breaking the symmetry between interaction and replacement in evolutionary dynamics on graphs we study the evolution of cooperation modeled as symmetric 2 2 games in a population whose structure is split into an interaction graph defining who plays with whom and a replacement graph specifying evolutionary competition we find it is always harder for cooperators to evolve whenever the two graphs do not coincide in the thermodynamic limit the dynamics on both graphs is given by a replicator equation with a rescaled payoff matrix in a rescaled time analytical results are obtained in the pair approximation and for weak selection their validity is confirmed by computer simulations

a predictive estimator of finite population proportion despite missing data abstract this paper considers the problem of estimating a finite population proportion when there are missing values the prediction approach is used to define a new estimator that presents desirable efficiency properties simulation studies are considered to evaluate the performance of the proposed estimator via empirical relative bias and empirical relative efficiency and favourable results are achieved

phase transition with the line tension effect we make the connection between the geometric model for capillarity with line tension and the cahn hilliard model of two phase fluids to this aim we consider the energies f eps u eps int o du 2 1 over eps int o w u lambda int bd o v u where u is a scalar density function and w and v are double well potentials we show that the behaviour of f e in the limit e 0 and depends on the limit of e log if this limit is finite and strictly positive then the singular limit of the energies f e leads to a coupled problem of bulk and surface phase transitions and under certain assumptions agrees with the relaxation of the capillary energy with line tension these results were announced in abs1 and abs2

variance estimation using auxiliary information abstract variance estimators under several sample designs are proposed and compared when auxiliary information is available improvement of the bias and mean squared error over some estimators commonly used in practice is illustrated a monte carlo comparison of the estimators is also presented

how to recognize convexity of a set from its marginals abstract we investigate the regularity of the marginals onto hyperplanes for sets of finite perimeter we prove in particular that if a set of finite perimeter has log concave marginals onto a e hyperplane then the set is convex our proof relies on measuring the perimeter of a set through a hilbertian fractional sobolev norm a fact that we believe has its own interest

improvement in estimating the population mean in simple random sampling using information on auxiliary attribute this paper proposes some estimators for the population mean by adapting the estimator in singh et al 2008 5 to the ratio estimators presented in kadilar and cingi 2006 2 we obtain mean square error mse equation for all proposed estimators and show that all proposed estimators are always more efficient than ratio estimator in naik and gupta 1996 3 and singh et al 2008 5 the results have been illustrated numerically by taking some empirical population considered in the literature

layer solutions in a half space for boundary reactions r n 1 are denoted by y y1 yn 1 our main goal is to study bounded solutions of 1 1 that are monotone increasing say from 1 to 1 in one of the y variables we call them layer solutions of 1 1 and we study their existence uniqueness symmetry and variational properties as well as their asymptotic behavior the interest in such increasing solutions comes from some models of boundary phase transitions when the nonlinearity f is given by f u sin cu for some constant c problem 1 1 in a half plane is called the peierls nabarro problem and it appears as a model of dislocations in crystals see 21 36 the peierls nabarro problem is also central to the analysis of boundary vortices in the paper 28 which studies a model for soft thin films in micromagnetism recently derived by kohn and slastikov 26 see also 27 our main result theorem 1 2 characterizes the nonlinearities f for which there exists a layer solution of 1 1 in dimension n 2 we prove that the necessary and sufficient condition is that the potential g defined by g f has two and only two absolute minima in the interval 1 1 located at 1 under the additional hypothesis g 1 0 we also establish the uniqueness of a layer solution up to translations in the y variable the proofs of both the necessity and the sufficiency of the condition on g for existence use new ingredients which we develop in this article a first one is a nonlocal estimate as well as a conserved or hamiltonian quantity satisfied by every layer solution in dimension 2 see theorem 1 3 the estimate can be seen as

iterated snowdrift game among mobile agents with myopic expected reward based decision rule numerical and analytical research abstract the iterated spatial game among the mobile population is an interesting problem in the fields of biological social and economic sciences inspired by some recent works this paper concentrates on the iterated snowdrift game among movable and myopic agents two different decision making schemes namely the utility maximum rule and the fermi rule are applied and examined in the former case cooperation is found to be enhanced by moving velocity with an upper bound the analytical results of the model are deduced at two extreme cases when agents cannot move or move quickly in the latter case the influences of velocity and temptation to defect are much more complicated these results allow a deeper insight of the related model as well as the emergence of cooperation

