Generic Criticality in a Model of Evolution

Using Monte Carlo simulations, we show that for a certain model of biological evolution, which is driven by non-extremal dynamics, active and absorbing phases are separated by a critical phase. In this phase both the density of active sites $\rho(t)$ and the survival probability of spreading $P(t)$ decay as $t^{-\delta}$, where $\delta \sim 0.5$. At the critical point, which separates the active and critical phases, $\delta\sim 0.29$, which suggests that this point belongs to the so-called parity-conserving universality class. The model has infinitely many absorbing states and, except for a single point, has no conservation law.Comment: 4 pages, 3 figures, minor grammatical change

Criticality of natural absorbing states

We study a recently introduced ladder model which undergoes a transition between an active and an infinitely degenerate absorbing phase. In some cases the critical behaviour of the model is the same as that of the branching annihilating random walk with $N\geq 2$ species both with and without hard-core interaction. We show that certain static characteristics of the so-called natural absorbing states develop power law singularities which signal the approach of the critical point. These results are also explained using random walk arguments. In addition to that we show that when dynamics of our model is considered as a minimum finding procedure, it has the best efficiency very close to the critical point.Comment: 6 page

WHO IS THE “MINER”? A BRIEF EXEGESIS OF JOB 28:4

There is a long tradition of researching the book of Job and the meaning behind the imagery presented. Job 28:4, is not without its own imagery especially the image of the ―miner‖ and ―foreigner.‖ Unpacking the meaning behind the ―miner‖ and its use in the Old Testament, is quite interesting. Addressing the image of the ―miner‖ within the context of the book of Job and other books in the Old Testament shows the complex meaning of the search for wisdom. The analysis of the text provides evidence for the meaning of the image of the ―miner‖ as well as the overall search for wisdom. What is verse 4 telling its readers? How does it fit into the larger work of the book of Job? This work will address these questions and show that the 4th verse in the book of Job does indeed fit into wisdom literature

WHO IS THE “MINER”? A BRIEF EXEGESIS OF JOB 28:4

There is a long tradition of researching the book of Job and the meaning behind the imagery presented. Job 28:4, is not without its own imagery especially the image of the ―miner‖ and ―foreigner.‖ Unpacking the meaning behind the ―miner‖ and its use in the Old Testament, is quite interesting. Addressing the image of the ―miner‖ within the context of the book of Job and other books in the Old Testament shows the complex meaning of the search for wisdom. The analysis of the text provides evidence for the meaning of the image of the ―miner‖ as well as the overall search for wisdom. What is verse 4 telling its readers? How does it fit into the larger work of the book of Job? This work will address these questions and show that the 4th verse in the book of Job does indeed fit into wisdom literature

Critical behaviour of a tumor growth model - Directed Percolation with a mean-field flavour

We examine the critical behaviour 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 (2012)), which suggested that the critical behaviour of the model differs from the expected Directed Percolation (DP) universality class. Surprisingly, only some of the critical exponents (beta, alpha, nu_perp, and z) take non-DP values while some others (beta', nu_||, and spreading-dynamics exponents Theta, delta, z') remain very close to their DP counterparts. The obtained exponents satisfy the scaling relations beta=alpha*nu_||, beta'=delta*nu_||, and the generalized hyperscaling relation Theta+alpha+delta=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 beta most likely takes the mean-field value beta=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.Comment: 8 pages, 15 figure

Crystallization of a supercooled liquid and of a glass - Ising model approach

Using Monte Carlo simulations we study crystallization in the three-dimensional Ising model with four-spin interaction. We monitor the morphology of crystals which grow after placing crystallization seeds in a supercooled liquid. Defects in such crystals constitute an intricate and very stable network which separate various domains by tensionless domain walls. We also show that the crystallization which occurs during the continuous heating of the glassy phase takes place at a heating-rate dependent temperature.Comment: 7 page

Glassy transition and metastability in four-spin Ising model

Using Monte Carlo simulations we show that the three-dimensional Ising model with four-spin (plaquette) interactions has some characteristic glassy features. The model dynamically generates diverging energy barriers, which give rise to slow dynamics at low temperature. Moreover, in a certain temperature range the model possesses a metastable (supercooled liquid) phase, which is presumably supported by certain entropy barriers. Although extremely strong, metastability in our model is only a finite-size effect and sufficiently large droplets of stable phase divert evolution of the system toward the stable phase. Thus, the glassy transitions in this model is a dynamic transition, preceded by a pronounced peak in the specific heat.Comment: extensively revised, with further simulations of metastability properties, response to referees tactfully remove

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.Comment: accepted in Phys. Rev.

Analytic study of the urn model for separation of sand

We present an analytic study of the urn model for separation of sand recently introduced by Lipowski and Droz (Phys. Rev. E 65, 031307 (2002)). We solve analytically the master equation and the first-passage problem. The analytic results confirm the numerical results obtained by Lipowski and Droz. We find that the stationary probability distribution and the shortest one among the characteristic times are governed by the same free energy. We also analytically derive the form of the critical probability distribution on the critical line, which supports their results obtained by numerically calculating Binder cumulants (cond-mat/0201472).Comment: 6 pages including 3 figures, RevTe