Ion transport through cell membrane channels (2007)
Gomulkiewicz, Jan, Miekisz, Jacek, Miekisz, Stanislaw
We discuss various models of ion transport through cell membrane channels. Recent experimental data shows that sizes of ion channels are compared to those of ions and that only few ions may be...
Evolutionary game theory and population dynamics (2007)
Many socio-economic and biological processes can be modeled as systems of interacting individuals. The behaviour of such systems can be often described within game-theoretic models. In these lecture...
Population dynamics with a stable efficient equilibrium (2007)
Miekisz, Jacek, Platkowski, Tadeusz
We propose a game-theoretic dynamics of a population of replicating individuals. It consists of two parts: the standard replicator one and a migration between two different habitats. We consider...
Stochastic stability in three-player games (2004)
Kaminski, Dominik, Miekisz, Jacek, Zaborowski, Marcin
Animal behavior and evolution can often be described by game-theoretic models. Although in many situations, the number of players is very large, their strategic interactions are usually decomposed...
Equilibrium transitions in finite populations of players (2004)
We discuss stochastic dynamics of finite populations of individuals playing games. We review recent results concerning the dependence of the long-run behavior of such systems on the number of players...
Long-run behavior of games with many players (2004)
We discuss similarities and differencies between systems of many interacting players maximizing their individual payoffs and particles minimizing their interaction energy. We analyze long-run...
Stochastic stability in spatial three-player games (2004)
We discuss long-run behavior of stochastic dynamics of many interacting agents. In particular, three-player spatial games are studied. The effect of the number of players and the noise level on the...
Stochastic stability in spatial games (2004)
We discuss similarities and differences between systems of interacting players maximizing their individual payoffs and particles minimizing their interaction energy. Long-run behavior of stochastic...
Evolutionary and asymptotic stability in symmetric multi-player games (2004)
Bukowski, Maciej, Miekisz, Jacek
We provide a classification of symmetric three-player games with two strategies and investigate evolutionary and asymptotic stability (in the replicator dynamics) of their Nash equilibria. We discuss...
Equilibrium selection in evolutionary games with random matching of players (2004)
We discuss stochastic dynamics of populations of individuals playing games. Our models possess two evolutionarily stable strategies: an efficient one, where a population is in a state with the...
Stability of evolutionarily stable strategies in discrete replicator dynamics with time delay (2004)
We construct two models of discrete-time replicator dynamics with time delay. In the social-type model, players imitate opponents taking into account average payoffs of games played some units of...
Statistical mechanics of spatial evolutionary games (2002)
We discuss the long-run behavior of stochastic dynamics of many interacting players in spatial evolutionary games. In particular, we investigate the effect of the number of players and the noise...
Devil's staircase for a nonconvex interaction (1999)
Jedrzejewski, Janusz, Miekisz, Jacek
We study ground-state orderings of particles in classical lattice-gas models of adsorption on crystal surfaces. In the considered models, the energy of adsorbed particles is a sum of two components,...
A symmetry group of a Thue-Morse quasicrystal (1999)
Gazeau, Jean-Pierre, Miekisz, Jacek
We present a method of coding general self-similar structures. In particular, we construct a symmetry group of a one-dimensional Thue-Morse quasicrystal, i.e., of a nonperiodic ground state of a...
Ground states of lattice gases with ``almost'' convex repulsive interactions (1999)
Jedrzejewski, Janusz, Miekisz, Jacek
To our best knowledge there is only one example of a lattice system with long-range two-body interactions whose ground states have been determined exactly: the one-dimensional lattice gas with purely...
Non-periodic long-range order for fast decaying interactions at positive temperatures (1997)
Van Enter, Aernout, Miekisz, Jacek, Zahradnik, Milos
We present the first example of an exponentially decaying interaction which gives rise to non-periodic long-range order at positive temperatures.
An Ultimate Frustration in Classical-Lattice Gas Models (1997)
We constructed an uncountable family of classical lattice-gas models with unique ground-state measures which are not uniquely ergodic measures of any tiling system, or more generally, of any system...
How Should One Define a (weak) Crystal? (1997)
. We compare two proposals for the study of positional longrange order: one in terms of the spectrum of the translation operator, the other in terms of the Fourier spectrum. We point out that only...
Low Temperature Stability of Nonperiodic Structures (1997)
. Complex ground states appearing in classical lattice gas models and their behaviour in the presence of thermal motions are discussed. Our examples consist of a nearest-neighbour model based on...
Non-Periodic Long-Range Order for Fast Decaying Interactions At Positive Temperatures (1997)
Introduction Since the discovery of quasicrystals [29], there has been an interest in understanding their occurrence in statistical mechanics models of interacting particles, see for example [18, 2,...
Stable Quasicrystalline Ground States (1997)
Jacek Miekisz, Stable Quasicrystalline, Ground States
. We give a strong evidence that noncrystalline materials such as quasicrystals or incommensurate solids are not exceptions but rather are generic in some regions of a phase space. We show this by...
The Global Minimum of Energy Is Not Always a Sum of Local Minima - a Note on Frustration (1997)
. A classical lattice gas model with translation-invariant finite range competing interactions, for which there does not exist an equivalent translation-invariant finite range nonfrustrated...
The Global Minimum of Energy Is Not Always a Sum of Local Minima - a Note on Frustration (1993)
A classical lattice gas model with translation-invariant finite range competing interactions, for which there does not exist an equivalent translation-invariant finite range nonfrustrated potential,...
Stable quasicrystalline ground states (1993)
We give a strong evidence that noncrystalline materials such as quasicrystals or incommensurate solids are not exceptions but rather are generic in some regions of a phase space. We show this by...
The unstable chemical structure of the quasicrystalline alloys, Phys (1986)
We show that a typical toy model of an ordered quasicrystalline alloy has a range of stoichiometries. We consider the low temperature ordered phases discrete model with nondegenerate periodic ground...
Evolutionary and asymptotic stability in symmetric multi-player games
Maciej Bukowski, Jacek Miekisz
We provide a classification of symmetric three-player games with two strategies and investigate evolutionary and asymptotic stability (in the replicator dynamics) of their Nash equilibria. We discuss...