Andrzej Pekalski networks of scientific interests with internal degrees of freedom through self-citation analysis

Old and recent theoretical works by Andrzej Pekalski (APE) are recalled as possible sources of interest for describing network formation and clustering in complex (scientific) communities, through self-organisation and percolation processes. Emphasis is placed on APE self-citation network over four decades. The method is that used for detecting scientists field mobility by focusing on author's self-citation, co-authorships and article topics networks as in [1,2]. It is shown that APE's self-citation patterns reveal important information on APE interest for research topics over time as well as APE engagement on different scientific topics and in different networks of collaboration. Its interesting complexity results from "degrees of freedom" and external fields leading to so called internal shock resistance. It is found that APE network of scientific interests belongs to independent clusters and occurs through rare or drastic events as in irreversible "preferential attachment processes", similar to those found in usual mechanics and thermodynamics phase transitions.Comment: 7 pages, 1 table, 44 references, submitted to Int J Mod Phys

Evolution of economic entities under heterogeneous political/environmental conditions within a Bak-Sneppen-like dynamics

A model for economic behavior, under heterogeneous spatial economic conditions is developed. The role of selection pressure in a Bak-Sneppen-like dynamics with entity diffusion on a lattice is studied by Monte-Carlo simulation taking into account business rule(s), like enterprise - enterprise short range location "interaction"(s), business plan(s) through spin-offs or merging and enterprise survival evolution law(s). It is numerically found that the model leads to a sort of phase transition for the fitness gap as a function of the selection pressure.Comment: 6 figures. to be published in Physica

Simple Model for the Dynamics of Correlations in the Evolution of Economic Entities Under Varying Economic Conditions

From some observations on economic behaviors, in particular changing economic conditions with time and space, we develop a very simple model for the evolution of economic entities within a geographical type of framework. We raise a few questions and attempt to investigate whether some of them can be tackled by our model. Several cases of interest are reported. It is found that the model even in its simple forms can lead to a large variety of situations, including: delocalization and cycles, but also pre-chaotic behavior.Comment: Presented at Bali IEC02 symposium, Aug. 2002; submitted to Physica A ; 8 pages, 5 figure

Monte Carlo simulations of the inside-intron recombination

Biological genomes are divided into coding and non-coding regions. Introns are non-coding parts within genes, while the remaining non-coding parts are intergenic sequences. To study the evolutionary significance of recombination inside introns we have used two models based on the Monte Carlo method. In our computer simulations we have implemented the internal structure of genes by declaring the probability of recombination between exons. One situation when inside-intron recombination is advantageous is recovering functional genes by combining proper exons dispersed in the genetic pool of the population after a long period without selection for the function of the gene. Populations have to pass through the bottleneck, then. These events are rather rare and we have expected that there should be other phenomena giving profits from the inside-intron recombination. In fact we have found that inside-intron recombination is advantageous only in the case when after recombination, besides the recombinant forms, parental haplotypes are available and selection is set already on gametes.Comment: 12 pages inc. 5 Figs., for Int. J. Mod. Phys. C 17, issue 4 (2006

Ferromagnetic Phase Transition in Barabasi-Albert Networks

Ising spins put onto a Barabasi-Albert scale-free network show an effective phase transition from ferromagnetism to paramagnetism upon heating, with an effective critical temperature increasing as the logarithm of the system size. Starting with all spins up and upon equilibration pinning the few most-connected spins down nucleates the phase with most of the spins down.Comment: 8 pages including figure

Comment on "Ising model on a small world network"

In the recent study of the Ising model on a small-world network by A. P\c{e}kalski [Phys. Rev. E {\bf 64}, 057104 (2001)], a surprisingly small value of the critical exponent $\beta \approx 0.0001$ has been obtained for the temperature dependence of the magnetization. We perform extensive Monte Carlo simulations of the same model and conclude, via the standard finite-size scaling of various quantities,that the phase transition in the model is of the mean-field nature, in contrast to the work by A. P\c{e}kalski but in accord with other existing studies.Comment: to be published in PR

The Role of Dominant Mutations in the Population Expansion

Abstract. We have studied the dynamics of expansion of diploid, sexually reproducing populations onto new territories demanding different genetic adaptations. Populations succeeded in the new habitats if the mutations of alleles responsible for adaptation to the new conditions were recessive. If behind the hostile territory another friendly habitat exists, several different scenarios are possible, including one in which the middle, most hostile, habitat remains empty, separating populated two, more friendly, ones

Bistability in a self-assembling system confined by elastic walls: Exact results in a one-dimensional lattice model

© 2015 AIP Publishing LLC. The impact of confinement on self-assembly of particles interacting with short-range attraction and long-range repulsion potential is studied for thermodynamic states corresponding to local ordering of clusters or layers in the bulk. Exact and asymptotic expressions for the local density and for the effective potential between the confining surfaces are obtained for a one-dimensional lattice model introduced by J. Pękalski et al. [J. Chem. Phys. 138, 144903 (2013)]. The simple asymptotic formulas are shown to be in good quantitative agreement with exact results for slits containing at least 5 layers. We observe that the incommensurability of the system size and the average distance between the clusters or layers in the bulk leads to structural deformations that are different for different values of the chemical potential μ. The change of the type of defects is reflected in the dependence of density on μ that has a shape characteristic for phase transitions. Our results may help to avoid misinterpretation of the change of the type of defects as a phase transition in simulations of inhomogeneous systems. Finally, we show that a system confined by soft elastic walls may exhibit bistability such that two system sizes that differ approximately by the average distance between the clusters or layers are almost equally probable. This may happen when the equilibrium separation between the soft boundaries of an empty slit corresponds to the largest stress in the confined self-assembling system.Peer Reviewe