Facultatea de Matematică şi Informatică / Faculty of Methematics and Informatics
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Item MACHINE GUESSING, PIGEON SUPERSTITION AND TRUST IN AI(CEP USM, 2020) Alvarado, RamónIn this paper I argue that the predictive prowess of artificial intelligence methods, such as machine learning, is not sufficient as an epistemic warrant for us to allocate trust in them. This is because of two reasons: 1) they are opaque in ways that other methodology is not and 2) they fail in ways that other methodology does not. In order to motivate my analysis, I compare the prowess of some machine learning methodology in image recognition to the ability for pattern identification by some animals, such as pigeons, and suggest that while useful in certain practical circumstances, their success does not constitute the kinds of epistemic warrants that we should aim for in more epistemically demanding contexts such as science, medicine, and/or policy-making.Item MEDITATIONS ABOUT THE MYSTIC OF MATHEMATICAL LANGUAGE(CEP USM, 2020) Pagliacci, Mario G.R.Mathematics is the science of measurement of greatness and form. It is fundamental for trying to understand, describe and explain phenomena, especially when they are chaotic and complex. Mathematical language is not true or false for itself. It is neutral in respect of truth or falsity of the described phenomena. However, it can give a distorted representation of reality when it is utilized in not correct way, by doing conceptual forcing or large approximations. Quantitative language can suggest in inexpert minds that anything is expressed in quantitative statement is more credible than qualitative one. The mystic conception that mathematical language is synonym of truth is confuted.Item ON RECURSIVELY DIFFERENTIABLE QUASIGROUPS(2015) Larionova-Cojocaru, IngaIf ( ),Q ⋅ is a binary groupoid then will denote its recursive derivative of order s by „ s ⋅ ”, hence 0 1 2 1 , , , ( ) ( ), s s s x y x y x y y xy x y x y x y − − ⋅ = ⋅ ⋅ = ⋅ ⋅ = ⋅ ⋅ ⋅K for every , .x y Q∈ If the recursive derivatives „ s ⋅ ”, s=1,2,…,k, of a binary quasigroup ( ),Q ⋅ are quasigroup operations, then ( ),Q ⋅ is called recursively k- differentiable. The notions of recursive derivatives and recursively differentiable quasigroups raised in the algebraic coding theory [1]. Recursively differentiable binary quasigroups in particular groups, are studied in the present paper. Proposition 1. If a quasigroup ( ),Q ⋅ , with the left unit, is recursively 1- differentiable then the mapping 2 x x→ is a bijection. Proposition 2. A diassociative loop ( ),Q ⋅ is recursively 1-differentiable if and only if the mapping 2 x x→ is a bijection. Corollary 1. A Moufang loop ( ),Q ⋅ , in particular a group, is recursively 1- differentiable if and only if the mapping 2 x x→ is a bijection on Q . Corollary 2. Finite groups of even order are not recursively 1-differentiable.Item SUBGRAFURILE B-STABILE ÎN ORIENTAREA TRANZITIVĂ A GRAFURILOR(2015) Grigoriu, NicolaeSe formulează rezultate noi ce țin de studierea problemei orientării tranzitive a grafurilor neorientate. Amintim că un graf 𝐺𝐺⃗ = 𝑋𝑋; 𝑈𝑈 este tranzitiv orientat dacă pentru oricare trei vârfuri 𝑥𝑥, 𝑦𝑦, 𝑧𝑧 ∈ 𝑋𝑋 este satisfăcută relația de tranzitivitate: [𝑥𝑥, 𝑦𝑦] ∈ 𝑈𝑈 & [𝑦𝑦, 𝑧𝑧] ∈ 𝑈𝑈 ⇒ [𝑥𝑥, 𝑧𝑧] ∈ 𝑈𝑈 [3]. Graful neorientat 𝐺𝐺 = (𝑋𝑋; 𝑈𝑈) este tranzitiv orientabil dacă atribuind o anumită orientare muchiilor sale obținem un graf tranzitiv orientat. Un subgraf determinat de o mulțime de vârfuri 𝐴𝐴, se va numi subgraf stabil dacă pentru orice vârf 𝑥𝑥 ∈ 𝑋𝑋 ∖ 𝐴𝐴 se verifică una din relațiile: [𝑥𝑥, 𝑦𝑦] ∈ 𝑈𝑈𝐺𝐺 sau [𝑦𝑦, 𝑥𝑥] ∉ 𝑈𝑈𝐺𝐺, unde ∀𝑦𝑦 ∈ 𝐴𝐴.[1], [3] Definiția 1.[2] Subgraful stabil 𝐹𝐹 se numește subgraf B-stabil dacă pentru orice subgraf stabil 𝑀𝑀 din 𝐺𝐺 = (𝑋𝑋; 𝑈𝑈) are loc una din relațiile: 𝐹𝐹 ⊆ 𝑀𝑀 ∨ 𝐹𝐹 ∩ 𝑀𝑀 = ∅ Reieșind din definiția subgrafului B-stabil rezultă, că dacă 𝐺𝐺 nu conține subgraf stabil atunci acesta nu conține nici subgraf B-stabil. Lema 1. Dacă graful 𝐺𝐺 conține subgraf stabil, atunci 𝐺𝐺 conține și subgraf B- stabil. Teorema 1. Subgraful 𝐹𝐹 al grafului tranzitiv orientabil 𝐺𝐺 este B-stabil dacă și numai dacă orientarea tranzitivă 𝐹𝐹⃗ se construiește în mod independent de orientarea tranzitivă a întregului graf 𝐺𝐺.Item SISTEME SUPORT PENTRU DECIZII APLICATE ÎN GESTIONAREA SIGURANŢEI RUTIERE(CEP USM, 2021) Bulmaga, ViorelOdată cu utilizarea sistemelor suport pentru decizii (SSD) întru susţinerea deciziilor manageriale în cadrul organizării proceselor de producere, un rol important revine aplicării SSD în abordarea problemei privind managementul