Institutul de Matematică şi Informatică "Vladimir Andrunachievici"
Permanent URI for this communityhttps://msuir.usm.md/handle/123456789/13368
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Item A Simple CAD System for Faculty Timetabling Design [Articol](2024) Rusu, Andrei; Rusu, ElenaA computer-aided design (CAD) system is proposed in order to help in designing the timetabling of courses in a faculty. It is based on already used technologies such as Google Spreadsheets and Microsoft Excel and tools built-in in them: Server JavaScript, Visual Basic for Applications (VBA). The idea is to use a single sheet ”Collision” in a spreadsheet in Microsoft Excel to deal with all information related to the timetable, and then, by parsing its cells, to generate all needed timetables for students, teachers, rooms, etc.Item About AC-Groupoids [Articol](2024) Izbas, Vladimir; Izbas, Ana-MariaThe concept of a right (left) AC-groupoid over an arbitrary group is defined and studied. Necessary and sufficient conditions which transform a right (left) AC-groupoid into a quasigroup are given. The AC-groupoids form a wide class of special groupoids and quasigroups that have a transitive subset of automorphisms.Item About Multiple Prolongations of Latin Cubes [Articol](2024) Sokhatsky, Fedir; Moroz, DariaWe propose an algorithm of prolongation of a Latin cube with k new elements (k ≥ 1).Item About Quadratic Functional Equations on Quasigroups [Articol](2024) Sokhatsky, Fedir; Krainichuk, HalynaFunctional equations over binary quasigroups are under consideration. An equation is called: quadratic, if each individual variable has either two appearances or none; cancellable, if a variable has two appearances and another none in a proper subterm; reducible, if it is equivalent to a system of equations such that every of which has less number of individual variables than the given one. Only the functional equations of unipotency, commutativity, associativity and mediality are noncancellable, and the irreducible ones are the same except the mediality. The criteria for the parastrophic equivalency of the equations up to the noncancellable equations were found.Item Algorithm to Minimize the Worst-Case Regret Function [Articol](2024) Godonoaga, Anatol; Chumakov, BorysThis paper examines mathematical model of decision-making under conditions of uncertainty, when Savage’s regret function is used as the objective function. Numerical algorithm for solving the corresponding problems are proposed, based on the implementation of parallel minimization of indicators for each state of nature and the indicator of greatest regret. The algorithms are developed based on the generalized gradient projection method.Item Alternative Clifford-like algebras [Articol](2024) Smith, Jonathan-DThe real, complex, and quaternion division algebras may be constructed as Clifford algebras. However, while the octonions and split octonions share many features with Clifford algebras, such as an involutary anti-automorphism, their nonassociativity prevents their realization as Clifford algebras. We now introduce Kingdon algebras: alternative Clifford-like algebras over vector spaces which are equipped with a symmetric bilinear form, such that the octonions and split octonions arise as Kingdon algebras. In the process, they acquire 2-graded (superalgebra) structure. A comparable construction yields 3-graded algebras over spaces equipped with an alternating trilinear form.Item Artificial Intelligence for Enhanced Medical Diagnosis: Developing Learning Models for Accurate Patient Diagnosis [Articol](2024) Olariu, Maria-EcaterinaThis paper explores the integration of Artificial Intelligence (AI) in healthcare, focusing on its applications in medical imaging and diagnosis. It presents a case study evaluating generative AI tools in cardiovascular diagnostics, comparing their performance with expert analysis. The research highlights the potential of AI to augment human expertise in healthcare decision-making. Furthermore, it proposes future work on developing an AI-driven adaptive clinical decision support system based on European Guidelines. This system aims to personalize recommendations for individual practitioners while maintaining adherence to standardized best practices, potentially revolutionizing AI support in medical practice across Europe.Item Automating Rhythm Game Level Design in Unity Through Beat Detection [Articol](2024) Irimia, Cosmin; Biceadă, StefanaTechnology is integral to our lives, impacting everything from daily tasks to critical fields like healthcare. While computers excel at technical tasks, translating intuitive concepts like rhythm into computer logic can be challenging. Detecting rhythm is natural for humans, as seen in activities like tapping or nodding to music. Over time, various beat detection algorithms have been developed for applications such as audio visualization and cardiology, where they monitor heartbeats and rhythms to identify diseases.Item Center Problem for Cubic Differential Systems with Two Affine Invariant Straight Lines of Total Transversal Multiplicity Tree [Articol](2024) Şubă, AlexandruIn this paper, using the first five Lyapunov quantities, we solve the center problem for cubic differential systems with two affine invariant straight lines one of which has transversal algebraic multiplicity two.Item Characteristic Function of the Markov Random Flight in Higher Dimensions [Articol](2024) Kolesnik, Alexander D.Two series representations of the characteristic function of the multidimensional symmetric Markov random flight, are presented. These series are the decompositions of the characteristic function with respect to Bessel functions and with respect to time variable, whose coefficients are given by recurrent relations, as well as in the form of special