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Pol Przegl Chir 2020 Jul;93(1):1-5

Department of Vascular Surgery, Multidisciplinary Hospital of SPZOZ in Nowa Sol.

In the current case report we present a novel case of a successful coil embolization of the left internal carotid artery aneurysm. The patient presented with neck pain and a palpable pulsating tumor and was admitted to the vascular surgery clinic where an angio-CT scan of the neck was performed. Angio-CT revealed a left internal carotid artery aneurysm with a narrow neck. The patient was admitted to the department of vascular surgery where she was enrolled into endovascular coil embolization. After the procedure, control angiography showed complete embolization of the aneurysm. Three months following the procedure, doppler ultrasonography of the carotid arteries showed no demonstrable flow into the aneurysm. Six months following the procedure, angio-CT confirmed complete aneurysm thrombosis. Based on this case, endovascular coil embolization of the carotid artery aneurysms is a safe and effective method of treatment.

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http://dx.doi.org/10.5604/01.3001.0014.3019 | DOI Listing |

July 2020

Entropy (Basel) 2021 Feb 28;23(3). Epub 2021 Feb 28.

Faculty of Physics, Adam Mickiewicz University in Poznań, 61-614 Poznań, Poland.

As an integral part of our culture and way of life, language is intricately related to the migrations of people. To understand whether and how migration shapes language formation processes, we examine the dynamics of the naming game with migrating agents. (i) When all agents may migrate, the dynamics generates effective surface tension that drives the coarsening. Such behaviour is very robust and appears for a wide range of densities of agents and their migration rates. (ii) However, when only multilingual agents are allowed to migrate, monolingual islands are typically formed. In such a case, when the migration rate is sufficiently large, the majority of agents acquire a common language that spontaneously emerges with no indication of surface-tension-driven coarsening. Relatively slow coarsening that takes place in a dense static population is very fragile, and an arbitrarily small migration rate can most likely divert the system towards the quick formation of monolingual islands. Our work shows that migration influences language formation processes, but additional details such as density or mobility of agents are needed to more precisely specify this influence.

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http://dx.doi.org/10.3390/e23030299 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC8001451 | PMC |

February 2021

Braz J Cardiovasc Surg 2020 12 1;35(6):859-868. Epub 2020 Dec 1.

Department of Cardiac Surgery, Medinet Heart Center Ltd, Nowa Sol, Poland.

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http://dx.doi.org/10.21470/1678-9741-2020-0313 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7731840 | PMC |

December 2020

Entropy (Basel) 2020 Nov 19;22(11). Epub 2020 Nov 19.

Faculty of Modern Languages and Literature, Adam Mickiewicz University in Poznań, 61-874 Poznań, Poland.

Using simulated annealing, we examine a bipartitioning of small worlds obtained by adding a fraction of randomly chosen links to a one-dimensional chain or a square lattice. Models defined on small worlds typically exhibit a mean-field behavior, regardless of the underlying lattice. Our work demonstrates that the bipartitioning of small worlds does depend on the underlying lattice. Simulations show that for one-dimensional small worlds, optimal partitions are finite size clusters for any fraction of additional links. In the two-dimensional case, we observe two regimes: when the fraction of additional links is sufficiently small, the optimal partitions have a stripe-like shape, which is lost for a larger number of additional links as optimal partitions become disordered. Some arguments, which interpret additional links as thermal excitations and refer to the thermodynamics of Ising models, suggest a qualitative explanation of such a behavior. The histogram of overlaps suggests that a replica symmetry is broken in a one-dimensional small world. In the two-dimensional case, the replica symmetry seems to hold, but with some additional degeneracy of stripe-like partitions.

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http://dx.doi.org/10.3390/e22111319 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC7712369 | PMC |

November 2020

Phys Rev E 2019 Jun;99(6-1):062129

Faculty of Modern Languages and Literature, Adam Mickiewicz University, Poznań 61-874, Poland.

