Games on graphs: A minor modification of payoff scheme makes a big difference

Various social dilemma games that follow different strategy updating rules have been studied on many networks.The reported results span the entire spectrum, from significantly boosting,to marginally affecting,to seriously decreasing the level of cooperation.Experimental results that are qualitatively different from theoretical prediction have also been reported.It is widely believed that the results are largely determined by three elements,including payoff matrices of the underlying 2*2 games,the way that the strategic states of the players are updated and the structure of the networks.Here we discuss the impact of a seemly non-essential mechanism -- what we refer to as a "payoff scheme". Specifically, in each round after the states of all of the players are determined,the payoff scheme is how each player's payoff is calculated.In addition to the two conventions in which either the accumulated or the averaged payoff is calculated from playing with all of the neighboring players,we here study the effects of calculating the payoff from pairing up with one random player from among the neighboring players. Based on probability theory, in a situation of uncorrelated events, the average payoff that involves all of the neighbors should,in principal,be equivalent to the payoff from pairing up with one neighbor.However,our simulation of games on graphs shows that, in many cases,the two payoff schemes lead to qualitatively different levels of cooperation.This finding appears to provide a possible explanation for a wide spectrum of observed behaviors in the literature.We have also observed that results from the randomly-pairing-one mechanism are more robust than the involving-all-neighbours mechanism because,in the former case, neither the other three main elements nor the initial states of the players have a large impact on the final level of cooperation compared with in the latter case.Comment: 23 pages,171 figure

Large-Scale Spectroscopic Mapping of the ρ\rho Ophiuchi Molecular Cloud Complex I. The C2_{2}H to N2_2H+^+ Ratio as a Signpost of Cloud Characteristics

We present 2.5-square-degree C$_{2}$H N=1-0 and N$_2$H$^+$ J=1-0 maps of the $\rho$ Ophiuchi molecular cloud complex. These are the first large-scale maps of the $\rho$ Ophiuchi molecular cloud complex with these two tracers. The C$_{2}$H emission is spatially more extended than the N$_2$H$^+$ emission. One faint N$_2$H$^+$ clump Oph-M and one C$_{2}$H ring Oph-RingSW are identified for the first time. The observed C$_{2}$H to N$_{2}$H$^{+}$ abundance ratio ([C$_{2}$H]/[N$_{2}$H$^{+}$]) varies between 5 and 110. We modeled the C$_{2}$H and N$_2$H$^+$ abundances with 1-D chemical models which show a clear decline of [C$_2$H]/[N$_2$H$^+$] with chemical age. Such an evolutionary trend is little affected by temperatures when they are below 40 K. At high density (n$_H$ $>$ 10$^5$ cm$^{-3}$), however, the time it takes for the abundance ratio to drop at least one order of magnitude becomes less than the dynamical time (e.g., turbulence crossing time $\rm \sim$10$^5$ years). The observed [C$_2$H]/[N$_2$H$^+$] difference between L1688 and L1689 can be explained by L1688 having chemically younger gas in relatively less dense regions. The observed [C$_{2}$H]/[N$_{2}$H$^{+}$] values are the results of time evolution, accelerated at higher densities. For the relative low density regions in L1688 where only C$_2$H emission was detected, the gas should be chemically younger.Comment: Accepted by ApJ, 45 pages, 10 figure

Complex Organic Molecules Formation in Cold Cores on Stochastically Heated Grains

We investigate the roles of stochastic grain heating in the formation of complex organic molecules (COMs) in cold cores, where COMs have been detected. Two different types of grain-size distributions are used in the chemical models. The first one is the MRN distribution, and the second one considers grain coagulation to study its effects on the chemical evolution in these environments. The macroscopic Monte Carlo method is used to perform the two-phase chemical model simulations. We find that (1) grain coagulation can affect certain gas-phase species, such as CO$_2$ and N$_2$H$^+$, in the cold core environments, which can be attributed to the volatile precursors originating from the small grains with temperature fluctuations; (2) grains with radii around 4.6 $\times$ 10$^{-3}$ $\mu$m contribute most to the production of COMs on dust grains under cold core conditions, while few species can be formed on even smaller grains with radii less than 2 $\times$ 10$^{-3}$ $\mu$m; (3) COMs formed on stochastically heated grains could help explain the observed abundances of gas-phase COMs in cold cores.Comment: 15 pages, 10 figures, 3 tables. Accepted by MNRA

Blind Image Restoration via the Integration of Stochastic and Deterministic Methods

This paper addresses the image restoration problem which remains a significant field of image processing. The fields of experts- (FoE-) based image restoration has been discussed and some open issues including noise estimation and parameter selection have been approached. The stochastic method FoE performs fairly well; meanwhile it might also produce unsatisfactory outcome especially when the noise is grave. To improve the final performance, we introduce the integration with deterministic method K-SVD. The FoE-treated image has been used to obtain the dictionary, and with the help of sparse and redundant representation over trained dictionary, the K-SVD algorithm can dramatically solve the problem, even though the pretreated result is of poor quality under severe noise condition. The experimental results via our proposed method are demonstrated and compared in detail. Meanwhile the test results from both qualitative and quantitative aspects are given, which present the better performance over current state-of-art related restoration algorithms