Serdica Journal of Computing

On a Bivariate Katz's Distribution Constructed by the Trivariate Reduction Method

Michel Koukouatikissa Diafouka, Chedly Gélin Louzayadio — Thu, 14 Dec 2023 00:00:00 +0200

In this paper, we propose the bivariate distribution of the Katz distribution [1] constructed by the trivariate reduction method, method developed in [6] and used in [5] to give an equivalent definition of the bivariate Poisson distribution [7, 8]. The constructed distribution includes, in particular, the bivariate Poisson distribution [5] and has interesting properties. For the estimation of the parameters, we used two methods: the method of moments and the maximum likelihood method using the EM algorithm. An application to concrete data has been made in order to carry out a comparative study between bivariate Poisson and Katz distributions, and we discuss the likelihood-ratio test, which assesses the goodness of fit of two competing statistical models.

Locally Two-weight Property for Linear Codes and Its Application

Hitoshi Kanda, Atsuya Kato, Tatsuya Maruta — Fri, 19 Jan 2024 00:00:00 +0200

A q-ary linear code is an [n,k,d]_q code, which is a linear code of length n, dimension k and minimum weight d over F_q, the field of order q. A fundamental problem in coding theory is to find n_q(k,d), the minimum length n for which an [n,k,d]_q code exists for given k,d and q. We introduce a new notion "e-locally 2-weight (mod q)" for linear codes over F_q and we give a necessary condition for the property. As an application, we prove the non-existence of some [n,4,d]₉ codes with d ≡ −1 (mod 9), which determines n₉(4,d) for some d.

Recognition of Handwritten Mathematical Expressions Using Systems of Convolutional Neural Networks

Tate Rowney, Alexander I. Iliev — Wed, 21 Feb 2024 00:00:00 +0200

Accurate recognition of handwritten mathematical expressions has proven difficult due to their two-dimensional structure. Various machine-learning techniques have previously been employed to transcribe handwritten math, including approaches based on convolutional neural networks (CNNs) and larger encoder/decoder-based models. In this work, we explore a CNN-based method for transcribing handwritten math expressions into the typesetting language known as LaTeX. This approach utilizes machine learning not only for classifying individual characters but also for extracting individual characters from handwritten inputs and determining what forms of two-dimensionality exist within the expression. This approach achieves significant reliability when recognizing common mathematical expressions.

Integer Linear Programming Models and Greedy Heuristic for the Minimum Weighted Independent Dominating Set Problem

Stefan Kapunac — Mon, 15 Apr 2024 00:00:00 +0300

This paper explores the Minimum Weighted Independent Dominating Set Problem and proposes novel approaches to tackle it. Namely, two integer linear programming formulations and a fast greedy heuristic as an alternative approach are proposed. Extensive computational experiments are conducted to evaluate the performance of these approaches on the established set of benchmark instances for the problem. The obtained results demonstrate that the introduced integer linear programming models are able to achieve optimal solutions on all instances with 100 nodes and significantly outperform existing exact methods on numerous other instances. Additionally, the greedy heuristic exhibits superior performance compared to competing greedy heuristics, particularly on random graphs. These findings suggest promising directions for future research, including the integration of these methods into hybrid algorithms or metaheuristic frameworks.