Mathematical Colloquium

 

PROGRAM


ODELJENJE ZA MATEMATIKU
MATEMATIČKOG INSTITUTA SANU

                      


PROGRAM ZA OKTOBAR 2020.


Četvrtak, 01.10.2020. u 15:30, sala 301f, MISANU, Kneza Mihaila 36
Riste Škrekovski, Fakulteta za matematiko in fiziko, Univeza v Ljubljani
SOME RESULTS ON UNIQUE-MAXIMUM COLORING OF PLANE GRAPHS
A unique-maximum coloring of a plane graph G is a proper vertex coloring by natural numbers such that each face α of G satisfies the propety: the maximal color that appears on α, appears precisely on one vertex of α (or shortly, the maximal color on a face is unique on that face). Fabrici and Göring proved that six colors are enough for any plane graph and conjectured that four colors suffice. Thus, this conjecture is a strengthening of the Four Color Theorem. Wendland later decreased the upper bound from six to five.
We first show that the conjecture holds for various subclasses of planar graphs but then we disprove it for planar graphs in general. Thus, the facial unique-maximum chromatic number of the sphere is not four but five. In the second part of the talk, we will consider various new directions and open problems.
Joint work with Vesna Andova, Bernard Lidický, Borut Lužar, and Kacy Messerschmidt.



Četvrtak, 08.10.2020. u 15:30, sala 301f, MISANU, Kneza Mihaila 36
Nataša Pržulj, RAF-Beograd i ICREA-Barcelona Supercomputing Center
UNTANGLING BIOLOGICAL COMPLEXITY: FROM OMICS DATA TO DATA-INTEGRATED MEDICINE
We are faced with a flood of molecular and clinical data. We are measuring interactions between various bio-molecules in and around a cell that form large, complex systems. Patient omics datasets are also increasingly becoming available. These systems-level network data provide heterogeneous, but complementary information about cells, tissues and diseases. The challenge is how to mine them collectively to answer fundamental biological and medical questions. This is nontrivial, because of computational intractability of many underlying problems on networks (also called /graphs/), necessitating the development of approximate algorithms (heuristic methods) for finding approximate solutions.
We develop methods for extracting new biomedical knowledge from the wiring patterns of systems-level, heterogeneous biomedical networks. Our methods uncover the patterns in molecular networks and in the multi-scale network organization indicative of biological function, translating the information hidden in the network topology into domain-specific knowledge. We also introduce a versatile data fusion (integration) framework to address key challenges in precision medicine from biomedical network data: better stratification of patients, prediction of driver genes in cancer, and re-purposing of approved drugs to particular patients and patient groups, including Covid-19 patients. Our new methods stem from novel network science algorithms coupled with graph-regularized non-negative matrix tri-factorization, a machine learning technique for dimensionality reduction and co-clustering of heterogeneous datasets. We utilize our new framework to develop methodologies for performing other related tasks, including disease re-classification from modern, heterogeneous molecular level data, inferring new Gene Ontology relationships, aligning multiple molecular networks, and uncovering new cancer mechanisms.

Petak, 23.10.2020. u 14:15, sala 301f, MISANU, Kneza Mihaila 36
Jelena Ivanović, Arhitektonski fakultet, Beograd
SUME MINKOVSKOG U SLUŽBI TRUNKIRANJA
Sumiranje Minkovskog je jedna od najelementarnijih operacija nad skupovima tačaka, pa time i nad politopima kao konveksnim omotačima svojih temena. Međutim, i pored njene jednostavnosti, rezultat joj je intuitivno vrlo nepredvidiv, naročito u opštem slučaju sabiranja više politopa različitih dimenzija sa velikim brojem temena. Uz pomoć ove operacije definisane su poznate familije zonotopa i nestoedara, ali do sada nema rezultata koji definiše vezu između ove operacije i operacije trunkiranja politopa u datoj strani. Naime, postavlja se pitanje koji politop treba sabrati sa zadatim proizvoljnim politopom, ne bi li njihov zbir bio trunkacija zadatog politopa u zadatoj strani, do na kombinatornu (normalnu) ekvivalenciju. Na predavanju ćemo odgovoriti na ovo pitanje i ilustrovati direktnu primenu ovog rezultata u generisanju familije prostih politopa proširenog intervala nestoedara, to jest geometrijskoj realizaciji simplicijalnih kompleksa sačinjenih od višestruko ugnježđenih skupova.

Obavezno je nošenje maski i održavanje distance. Broj prisutnih na predavanju ograničen na najviše 10 (uključujući i predavača).


Odeljenje za matematiku je opsti matematicki seminar namenjen sirokoj publici. Predavanja su prilagodjena matematicarima i onima koji zele da to postanu.


Zoran Petric, Odeljenje za matematiku Matematickog instituta SANU