siguranţei publice sau al situaţiilor de urgenţă. A fost studiată aplicabilitatea SSD în domeniul managementului siguranţei rutiere pentru a fundamenta deciziile manageriale, în vederea optimizării raportului cost-eficienţă pe următoarele segmente: (1) Identificarea şi clasificarea sectoarelor periculoase pe arterele rutiere, determinând modul şi termenele de intervenţie în proiectarea infrastructurii rutiere pentru a reduce pericolul acestor sectoare; (2) Sprijinirea în timp real a deciziilor conducătorului de vehicul, în baza informaţiilor interne (parametrii vehiculului) şi externe (mesaje privind infrastructura rutieră), pentru a oferi avertismente sau recomandări utile cu privire la pericolele potenţiale ale mediului de conducere; (3) Evaluarea amplorii şi clasificarea situaţiilor de urgenţă în cazul accidentelor de circulaţie, pentru implicarea forţei de muncă şi a resurselor serviciilor de salvare. Urmând exemplele studiate, a fost dedusă posibilitatea aplicării unei reţele neuronale artificiale în scopul de comparare, uniformizare şi de export de date din/în tabele de date cu seturi de variabile şi valori de format diferit (definite diferit). Acest instrument permite realizarea practică a unui Sistem suport pentru decizii aplicat întru soluţionarea unei astfel de probleme nestructurate, precum exportul datelor din Sistemul informaţional automatizat „Registrul de stat al accidentelor rutiere” în formatul CADaS al Uniunii Europene.Item PARALLEL ALGORITHM TO SOLVING 2D BLOCK-CYCLIC PARTITIONED BIMATRIX GAMES(CEP USM, 2021) Hâncu, Boris; Cataranciuc, EmilThe article presents a theoretical and practical study of the ways of determining solutions in bimatrix games divided into blocks of submatrices using 2D block-cyclic matrix dividing and distribution algorithm. The proved theorems represent the foundation on which the bimatrix game solution can be built using the sub-games solutions generated by the 2D-cyclic matrix distribution algorithm.Item ON INTELLIGENT SOFTWARE TOOLS IN SOLVING OF INTEGRAL EQUATIONS OF SECOND KIND(2015) Carmocanu, Gheorghe; Căpăţână, Gheorghe; Seiciuc, Eleonora; Seiciuc, VladislavThe Intelligent Support System for approximate solving of the Fredholm and Volterra integral equations of the second kind are developed. Some components for Computing Modules of the Intelligent Support System for solving of regular integral equations of second kind with spline-collocations, splinequadratures and degenerated kernel methods are proposed.Item IDENTITIES AND GENERALIZED DERIVATIVES OF QUASIGROUPS(2022) Horosh, Grigorii; Malyutina, Nadeghda; Scerbacova, Alexandra; Shcherbacov, VictorWe associate a partial (autostrophical) identity with every generalized derivative. We research when a quasigroup that satisfies an autostrophic identity has a unit (left or/and right or/and middle).Item SOLVING THE NON-LINEAR MULTI-INDEX TRANSPORTATION PROBLEMS WITH GENETIC ALGORITHMS(2022) Pașa, TatianaIn this paper we study the non-linear multi-index transportation problem with concave cost functions. We solved thnon-linear transportation problem on a network with 5 in- dices (NTPN5I) described by sources, destinations, intermediate nodes, types of products, and types of transport, that is formulated as a non-linear transportation problem on a network with 3 indices (NTPN3I) described by arcs, types of products, and types of transport. We propose a genetic algorithm for solving the large-scale problems in reasonable amount of time, which was proven by the various tests shown in this paper. The convergence theorem of the algorithm is formulated and proved. The algorithm was implemented in Wolfram Language and tested in Wolfram Mathematica.Item MIDDLE BRUCK LOOPS AND THE TOTAL MULTIPLICATION GROUP(Springer, 2022) Drapal, Ales; Syrbu, ParascoviaLet Q be a loop. The mappings x↦ ax, x↦ xa and x↦ a/ x are denoted by La, Ra and Da, respectively. The loop is said to be middle Bruck if for all a, b∈ Q there exists c∈ Q such that DaDbDa= Dc. The right inverse of Q is the loop with operation x/ (y\ 1). It is proved that Q is middle Bruck if and only if the right inverse of Q is left Bruck (i.e., a left Bol loop in which (xy) - 1= x- 1y- 1). Middle Bruck loops are characterized in group theoretic language as transversals T to H≤ G such that ⟨ T⟩ = G, TG= T and t2= 1 for each t∈ T. Other results include the fact that if Q is a finite loop, then the total multiplication group⟨ La, Ra, Da; a∈ Q⟩ is nilpotent if and only if Q is a centrally nilpotent 2-loop, and the fact that total multiplication groups of paratopic loops are isomorphic.