © 2013 Pleiades Publishing, Ltd

Приближенные алгоритмы с гарантированными оценками точности для пересечения множеств ребер некоторых метрических графов равными кругами

Polynomial-time approximation algorithms with constant approximation ratio are proposed for the problem of intersection of a given set of n planar straight line segments with the least number of equal disks. In the case where the segments have at most k different orientations, a simple 4k-approximate algorithm with time complexity O(n log n) is known. In addition, a 100-approximate algorithm with time complexity O(n4 log n) is known for the case of the problem on the edge sets of plane graphs. In this paper, for instances of the problem on the edge sets of Gabriel graphs, relative neighbourhood graphs, and Euclidean minimum spanning trees, in which the number of different edge orientations is, in general, unbounded, we construct simple O(n2)-time approximation algorithms with approximation ratios 14, 12, and 10, respectively. These algorithms outperform the aforementioned approximation algorithm for the general setting of the problem for edge sets of plane graphs. © 2019 Krasovskii Institute of Mathematics and Mechanics. All rights reserved

Modification of the algorithm for beat tracking of a musical melody

A new efficient modification of the known heuristic algorithm for real-time beat tracking is proposed. An improved formula for updating the relative frequencies of time intervals between adjacent onsets is used in the modification. The algorithm has shown good performance on the MIREX Beat Tracking test base. © 2013 Pleiades Publishing, Ltd

A survey on software defect prediction using deep learning

Defect prediction is one of the key challenges in software development and programming language research for improving software quality and reliability. The problem in this area is to properly identify the defective source code with high accuracy. Developing a fault prediction model is a challenging problem, and many approaches have been proposed throughout history. The recent breakthrough in machine learning technologies, especially the development of deep learning techniques, has led to many problems being solved by these methods. Our survey focuses on the deep learning techniques for defect prediction. We analyse the recent works on the topic, study the methods for automatic learning of the semantic and structural features from the code, discuss the open problems and present the recent trends in the field. © 2021 by the authors. Licensee MDPI, Basel, Switzerland