# Raziskovalni matematični seminar - Arhiv

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**Datum in ura**/ Date and time: 25.3.13

**Predavalnica**/ Location: FAMNIT-SEMIN

**Predavatelj**/ Lecturer: Nina Chiarelli

**Naslov**/ Title: Linear separation of totoal dominating sets in graphs

**Vsebina**/ Abstract:

A total dominating set in a graph is a set of vertices such that every vertex of the graph has a neighbor in the set. We introduce and study graphs that admit non-negative real weights associated to their vertices so that a set of vertices is a total dominating set if and only if the sum of corresponding weights exceeds a certain threshold. These graphs, which we call total domishold graphs, form a non-hereditary class. We also obtain partial results towards a characterisation of graphs in which the above property holds in a hereditary sense.

**Datum in ura**/ Date and time: 25.3.13

**Predavalnica**/ Location: FAMNIT-SEMIN

**Predavatelj**/ Lecturer: dr. Barbara Boldin

**Naslov**/ Title: An extension of the classification of evolutionarily singular strategies in Adaptive Dynamics

**Vsebina**/ Abstract:

The existing classification of evolutionarily singular strategies in Adaptive Dynamics assumes an invasion exponent that is differentiable twice as a function of both the resident and the invading trait. Motivated by nested models for studying the evolution of infectious diseases, we consider an extended framework in which the selection gradient exists (so the definition of evolutionary singularities extends verbatim), but where the invasion fitness may lack the smoothness necessary for the classification `a la Geritz et al. We derive the classification of singular strategies with respect to their convergence stability and invadability and determine the condition forthe existence of nearby dimorphisms. Contrary to the standard setting of Adaptive Dynamics, the fate of dimorphisms nearby a singular strategy can, in general, not be deduced from the monomorphic invasion exponent. We will present a formula that allows one to deduce the fate of dimorphisms from the dimorphic invasion exponent and demonstrate our findings on a specific example from evolutionary epidemiology.

**Datum in ura**/ Date and time: 18.3.13

**Predavalnica**/ Location: FAMNIT-SEMIN

**Predavatelj**/ Lecturer: Prof. Alexander A. Ivanov (Imperial College London, UK)

**Naslov**/ Title: Method to construct groups using group amalgams

**Vsebina**/ Abstract:

It is our pleasure to inform you that there will be a minicourse

"Method to construct groups using group amalgams" (5 lectures) given by

Prof. Alexander A. Ivanov (Imperial College London, UK) at UP FAMNIT

Timetable:

Monday, March 18, 11:00 - 12:00 FAMNIT-SEMIN

Thursday, March 21, 14:00 - 15:00 FAMNIT-POŠTA

Monday, March 25, 11:00 - 12:00 FAMNIT-SEMIN

Thursday, March 28, 14:00 - 15:00 FAMNIT-VP

Thursday, April 4, 14:00 - 15:00 FAMNIT-VP

Welcome!

**Datum in ura**/ Date and time: 18.3.13

**Predavalnica**/ Location: FAMNIT-SEMIN

**Predavatelj**/ Lecturer: Karla Počkaj

**Naslov**/ Title: Construction of G^1 Hermite rational spline motion of degree six

**Vsebina**/ Abstract:

Geometric interpolation techniques have many advantages, such as automatically chosen parametrization, lower degree of interpolants and optimal approximation order.

In this talk a geometric continuous Hermite rational spline motion of degree six will be presented. The nonlinear equations that determine the spherical part of the motion turn out to have a nice explicit solution. Particular emphasis will be placed on the construction of the translational part of the motion. Since the geometric continuity of the motion is preserved while changing the lengths of the tangent vectors to the center trajectory, additional free parameters are obtained, which affect the shape of the motion significantly. Numerical examples which confirm the theoretical results, will be presented.

**Datum in ura**/ Date and time: 15.10.12

**Predavalnica**/ Location: FAMNIT-SEMIN

**Predavatelj**/ Lecturer: Dr. Pim van 't Hof (University of Bergen, Norway)

**Naslov**/ Title: Obtaining Planarity by Contracting Few Edges

**Vsebina**/ Abstract:

The contraction of an edge uv in a graph G is the operation that deletes u and v from G, and replaces them by a new vertex that is made adjacent to precisely those vertices that were adjacent to either u or v in G. The Planar Contraction problem takes as input a graph G

and an integer k, and asks whether G can be made planar by using at most k edge contractions. This problem is known to be NP-complete. We show that it is fixed-parameter tractable when parameterized by k. More precisely, we show that for every fixed \epsilon>0 and every

fixed integer k, it can be decided in O(n^{2+\epsilon}) time whether a graph can be made planar by contracting at most k edges.

Slides from the talk are available here: DOWNLOAD SLIDES!

**Datum in ura**/ Date and time: 11.3.13

**Predavalnica**/ Location: FAMNIT-SEMIN

**Predavatelj**/ Lecturer: Marcin Anholcer

**Naslov**/ Title: On Some Surprising Application of Graphs in Decision Making: Pairwise Comparisons

**Vsebina**/ Abstract:

In many multiple criteria decision making problems (in particular in the case of group expert decisions) the Pairwise Comparison Matrices (PCM) are used. In almost all the cases such matrices are inconsistent (i.e. they do not satisfy some axioms). In such a situation, it is necessary to find a consistent matrix that is closest to the given one with respect to some distance measure. In the case of the measure L_{2}, the resulting optimization problem is non-convex and multiple local optima are possible. In the talk some results for the case of the measure L_{∞} will be presented. Rather surprisingly, after using the logarithmic transformation, the subproblems become equivalent to the instances of the Shortest Path Problem (some of which can be divergent). Using this property we propose eﬀective method of deriving the consistent PCM.

This is a joint work with Janos Fulop.