PLAN RADA SEMINARA ZA OKTOBAR 2021. GODINE
Zbog trenutne epidemiološke situacije, predavanja na seminaru će se održavati na daljinu, a slušaoci mogu da ih prate preko linka https://miteam.mi.sanu.ac.rs/asset/YoqHWKALRkRTbK9So.
UTORAK, 05.10.2021. u 10:30, Online
SVEČANI SASTANAK ODELJENJA ZA RAČUNARSTVO I PRIMENJENU MATEMATIKU POVODOM PROSLAVE 75 GODINA OD OSNIVANJA MATEMATIČKOG INSTITUTA SANU
Registracija za on-line praćenje predavanja na Seminaru je na linku https://miteam.mi.sanu.ac.rs/asset/xzGqvSp7aWbg8WpYX.
10:45-11:15 Endre Süli, University of Oxford, United Kingdom
DISCRETE DE GIORGI ESTIMATES AND THE FINITE ELEMENT
APPROXIMATION OF CHEMICALLY REACTING BIOLOGICAL FLUIDS
The talk is concerned with the convergence analysis of finite element methods for the approximate solution of a system of nonlinear elliptic partial differential equations that arise in models of chemically reacting viscous incompressible biological fluids. The shear-stress appearing in the model involves a power-law type nonlinearity, where, instead of being a fixed constant, the power law-exponent is a function of a spatially varying nonnegative concentration function, which, in turn, solves a nonlinear convection-diffusion equation. In order to prove the convergence of the sequence of finite element approximations to a solution of this coupled system of nonlinear PDEs, a uniform Holder norm bound needs to be derived for the sequence of finite element approximations to the concentration in a setting, where the diffusion coefficient in the convection-diffusion equation satisfied by the concentration is merely an function. This necessitates the development of a finite element counterpart of the De Giorgi-Nash-Moser theory. Motivated by an early paper by Aguilera and Caffarelli (1986) in the simpler setting of Laplace's equation, we derive such uniform Holder norm bounds on the sequence of continuous piecewise linear finite element approximations to the concentration. We then use results from the theory of variable-exponent Sobolev spaces, Minty's method for monotone operators, and an extension to variable-exponent Sobolev spaces of the finite element version of the Acerbi Fusco Lipschitz-truncation method, to pass to the limit in the coupled system of nonlinear PDEs under consideration.
11:15-11:45 Nenad Mladenović, Khalifa University, United Arab Emirates
FORMULATION SPACE SEARCH METAHEURISTIC (Slides)
Many methods for solving discrete and continuous global optimization problems are based on changing one formulation to another, which is either equivalent or very close to it. These types of methods include dual, primal-dual, Lagrangian, linearization, surrogation, convexification methods, coordinate system change, discrete/continuous reformulations, to mention a few. However, in all those classes, the set of formulations of one problem are not considered as a set having some structure provided with some order relation among formulations.
The main idea of Formulation Space Search (FSS) is to provide the set of formulations with some metric or quasi-metric relations, used for solving a given class or type of problem. In that way, the (quasi) distance between formulations is introduced, and the search space is extended to the set of formulations as well. In this talk I will present the general methodology of FSS, and give an overview of several applications taken from the literature that fall within this framework.
This is a joint work with Jack Brimberg, Frank Plastria and Dragan Urosević.
11:45-12:15 Dragan Stevanović, Mathematical Institute SANU
ON HOSOYA'S DORMANTS AND SPROUTS (Slides)
The study of cospectral graphs is one of the traditional topics of spectral graph theory. Initial expectation by theoretical chemists Günthard and Primas in 1956 that molecular graphs are characterized by the multiset of eigenvalues of the adjacency matrix was quickly refuted by the existence of numerous examples of cospectral graphs in both chemical and mathematical literature. This work was further motivated by Fisher in 1966 in the influential study that investigated whether one can “hear” the shape of a (discrete) drum, which has led over the years to the construction of many cospectral graphs. These findings culminated in setting the ground for the Godsil-McKay local switching and the Schwenk’s use of coalescences, both of which were used to show (around the 1980s) that almost all trees have cospectral mates. Recently, enumerations of cospectral graphs with up to 12 vertices by Haemers and Spence and by Brouwer and Spence have led to the conjecture that, on the contrary, “almost all graphs are likely to be determined by their spectrum”. This conjecture paved the way for myriad of results showing that various special types of graphs are determined by their spectra. On the other hand, in a recent series of papers, Hosoya drew the attention to a particular aspect of constructing cospectral graphs by using coalescences: that cospectral graphs can be constructed by attaching multiple copies of a rooted graph in different ways to subsets of vertices of an underlying graph.