enhancement of cooperation in prisoner s dilemma game on weighted lattices abstract we introduce the vertex weight into the spatial prisoners dilemma game to investigate the evolution of cooperation each player on a square lattice is assigned to a particular weight followed by three types of distributions which include the exponential power law and uniform ones compared with the traditional version we find that the cooperation level is markedly enhanced under the weighted square lattice for most ranges of b the highest cooperation level can be obtained under the uniform distribution while power law distribution usually leads to the lowest cooperation the distributed weight can produce a heavy heterogeneity among the individuals payoff some cooperators with higher weight will foster the cooperative clusters and even spread the cooperation strategy around the clusters while defectors have no such advantages in addition we still investigate the impact of the amplitude of undulation of weight distribution on the cooperation and the non monotonic behavior about b is observed finally the influence of noise on the cooperation is also studied for these types of distribution of weight to some extent our weighted scheme can characterize the difference or diversity of players which will be beneficial to further understand the role of individuals during the evolution of cooperation

stochastic dynamics of invasion and fixation we study evolutionary game dynamics in finite populations we analyze an evolutionary process which we call pairwise comparison for which we adopt the ubiquitous fermi distribution function from statistical mechanics the inverse temperature in this process controls the intensity of selection leading to a unified framework for evolutionary dynamics at all intensities of selection from random drift to imitation dynamics we derive a simple closed formula that determines the feasibility of cooperation in finite populations whenever cooperation is modeled in terms of any symmetric two person game in contrast with previous results the present formula is valid at all intensities of selection and for any initial condition we investigate the evolutionary dynamics of cooperators in finite populations and study the interplay between intensity of selection and the remnants of interior fixed points in infinite populations as a function of a given initial number of cooperators showing how this interplay strongly affects the approach to fixation of a given trait in finite populations leading to counterintuitive results at different intensities of selection

on stable solutions for boundary reactions a de giorgi type result in dimension 4 1 we prove that every bounded stable solution of begin aligned delta 1 2 u f u 0 qquad text in mathbb r 3 end aligned is a 1d profile i e u x phi e cdot x for some e in mathbb s 2 where phi mathbb r rightarrow mathbb r is a nondecreasing bounded stable solution in dimension one equivalently stable critical points of boundary reaction problems in mathbb r d 1 mathbb r d 1 cap x d 1 ge 0 of the form begin aligned int x d 1 ge 0 frac 1 2 nabla u 2 dx dx d 1 int x d 1 0 f u dx end aligned are 1d when d 3 these equations have been studied since the 1940 s in crystal dislocations also as it happens for the allen cahn equation the associated energies enjoy a gamma convergence result to the perimeter functional in particular when f u u 3 u or equivalently when f u frac 1 4 1 u 2 2 our result implies the analogue of the de giorgi conjecture for the half laplacian in dimension 4 namely that monotone solutions are 1d note that our result is a pde version of the fact that stable embedded minimal surfaces in mathbb r 3 are planes it is interesting to observe that the corresponding statement about stable solutions to the allen cahn equation namely when the half laplacian is replaced by the classical laplacian is still unknown for d 3

costly punishment and cooperation in the evolutionary snowdrift game abstract the role of punishments in promoting cooperation is an important issue we incorporate costly punishments into the snowdrift game sg by introducing a third punishing p character and study the effects the punishers who carry basically a cooperative c character are willing to pay a cost so as to punish a non cooperative d opponent by depending on the initial fractions of the characters and the cost to benefit ratio r in the sg the three character system evolves into a steady state consisting either only of c and p characters or only of c and d characters in a well mixed population the former situation represents an enhancement in cooperation relative to the sg while the latter is similar to the sg the dynamics in approaching these different steady states are found to be different analytically the key features in the dynamics and the steady states observed in simulations are captured by a set of differential equations the sensitivity to the initial distribution of characters is studied by depicting the flow in a phase portrait and analyzing the nature of fixed points the analysis also shows the role of p character agents in preventing a system from invasion by d character agents starting from a population consisting only of c and p agents a d character agent intended to invade the system cannot survive when the initial fraction of p agents is greater than r our model defined intentionally as a simulation algorithm can be readily generalized to incorporate many interesting effects such as those in a networked population

