Jacek Miekisz | University of Warsaw (original) (raw)

PAPERS by Jacek Miekisz

We introduce quasilattice-gas models in which every vertex of certain two-dimensional grids can b... more We introduce quasilattice-gas models in which every vertex of certain two-dimensional grids can be occupied by one of two different types of particles interacting through Lennard-Jones potentials. Such grids are quasiperiodic analogs of regular lattices present in periodic systems. To find ground-state configurations of our models, we performed Monte Carlo simulations and obtained structures with local five-fold symmetries and five-fold diffraction patterns.

Lecture Notes in Computer Science, 2014

Lecture Notes in Computer Science, 2012

The goal of the ramified optimal transport is to find an optimal transport path between two given... more 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. The problem is well known to be NP-hard. We develop an algorithm for solving a ramified optimal transport problem within the framework of Bayesian networks. It is based on the decision strategy optimisation technique that utilises self-annealing ideas of Chen-style stochastic optimisation. Resulting transport paths are represented in the form of treeshaped structures. The effectiveness of the algorithm has been tested on computer-generated examples.

Lecture Notes in Computer Science, 2012

The problem of learning Bayesian network structure is well known to be NP-hard. It is therefore v... more The problem of learning Bayesian network structure is well known to be NP-hard. It is therefore very important to develop efficient approximation techniques. We introduce an algorithm that within the framework of influence diagrams translates the structure learning problem into the strategy optimisation problem, for which we apply the Chen's self-annealing stochastic optimisation algorithm. The effectiveness of our method has been tested on computer-generated examples.

Biophysical Journal

The phenomena of stochasticity in biochemical processes have been intriguing life scientists for ... more The phenomena of stochasticity in biochemical processes have been intriguing life scientists for the past few decades. We now know that living cells take advantage of stochasticity in some cases and counteract stochastic effects in others. The source of intrinsic stochasticity in biomolecular systems are random timings of individual reactions, which cumulatively drive the variability in outputs of such systems. Despite the acknowledged relevance of stochasticity in the functioning of living cells no rigorous method have been proposed to precisely identify sources of variability. In this paper we propose a novel methodology that allows us to calculate contributions of individual reactions into the variability of a system's output. We demonstrate that some reactions have dramatically different effects on noise than others. Surprisingly, in the class of open conversion systems that serve as an approximate model of signal transduction, the degradation of an output contributes half o...

Dynamic Games and Applications, 2012

We construct a symmetric version of the ultimatum mini game and analyze the stability of its equi... more We construct a symmetric version of the ultimatum mini game and analyze the stability of its equilibria in the replicator dynamics. We show that the mere symmetry does not lead to a unique social norm consistent with the observed experimental results. Moreover, the average offer in the population has to be lower than 50 % in order to have one of the equilibria consistent with the experimental data.

Physical review. B, Condensed matter, Jan 15, 1989

Dynamic Games and Applications, 2012

We propose a dynamic three-strategy symmetric model of the Ultimatum Game with players using a sa... more We propose a dynamic three-strategy symmetric model of the Ultimatum Game with players using a sampling procedure. We allow an intermediate strategy, interpreted as a social norm, to evolve in time according to beliefs of players about an average offer. We show that a social norm converges to a self-consistent offer of about 15 % in the unique globally asymptotically stable equilibrium of our model.

Mathematica Applicanda, 2014

We discuss various models of ion transport through cell membrane channels.

Lecture Notes in Computer Science, 2011

We propose an algorithm for determining optimal transition paths between given configurations of ... more We propose an algorithm for determining optimal transition paths between given configurations of systems consisting of many objects. It is based on the Principle of Least Action and variational equations for Freidlin-Wentzell action functionals in Gaussian networks set-up. We use our method to construct a system controlling motion and redeployment between unit's formations. Another application of the algorithm allows a realistic transformation between two sequences of character animations in a virtual environment. The efficiency of the algorithm has been evaluated in a simple sandbox environment implemented with the use of the NVIDIA CUDA technology.

