Seminar za biomatematiko in matematično kemijo - Arhiv
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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.
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.
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.