We examine a two-dimensional nonequilibrium lattice model where particles adsorb at empty sites and desorb when the number of neighboring particles is greater than a given threshold. In a certain range of parameters the model exhibits entropic ordering similar to some hard-core systems. However, contrary to hard-core systems, on increasing the density of particles the ordering is destroyed. In the heterogenous version of our model, a regime with slow dynamics appears that might indicate formation of some kind of glassy structures.

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http://dx.doi.org/10.1103/PhysRevE.99.062129 | DOI Listing |

June 2019

PLoS One 2018 29;13(11):e0208095. Epub 2018 Nov 29.

Faculty of Physics, Adam Mickiewicz University, Poznań, Poland.

Recently, emergence of signaling conventions, among which language is a prime example, draws a considerable interdisciplinary interest ranging from game theory, to robotics to evolutionary linguistics. Such a wide spectrum of research is based on much different assumptions and methodologies, but complexity of the problem precludes formulation of a unifying and commonly accepted explanation. We examine formation of signaling conventions in a framework of a multi-agent reinforcement learning model. When the network of interactions between agents is a complete graph or a sufficiently dense random graph, a global consensus is typically reached with the emerging language being a nearly unique object-word mapping or containing some synonyms and homonyms. On finite-dimensional lattices, the model gets trapped in disordered configurations with a local consensus only. Such a trapping can be avoided by introducing a population renewal, which in the presence of superlinear reinforcement restores an ordinary surface-tension driven coarsening and considerably enhances formation of efficient signaling.

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http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0208095 | PLOS |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC6264146 | PMC |

April 2019

Phys Rev E 2017 Sep 29;96(3-1):032145. Epub 2017 Sep 29.

Departamento de Física, I3N, Universidade de Aveiro, 3810-193 Aveiro, Portugal.

We examine an opinion formation model, which is a mixture of Voter and Ising agents. Numerical simulations show that even a very small fraction (∼1%) of the Ising agents drastically changes the behavior of the Voter model. The Voter agents act as a medium, which correlates sparsely dispersed Ising agents, and the resulting ferromagnetic ordering persists up to a certain temperature. Upon addition of the Ising agents, a logarithmically slow coarsening of the Voter model (d=2), or its active steady state (d=3), change into an Ising-type power-law coarsening.

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http://dx.doi.org/10.1103/PhysRevE.96.032145 | DOI Listing |

September 2017

Phys Rev E 2017 May 11;95(5-1):052308. Epub 2017 May 11.

Faculty of Physics, Adam Mickiewicz University, Poznań, Poland.

Influencing various aspects of human activity, migration is associated also with language formation. To examine the mutual interaction of these processes, we study a Naming Game with migrating agents. The dynamics of the model leads to formation of low-mobility clusters, which turns out to break the symmetry of the model: although the Naming Game remains symmetric, low-mobility languages are favored. High-mobility languages are gradually eliminated from the system, and the dynamics of language formation considerably slows down. Our model is too simple to explain in detail language competition of migrating human communities, but it certainly shows that languages of settlers are favored over nomadic ones.

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http://dx.doi.org/10.1103/PhysRevE.95.052308 | DOI Listing |

May 2017

Phys Rev E Stat Nonlin Soft Matter Phys 2015 Nov 23;92(5):052811. Epub 2015 Nov 23.

Faculty of Physics, Adam Mickiewicz University, Poznań, Poland.

We examine Ising models with heat-bath dynamics on directed networks. Our simulations show that Ising models on directed triangular and simple cubic lattices undergo a phase transition that most likely belongs to the Ising universality class. On the directed square lattice the model remains paramagnetic at any positive temperature as already reported in some previous studies. We also examine random directed graphs and show that contrary to undirected ones, percolation of directed bonds does not guarantee ferromagnetic ordering. Only above a certain threshold can a random directed graph support finite-temperature ferromagnetic ordering. Such behavior is found also for out-homogeneous random graphs, but in this case the analysis of magnetic and percolative properties can be done exactly. Directed random graphs also differ from undirected ones with respect to zero-temperature freezing. Only at low connectivity do they remain trapped in a disordered configuration. Above a certain threshold, however, the zero-temperature dynamics quickly drives the model toward a broken symmetry (magnetized) state. Only above this threshold, which is almost twice as large as the percolation threshold, do we expect the Ising model to have a positive critical temperature. With a very good accuracy, the behavior on directed random graphs is reproduced within a certain approximate scheme.