After briefly surveying the history of constructing cospectral graphs, we focus on the expectations and questions about cospectrality of multiple coalescences that were raised in Hosoya's papers. In particular, we discuss the characteristic polynomial of such multiple coalescences, from which a necessary and sufficient condition for their cospectrality follows. We enumerate such pairs of cospectral multiple coalescences for a few families of underlying graphs, and show the infinitude of cospectral multiple coalescences having paths as underlying graphs, which were deemed rare by Hosoya.
This is a joint work with Salem Al-Yakoob.
12:15-12:30 Coffee break
12:30-13:00 Veljko Milutinović, Profesor u penziji, Elektrotehničkog fakulteta u Beogradu, Adjunct Professor, University of Indiana, Bloomingtom, IND, USA, Gostujuci Profesor Univerziteta u Beogradu (Matematicki faklutet, Elektrotehnički fakultet, i FON)
OPTIMALNA ARHITEKTURA ZA SUPERKOMPJUTER NA ČIPU OD TRILION TRANZISTORA
Čip od trilion (10**12) tranzistora postao je realnost počev od 2021. godine i osnovno je pitanje kako kreirati arhitekturu takvog čipa, da bi se postigla maksimalna efikasnost za aplikacije od interesa, a sada su to uglavnom aplikacije orijentisane ka veštačkoj inteligenciji koja se primenjuje nad izuzetno velikim skupovima podataka. Ova prezentacija daje jedan mogući odgovor na dato pitanje i predlaže da to bude arhitektura koja uključuje dve ControlFlow paradigme (MultiCore i ManyCore) i dve DataFlow paradigme (Flexible Execution Graph i Fixed Systolic Array). Takođe, i adekvatni interfejs, kako prema izvorima podataka (memorija, klasični I/O, WSN i IoT), tako i prema mogućim spoljnim akceleratorima (opto, bio, molecular i quantum). Predložena je i originalna metodologija za raspodelu tranzistora između svih pomenutih resursa na čipu. Ova prezentacija diskutuje i moguće modele programiranja koji objedinjuju sve navedene pristupe: Predložena su proširenja postojećih modela (ControlFlow i DataFlow), kao i dva nova modela (DiffusionFlow i EnergyFlow).
13:00-13:30 Zoran Obradović, Laura H. Carnell Professor of Data Analytics, Data Analytics and Biomedical Informatics Center, Computer and Information Sciences Department, Statistics Department, Temple University
EVENT DETECTION AND CLASSIFICATION IN TEMPORAL NETWORKS FROM SCARCE AND
IMPRECISE LABELS (Slides)
Accurate predictions at multiple temporal and spatial scales from multi-source data can potentially enable innovations across many industries. For example, moving from corrective to predictive maintenance of complex infrastructure could be more cost effective since early and interpretable risk predictions with uncertainty estimates allow optimization of damage mitigation and prevention strategies. Similarly, in proactive emergency monitoring, operating conditions are identified before they occur, which can direct deployment of control measures for avoiding undesirable outcomes. In this talk an overview of our recently developed methods to facilitate such end-to-end solutions will be discussed within the context of our ongoing DOE funded project aimed at predictive analytics in a large electricity grid. Challenges and the proposed solutions will be discussed related to (1) deep-learning based detection and classification of local and system-wide events using rapidly refined, partially inspected event labels; (2) digital-twin based data enhancement for events insufficiently represented in field-recordings over the training period; and (3) transfer learning to leverage relevant labeled events from a different network to minimize additional labeling effort.
ČETVRTAK, 07.10.2021. u 13:00, Live stream Niš
Milan Todorović, Matematički Institut SANU
COMBINATORIAL OPTIMIZATION FOR SELF CONTAINED BLOCKCHAIN: AN EXAMPLE OF USEFUL SYNERGY
With the increasing number of applications and systems that use Blockchain it is important to deal with its downsides. We are considering combinatorial optimization ideas to motivate and address two main issues in maintaining Blockhain. The first issue refers to economic usage of resources, and we propose a new consensus protocol exploring the Proof-of-Useful-Work concept. Deanonymization problem is considered as a second issue. It reduces to community detection in directed graphs which we propose to be consensus protocol’s useful work. In order to implement the proposed ideas we provide a short targeted literature review and identify the steps that need to be performed within the implementation.
This is joint work with Dušan Ramljak, Tatjana Davidović, Dragan Urošević, Tatjana Jakšić Krüger, Luka Matijević and Đorđe Jovanović.