diversity optimized cooperation on complex networks we propose a strategy for achieving maximum cooperation in evolutionary games on complex networks each individual is assigned a weight that is proportional to the power of its degree where the exponent is an adjustable parameter that controls the level of diversity among individuals in the network during the evolution every individual chooses one of its neighbors as a reference with a probability proportional to the weight of the neighbor and updates its strategy depending on their payoff difference it is found that there exists an optimal value of for which the level of cooperation reaches maximum this phenomenon indicates that although high degree individuals play a prominent role in maintaining the cooperation too strong influences from the hubs may counterintuitively inhibit the diffusion of cooperation other pertinent quantities such as the payoff the cooperator density as a function of the degree and the payoff distribution are also investigated computationally and theoretically our results suggest that in order to achieve strong cooperation on a complex network individuals should learn more frequently from neighbors with higher degrees but only to a certain extent

improved estimation of population variance using information on auxiliary attribute in simple random sampling singh and kumar 2011 19 suggested estimators for calculating population variance using auxiliary attributes this paper proposes a family of estimators based on an adaptation of the estimators presented by kadilar and cingi 2004 5 and singh et al 2007 16 and introduces a new family of estimators using auxiliary attributes the expressions of the mean square errors mses of the adapted and proposed families are derived it is shown that adapted estimators and suggested estimators are more efficient than singh and kumar 2011 19 estimators the theoretical findings are supported by a numerical example

an improved estimator using two auxiliary attributes in the present study we propose two new estimators for population mean using kadilar and cingi 2005 2 and lu et al 2010 9 estimators in the case when the information is available in form of attributes expressions for the mse s of the proposed estimator are derived up to the first degree of approximation the theoretical conditions have also been verified by a numerical example it has been shown that the proposed estimators are more efficient than usual regression estimators

positive correlation between strategy persistence and teaching ability promotes cooperation in evolutionary prisoner s dilemma games abstract strategy persistence and heterogeneous teaching ability are two factors that play important roles in promoting cooperation in this work we simultaneously take the strategy persistence and heterogeneous teaching ability into account in evolutionary prisoner s dilemma games we introduce the correlation between strategy persistence and teaching ability by partitioning a population into two groups in the positive negative correlation scheme individuals in one group are assigned with large and 1 reduced teaching ability 1 and those in the other with 0 and 1 1 the simulation results show that compared to negative correlation positive correlation between strategy persistence and teaching ability can greatly enhance cooperation and result in a much higher cooperation level furthermore we show that the finding is robust with respect to reduced teaching ability initial cooperator fraction f 0 amplitude of noise k and underlying network topology

effects of strategy migration direction and noise in the evolutionary spatial prisoner s dilemma spatial games are crucial for understanding patterns of cooperation in nature and to some extent society they are known to be more sensitive to local symmetries than e g spin models this paper concerns the evolution of the prisoner s dilemma game on regular lattices with three different types of neighborhoods char22 the von neumann moore and kagom e types we investigate two kinds of dynamics for the players to update their strategies that can be unconditional cooperator or defector depending on the payoff difference an individual can adopt the strategy of a random neighbor a voter model like dynamics vmld or impose its strategy on a random neighbor i e invasion process like dynamics ipld in particular we focus on the effects of noise in combination with the strategy dynamics on the evolution of cooperation we find that vmld compared to ipld better supports the spreading and sustaining of cooperation we see that noise has nontrivial effects on the evolution of cooperation maximum cooperation density can be realized either at a medium noise level in the limit of zero noise or in both these regions the temptation to defect and the local interaction structure determine the outcome especially in the low noise limit the local interaction plays a crucial role in determining the fate of cooperators we elucidate these both by numerical simulations and mean field cluster approximation methods

ordering in spatial evolutionary games for pairwise collective strategy updates evolutionary 2 ifmmode times else texttimes fi 2 games are studied with players located on a square lattice during the evolution the randomly chosen neighboring players try to maximize their collective income by adopting a random strategy pair with a probability dependent on the difference of their summed payoffs between the final and initial states assuming quenched strategies in their neighborhood in the case of the anticoordination game this system behaves like an antiferromagnetic kinetic ising model within a wide region of social dilemmas this dynamical rule supports the formation of similar spatial arrangement of the cooperators and defectors ensuring the optimum total payoff if the temptation to choose defection exceeds a threshold value dependent on the sucker s payoff the comparison of the results with those achieved for pairwise imitation and myopic strategy updates has indicated the relevant advantage of pairwise collective strategy update in the maintenance of cooperation