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http://dx.doi.org/10.1103/PhysRevE.92.052811 | DOI Listing |

November 2015

Phys Rev E Stat Nonlin Soft Matter Phys 2015 Jun 2;91(6):062801. Epub 2015 Jun 2.

Faculty of Modern Languages and Literature, Adam Mickiewicz University, Poznań, Poland.

We show that preferential rewiring, which is supposed to mimic the behavior of financial agents, changes a directed-network Ising ferromagnet with a single critical point into a model with robust critical behavior. For the nonrewired random graph version, due to a constant number of out-links for each site, we write a simple mean-field-like equation describing the behavior of magnetization; we argue that it is exact and support the claim with extensive Monte Carlo simulations. For the rewired version, this equation is obeyed only at low temperatures. At higher temperatures, rewiring leads to strong heterogeneities, which apparently invalidates mean-field arguments and induces large fluctuations and divergent susceptibility. Such behavior is traced back to the formation of a relatively small core of agents that influence the entire system.

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http://dx.doi.org/10.1103/PhysRevE.91.062801 | DOI Listing |

June 2015

Phys Rev E Stat Nonlin Soft Matter Phys 2014 Sep 29;90(3):032817. Epub 2014 Sep 29.

Department of Physics and I3N, University of Aveiro, 3810-193 Aveiro, Portugal.

We examine a weighted-network multiagent model with preferential selection such that agents choose partners with probability p(w), where w is the number of their past selections. When p(w) increases sublinearly with the number of past selections [p(w)∼w(α),α<1], agents develop a uniform preference for all other agents. At α=1, this state loses stability and more complex structures form. For a superlinear increase (α>1), strong heterogeneities emerge and agents make selections mainly within small and sometimes asymmetric clusters. Even in a few-agent case, the formation of such clusters resembles phase transitions with spontaneous symmetry breaking.

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http://dx.doi.org/10.1103/PhysRevE.90.032817 | DOI Listing |

September 2014

Phys Rev E Stat Nonlin Soft Matter Phys 2014 Sep 25;90(3):032815. Epub 2014 Sep 25.

Faculty of Modern Languages and Literature, Adam Mickiewicz University, 61-614 Poznań, Poland.

We examine a community structure in random graphs of size n and link probability p/n determined with the Newman greedy optimization of modularity. Calculations show that for p<1 communities are nearly identical with clusters. For p=1 the average sizes of a community s(av) and of the giant community s(g) show a power-law increase s(av)∼n(α') and s(g)∼n(α). From numerical results we estimate α'≈0.26(1) and α≈0.50(1) and using the probability distribution of sizes of communities we suggest that α'=α/2 should hold. For p>1 the community structure remains critical: (i) s(av) and s(g) have a power-law increase with α'≈α<1 and (ii) the probability distribution of sizes of communities is very broad and nearly flat for all sizes up to s(g). For large p the modularity Q decays as Q∼p(-0.55), which is intermediate between some previous estimations. To check the validity of the results, we also determine the community structure using another method, namely, a nongreedy optimization of modularity. Tests with some benchmark networks show that the method outperforms the greedy version. For random graphs, however, the characteristics of the community structure determined using both greedy and nongreedy optimizations are, within small statistical fluctuations, the same.

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http://dx.doi.org/10.1103/PhysRevE.90.032815 | DOI Listing |

September 2014

Phys Rev E Stat Nonlin Soft Matter Phys 2012 Nov 26;86(5 Pt 1):051129. Epub 2012 Nov 26.

Faculty of Physics, Adam Mickiewicz University, 61-614 Poznań, Poland.

