Seminarul Științific de Matematică și Informatică

Centrul de Cercetare în Matematică și Informatică (CCMI) din cadrul Departamentului de Matematică și Informatică (DMI),

Evenimente anterioare:

Miercuri, 20 Decembrie 2023, ora 12:00

„From Big Data to Artificial Intelligence” susținut de Profesor Mihail Barbosu, Fulbright Scholar, UBB Cluj-Napoca, Professor and Director, Data and Predictive Analytics Center, School of Mathematics and Statistics, Rochester Institute of Technology (RIT), Rochester, NY, USA.

Abstract:
This presentation will start with a brief introduction to Data Science, the application domains linked to this field and the data scientist profession, ranked number 1 job for the past several years. Furthermore, challenges and opportunities for new academic programs in this area will be discussed along with ethical issues and ways to lead and mislead with data. We will also have an opportunity to interact about controversial matters on how data is handled, analyzed and presented, while examining the trends in human-to-computer and machine-to-machine interactions.

Marți, 01 noiembrie 2022, ora 16:00

„Simple Proofs for the Hermite-Lindemann Results on the Transcendence of e and π” susținut de Profesor Emerit Angel Popescu, Universitatea Tehnică de Construcții București.

Abstract:
In this note we give some simple proofs for the irrationality of π^2 and e^q where q is a nonzero rational number. We also use some basic ideas of Hermite [4], Hilbert [5], Hurwitz [6] and Lindemann [8] to give simple proofs for the transcendence of e and of e^a where a a is a nonzero algebraic number. In particular, we obtain the transcendence of π. In the end we apply our previous results to develop a great idea of Wantzel [11] for a complete solution of the three famous Greek geometrical problem: squaring a circle, duplicate a cube and trisection of an angle. We also supply all the elementary prerequisites of algebraic number theory such that the famous Lindemann’s idea be easily understood even by an undergraduate student with some basic knowledge in Calculus and Algebra.
References:
[1] M. Aigner and G.H. Ziegler, Proofs from THE BOOK, Sixth Edition, Springer, 2018.
[2] A. Baker, Transcendental number theory, Cambridge University Press, New York, 1975.
[3] C. Fefferman, An Easy Proof of the Fundamental Theorem of Algebra, The Amer. Math. Monthly, 74 No. 7 (Aug.-Spt.)(1967), 854-855.
[4] C. Hermite, Sur la fonction exponentielle, C. R. Acad. Sci. (Paris) 77 (1873), 18-24.
[5] D. Hilbert, Über die Transcendenz der Zahlen e und π, Math. Ann. 43 (1893), 216-219.
[6] A. Hurwitz, Beweis der Transcendenz der Zahl e, Math. Ann. 43 (1893), 220-222.
[7] S. Lang, Algebra, Springer, 2002.
[8] F. Lindemann, Über die Zahl π, Math. Ann. 20 (1882), 213-225.
[9] I. Niven, A simple proof that π is irrational, Bull. Amer. Math. Soc. 53 (1947), 509-509.
[10] M. Waldschmidt, La méthode de Charles Hermite en théorie des nombres transcendents,
http://journals.openedition.org/bibnum/893?lang=en.
[11] P.L. Wantzel, Recherches sur les moyens de reconnaître si un problème de géométrie peut se résoudre avec la règle et le compas, Journal de Mathématiques pures et appliquées, 2 (1837), 366-372.

20 aprilie 2022, ora 16:00

„Applications of Riemannian Geometry in Machine Learning” susținut de Professor Inan Ünal, Department of Computer Engineering Munzur University, Tunceli, Turcia.

Abstract:
One of the most basic purposes of human beings is to understand the universe. We want to model events in the universe and to make predictions about the future by obtaining useful results from these models. Undoubtedly, mathematics is our greatest helper on this path. In generally, we know that mathematics is divided into two distinct subtitles: pure mathematics and applied mathematics. This uncertain distinction is getting vaguer and vaguer day by day. Today, we see that many sub elds of mathematics as seen as purely theoretical sciences such as topology and algebra have very important applications. In the period when non-Euclidean geometry emerged, one of the most important questions was whether the results obtained would be applicable. One of the first to give a clear answer to this question was Albert Einstein with his theory of relativity. Einstein made use of Riemannian geometry, one of the most important examples of non-Euclidean geometry. We all know that the universe we live in is not Euclidean. Therefore, it is inevitable for non-Euclidean geometry to be placed at the center of applied mathematics.
Another important interest of ours is understanding and modeling human behavior. We call machine learning the field where studies are carried out on this subject. In recent years, there have been significant developments in machine learning algorithms and techniques. Running these algorithms on non-Euclidean data required Riemann geometry techniques. Thus, the field we call Geometric Deep Learning today emerged. The purpose of this talk is to summarize the use of Riemannian geometry in the field of machine learning through the concept of geometric deep learning.