Dynamic Games and Applications, 2014

We discuss combined effects of stochasticity and time delays in finite-population three-player ga... more We discuss combined effects of stochasticity and time delays in finite-population three-player games with two mixed Nash equilibria and a pure one. We show that if basins of attraction of the stable interior equilibrium and the stable pure one are equal, then an arbitrary small time delay makes the pure one stochastically stable. Moreover, if the basin of attraction of the interior equilibrium is bigger than the one of the pure equilibrium, then there exists a critical time delay where the pure equilibrium becomes stochastically stable.

Dynamic Games and Applications, 2011

We discuss combined effects of stochasticity and time delays in simple evolutionary games with a ... more We discuss combined effects of stochasticity and time delays in simple evolutionary games with a unique mixed evolutionarily stable strategy. We present three models of time-delay stochastic dynamics of finite well-mixed or random-matching populations. We show that in the first two models the evolutionarily stable strategy loses its stability and there appears a stable cycle around it with the time period and the amplitude proportional to the delay. In the third model, only one randomly chosen individual can update his strategy at a time. This slows down the dynamics and makes the evolutionarily stable strategy stable with respect to both time delay and stochastic perturbations.

We introduce quasilattice-gas models in which every vertex of certain two-dimensional grids can b... more We introduce quasilattice-gas models in which every vertex of certain two-dimensional grids can be occupied by one of two different types of particles interacting through Lennard-Jones potentials. Such grids are quasiperiodic analogs of regular lattices present in periodic systems. To find ground-state configurations of our models, we performed Monte Carlo simulations and obtained structures with local five-fold symmetries and five-fold diffraction patterns.

Physics Letters A, 1986

We show that a typical toy model of an ordered quasicrystalline alloy has a range of stoichiometr... more We show that a typical toy model of an ordered quasicrystalline alloy has a range of stoichiometries.

Modern Physics Letters B, 1987

ABSTRACT

We introduce quasilattice-gas models in which every vertex of certain two-dimensional grids can b... more We introduce quasilattice-gas models in which every vertex of certain two-dimensional grids can be occupied by one of two different types of particles interacting through Lennard-Jones potentials. Such grids are quasiperiodic analogs of regular lattices present in periodic systems. To find ground-state configurations of our models, we performed Monte Carlo simulations and obtained structures with local five-fold symmetries and five-fold diffraction patterns.

Lecture Notes in Computer Science, 2014

Lecture Notes in Computer Science, 2012

The goal of the ramified optimal transport is to find an optimal transport path between two given... more 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. The problem is well known to be NP-hard. We develop an algorithm for solving a ramified optimal transport problem within the framework of Bayesian networks. It is based on the decision strategy optimisation technique that utilises self-annealing ideas of Chen-style stochastic optimisation. Resulting transport paths are represented in the form of treeshaped structures. The effectiveness of the algorithm has been tested on computer-generated examples.

Lecture Notes in Computer Science, 2012

The problem of learning Bayesian network structure is well known to be NP-hard. It is therefore v... more The problem of learning Bayesian network structure is well known to be NP-hard. It is therefore very important to develop efficient approximation techniques. We introduce an algorithm that within the framework of influence diagrams translates the structure learning problem into the strategy optimisation problem, for which we apply the Chen's self-annealing stochastic optimisation algorithm. The effectiveness of our method has been tested on computer-generated examples.

Biophysical Journal

The phenomena of stochasticity in biochemical processes have been intriguing life scientists for ... more The phenomena of stochasticity in biochemical processes have been intriguing life scientists for the past few decades. We now know that living cells take advantage of stochasticity in some cases and counteract stochastic effects in others. The source of intrinsic stochasticity in biomolecular systems are random timings of individual reactions, which cumulatively drive the variability in outputs of such systems. Despite the acknowledged relevance of stochasticity in the functioning of living cells no rigorous method have been proposed to precisely identify sources of variability. In this paper we propose a novel methodology that allows us to calculate contributions of individual reactions into the variability of a system's output. We demonstrate that some reactions have dramatically different effects on noise than others. Surprisingly, in the class of open conversion systems that serve as an approximate model of signal transduction, the degradation of an output contributes half o...