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. Although 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.

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http://dx.doi.org/10.1103/PhysRevE.86.051129 | DOI Listing |

November 2012

Phys Rev E Stat Nonlin Soft Matter Phys 2012 Oct 22;86(4 Pt 1):041138. Epub 2012 Oct 22.

Faculty of Physics, Adam Mickiewicz University, Poznań, Poland.

We examine the critical behavior of a lattice model of tumor growth where supplied nutrients are correlated with the distribution of tumor cells. Our results support the previous report [Ferreira et al., Phys. Rev. E 85, 010901(R) (2012)], which suggested that the critical behavior of the model differs from the expected directed percolation (DP) universality class. Surprisingly, only some of the critical exponents (β, α, ν([perpendicular]), and z) take non-DP values while some others (β', ν(||), and spreading-dynamics exponents Θ, δ, z') remain very close to their DP counterparts. The obtained exponents satisfy the scaling relations β=αν(||), β'=δν(||), and the generalized hyperscaling relation Θ+α+δ=d/z, where the dynamical exponent z is, however, used instead of the spreading exponent z'. Both in d=1 and d=2 versions of our model, the exponent β most likely takes the mean-field value β=1, and we speculate that it might be due to the roulette-wheel selection, which is used to choose the site to supply a nutrient.

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http://dx.doi.org/10.1103/PhysRevE.86.041138 | DOI Listing |

October 2012

Artif Life 2012 4;18(3):311-23. Epub 2012 Jun 4.

Adam Mickiewicz University, Poznan, Poland.

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 essentially 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 important 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 present. A comparison of distribution of languages in our model and in the human population is discussed.

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http://dx.doi.org/10.1162/artl_a_00067 | DOI Listing |

September 2012

Phys Rev E Stat Nonlin Soft Matter Phys 2012 Jan 10;85(1 Pt 1):010901. Epub 2012 Jan 10.

Departamento de Fisica and I3N, Universidade de Aveiro, 3810-193 Aveiro, Portugal.

We examine a lattice model of tumor growth where the 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 the distribution of tumor cells, which as we suggest might mimic the angiogenic growth, the extinction shows different critical behavior. Such a correlation affects also the morphology of the growing tumors and drastically raises tumor-survival probability.

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http://dx.doi.org/10.1103/PhysRevE.85.010901 | DOI Listing |

January 2012

Phys Rev E Stat Nonlin Soft Matter Phys 2011 Jun 13;83(6 Pt 1):061115. Epub 2011 Jun 13.

Faculty of Physics, Adam Mickiewicz University, Poznań, Poland.

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 (r(2)) 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 Lévy flights. Our results suggest that broad and Lévy-like distributions in such systems might appear due to dimension-dependent properties of a search space.

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http://dx.doi.org/10.1103/PhysRevE.83.061115 | DOI Listing |

June 2011

Phys Rev E Stat Nonlin Soft Matter Phys 2011 Mar 7;83(3 Pt 1):031904. Epub 2011 Mar 7.

Faculty of Physics, Adam Mickiewicz University, PL-61-614 Poznań, Poland.

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 different morphologies are presented. In the d = 1 and d = 2 models, we analyze 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 that differ from 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 behavior occurs in the present model but only for d ≳ 2. For d ≥ 2, a steady state depends on the initial configuration in some cases.

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http://dx.doi.org/10.1103/PhysRevE.83.031904 | DOI Listing |

March 2011

Phys Rev E Stat Nonlin Soft Matter Phys 2009 Nov 19;80(5 Pt 2):056107. Epub 2009 Nov 19.

Faculty of Physics, Adam Mickiewicz University, 61-614 Poznań, Poland.

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.

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http://dx.doi.org/10.1103/PhysRevE.80.056107 | DOI Listing |

November 2009

Phys Rev E Stat Nonlin Soft Matter Phys 2009 Jun 17;79(6 Pt 1):060102. Epub 2009 Jun 17.

