arXiv subjects

Adam Lipowski

Publications and source records attributed to Adam Lipowski.

At least 37 records · Page 2Linked to original sources

arXiv2012

Stretched exponentials and tensionless glass in the plaquette Ising model

Using Monte Carlo simulations we show that the autocorrelation function $C(t)$ in the d=3 Ising model with a plaquette interaction has a stretched-exponential decay in a supercooled liquid phase. Such a decay characterizes also some ground-state probability distributions obtained from the numerically exact counting of up to 10^450 configurations. A related model with a strongly degenerate ground state but lacking glassy features does not exhibit such a decay. Althoug the stretched exponential decay of C(t) in the three-dimensional supercooled liquid is inconsistent with the droplet model, its modification that considers tensionless droplets might explain such a decay. An indication that tensionless droplets might play some role comes from the analysis of low-temperature domains that compose the glassy state. It shows that the energy of a domain of size l scales as l^1.15, hence these domains are indeed tensionless .

cond-mat.stat-mech↗

arXiv2012

Naming Game on Adaptive Weighted Networks

We examine a naming game on an adaptive weighted network. A weight of connection for a given pair of agents depends on their communication success rate and determines the probability with which the agents communicate. In some cases, depending on the parameters of the model, the preference toward successfully communicating agents is basically negligible and the model behaves similarly to the naming game on a complete graph. In particular, it quickly reaches a single-language state, albeit some details of the dynamics are different from the complete-graph version. In some other cases, the preference toward successfully communicating agents becomes much more relevant and the model gets trapped in a multi-language regime. In this case gradual coarsening and extinction of languages lead to the emergence of a dominant language, albeit with some other languages still being present. A comparison of distribution of languages in our model and in the human population is discussed.

cond-mat.stat-mech↗

arXiv2012

Statistical mechanics model of angiogenic tumor growth

We examine a lattice model of tumor growth where survival of tumor cells depends on the supplied nutrients. When such a supply is random, the extinction of tumors belongs to the directed percolation universality class. However, when the supply is correlated with distribution of tumor cells, which as we suggest might mimick the angiogenic growth, the extinction shows different, and most likely novel critical behaviour. Such a correlation affects also the morphology of the growing tumors and drastically raise tumor survival probability.

cond-mat.stat-mech↗

arXiv2011

Roulette-wheel selection via stochastic acceptance

Roulette-wheel selection is a frequently used method in genetic and evolutionary algorithms or in modeling of complex networks. Existing routines select one of N individuals using search algorithms of O(N) or O(log(N)) complexity. We present a simple roulette-wheel selection algorithm, which typically has O(1) complexity and is based on stochastic acceptance instead of searching. We also discuss a hybrid version, which might be suitable for highly heterogeneous weight distributions, found, for example, in some models of complex networks. With minor modifications, the algorithm might also be used for sampling with fitness cut-off at a certain value or for sampling without replacement.

cs.NE↗

arXiv2011

Diffusive behavior of a greedy traveling salesman

Using Monte Carlo simulations we examine the diffusive properties of the greedy algorithm in the d-dimensional traveling salesman problem. Our results show that for d=3 and 4 the average squared distance from the origin is proportional to the number of steps t. In the d=2 case such a scaling is modified with some logarithmic corrections, which might suggest that d=2 is the critical dimension of the problem. The distribution of lengths also shows marked differences between d=2 and d>2 versions. A simple strategy adopted by the salesman might resemble strategies chosen by some foraging and hunting animals, for which anomalous diffusive behavior has recently been reported and interpreted in terms of Levy flights. Our results suggest that broad and Levy-like distributions in such systems might appear due to dimension-dependent properties of a search space.

cond-mat.stat-mech↗

arXiv2011

Coexistence and critical behaviour in a lattice model of competing species

In the present paper we study a lattice model of two species competing for the same resources. Monte Carlo simulations for d=1, 2, and 3 show that when resources are easily available both species coexist. However, when the supply of resources is on an intermediate level, the species with slower metabolism becomes extinct. On the other hand, when resources are scarce it is the species with faster metabolism that becomes extinct. The range of coexistence of the two species increases with dimension. We suggest that our model might describe some aspects of the competition between normal and tumor cells. With such an interpretation, examples of tumor remission, recurrence and of different morphologies are presented. In the d=1 and d=2 models, we analyse the nature of phase transitions: they are either discontinuous or belong to the directed-percolation universality class, and in some cases they have an active subcritical phase. In the d=2 case, one of the transitions seems to be characterized by critical exponents different than directed-percolation ones, but this transition could be also weakly discontinuous. In the d=3 version, Monte Carlo simulations are in a good agreement with the solution of the mean-field approximation. This approximation predicts that oscillatory behaviour occurs in the present model, but only for d>2. For d>=2, a steady state depends on the initial configuration in some cases.

