ὅδε οἶκος, ὦ ἑταῖρε, μνημεῖον ἐστιν ζῴων τῶν σοφῶν ἀνδρῶν, καὶ τῶν ἔργων αὐτῶν

Seminar on Applied Mathematics

 

PROGRAM


Matematički Institut
Matematički fakultet
Fakultet organizacionih nauka
JUPIM
IEEE Computer Chapter, Srbija

SEMINAR ZA PRIMENJENU I INDUSTRIJSKU MATEMATIKU

MI SANU, Knez Mihailova 36, sala 301f

PLAN RADA SEMINARA ZA OKTOBAR 2011. GODINE

Ponedeljak, 03.10.2011. u 12:00, Sala 301f, MI SANU:

Laureano F. Escudero Dept. of Statistics and Operations Research U. Rey Juan Carlos, Madrid, Spain
RISK MINIMIZATION STRATEGIES FOR SUPPLY CHAIN MANAGEMENT UNDER UNCERTAINTY

Abstract: Supply Chain Management (SCM) is concerned with determining supply, production and stock levels in raw materials, subassemblies at different levels of the given Bills of Materials, end products and information exchange through a set of factories, depots and dealer centres of a given production and service network to meet fluctuating demand requirements. Key aspects of the problem are the supply chain topology, time, uncertainty and cost. Uncertainty is due to the inherent stochasticity in some parameters for dynamic (multiperiod) planning problems, mainly, product demand and price, raw material supply costs and production costs. We treat it via scenario analysis. Strategic planning for supply chains, basically, consists of deciding on the production topology, plant sizing, product selection, product allocation among plants and vendor selection for crucial raw materials. The objective is the maximization of the expected global product net profit over the time horizon and, simultaneously, minimizing the weighted risk of having scenarios of the uncertain parameters with the related net profit below given sets of thresholds. Tactical supply chain planning consists of deciding on the utilization of the available resources included by vendors, factories, depots and dealer centres along the time horizon, such that given targets are met at a minimum cost. It assumes that the supply chain topology is given. Both planning activities should be considered together. In this talk we present a set of averse risk measures as alternatives to the maximization of the (risk neutral) expected net profit along a given time horizon over a set of representative scenarios in SCM, where the uncertainty is represented in a multiperiod nonsymmetric scenario tree. The main risk averse control strategies analyzed are: min-max regret, VaR strategy, Conditional VaR, mean-risk immunization, stochastic dominance constraints, and the new one, a mixture of VaR \& stochastic dominance. Most of these measures require from the modeller a threshold for the net profit to be achieved for each scenario and a failure's probability for not reaching the threshold or, at least, a weight for that probability to show the importance of each threshold. We shall also present a risk averse multistage mixed 0-1 stochastic optimization model for SCM by considering both the strategic and tactical decisions.

Utorak, 04.10.2011. u 14:15, Sala 301f, MI SANU:

Dragos Cvetkovic, Matematicki institut SANU
GRAFOVSKI PRISTUP U NASTAVI LINEARNE ALGEBRE UZ KORISCENJE SLAJDOVA - ISKUSTVA I SUGESTIJE

Sadrzaj: Predavanje pocinje podsecanjem na osnovne ideje zasnivanja teorije matrica kombinatornim sredstvima, tj. sredstvima teorije grafova. Takav pristup je primenjen u knjizi:

Brualdi R.A., Cvetkovic D., A Combinatorial Approach to Matrix Theory and Its Applications}, CRC Press, Boca Raton, 2008,

a takodje i u knjizi:

Cvetkovic D., Kombinatorna teorija matrica sa primenama u elektrotehnici, hemiji i fizici, Naucna knjiga, Beograd, 1980; II izdanje, 1987; III izdanje, Zavod za udzbenike, Beograd, 2011.

Elementi kombinatornog nacina uvodjenja pojmova u teoriji matrica ukljuceni su u udzbenik

Cvetkovic D., Lackovic I., Merkle M., Radosavljevic Z., Simic S., Vasic P., Matematika I - Algebra, IX izdanje, Akademska misao, Beograd, 2005.

i nastavu za studente Elektrotehnickog fakulteta u Beogradu znatno ranije.