Faculty of Physics, Adam Mickiewicz University, 61-614 Poznań, Poland.

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=qc. 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).

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http://dx.doi.org/10.1103/PhysRevE.79.060102 | DOI Listing |

June 2009

Phys Rev E Stat Nonlin Soft Matter Phys 2007 May 31;75(5 Pt 1):052201. Epub 2007 May 31.

Faculty of Physics, Adam Mickiewicz University, Poznań, Poland.

Using molecular dynamics we study heat conduction and diffusion of hard disks in one-dimensional narrow channels. When collisions preserve momentum the heat conduction kappa diverges with the number of disks N as kappa approximately N alpha (alpha approximately 1/3) . Such a behavior 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 behavior 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, kappa remains finite and sound-wave effects are absent.

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http://dx.doi.org/10.1103/PhysRevE.75.052201 | DOI Listing |

May 2007

Theory Biosci 2006 Aug 20;125(1):67-77. Epub 2006 Mar 20.

Faculty of Physics, Department of Physics, Adam Mickiewicz University, 61-614 Poznań, Poland.

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.

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http://dx.doi.org/10.1016/j.thbio.2006.01.001 | DOI Listing |

August 2006

Phys Rev E Stat Nonlin Soft Matter Phys 2006 Mar 31;73(3 Pt 1):032102. Epub 2006 Mar 31.

Faculty of Physics, Adam Mickiewicz University, 61-614 Poznań, Poland.

Using event-driven molecular dynamics we study one- and two-dimensional ballistic annihilation. We estimate exponents xi and gamma, which describe the long-time decay of the number of particles [n(t) approximately t-xi] and of their typical velocity [v(t) approximately t-gamma]. To a good accuracy our results confirm the scaling relation xi+gamma=1. In the two-dimensional case our results are in good agreement with those obtained from Boltzmann kinetic theory.

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http://dx.doi.org/10.1103/PhysRevE.73.032102 | DOI Listing |

March 2006

Phys Rev E Stat Nonlin Soft Matter Phys 2005 Jun 10;71(6 Pt 2):067701. Epub 2005 Jun 10.

Faculty of Physics, Adam Mickiewicz University, 61-614 Poznań, Poland.

We study a traveling 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 behavior of L and C, in efficiency of SA, and in the shape of minimal paths.

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http://dx.doi.org/10.1103/PhysRevE.71.067701 | DOI Listing |

June 2005

Phys Rev E Stat Nonlin Soft Matter Phys 2005 May 20;71(5 Pt 1):052902. Epub 2005 May 20.

Faculty of Physics, Adam Mickiewicz University, 61-614 Pozńan, Poland.

We study a lattice model of a multispecies prey-predator system. Numerical results show that for a small mutation rate the model develops irregular long-period oscillatory behavior with sizeable changes in a number of species. The periodicity of extinctions on Earth was suggested by Raup and Sepkoski [Proc. Natl. Acad. Sci. 81, 801 (1984)], but thus far is lacking a satisfactory explanation. Our model indicates that this might be a natural consequence of the ecosystem dynamics and not the result of any extraterrestrial cause.

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http://dx.doi.org/10.1103/PhysRevE.71.052902 | DOI Listing |

May 2005

Phys Rev E Stat Nonlin Soft Matter Phys 2003 Nov 24;68(5 Pt 2):056119. Epub 2003 Nov 24.

Department of Physics, University of Geneva, CH 1211 Geneva 4, Switzerland.

We study a solid-on-solid (SOS) model whose dynamics is inspired by recent studies of the synchronization transition in coupled map lattices (CML). The synchronization of CML is thus related with a depinning of interface from a binding wall. Critical behavior of our SOS model depends on a specific form of binding (i.e., transition rates of the dynamics). For an exponentially decaying binding the depinning belongs to the directed percolation universality class. Other types of depinning, including the one with a line of critical points, are observed for a power-law binding.

