Phase transitions in dependence of apex predator decaying ratio in a cyclic dominant system

Cyclic dominant systems, like rock-paper-scissors game, are frequently used to explain biodiversity in nature, where mobility, reproduction and intransitive competition are on stage to provide the coexistence of competitors. A significantly new situation emerges if we introduce an apex predator who can superior all members of the mentioned three-species system. In the latter case the evolution may terminate into three qualitatively different destinations depending on the apex predator decaying ratio $q$. In particular, the whole population goes extinct or all four species survive or only the original three-species system remains alive as we vary the control parameter. These solutions are separated by a discontinuous and a continuous phase transitions at critical $q$ values. Our results highlight that cyclic dominant competition can offer a stable way to survive even in a predator-prey-like system that can be maintained for large interval of critical parameter values.Comment: version to appear in EPL. 7 pages, 7 figure

Invasion controlled pattern formation in a generalized multi-species predator-prey system

Rock-scissors-paper game, as the simplest model of intransitive relation between competing agents, is a frequently quoted model to explain the stable diversity of competitors in the race of surviving. When increasing the number of competitors we may face a novel situation because beside the mentioned unidirectional predator-prey-like dominance a balanced or peer relation can emerge between some competitors. By utilizing this possibility in the present work we generalize a four-state predator-prey type model where we establish two groups of species labeled by even and odd numbers. In particular, we introduce different invasion probabilities between and within these groups, which results in a tunable intensity of bidirectional invasion among peer species. Our study reveals an exceptional richness of pattern formations where five quantitatively different phases are observed by varying solely the strength of the mentioned inner invasion. The related transition points can be identified with the help of appropriate order parameters based on the spatial autocorrelation decay, on the fraction of empty sites, and on the variance of the species density. Furthermore, the application of diverse, alliance-specific inner invasion rates for different groups may result in the extinction of the pair of species where this inner invasion is moderate. These observations highlight that beyond the well-known and intensively studied cyclic dominance there is an additional source of complexity of pattern formation that has not been explored earlier.Comment: 8 pages, 8 figures. To appear in PR

Three dimensional Lifshitz black hole and the Korteweg-de Vries equation

We consider a solution of three dimensional New Massive Gravity with a negative cosmological constant and use the AdS/CTF correspondence to inquire about the equivalent two dimensional model at the boundary. We conclude that there should be a close relation with the Korteweg-de Vries equation.Comment: 4 page

The Likelihood Ratio Test and Full Bayesian Significance Test under small sample sizes for contingency tables

Hypothesis testing in contingency tables is usually based on asymptotic results, thereby restricting its proper use to large samples. To study these tests in small samples, we consider the likelihood ratio test and define an accurate index, the P-value, for the celebrated hypotheses of homogeneity, independence, and Hardy-Weinberg equilibrium. The aim is to understand the use of the asymptotic results of the frequentist Likelihood Ratio Test and the Bayesian FBST -- Full Bayesian Significance Test -- under small-sample scenarios. The proposed exact P-value is used as a benchmark to understand the other indices. We perform analysis in different scenarios, considering different sample sizes and different table dimensions. The exact Fisher test for $2 \times 2$ tables that drastically reduces the sample space is also discussed. The main message of this paper is that all indices have very similar behavior, so the tests based on asymptotic results are very good to be used in any circumstance, even with small sample sizes

Holographic Superconductors with various condensates in Einstein-Gauss-Bonnet gravity

We study holographic superconductors in Einstein-Gauss-Bonnet gravity. We consider two particular backgrounds: a $d$-dimensional Gauss-Bonnet-AdS black hole and a Gauss-Bonnet-AdS soliton. We discuss in detail the effects that the mass of the scalar field, the Gauss-Bonnet coupling and the dimensionality of the AdS space have on the condensation formation and conductivity. We also study the ratio $\omega_g/T_c$ for various masses of the scalar field and Gauss-Bonnet couplings.Comment: 21 pages, 10 figures. accepted for publication in PR

Inclusive hadron and photon production at LHC in dipole momentum space

Using a momentum space model for the dipole scattering amplitude we present an analysis of the saturation effects at LHC energies, describing the data on proton-proton and proton-lead collisions. The model is based on the asymptotic solutions of the Balitsky-Kovchegov equation, being ideal in the saturation domain where the target wave function has a high occupation number. We also make predictions for the nuclear modification ratios on charged hadron and prompt photon production in the forward region, where the high parton density effects are important.Comment: New section added and typos corrected. To be published in PR

Structural anomalies for a three dimensional isotropic core-softened potential

Using molecular dynamics simulations we investigate the structure of a system of particles interacting through a continuous core-softened interparticle potential. We found for the translational order parameter, t, a local maximum at a density $\rho_{t-max}$ and a local minimum at $\rho_{t-min} > \rho_{t-max}$. Between $\rho_{t-max}$ and $\rho_{t-min}$, the $t$ parameter anomalously decreases upon pressure. For the orientational order parameter, $Q_6$, was observed a maximum at a density $\rho_{t-max}< \rho_{Qmax} < \rho_{t-min}$. For densities between $\rho_{Qmax}$ and $\rho_{t-min}$, both the translational (t) and orientational ($Q_6$) order parameters have anomalous behavior. We know that this system also exhibits density and diffusion anomaly. We found that the region in the pressure-temperature phase-diagram of the structural anomaly englobes the region of the diffusion anomaly that is larger than the region limited by the temperature of maximum density. This cascade of anomalies (structural, dynamic and thermodynamic) for our model has the same hierarchy of that one observed for the SPC/E water.Comment: 19 pages, 8 figure