q-bio.PE↗

arXiv2010

Computational approach to the emergence and evolution of language - evolutionary naming game model

Computational modelling with multi-agent systems is becoming an important technique of studying language evolution. We present a brief introduction into this rapidly developing field, as well as our own contributions that include an analysis of the evolutionary naming-game model. In this model communicating agents, that try to establish a common vocabulary, are equipped with an evolutionarily selected learning ability. Such a coupling of biological and linguistic ingredients results in an abrupt transition: upon a small change of the model control parameter a poorly communicating group of linguistically unskilled agents transforms into almost perfectly communicating group with large learning abilities. Genetic imprinting of the learning abilities proceeds via Baldwin effect: initially unskilled communicating agents learn a language and that creates a niche in which there is an evolutionary pressure for the increase of learning ability. Under the assumption that communication intensity increases continuously with finite speed, the transition is split into several transition-like changes. It shows that the speed of cultural changes, that sets an additional characteristic timescale, might be yet another factor affecting the evolution of language. In our opinion, this model shows that linguistic and biological processes have a strong influence on each other and this effect certainly has contributed to an explosive development of our species.

physics.soc-ph↗

arXiv2010

The crystallization of hard disks induced by a temperature gradient

While uniform temperature has no effect on equilibrium properties of hard-core systems, its gradient might substantially change their behaviour. In particular, in hard-disk system subject to temperature difference $ΔT$ disks are repelled from the hot boundary of the system and accumulate at the cold one. Using event-driven molecular dynamics simulations we show that for sufficiently large $ΔT$ or coverage ratio $ρ^*$, crystal forms at the cold boundary. In this spatially inhomogeneous system a significant decrease of diffusivity of disks clearly marks the stationary interface between liquid and crystal. Such a behaviour is also supported through calculation of the radial distribution function and the bond order parameter. Simulations show that for this nonequilibrium system the equipartition of energy holds and velocity obeys the Boltzmann distribution.

cond-mat.stat-mech↗

arXiv2009

Language structure in the n-object naming game

We examine a naming game with two agents trying to establish a common vocabulary for n objects. Such efforts lead to the emergence of language that allows for an efficient communication and exhibits some degree of homonymy and synonymy. Although homonymy reduces the communication efficiency, it seems to be a dynamical trap that persists for a long, and perhaps indefinite, time. On the other hand, synonymy does not reduce the efficiency of communication, but appears to be only a transient feature of the language. Thus, in our model the role of synonymy decreases and in the long-time limit it becomes negligible. A similar rareness of synonymy is observed in present natural languages. The role of noise, that distorts the communicated words, is also examined. Although, in general, the noise reduces the communication efficiency, it also regroups the words so that they are more evenly distributed within the available "verbal" space.

cs.CL↗

arXiv2009

Slow dynamics in a driven two-lane particle system

We study a two-lane model of two-species of particles that perform biased diffusion. Extensive numerical simulations show that when bias q is strong enough oppositely drifting particles form some clusters that block each other. Coarsening of such clusters is very slow and their size increases logarithmically in time. For smaller q particles collapse essentially on a single cluster whose size seems to diverge at a certain value of q=q_c. Simulations show that despite slow coarsening, the model has rather large power-law cooling-rate effects. It makes its dynamics different from glassy systems, but similar to some three-dimensional Ising-type models (gonihedric models).

cond-mat.stat-mech↗

arXiv2008

Computational modelling of evolution: ecosystems and language

Recently, computational modelling became a very important research tool that enables us to study problems that for decades evaded scientific analysis. Evolutionary systems are certainly examples of such problems: they are composed of many units that might reproduce, diffuse, mutate, die, or in some cases for example communicate. These processes might be of some adaptive value, they influence each other and occur on various time scales. That is why such systems are so difficult to study. In this paper we briefly review some computational approaches, as well as our contributions, to the evolution of ecosystems and language. We start from Lotka-Volterra equations and the modelling of simple two-species prey-predator systems. Such systems are canonical example for studying oscillatory behaviour in competitive populations. Then we describe various approaches to study long-term evolution of multi-species ecosystems. We emphasize the need to use models that take into account both ecological and evolutionary processes. Finally, we address the problem of the emergence and development of language. It is becoming more and more evident that any theory of language origin and development must be consistent with darwinian principles of evolution. Consequently, a number of techniques developed for modelling evolution of complex ecosystems are being applied to the problem of language. We briefly review some of these approaches.

