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Schreiber and Yukich [Ann. Probab. 36 (2008) 363–396] establish an asymptotic representation for random convex polytope geometry in the unit ball Bd , d ≥ 2, in terms of the general theory of… (More)

- Tomasz Schreiber
- 2008

In Piekniewski & Schreiber (2008) we have developed a simple mathematical model for information flow structure in a class of recurrent neural networks and shown that its asymptotic behaviour is… (More)

- Tomasz Schreiber
- 2005

We construct random dynamics on collections of non-intersecting planar contours, leaving invariant the distributions of lengthand area-interacting polygonal Markov fields with V-shaped nodes. The… (More)

- Tomasz Schreiber
- 2006

We consider the so-called length-interacting Arak-Surgailis polygonal Markov fields with V-shaped nodes – a continuum and isometry invariant process in the plane sharing a number of properties with… (More)

The paper [40] establishes an asymptotic representation for random convex polytope geometry in the unit ball Bd, d ≥ 2, in terms of the general theory of stabilizing functionals of Poisson point… (More)

- Filip Piekniewski, Tomasz Schreiber
- 2007 IEEE Symposium on Foundations of…
- 2007

In recent two decades neuroscience and computational intelligence has experienced a large progress, with some new important concepts being developed like spiking (Bohte, 2003) and dynamical neurons… (More)

- Jaroslaw Piersa, Filip Piekniewski, Tomasz Schreiber
- IEEE Transactions on Neural Networks
- 2010

In this paper, we provide theoretical and numerical analysis of a geometric activity flow network model which is aimed at explaining mathematically the scale-free functional graph self-organization… (More)

- Michal Matuszak, Jacek Miekisz, Tomasz Schreiber
- ICAISC
- 2012

The goal of the ramified optimal transport is to find an optimal transport path between two given probability measures. One measure can be identified with a source while the other one with a target.… (More)

In this paper, we are interested in the behavior of the typical Poisson–Voronoi cell in the plane when the radius of the largest disk centered at the nucleus and contained in the cell goes to… (More)

Functionals of spatial point process often satisfy a weak spatial dependence condition known as stabilization. In this paper we prove process level moderate deviation principles (MDP) for such… (More)