Dynamic Games and Applications, 2012

We construct a symmetric version of the ultimatum mini game and analyze the stability of its equi... more We construct a symmetric version of the ultimatum mini game and analyze the stability of its equilibria in the replicator dynamics. We show that the mere symmetry does not lead to a unique social norm consistent with the observed experimental results. Moreover, the average offer in the population has to be lower than 50 % in order to have one of the equilibria consistent with the experimental data.

Physical review. B, Condensed matter, Jan 15, 1989

Dynamic Games and Applications, 2012

We propose a dynamic three-strategy symmetric model of the Ultimatum Game with players using a sa... more We propose a dynamic three-strategy symmetric model of the Ultimatum Game with players using a sampling procedure. We allow an intermediate strategy, interpreted as a social norm, to evolve in time according to beliefs of players about an average offer. We show that a social norm converges to a self-consistent offer of about 15 % in the unique globally asymptotically stable equilibrium of our model.

Mathematica Applicanda, 2014

We discuss various models of ion transport through cell membrane channels.

Lecture Notes in Computer Science, 2011

We propose an algorithm for determining optimal transition paths between given configurations of ... more We propose an algorithm for determining optimal transition paths between given configurations of systems consisting of many objects. It is based on the Principle of Least Action and variational equations for Freidlin-Wentzell action functionals in Gaussian networks set-up. We use our method to construct a system controlling motion and redeployment between unit's formations. Another application of the algorithm allows a realistic transformation between two sequences of character animations in a virtual environment. The efficiency of the algorithm has been evaluated in a simple sandbox environment implemented with the use of the NVIDIA CUDA technology.

Dynamic Games and Applications, 2014

We discuss combined effects of stochasticity and time delays in finite-population three-player ga... more We discuss combined effects of stochasticity and time delays in finite-population three-player games with two mixed Nash equilibria and a pure one. We show that if basins of attraction of the stable interior equilibrium and the stable pure one are equal, then an arbitrary small time delay makes the pure one stochastically stable. Moreover, if the basin of attraction of the interior equilibrium is bigger than the one of the pure equilibrium, then there exists a critical time delay where the pure equilibrium becomes stochastically stable.

Dynamic Games and Applications, 2011

We discuss combined effects of stochasticity and time delays in simple evolutionary games with a ... more We discuss combined effects of stochasticity and time delays in simple evolutionary games with a unique mixed evolutionarily stable strategy. We present three models of time-delay stochastic dynamics of finite well-mixed or random-matching populations. We show that in the first two models the evolutionarily stable strategy loses its stability and there appears a stable cycle around it with the time period and the amplitude proportional to the delay. In the third model, only one randomly chosen individual can update his strategy at a time. This slows down the dynamics and makes the evolutionarily stable strategy stable with respect to both time delay and stochastic perturbations.

We introduce quasilattice-gas models in which every vertex of certain two-dimensional grids can b... more We introduce quasilattice-gas models in which every vertex of certain two-dimensional grids can be occupied by one of two different types of particles interacting through Lennard-Jones potentials. Such grids are quasiperiodic analogs of regular lattices present in periodic systems. To find ground-state configurations of our models, we performed Monte Carlo simulations and obtained structures with local five-fold symmetries and five-fold diffraction patterns.

Physics Letters A, 1986

We show that a typical toy model of an ordered quasicrystalline alloy has a range of stoichiometr... more We show that a typical toy model of an ordered quasicrystalline alloy has a range of stoichiometries.

Modern Physics Letters B, 1987

ABSTRACT