determinants. Basing on these series representations, an asymptotic formula for the second moment function of the process, is obtained.Item Collocation Method for Solving Singular Integral Equations with Discontinuous Coefficients [Articol](2024) Capcelea, Maria; Capcelea, TituThe paper presents an efficient method for solving the Cauchy singular integral equation, which is defined on a closed and smooth contour in the complex plane. The coefficients and the right-hand side of the equation are piecewise continuous functions, numerically defined on a finite set of points along the contour.Item Combinatorial Symmetry of Twisty Puzzles and Twist Axes of Order 4, 6, 8, 9, 10 and 11 [Articol](2024) Popa, AlexandruThis paper introduces the notion of conbinatorial symmetry of twisty puzzles, presents geometric principles of searching for twisty puzzles with sun mechanism. Additionally, some geometrical and combinatorial properties of such puzzles and their polyhedra are discussed.Item Combined Encryption Algorithm Using a Generalization of the Markovski Algorithm [Articol](2024) Malyutina, Nadezhda; Shcherbacov, VictorThis article is devoted to the construction of a generalization of a cryptographic algorithm based on the use of quasigroups of a special type. Here is a more detailed description of the algorithm proposed in [1]. An example is given to illustrate the operation of the developed algorithm. Our task was to show the effectiveness and advantages of using quasigroups of a special type in cryptology.Item A Comparative Analysis of Machine Learning Algorithms for Text Analysis [Articol](2024) Parahonco, Alexandr; Petic, MirceaThis article proposes a system of metrics for estimating text fetched from the Internet and selecting the one that should be further summarized. The research examines algorithms and software for determining user preferences, employing natural language processing (NLP) and supervised learning classification methods. An empirical assessment is conducted across academic, security, and non-security domains. The paper concludes with insights on the experimental results and the potential future of the implemented metric system.Item Comparison of Large Language Models and Traditional Neural Networks in Optical Character Recognition for Old Alphabets [Articol](2024) Cerescu, Marius; Bumbu, TudorThis study compares large language models (LLMs) and traditional neural networks (TNNs) in Optical Character Recognition (OCR) for historical alphabets. While deep learning has advanced OCR technology, recognizing old scripts remains challenging due to their complexity. LLMs, with vision capabilities, offer a novel approach by integrating visual and linguistic understanding. This research evaluates the accuracy and robustness of both models on a dataset of an ancient alphabet, highlighting the potential of LLMs to improve OCR in historical linguistics and digital preservation. The findings provide valuable insights for applying modern AI to the preservation of historical texts.Item The Computing Quantum Universe and Einstein-Landauer’s Principle of Mass-Energy-Information Equivalence [Articol](2024) Albu, VeaceslavThe proposed paper advocates the formulated Einstein-Landauer’s mass-energy-information equivalence principle against criticism, provides evidence for its consistency with Standard Model theory, and formulates the concept of the self-computing Universe by natural kinds.Item Credibility of Textual Information Generated by AI Tools [Articol](2024) Gorea, Adela; Petic, MirceaThe paper refers to the topic of information credibility in the context of the increasingly active use of AI tools. Starting from the notion of the credibility of the information, the examples of AI tools that generate credible text content are presented. At the same time, the particularities of generating credible textual content with the help of AI tools were discussed, as well as the way we can detect texts produced by AI tools.Item Darboux Integrability of a Cubic Differential System with One Invariant Straight Line and One Invariant Cubic [Articol](2024) Cozma, Dumitru; Matei, AngelaWe find conditions for a singular point O(0; 0) of a center or a focus type to be a center, in a cubic differential system with one invariant straight line and one invariant cubic. The presence of a center at O(0; 0) is proved by method of Darboux integrability.Item Data Parallelization for Solving Bimatrix Games [Articol](2024) Hâncu, Boris; Turcanu, CalinContemporary decision-making problems are very complex and require the processing of a very large volume of data. Thus, for the mathematical modelling of these processes, it is necessary to take into account the big data problems. The data is too big to be stored and processed by a single machine. In many large-scale solutions, data is divided into partitions that can be managed and accessed separately. In order to solve such problems in real time, parallel algorithms are built and then implemented on various types of parallel computing systems. In this paper, we will analyze the ways to build parallel algorithms, and especially, data parallelization, for a class of noncooperative games, bimatrix games.Item Digitization of Moldovan folklore texts using the HeDy platform [Articol](2024) Colesnicova, Vlada; Caftanatov, Olesea; Cojocaru, Svetlana; Colesnicov, Alexandru; Malahov, LudmilaThis paper discusses the use of the digitization platform HeDy to produce electronic resources of Moldavian proverbs and sayings. It will promote the development and enrichment of annotated corpora and other electronic resources of philological data on regional folklore and nonstandard texts from Moldova. The results should be uniform in terms of formats and standards, in particular, to be incorporated into the Universal Dependency (UD) repository.