memory based snowdrift game on networks we present a memory based snowdrift game mbsg taking place on networks we found that when a lattice is taken to be the underlying structure the transition of spatial patterns at some critical values of the payoff parameter is observable for both four and eight neighbor lattices the transition points as well as the styles of spatial patterns can be explained by local stability analysis in sharp contrast to previously reported results cooperation is promoted by the spatial structure in the mbsg interestingly we found that the frequency of cooperation of the mbsg on a scale free network peaks at a specific value of the payoff parameter this phenomenon indicates that properly encouraging selfish behaviors can optimally enhance the cooperation the memory effects of individuals are discussed in detail and some nonmonotonous phenomena are observed on both lattices and scale free networks our work may shed some new light on the study of evolutionary games over networks

co evolving prisoner s dilemma performance indicators and analytic approaches understanding the intrinsic relation between the dynamical processes in a co evolving network and the necessary ingredients in formulating a reliable theory is an important question and a challenging task using two slightly different definitions of performance indicator in the context of a co evolving prisoner s dilemma game it is shown that very different cooperative levels result and theories of different complexity are required to understand the key features when the payoff per opponent is used as the indicator case a non cooperative strategy has an edge and dominates in a large part of the parameter space formed by the cutting and rewiring probability and the strategy imitation probability when the payoff from all opponents is used case b cooperative strategy has an edge and dominates the parameter space two distinct phases one homogeneous and dynamical and another inhomogeneous and static emerge and the phase boundary in the parameter space is studied in detail a simple theory assuming an average competing environment for cooperative agents and another for non cooperative agents is shown to perform well in case a the same theory however fails badly for case b it is necessary to include more spatial correlation into a theory for case b we show that the local configuration approximation which takes into account of the different competing environments for agents with different strategies and degrees is needed to give reliable results for case b the results illustrate that formulating a proper theory requires both a conceptual understanding of the effects of the adaptive processes in the problem and a delicate balance between simplicity and accuracy

the evolutionary public goods game on scale free networks with heterogeneous investment abstract the public goods game pgg is generally considered as a suitable paradigm to explain ubiquitous cooperative behavior in this study we investigated the evolutionary pgg on scale free networks and studied the effect of individual heterogeneity by setting the cooperator x an investment value correlated to its degree as i x n k x j k j where k x is the degree of x j runs over all players and is a tunable parameter it is shown that the cooperation level is remarkably promoted by negative values of whereas it is highly depressed by positive values of moreover the effect of environmental noise has also been investigated our result may sharpen the understanding of cooperation induced by the individual diversity

to model or not to model competing modes of inference for finite population sampling finite population sampling is perhaps the only area of statistics in which the primary mode of analysis is based on the randomization distribution rather than on statistical models for the measured variables this article reviews the debate between design based and model based inference the basic features of the two approaches are illustrated using the case of inference about the mean from stratified random samples strengths and weakness of design based and model based inference for surveys are discussed it is suggested that models that take into account the sample design and make weak parametric assumptions can produce reliable and efficient inferences in surveys settings these ideas are illustrated using the problem of inference from unequal probability samples a model based regression analysis that leads to a combination of design based and model based weighting is described

regularity of flat level sets in phase transitions we consider local minimizers of the ginzburg landau energy functional 1 2 u 2 1 4 1 u 2 2 dx and prove that if the 0 level set is included in a flat cylinder then in the interior it is included in a flatter cylinder as a consequence we prove a conjecture of de giorgi which states that level sets of global solutions of u u 3 u such that u 1 n u 0 lim u x x n 1 x n are hyperplanes in dimension n 8

enhanced cooperation and harmonious population in an evolutionary n person snowdrift game abstract the n person evolutionary snowdrift game nesg is generalized to study the effects of the additional benefit to all agents in a competing group of size n resulting from an earlier completion of a task when more agents are willing to share the work following replicator dynamics an equation that can be used to solve for the steady state frequency of cooperation x in a well mixed population as a function of the parameters representing the cost to benefit ratio c b additional reward w b and n is derived cooperation is enhanced in general for w 0 and a stable state with all cooperative agents allc state emerges for small groups n and small c b in contrast such a harmonious allc state does not exist in the original nesg for c 0 the condition for the existence of an allc state is estimated to be n 1 c w and good agreement is found when compared with numerical solutions the observed disappearance of an allc state and the drop in x with n are discussed in terms of the change in the stability of the allc state as n increases previous results in nesg are recovered as the w 0 case of our model thus the pleasure of enjoying the completed task earlier promotes cooperation and the effects are more pronounced when small group collective interactions are considered