Predstavice se specijalno izradjeni slajdovi za visokoskolsku nastavu linearne algebre (definicija i osobine determinanata, operacije sa matricama, sistemi linearnih algebarskih jednacina i dr.).

Predavanje ima za cilj da pomogne nastavnicima koji zele da u svoja predavanja linearne algebre unesu elemente kombinatornog pristupa.

Sreda, 12.10.2011. u 14:15, sala 301f, MI:

Willem Haemers, Tilburg University, Holandija
THE MAXIMUM ORDER OF ADJACENCY MATRICES WITH A GIVEN RANK

Abstract: We look for the maximum order $m(r)$ of the adjacency matrix $A$ of a graph $G$ with a fixed rank $r$, provided $A$ has no repeated rows or all-zero row. Akbari, Cameron and Khosrovshahi conjecture that $m(r)=2^{(r+2)/2}-2$ if $r$ is even, and $m(r)=5\cdot 2^{(r-3)/2}-2$ if $r$ is odd. We prove the conjecture and characterize $G$ in the case that $G$ contains an induced subgraph $\frac{r}{2}K_2$, or $\frac{r-3}{2}K_2+K_3$. (Joint work with Rene Peeters). UNIVERSAL ADJACENCY MATRICES WITH TWO EIGENVALUES Abstract: Consider a graph $G$ on $n$ vertices with adjacency matrix $A$ and degree sequence $( d_1, \dots ,d_n )$. A universal adjacency matrix of $G$ is any matrix in Span$\{ A,D,I,J \}$ with a nonzero coefficient for $A$, where $D = \mbox{diag}(d_1, \ldots ,d_n)$ and $I$ and $J$ are the identity and all-ones matrix, respectively. Thus a universal adjacency matrix is a common generalization of the adjacency, the Laplacian, the signless Laplacian and the Seidel matrix. We investigate graphs for which some universal adjacency matrix has just two eigenvalues. The regular ones are strongly regular, complete or empty, but several other interesting classes occur. (Joint work with Reza Omidi).

Utorak, 18.10.2011. u 14:15, sala 301f, MI SANU:

Jasmina Novakovic, Megatrend Unverzitet, Beograd
TACNOST KLASIFIKACIJE KORISCENJEM ANALIZE GLAVNIH KOMPONENTI-SLUCAJEVI KORISCENJA U BIOMEDICINI I PREPOZNAVANJU EMOCIJA

Sadrzaj: Koriscena je analiza glavnih komponenti (Principal Component Analysis - PCA) za redukciju atributa sa razlicitim vrednostima razlomka R. Cilj je bio da se u podacima kovarijansa (zavisnost) medju atributima ukloni, a da se poveca varijansa otkrivenih komponenti i faktora. Izvrsena je uporedna analiza dobijenih rezultata uz pomoc razlicitih klasifikatora sa velikim brojem setova podataka. U nasem slucaju, redukcija atributa je posebno bila efikasna kod algoritama koji nisu imali ugradjene metode selekcije i ekstrakcije, kao na primer k-NN ili neki tipovi neuralnih mreza. Tako na primer, eksperimentalni rezultati u tumacenju digitalnih mamografskih snimaka raka dojke kod zena i predvidjanju rezultata biopsije tkiva, potvrdili su efikasnost koriscenja analize glavnih komponenti, uz tacnost klasifikacije od priblizno 83%. Takodje, analiza glavnih komponenti je uspesno koriscenjena u prepoznavanju osnovnih emotivnih stanja na osnovu facijalne ekspresije, tako sto je postignuta tacnost prepoznavanja od priblizno 85% koriscenjem neuralne mreze.

Utorak, 25.10.2011. u 14:15, sala 301f, MI SANU:

Vasily Borisovich Demidovich, Faculty of Mechanics and Mathematics, M. V. Lomonosov Moscow State University, Moscow
O UOPSTENIM POLINOMIMA NAJMANJEG ODSTUPANJA OD NULE U CEBISOVLJEVIM PROSTORIMA

Abstract: Detalji o predavanju bice dostavljeni naknadno.

RUKOVODIOCI SEMINARA

Vera Kovačević-Vujčić
Milan Dražić