The research activities of the laboratory involve various fields of mathematics with special emphasis on applications to computer and information science. The following areas of mathematics are studied: scientific computing and numerical solutions of differential equations, in particular, methods for geometric integration, graph theory, mostly topological and structural properties of graphs, vertex colorings of graphs and weighted graphs as a natural generalization of the channel assignment problem, algebraic topology, in particular cohomology of topological spaces with group actions, applications of topology to computer science, and computational topology, nonlinear dynamical systems and their application in geometry, physics and mechanics, linear and nonlinear mathematical techniques in computer vision (in cooperation with the Computer vision laboratory), computational geometry and geometry of cycles (in cooperation the Faculty of Electrical Engineering and the Faculty of Mathematics and Physics) with applications to surface modeling, in the area of incidence structures we study problems related to combinatorial and geometric configurations (the study of combinatorial properties of configurations via their incidence graphs, and the study of possibility of the realization of configurations in other incidence structures), CFD programs and their use in sailing simulations

The laboratory organizes the Mathematical seminar at the FRI, where members of the lab and other researchers report on current work, connected to the research and teaching activities of the lab. Several members of the lab are also members of research groups of the Institute of Mathematics, Physics, and Mechanics.

Members of the lab are involved in joint research work with other research groups at the Faculty of Computer and Information Science and the Faculty of Electrical Engineering and with the following institutions: NTNU Trondheim, Norway, and University in Bergen, Norway.

## Where are we?

We are located on Jadranska 21 on the ground floor. To get to our lab use the South entry into the building, at the entrance turn left.

## Collaborators

- Prof. Gašper Fijavž, PhD, Head
- Prof. Neža Mramor Kosta, PhD
- Prof. Bojan Orel, PhD
- Assist. Prof. Marko Boben, PhD
- as. Martin Vuk, PhD
- as. Peter Marjan Kink, PhD
- Damjan Vrenčur
- as. Gregor Jerše, PhD
- Assoc. Prof. Polona Oblak, PhD
- Assist. Prof. Ganna Kudryavtseva, PhD
- Assist. Prof. Žiga Virk, PhD