bistable boundary reactions in two dimensions in a bounded domain omega subset mathbb r 2 with smooth boundary we consider the problem delta u 0 quad rm in omega qquad frac partial u partial nu frac1 varepsilon f u quad rm on partial omega where is the unit normal exterior vector e 0 is a small parameter and f is a bistable nonlinearity such as f u sin u or f u 1 u2 u we construct solutions that develop multiple transitions from 1 to 1 and vice versa along a connected component of the boundary we also construct an explicit solution when is a disk and f u sin u

a two parameter variance estimator using auxiliary information we propose a two parameter ratio product ratio estimator for estimating a finite population variance based on simple random sampling without replacement the bias and mean square error of the proposed estimator are obtained to the first degree of approximation we have derived the conditions for the parameters under which the proposed estimator has smaller mean square error than the sample variance ratio and product estimators we carry out an application showing that the proposed estimator outperforms the traditional estimators using different data sets

cooperative behavior in evolutionary snowdrift games with the unconditional imitation rule on regular lattices we study an evolutionary snowdrift game with the unconditional imitation updating rule on regular lattices detailed numerical simulations establish the structure of plateaus and discontinuous jumps of the equilibrium cooperation frequency f c as a function of the cost to benefit ratio r by analyzing the stability of local configurations it is found that the transitions occur at values of r at which there are changes in the ranking of the payoffs to the different local configurations of agents using different strategies nonmonotonic behavior of f c r at the intermediate range of r is analyzed in terms of the formation of blocks of agents using the cooperative strategy that are stabilized by agents inside the block due to the updating rule for random initial condition with 50 50 agents of different strategies randomly dispersed cooperation persists in the whole range of r and the level of cooperation is higher than that in the well mixed case in a wide range of r these results are in sharp contrast to those based on the replicator updating rule the sensitivity to initial states with different fractions of cooperative agents is also discussed the results serve to illustrate that both the spatial structure and the updating rule are important in determining the level of cooperation in a competing population when extreme initial states are used where there are very few agents of a strategy in a background of the opposite strategy the result would depend on the stability of the clusters formed by the initially minority agents

effect of memory on the prisoner s dilemma game in a square lattice we have studied the effect of memory on the evolution of the prisoner s dilemma game in square lattice networks based on extensive simulations we found that the density of cooperators was enhanced by an increasing memory effect for most parameters however we also observed that the density of cooperators decreased with an increased memory effect in the case of a large memory and moderate temptation it is interesting to note that memory makes cooperators immune from temptation the strength of protection reaches its maximal value only for a moderate memory effect

three strategy n person snowdrift game incorporating loners the nn person snowdrift game is generalized to incorporate a third strategy in addition to the cooperative cc and non cooperative dd strategies a strategy ll representing a loner behavior is introduced agents taking on the ll strategy ll agents do not contribute to the game as the cc agents do but they do not take advantage of the cc agents instead they would rather settle with a fixed payoff ll dynamical equations governing the time evolution of the frequencies of the strategies in a well mixed population are derived the dynamics and the frequencies of the steady state reveal the rich behavior resulting from the interplay between the payoff rr which promotes the non cooperative behavior and ll detailed studies on how a system evolves indicated that the steady state could be an alll allc or c d state depending on the parameters rr ll and group size nn in contrast only a c d state results for r 0r 0 and an allc state is possible only at r 0r 0 without the strategy ll with the strategy ll the allc phase occupies a finite though tiny region of the rr ll parameter space the ll agents play an important role in the dynamics leading to the allc phase they help eliminate the dd strategy in the transient and later only to be replaced by the cc strategy phase diagrams in the rr ll space are presented for different values of nn the strategy ll plays two roles it leads to an alll phase and helps give an allc phase an algorithm for simulating the model numerically is described and validated the algorithm will be useful in studying our model in various structured populations