Zajednički sastanak sa Seminarom Odlučivanje - teorija, tehnologija, praksa
UTORAK, 12.10.2021. u 14:15, Live stream Niš
Milica Knežević i Siniša Tomović, Matematički Institut SANU
MAN-IN-THE-MIDDLE ATTACK AGAINST LPN-BASED AUTHENTICATION PROTOCOLS: RE-EVALUATION AND CORRECTION
Authentication is one of the key cryptology problems and it constitutes the basis of protection needed for secure communication within computer networks. RFID (Radio Frequency IDentification) is a technology applied in various fields, such as supply chain management, payment and transportation systems, access control, animal identification, etc. The necessity to provide some level of security and privacy in RFID systems, on one hand, and inherent constraints of the RFID devices, on the other, have made RFID authentication a very active and challenging research topic. As a solution, a number of lightweight authentication protocols have been proposed, and one of the significant families of protocols among these is the HB-family, whose security is based on the hardness of the LPN (Learning Parity with Noise) problem. In the focus of our research is a well-known Man-in-the-middle attack against the HB\# and Random-HB\# protocols, two prominent members of the HB-family. We show that the attack does not achieve the claimed precision and complexity, and further identify the root cause of the detected problem, which lies in reasoning based on improper approximations of the probability distributions of the central attack events. After establishing the exact distributions of these events, we rectify the attack and prove correctness of the proposed solution.
Zajednički sastanak sa Seminarom Odlučivanje - teorija, tehnologija, praksa
UTORAK, 19.10.2021. u 14:15, Online
Stefan Kostić, Elektrotehnički fakultet
CUSTOMER CHURN PREDICTION IN MOBILE TELECOMMUNICATION NETWORKS APPLYING UNSUPERVISED MACHINE LEARNING
Due to telecommunications market saturation, it is very important for telco operators to always have fresh insights into their customer’s dynamics. In that regard, social network analytics and its application with graph theory can be very useful. In this paper we analyze a social network that is represented by a large telco network graph and perform clustering of its nodes by studying a broad set of metrics, e.g., node in/out degree, first and second order influence, eigenvector, authority and hub values. This paper demonstrates that it is possible to identify some important nodes in our social network (graph) that are vital regarding churn prediction. We show that if such a node leaves a monitored telco operator, customers that frequently interact with that specific node will be more prone to leave the monitored telco operator network as well; thus, by analyzing existing churn and previous call patterns, we proactively predict new customers that will probably churn. The churn prediction results are quantified by using top decile lift metrics. The proposed method is general enough to be readily adopted in any field where homophilic or friendship connections can be assumed as a potential churn driver.
UTORAK, 26.10.2021. u 14:15, Online
Snežana Knežević, Fakultet organizacionih nauka
PREDSTAVLJANJE UDŽBENIKA "FORENZIČKO RAČUNOVODSTVO, ISTRAŽNE RADNJE, LJUDSKI FAKTOR I PRIMENJENI ALATI"
Nezavisno od toga što postoje mnogi akademski i stručni izvori koji opisuju primarne funkcionalne aspekte forenzičkog računovodstva ili istrage prevarnih i koruptivnih radnji, ova knjiga je prva ove vrste po svom specifičnom pristupu. Udžbenik pod nazivom „Forenzičko računovodstvo, istražne radnje, ljudski faktor i primenjeni alati“ koji daje pregled teorijskih koncepata i njihove praktične primene, a koji su organizovani u četiri dela: (1) Forenzičko računovodstvo, Revizija, Interna Kontrola, Finansijska analiza, Upravljačko računovodstvo i etika, Forenzika javnih nabavki i Statistika; (2) Istražne radnje, Poreska evazija, Veštačenje, Pranje novca i finansiranje terorizma; (3) Ljudski faktor, Forenzička fonetika, Bezbednost; (4) Primenjeni alati, Poslovni modeli, Digitalizacija, Korporativna društvena odgovornost.
Udžbenik je rezultat dugogodišnjeg rada istaknutih eksperata iz oblasti računovodstva i revizije, bezbednosti, prava, zdravstva i drugih disciplina sa višegodišnjim iskustvom, među kojima je i veći broj univerzitetskih profesora, docenata i asistenata (Fakultet organizacionih nauka, Fakultet za hotelijerstvo i turizam u Vrnjačkoj Banji, Ekonomski fakultet u Beogradu, Pravni fakultet u Novom Sadu, Kriminalističko policijski univerzitet, Fakultet bezbednosti, Fakultet za specijalnu edukaciju i rehabilitaciju, Ekonomski fakultet u Kragujevcu). Takođe, veliku podršku u izrade ovog udžbenika pružili su profesori i docenti iz inostranstva (Ekonomski fakultet u Banja Luci, Pravni fakultet “Iustinianus Primus,” „S. Univerzitet Ćirila i Metodija, Univerzitet Goce Delčev-Štip“). U izradi ovog udžbenika značajan doprinos su dali i profesori i predavači na strukovnim studijama (Beogradska akademija poslovnih i umetničkih strukovnih studija, Visoka poslovna škola strukovnih studija u Novom Sadu, Akademija strukovnih studija Južna Srbija, Odsek za poslovne studije Blace i dr). Urednik udžbenika je prof. dr Snežana Knežević.