# Seminar za biomatematiko in matematično kemijo

Tedenski raziskovalni seminar za biomatematiko in matematično kemijo je namenjen formalnemu in neformalnemu seznanjanju z najnovejšimi dosežki na področjih, ki prepletajo uporabo predvsem diskretnih matematičnih in računalniških metod v kemiji in bioznanosti. Na seminarju domači raziskovalci, njihovi gostje ter doktorski študentje poročajo o svojih rezultatih. Seminar služi tudi kot pripravljalnica na predavanja na mednarodnih konferencah. Po drugi strani pa omogoča tudi neformalno sestajanje zainteresiranih za skupno raziskovalno delo na konkretnih odprtih problemih.

**Datum in ura**/ Date and time: 5.12.18

**Predavalnica**/ Location: FAMNIT-VP2

**Predavatelj**/ Lecturer: Guillermo Restrepo (Max Planck Institute for Mathematics in the Sciences & Leipzig University)

**Naslov**/ Title: Graphs and chemical reactions

**Vsebina**/ Abstract:

Chemical reactions encode a wealth amount of information on the transformation of chemical substances. In this talk we will discuss how to mathematically model them at the level of atoms involved in the molecules interacting in the chemical reaction. Here molecules are regarded as graphs, whose transformation are modelled by rewriting rules acting upon the graph of starting materials and yielding the graph of products of the chemical reaction. Leaving aside reactions as ensembles of atoms and their transformations, reactions can also be modelled at the level of substances, where the important information is which starting materials relate to each other to produce the final products. Here, the model we use is that of directed hypergraphs.

As chemical reactions reported by chemists grow exponentially, the hypergraph representing them turns very large. In general, large networks are treated by devising statistics gauging several aspects of such structures, some statistics are, e.g. vertex degree distributions, centrality, and several others. Recently, curvature of edges and vertices has been incorporated to this statistics and we will show how the curvature can be extended to hypergraphs, which actually generalise graph results.

In the last part of the talk we will discuss open questions about the growth of chemical reaction networks and how to model them.

**Datum in ura**/ Date and time: 16.10.18

**Predavalnica**/ Location: FAMNIT-Muzejski3

**Predavatelj**/ Lecturer: Tomaž Pisanski

**Naslov**/ Title: Some questions about nut graphs

**Vsebina**/ Abstract:

I will present basic facts about *nut graphs* and *core graphs* using four papers by Irene Sciriha. I will also give a demonstrtion of a short SageMath program that tests whether a given graph is a nut graph. The talk will be concluded by some questions about nut graphs.

**Datum in ura**/ Date and time: 23.4.18

**Predavalnica**/ Location: FAMNIT-MP1

**Predavatelj**/ Lecturer: Boštjan Šimunič

**Naslov**/ Title: Skeletal muscle mechanics: the need for new approaches

**Vsebina**/ Abstract:

Already in 1923 science confirmed that “the analysis of the mechanical effects of muscle excitements would be incomplete if only changes in muscle length were examined disregarding changes in muscle thickness”. Distortions of muscle contraction mechanics due to longitudinal signal pathways were recently overcame by the mechanomyographic methods, where one of them, the Tensiomyography is a non-invasive method for detecting skeletal muscle contractile properties using a linear displacement sensor. It was designed to assess skeletal muscle thickening and low frequency lateral oscillations of active skeletal muscle fibres during twitch contractions and overcomes the limitations of mechanomyographic methods (low signal to noise ratio; low reliability; complex measuring setup; the need for complex post-processing) and dynamometry (low signal to noise ratio; pain; signal distortion, muscle cross-talk). Since its first scientific publication in 1990 more than 100 SCI articles show its use and purpose: in the estimation of muscle composition; for evaluating muscle atrophy and tone; for measuring adaptation to different pathologies; for measuring adaptation to specific training; and for measuring muscle fatigue.

The lecture will focus on the presentation of the scientific background of the Tensiomyography as well as the motivation for its development. Furthermore, we will focus on reliability and validity studies, together with its applications. During the lecture many future directions of TMG-based research will be proposed, focusing on mathematical and medical grounds.

**Datum in ura**/ Date and time: 9.11.17

**Predavalnica**/ Location: FAMNIT-Galeb-Sejna

**Predavatelj**/ Lecturer: Nino Bašić

**Naslov**/ Title: On the Clar number of benzenoid graphs

**Vsebina**/ Abstract:

A Clar set of a benzenoid graph *B* is a maximum set of independent alternating hexagons over all perfect matchings of *B*. The Clar numberof *B*, denoted Cl(*B*), is the number of hexagons in a Clar set for *B*.

In this talk, an upper bound for the Clar number of catacondensed benzenoid graphs and a characterization of the graphs that attain this bound will be presented.

This is joint work with István Estélyi, Riste Škrekovski and Niko Tratnik.

**Datum in ura**/ Date and time: 30.10.17

**Predavalnica**/ Location: FAMNIT-Galeb-Sejna

**Predavatelj**/ Lecturer: doc. dr. Rok Požar

**Naslov**/ Title: Grafovski pristop za analizo delovanja možganov

**Vsebina**/ Abstract:

Električno aktivnost, ki jo živčne celice generirajo v možganih, lahko merimo na površini glave s pomočjo kape z vgrajenimi elektrodami. S tem se ukvarja elektroencefalografija (EEG), ki je uporabna ne le pri kliničnem delu, ampak tudi pri raziskovanju različnih kognitivnih procesov. V predavanju predstavimo, kako lahko teorijo grafov uporabimo za analizo EEG podatkov. Učinkovitost grafovskega pristopa ilustriramo na primeru blage kognitivne motnje.

**Datum in ura**/ Date and time: 20.3.17

**Predavalnica**/ Location: FAMNIT-Muzejski4

**Predavatelj**/ Lecturer: Nino Bašić

**Naslov**/ Title: A dynamic programming approach to generation of strong traces

**Vsebina**/ Abstract:

In 2013 Gradišar et al. (National Institute of Chemistry, Slovenia) successfully designed a self-assembly tetrahedral polypeptide called TET12. It is a linear chain of twelve peptides, separated by flexible links, such that certain pairs of peptides “glued” together and formed coiled coil dimers. The end result was a stable tetrahedron in which each of its six edges was a coiled coil dimer.

In the following years mathematical models behind the self-assembly were studied by many researches and a number of theoretical results were obtained. Here, we are going to present the concept of *strong traces* and a dynamic programming algorithm for their generation.

This is joint work with Drago Bokal, Tomaž Pisanski and Jernej Rus.

Properties of fullerenes are critically dependent on the distribution of their 12 pentagonal faces. It is well known that there are infinitely many IPR-fullerenes. IPR-fullerenes can be described as fullerenes in which each connected cluster of pentagons has size 1.

We studied the combinations of cluster sizes that can occur in fullerenes (and whether the clusters can be at an arbitrarily large distance from each other). For each possible partition of the number 12, we are able to decide whether the partition describes the sizes of pentagon clusters in a possible fullerene.

This is joint work with Gunnar Brinkmann, Patrick W. Fowler and Nico Van Cleemput.