Heterogeneity in evolutionary games: an analysis of the risk perception

In this work, we analyse the relationship between heterogeneity and cooperation. Previous investigations suggest that this relation is nontrivial, as some authors found that heterogeneity sustains cooperation, while others obtained different results. Among the possible forms of heterogeneity, we focus on the individual perception of risks and rewards related to a generic event, that can show up in a number of social and biological systems. The modelling approach is based on the framework of Evolutionary Game Theory. To represent this kind of heterogeneity, we implement small and local perturbations on the payoff matrix of simple 2-strategy games, as the Prisoner's Dilemma. So, while usually the payoff is considered as a global and time-invariant structure, i.e. it is the same for all individuals of a population at any time, in our model its value is continuously affected by small variations, both in time and space (i.e. position on a lattice). We found that such perturbations can be beneficial or detrimental to cooperation, depending on their setting. Notably, cooperation is strongly supported when perturbations act on the main diagonal of the payoff matrix, whereas when they act on the off-diagonal the resulting effect is more difficult to quantify. To conclude, the proposed model shows a rich spectrum of possible equilibria, whose interpretation might offer insights and enrich the description of several systems.Comment: 7 pages, 5 figure

Cooperation in public goods games: stay, but not for too long

Cooperation in repeated public goods game is hardly achieved, unless contingent behavior is present. Surely, if mechanisms promoting positive assortment between cooperators are present, then cooperators may beat defectors, because cooperators would collect greater payoffs. In the context of evolutionary game theory, individuals that always cooperate cannot win the competition against defectors in well-mixed populations. Here, we study the evolution of a population where fitness is obtained in repeated public goods games and players have a fixed probability of playing the next round. As a result, the group size decreases during the game. The population is well-mixed and there are only two available strategies: always cooperate (ALLC) or always defect (ALLD). Through numerical calculation and analytical approximations we show that cooperation can emerge if the players stay playing the game, but not for too long. The essential mechanism is the interaction between the transition from strong to weak altruism, as the group size decreases, and the existence of an upper limit to the number of rounds representing limited time availability

Comment on: Kinetic Roughening in Slow Combustion of Paper

We comment on a recent Letter by Maunuksela et al. [Phys. Rev. Lett. 79, 1515 (1997)].Comment: 1 page, 1 figure, http://polymer.bu.edu/~hmakse/Home.htm

Classes of complex networks defined by role-to-role connectivity profiles

Interactions between units in phyical, biological, technological, and social systems usually give rise to intrincate networks with non-trivial structure, which critically affects the dynamics and properties of the system. The focus of most current research on complex networks is on global network properties. A caveat of this approach is that the relevance of global properties hinges on the premise that networks are homogeneous, whereas most real-world networks have a markedly modular structure. Here, we report that networks with different functions, including the Internet, metabolic, air transportation, and protein interaction networks, have distinct patterns of connections among nodes with different roles, and that, as a consequence, complex networks can be classified into two distinct functional classes based on their link type frequency. Importantly, we demonstrate that the above structural features cannot be captured by means of often studied global properties

Modularity from Fluctuations in Random Graphs and Complex Networks

The mechanisms by which modularity emerges in complex networks are not well understood but recent reports have suggested that modularity may arise from evolutionary selection. We show that finding the modularity of a network is analogous to finding the ground-state energy of a spin system. Moreover, we demonstrate that, due to fluctuations, stochastic network models give rise to modular networks. Specifically, we show both numerically and analytically that random graphs and scale-free networks have modularity. We argue that this fact must be taken into consideration to define statistically-significant modularity in complex networks.Comment: 4 page

A Study of Cool White Dwarfs in the Sloan Digital Sky Survey Data Release 12

In this work we study white dwarfs where $30\,000\,\text{K} {>} \mathrm{T}_{\rm{eff}} {>} 5\,000\,\text{K}$ to compare the differences in the cooling of DAs and non-DAs and their formation channels. Our final sample is composed by nearly $13\,000$ DAs and more than $3\,000$ non-DAs that are simultaneously in the SDSS DR12 spectroscopic database and in the \textit{Gaia} survey DR2. We present the mass distribution for DAs, DBs and DCs, where it is found that the DCs are ${\sim}0.15\,\mathrm{M}_\odot$ more massive than DAs and DBs on average. Also we present the photometric effective temperature distribution for each spectral type and the distance distribution for DAs and non-DAs. In addition, we study the ratio of non-DAs to DAs as a function of effective temperature. We find that this ratio is around ${\sim}0.075$ for effective temperature above ${\sim}22\,000\,\text{K}$ and increases by a factor of five for effective temperature cooler than $15\,000\,\text{K}$. If we assume that the increase of non-DA stars between ${\sim}22\,000\,\text{K}$ to ${\sim}15\,000\,\text{K}$ is due to convective dilution, $14{\pm}3$ per cent of the DAs should turn into non-DAs to explain the observed ratio. Our determination of the mass distribution of DCs also agrees with the theory that convective dilution and mixing are more likely to occur in massive white dwarfs, which supports evolutionary models and observations suggesting that higher mass white dwarfs have thinner hydrogen layers.Comment: 9 pages, 10 figures, accepted by MNRA