q-bio.PE↗

arXiv2008

Statistical-mechanics approach to a reinforcement learning model with memory

We introduce a two-player model of reinforcement learning with memory. Past actions of an iterated game are stored in a memory and used to determine player's next action. To examine the behaviour of the model some approximate methods are used and confronted against numerical simulations and exact master equation. When the length of memory of players increases to infinity the model undergoes an absorbing-state phase transition. Performance of examined strategies is checked in the prisoner' dilemma game. It turns out that it is advantageous to have a large memory in symmetric games, but it is better to have a short memory in asymmetric ones.

cond-mat.stat-mech↗

arXiv2007

Bio-linguistic transition and Baldwin effect in an evolutionary naming-game model

We examine an evolutionary naming-game model where communicating agents are equipped with an evolutionarily selected learning ability. Such a coupling of biological and linguistic ingredients results in an abrupt transition: upon a small change of a model control parameter a poorly communicating group of linguistically unskilled agents transforms into almost perfectly communicating group with large learning abilities. When learning ability is kept fixed, the transition appears to be continuous. Genetic imprinting of the learning abilities proceeds via Baldwin effect: initially unskilled communicating agents learn a language and that creates a niche in which there is an evolutionary pressure for the increase of learning ability.Our model suggests that when linguistic (or cultural) processes became intensive enough, a transition took place where both linguistic performance and biological endowment of our species experienced an abrupt change that perhaps triggered the rapid expansion of human civilization.

cs.CL↗

arXiv2007

Heat conduction and diffusion of hard disks in a narrow channel

Using molecular dynamics we study heat conduction and diffusion of hard disks in one dimensional narrow channels. When collisions preserve momentum the heat conduction $κ$ diverges with the number of disks $N$ as $κ\sim N^α$ $(α\approx 1/3)$. Such a behaviour is seen both when the ordering of disks is fixed ('pen-case' model), and when they can exchange their positions. Momentum conservation results also in sound-wave effects that enhance diffusive behaviour and on an intermediate time scale (that diverges in the thermodynamic limit) normal diffusion takes place even in the 'pen-case' model. When collisions do not preserve momentum, $κ$ remains finite and sound-wave effects are absent.

cond-mat.stat-mech↗

arXiv2006

Molecular dynamics simulations of ballistic annihilation

Using event-driven molecular dynamics we study one- and two-dimensional ballistic annihilation. We estimate exponents $ξ$ and $γ$ that describe the long-time decay of the number of particles ($n(t)\sim t^{-ξ}$) and of their typical velocity ($v(t)\sim t^{-γ}$). To a good accuracy our results confirm the scaling relation $ξ+ γ=1$. In the two-dimensional case our results are in a good agreement with those obtained from the Boltzmann kinetic theory.

cond-mat.stat-mech↗

arXiv2006

Long-term evolution of an ecosystem with spontaneous periodicity of mass extinctions

Twenty years ago, after analysing palaeontological data, Raup and Sepkoski suggested that mass extinctions on Earth appear cyclically in time with a period of approximately 26 million years (My). To explain the 26My period, a number of proposals were made involving, e.g., astronomical effects, increased volcanic activity, or the Earth's magnetic field reversal, none of which, however, has been confirmed. Here we study a spatially extended discrete model of an ecosystem and show that the periodicity of mass extinctions might be a natural feature of the ecosystem's dynamics and not the result of a periodic external perturbation. In our model, periodic changes of the diversity of an ecosystem and some of its other characteristics are induced by the coevolution of species. In agreement with some palaeontological data, our results show that the longevity of a species depends on the evolutionary stage at which the species is created. Possible further tests of our model are also discussed.

q-bio.PE↗

arXiv2005

Statistical Mechanics of Equilibrium and Nonequilibrium Phase Transitions: The Yang-Lee Formalism

Showing that the location of the zeros of the partition function can be used to study phase transitions, Yang and Lee initiated an ambitious and very fruitful approach. We give an overview of the results obtained using this approach. After an elementary introduction to the Yang-Lee formalism, we summarize results concerning equilibrium phase transitions. We also describe recent attempts and breakthroughs in extending this theory to nonequilibrium phase transitions.

cond-mat.stat-mech↗

arXiv2005

Travelling Salesman Problem with a Center

We study a travelling salesman problem where the path is optimized with a cost function that includes its length $L$ as well as a certain measure $C$ of its distance from the geometrical center of the graph. Using simulated annealing (SA) we show that such a problem has a transition point that separates two phases differing in the scaling behaviour of $L$ and $C$, in efficiency of SA, and in the shape of minimal paths.

cond-mat.stat-mech↗