Finite-size scaling considerations on the ground state microcanonical temperature in entropic sampling simulations

In this work we discuss the behavior of the microcanonical temperature $\frac{\partial S(E)}{\partial E}$ obtained by means of numerical entropic sampling studies. It is observed that in almost all cases the slope of the logarithm of the density of states $S(E)$ is not infinite in the ground state, since as expected it should be directly related to the inverse temperature $\frac{1}{T}$. Here we show that these finite slopes are in fact due to finite-size effects and we propose an analytic expression $a\ln(bL)$ for the behavior of $\frac{\varDelta S}{\varDelta E}$ when $L\rightarrow\infty$. To test this idea we use three distinct two-dimensional square lattice models presenting second-order phase transitions. We calculated by exact means the parameters $a$ and $b$ for the two-states Ising model and for the $q=3$ and $4$ states Potts model and compared with the results obtained by entropic sampling simulations. We found an excellent agreement between exact and numerical values. We argue that this new set of parameters $a$ and $b$ represents an interesting novel issue of investigation in entropic sampling studies for different models

Analysing and controlling the tax evasion dynamics via majority-vote model

Within the context of agent-based Monte-Carlo simulations, we study the well-known majority-vote model (MVM) with noise applied to tax evasion on simple square lattices, Voronoi-Delaunay random lattices, Barabasi-Albert networks, and Erd\"os-R\'enyi random graphs. In the order to analyse and to control the fluctuations for tax evasion in the economics model proposed by Zaklan, MVM is applied in the neighborhod of the noise critical $q_{c}$. The Zaklan model had been studied recently using the equilibrium Ising model. Here we show that the Zaklan model is robust and can be reproduced also through the nonequilibrium MVM on various topologies.Comment: 18 pages, 7 figures, LAWNP'09, 200

Astrobiological Complexity with Probabilistic Cellular Automata

Search for extraterrestrial life and intelligence constitutes one of the major endeavors in science, but has yet been quantitatively modeled only rarely and in a cursory and superficial fashion. We argue that probabilistic cellular automata (PCA) represent the best quantitative framework for modeling astrobiological history of the Milky Way and its Galactic Habitable Zone. The relevant astrobiological parameters are to be modeled as the elements of the input probability matrix for the PCA kernel. With the underlying simplicity of the cellular automata constructs, this approach enables a quick analysis of large and ambiguous input parameters' space. We perform a simple clustering analysis of typical astrobiological histories and discuss the relevant boundary conditions of practical importance for planning and guiding actual empirical astrobiological and SETI projects. In addition to showing how the present framework is adaptable to more complex situations and updated observational databases from current and near-future space missions, we demonstrate how numerical results could offer a cautious rationale for continuation of practical SETI searches.Comment: 37 pages, 11 figures, 2 tables; added journal reference belo

Fine-structured multi-scaling long-range correlations in completely sequenced genomes—features, origin, and classification

The sequential organization of genomes, i.e. the relations between distant base pairs and regions within sequences, and its connection to the three-dimensional organization of genomes is still a largely unresolved problem. Long-range power-law correlations were found using correlation analysis on almost the entire observable scale of 132 completely sequenced chromosomes of 0.5 × 106 to 3.0 × 107 bp from Archaea, Bacteria, Arabidopsis thaliana, Saccharomyces cerevisiae, Schizosaccharomyces pombe, Drosophila melanogaster, and Homo sapiens. The local correlation coefficients show a species-specific multi-scaling behaviour: close to random correlations on the scale of a few base pairs, a first maximum from 40 to 3,400 bp (for Arabidopsis thaliana and Drosophila melanogaster divided in two submaxima), and often a region of one or more second maxima from 105 to 3 × 105 bp. Within this multi-scaling behaviour, an additional fine-structure is present and attributable to codon usage in all except the human sequences, where it is related to nucleosomal binding. Computer-generated random sequences assuming a block organization of genomes, the codon usage, and nucleosomal binding explain these results. Mutation by sequence reshuffling destroyed all correlations. Thus, the stability of correlations seems to be evolutionarily tightly controlled and connected to the spatial genome organization, especially on large scales. In summary, genomes show a complex sequential organization related closely to their three-dimensional organization