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http://dx.doi.org/10.1103/PhysRevE.68.056119 | DOI Listing |

November 2003

Phys Rev E Stat Nonlin Soft Matter Phys 2003 May 13;67(5 Pt 2):056204. Epub 2003 May 13.

Department of Physics, University of Geneva, CH 1211 Geneva 4, Switzerland.

We use spreading dynamics to study the synchronization transition (ST) of one-dimensional coupled map lattices (CML's). Recently, Baroni et al. [Phys. Rev. E 63, 036226 (2001)] have shown that the ST belongs to the directed percolation (DP) universality class for discontinuous CML's. This was confirmed by accurate numerical simulations for the Bernoulli map by Ahlers and Pikovsky [Phys. Rev. Lett. 88, 254101 (2002)]. Spreading dynamics confirms such an identification only for random synchronized states. For homogeneous synchronized states the spreading exponents eta and delta are different from the DP exponents but their sum equals the corresponding sum of the DP exponents. Such a relation is typical of models with infinitely many absorbing states. Moreover, we calculate the spreading exponents for the tent map for which the ST belongs to the bounded Kardar-Parisi-Zhang (BKPZ) universality class. The estimation of spreading exponents for random synchronized states is consistent with the hyperscaling relation, while it is inconsistent for the homogeneous ones. Finally, we examine the asymmetric tent map. For small asymmetry the ST remains of the BKPZ type. However, for large asymmetry a different critical behavior appears, with exponents being relatively close to those for DP.

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http://dx.doi.org/10.1103/PhysRevE.67.056204 | DOI Listing |

May 2003

Phys Rev E Stat Nonlin Soft Matter Phys 2003 May 13;67(5 Pt 2):056108. Epub 2003 May 13.

Department of Physics, University of Geneva, CH 1211 Geneva 4, Switzerland.

Recently some two-dimensional models with double symmetric absorbing states were shown to share the same critical behavior that was called the voter universality class. We show that, for an absorbing-states Potts model with finite but further than nearest-neighbor range of interactions, the critical point is split into two critical points: one of the Ising type and the other of the directed percolation universality class. Similar splitting takes place in the three-dimensional nearest-neighbor model.

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http://dx.doi.org/10.1103/PhysRevE.67.056108 | DOI Listing |

May 2003

Phys Rev E Stat Nonlin Soft Matter Phys 2002 Dec 9;66(6 Pt 2):066107. Epub 2002 Dec 9.

Department of Physics, A. Mickiewicz University, 61-614 Poznań, Poland.

Using Monte Carlo simulations we study two-dimensional prey-predator systems. Measuring the variance of densities of prey and predators on the triangular lattice and on the lattice with eight neighbors, we conclude that temporal oscillations of these densities vanish in the thermodynamic limit. This result suggests that such oscillations do not exist in two-dimensional models, at least when driven by local dynamics. Depending on the control parameter, the model could be either in an active or in an absorbing phase, which are separated by the critical point. The critical behavior of this model is studied using the dynamical Monte Carlo method. This model has two dynamically nonsymmetric absorbing states. In principle both absorbing states can be used for the analysis of the critical point. However, dynamical simulations which start from the unstable absorbing state suffer from metastablelike effects, which sometimes renders the method inefficient.

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http://dx.doi.org/10.1103/PhysRevE.66.066107 | DOI Listing |

December 2002

Phys Rev E Stat Nonlin Soft Matter Phys 2002 Dec 18;66(6 Pt 1):062301. Epub 2002 Dec 18.

Department of Physics, University of Geneva, CH 1211 Geneva 4, Switzerland.

The problem of the steady-state velocity distribution in a driven inelastic Maxwell model of shaken granular material is revisited. Numerical solution of the master equation and analytical arguments show that the model has bilateral exponential velocity tails [P(v) approximately e(-|v|/sqrt[D])], where D is the amplitude of the noise. Previous study of this model predicted Gaussian tails [P(v) approximately e(-av(2))].

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http://dx.doi.org/10.1103/PhysRevE.66.062301 | DOI Listing |

December 2002

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