## Selected References

- D. Bokal, G. Fijavž and B. Mohar, The minor crossing number, SIAM Journal on Discrete Mathematics. Accepted for publication, 2006.
- S. Fidler, D. Skočaj, and A. Leonardis, Combining reconstructive and discriminative subspace methods for robust classification and regression by subsampling,
*IEEE Transactions on Pattern Analysis and Machine Intelligence*. Mar. 2006, vol. 28, no. 3, str. 337-350. - N. Mramor Kosta. A strong excision theorem for generalized Tate cohomology.
*Bull. Aust. Math. Soc.*, 2005, vol. 72, 7-15. - M. Boben, B. Grünbaum, T. Pisanski, A. Žitnik, Small triangle-free configurations of points and lines,
*Discrete and Computational Geometry*, Accepted for publication, 2005. - M. Boben, T. Pisanski, A. Žitnik. I-graphs and the corresponding configurations.
*J. Comb. Des*. 2005 (13), 406–424. - D. Bokal, G. Fijavž, B. Mohar. Minor-monotone crossing number.
*European Conference on Combinatorics, Graph Theory and Applications, EuroComb 2005*, Technische Universität, Berlin, September 5-9, 2005.*MathComb 2005*, (DMTCS, Vol. AE). Nancy: DMTCS, 2005, str. 123-128. - H. King, K. Knudson, N. Mramor Kosta. Generating discrete Morse functions from point data.
*Experimental Math.*14 (2005), 441--450. - M. Boben, T. Pisanski, D. Marušič, A. Orbanić, A. Graovac, The 10-cages and derived configurations. Discrete Math. 2004 (275), 265–276.
- D. Bokal, G. Fijavž, M. Juvan, M. Kayll, R. Škrekovski. The circular chromatic number of a digraph, J. Graph Theory, 2004, vol. 46, no. 3, pp. 227–240.
- M. Boben, T. Pisanski, D. Marušič, A. Orbanić, A. Graovac. The 10-cages and derived configurations. Discrete Math. 2004 (275), 265–276.
- D. Bokal, G. Fijavž, M. Juvan, M. Kayll, R. Škrekovski. The circular chromatic number of a digraph, J. Graph Theory, 2004, vol. 46, no. 3, str. 227-240.
- G. Fijavž, B. Mohar, Rigidity and separation indices of Paley graphs. Discrete math., 2004, vol. 289, no. 1-3, str. 157-161.
- G. Fijavž. Minor-minimal 6-regular graphs in the Klein bottle. Eur. J. Comb., 2004, vol. 25, no. 6, str. 893-898.
- A. Orbanić, M. Boben, G. Jaklič, T. Pisanski, Algorithms for drawing polyhedra from 3-connected planar graphs. Informatica (Ljublj.), 2004, (28), 239–243.
- M. Vilfan, M. Vuk, Nuclear spin relaxation of mesogenic fluids in spherical microcavities, J. Chem. Phys., 2004, vol. 120, 8638-8644.
- M. Boben, T. Pisanski. Polycyclic configurations, Eur.J Comb., 2003, (24), 431–457.
- G. Fijavž, B. Mohar, K6 minors in projective planar graphs, Combinatorica 23(2003), 453–465.
- S. Fidler, A. Leonardis. Robust LDA classification by subsampling, In Proceedings of the Conference on Computer Vision and Pattern Recognition, 2003.
- M. Boben, T. Pisanski. Polycyclic configurations, Eur.J Comb., 2003, (24), 431–457.
- E. Celledoni, A. Iserles, S.P. Norsett, B. Orel. Complexity Theory for Lie Group Solvers, J. of Complexity 18 (2002), 242–286.
- M. Cencelj, N. Mramor Kosta. CW decompositions of equivariant complexes, Bull. Australian Math. Soc. 65 (2002), 45–53.
- E. Celledoni, A. Iserles, S.P. Norsett, B. Orel. Complexity Theory for Lie Group Solvers, J. of Complexity 18 (2002), 242–286.
- B. Orel, Extrapolated Magnus methods. BIT 41, 2001, 1089–1100.
- B. Orel. Parallel Runge-Kutta methods with real eigenvalues. Applied Numerical Mathematics, 11(1993), 241–250.
- B. Orel, Real pole approximations to the exponential function. BIT, 1991, vol. 31, 144–159.

## Projects

### Current Projects

- Representations of Quantum Groups via Computational Linear Algebra, Bilateral Collaboration Project (BI-BA/16-17-025), 2016−2017
- Advancement of computationally intensive methods for efficient modern general-purpose statistical analysis and inference, Basic Research and Application Project (L1-7542), 2016−2019

### Closed Projects

- Algorithms for control of scnning probe microscopes using quartz tuning forks , Basic Research and Application Project (L2-6045), 2004−2006
- MOBVIS, Vision Technologies and Intelligent Maps for Mobile Attentive Interfaces in Urban Scenario, European Project (Framework Programmes) (FP6-511051), 2005−2008
- Optimization of the shape of yacht hulls, Industry-Funded Project , 2007−2008
- Randomness verification and irregularity analysis of a mechanical random generator that is to be part of a game machine, Industry-Funded Project , 2008−2008
- Holomorphic mappings and foliations, harmonic analysis and hamiltonian systems, Basic Research and Application Project (J1-2152), 2009−2012
- Learning a large number of visual object categories for content-based retrieval in image and video databases, Basic Research and Application Project (J2-3607), 2010−2013
- Applied computational and algebraic topology (ACAT), International Project , 2011−2015
- KUL - KAKOVOST – UNIVERZA V LJUBLJANI, Structural Funds Project , 2013−2015
- Overcoming the curse of dimensionality with the use of background knowledge, Basic Research and Application Project (J2-5480), 2013−2016
- Creative Path to Practical Knowledge, Structural Funds Project , 2014−2014