Joi, 24 martie 2022, ora 17:00

„Lamé-Gielis Transformations in the natural sciences and geometry” susținut de Professor Johan Gielis, Department of Biosciences Engineering, University of Antwerp, Belgium & Simon Stevin Institute for Geometry, Antwerpen, Belgium.

Abstract:
In the study of natural shapes and phenomena, the search for a unifying description is one of the key strategies. At the age of 21 Gabriel Lamé (1795-1860) published a small booklet on geometrical methods [1]. To apply geometry to crystallography, he introduced supercircles and superellipses, a subset of what are now known as Lamé curves. A generalization of Lamé curves to Gielis curves enlarges the scope of a unified geometric description to many more natural shapes [2]. In the past decade, this model has been tested successfully on over 40000 biological specimen including tree rings, culms of bamboos, starfish and avian eggs [3]. From a geometrical point of view, Gielis Transformations are a generalization of the Euclidean circle, and related to Minkowski and the simplest Riemann-Finsler geometries. Notably, it is a continuous transformation, also between shapes and the spaces in which they reside. Among others, this has opened the door for the application of classical Fourier projection methods to solve boundary value problems (Laplace, Helmholtz,…) on starlike domains in 2D and 3D [4].
These developments have also found their way in various applications in science and technology. Examples will include minimal surfaces, antenna design and information sciences.
References:
[1] G. Lamé (1818) Examen des différentes méthodes employées pour résoudre les problèmes de géométrie.
[2] J. Gielis (2003) A generic geometric transformation that unifies a wide range of natural and abstract shapes. American Journal of Botany.
[3] J. Gielis, J., P. Shi, B. Beirinckx, D. Caratelli, & P.E. Ricci (2021). Lamé-Gielis curves in biology and geometry. In: (Eds. Mihai A., Mihai I.) Proceedings of the Conference Riemannian Geometry and Applications RIGA (pp. 139-164).
[4] P.E. Ricci, J. Gielis (2022). From Pythagoras to Fourier and from Geometry to Nature. Athena Publishing, Amsterdam.

Vineri, 14 ianuarie 2022, ora 15:00

„O nouă caracterizare a curbelor rectificante” susținut de Lect. Dr. Marilena Jianu, UTCB.

Abstract:
O curbă rectificantă este o curbă în spațiu cu proprietatea că toate planele rectificante la curbă trec printr-un punct fix. Dacă acest punct este originea sistemului de coordonate, atunci vectorul de poziție al unei curbe rectificante se află întotdeauna în planul rectificant.
O proprietate remarcabilă a curbelor rectificante este aceea că raportul dintre torsiune și curbură este o funcție liniară neconstantă de parametrul natural s: În această prezentare, demonstrăm o nouă caracterizare a curbelor de rectificante: o curbă este rectificantă dacă și numai dacă admite o involută sferică. Prin urmare, curbele rectificante pot fi construite ca evolute ale unor curbe sferice. Un exemplu ilustrativ este cel al curbelor rectificante construite ca evolute ale unei spirale sferice.
Alte rezultate obținute sunt expresiile curburii și torsiunii unei curbe sferice rectificante, precum și determinarea unor condiții necesare si suficiente pentru ca o curbă și involuta ei să fie ambele curbe rectificante.

Joi, 25 Martie 2021, ora 15:00

„Testare repetată pe scară largă: lecții din trecutul pandemic apropiat” susținut de Prof. Dr. Monica Cojocaru, Department of Mathematics and Statistics, University of Guelph, Canada.

Abstract: In aceasta prezentare folosim incidența raportată de cazuri COVID în patru țări dezvoltate, de la începutul pandemiei (Feb-Mar 2020) până la sfirșitul lui noiembrie 2020. Prezentăm efectele izolării sociale, a purtatului de mască, a închiderii școlilor etc., prin calibrarea unei variante de model SEIR la datele de incidență din Italia, Canada, U.S. si Korea de Sud. Apoi propunem și testăm o măsură sociala diferită de cele implementate în majoritatea țărilor din lume: anume testarea repetată pe scară largă a populației pentru determinarea si izolarea cazurilor pre- si asimptomatice. Evaluăm și calculăm ratele medii necesare pentru testare și ratele medii asociate „contact tracing”-ului în așa fel încât rata de creștere a noilor infecții evită nivelul de outbreak (i.e., asa incit numărul efectiv the reproducere de noi infecții este aproximativ 1).
În final, arătăm că aceasta măsură este foarte eficientă și ușor de aplicat la scara mai mică, de pildă în școli. Încheiem cu o discuție a posibilităților și circumstanțelor de aplicare ale acestor măsuri.