Topological methods based on topological invariants such as fixed point index or Lefschetz number are useful instruments in studying dynamical systems, which model physical and biological phenomena.

There are many studies that have found correlates of neuronal activity and behavior using single-cell electrophysiology. However, these studies have left behind the problem of what is the relationship of the activity of ensembles of neurons to behavior. The goal of this project is to study the impact of spiking variability of small neuronal populations on decision making.

Teoria półgrup operatorów i jej bliska krewniaczka, teoria operatorowych funkcji kosinusowych jest zaawansowanym, nowoczesnym językiem opisu rozwiązań równań różniczkowych w przestrzeniach Banacha.

Voting theory is one of those rare evergreen topics. It has been around for a long time, and yet has never become outdated. This is not surprising, given that it has connections to preference modeling and database querying theory (see the paper by Chomicki), among other

The future of fuzzy set theory greatly depends on the development of systematic ways of generalizing classical results to a graded setting. Far too often, such a generalization is done on a case by case basis, reinventing the wheel over and over again. However, instead of looking for multiple theorems, one should rather aim for a single powerful meta-theorem.

Cellular Automata (CAs) form an interesting class of dynamical systems. Whereas partial differential equations are prototypical examples of the continuous modelling paradigm (as state, time and space are continuous), CAs are to be situated at the extreme end of the discrete modelling paradigm (as state, time and space are discrete).

In many settings, random variables need to be ordered, at least partially. To that end, various notions of so-called stochastic dominance have been put forward. Most of them are based on the pairwise comparison of performance functions, such as the cumulative distribution functions of the random variables, and are related to orderings on expected values.

Reciprocal relations can be considered as generalizations of complete relations, more specifically as mappings Q:X^2->[0,1] satisfying Q(a,b)+Q(b,a)=1. They have applications both in fuzzy set theory (as preference relations), probability theory (as winning probability relations) and decision making.

W pracy należy opracować metodykę określenia optymalnych topologii sieci sensorów bezprzewodowych WSN (ang. Wireless Sensor Network) w niestandardowych środowiskach pracy. Przykładem takiego środowiska jest wnętrze rakiety kosmicznej, samolotu czy pociągu.

Problem dotyczy zagadnienia wyznaczania prędkości (pierwsza całka po czasie) oraz drogi (druga całka po czasie), z pomiarów przyspieszeń w funkcji czasu, zarejestrowanych przez akcelerometry umieszczone w różnych punktach obiektów latających.

The formation/annihilation of new phases during interdiffusion in multicomponent alloys is the fundamental process in metallurgy and material science. Present mathematical methods combine simple diffusion formalism with highly developed thermodynamic solutions (Thermocalc).

A noncommutative probability space is a quantum analog of the classical Kolmogorov construction. Unlike its classical counterpart, a noncommutative probability space has an important feature: quantum correlations. Our aim will be to construct some concrete examples of such objects and to describe their properties.