the peierls nabarro and benjamin ono equations abstract an intimate connection between the peierls nabarro equation in crystal dislocation theory and the travelling wave form of the benjamin ono equation in hydro dynamics is uncovered it is used to prove the essential uniqueness of peierls solution of the peierls nabarro equation and to give in closed form all solutions of the analogous periodic problem the latter problem is shown to be an example of global bifurcation with no secondary symmetry breaking bifurcations for a nonlinear neumann boundary value problem or equivalently for an equation involving the conjugate operator which is the hilbert transform of functions on the unit circle

efficient estimators of population mean using auxiliary attributes abstract abd elfattah et al 1 suggested a set of estimators for calculating population mean using auxiliary attributes this paper proposes a family of estimators based on an adaptation of the estimators presented by koyuncu and kadilar 2 and introduces a new family of exponential estimators using auxiliary attributes the expressions of the mean square errors mses of the adapted and proposed families are derived in a general form it is shown that the adapted version of the koyuncu and kadilar 2 estimators is always more efficient than that of abd elfattah et al 1 moreover the new exponential estimators based on auxiliary attributes are more efficient than those of koyuncu and kadilar 2 and abd elfattah et al 1 the theoretical findings are supported by a numerical example using original data

improved estimation of population mean in simple random sampling using information on auxiliary attribute abstract this paper addresses the problem of estimating the population mean with known population proportion of an auxiliary variable a class of estimators is defined which includes the estimators recently proposed by shabbir and gupta 2007 10 and abd elfattah et al 2010 1 the usual unbiased estimator and naik and gupta 1996 15 estimator are also the member of the proposed class of the estimators the bias and mean square error mse expressions of the proposed class are obtained up to first order of approximation asymptotically optimum estimator aoe in the class of estimators is identified alongwith its mean square error formula the correct mse and minimum mse expressions of shabbir and gupta 2007 10 estimator are also given it has been shown that the proposed class of estimators is more efficient than the usual unbiased estimator usual linear regression estimator and estimators classes of estimators due to naik and gupta 1996 15 jhajj et al 2008 9 shabbir and gupta 2007 10 estimator singh et al 2008 13 and abd elfattah et al 2010 1 the double sampling version of the proposed class of estimators is proposed alongwith its properties numerical illustrations are given in support of the present study

ratio estimators for the population variance in simple and stratified random sampling we propose some ratio type variance estimators using ratio estimators for the population mean in literature we obtain mean square error mse equations of proposed estimators and show that proposed estimators are more efficient than the traditional ratio estimator suggested by c t isaki variance estimation using auxiliary information journal of the american statistical association 78 1983 117 123 under certain conditions we also adapt the proposed estimators in the simple random sampling to the stratified random sampling in addition we support the theoretical results with the aid of numerical examples

age based model for weighted network with general assortative mixing abstract in this paper we propose an evolutionary model for weighted networks by introducing an age based mutual selection mechanism our model generates power law distributions of degree weight and strength which are confirmed by analytical predictions and are consistent with real observations the investigation of the relationship between clustering and the connectivity of nodes suggests hierarchical organization in the weighted networks furthermore both assortative and disassortative properties can be naturally obtained by tuning a parameter which controls the strength of age based preferential attachments since the age information of nodes is easier to acquire than the degree and strength of nodes and almost all empirically observed structural and weighted properties can be reproduced by the simple evolutionary regulation our model may reveal some underlying mechanisms that are key for the evolution of weighted complex networks

an improved exponential estimator of finite population mean in simple random sampling using an auxiliary attribute abstract in this paper we propose an exponential ratio type estimator of the finite population mean when auxiliary information is qualitative in nature under simple random sampling without replacement scheme the expressions for the bias and the mean square error of the proposed estimator have been obtained up to first order of approximation to show that our proposed estimator is more efficient as compared to the existing estimators we have made a comparative study with respect to their mean square errors theoretically and numerically we have found that our proposed estimator is always more efficient as compared to its competitor estimators including all the estimators of abd elfattah et al 1 a m abd elfattah e a el sherpieny s m mohamed and o f abdou improvement in estimating the population mean in simple random sampling using information on auxiliary attribute applied mathematics and computation 215 2010 4198 4202

asymptotics for the fractional allen cahn equation and stationary nonlocal minimal surfaces this article is mainly devoted to the asymptotic analysis of a fractional version of the elliptic allen cahn equation in a bounded domain omega subseteq mathbb r n with or without a source term in the right hand side of the equation commonly called chemical potential in contrast to the usual allen cahn equation the laplace operator is here replaced by the fractional laplacian delta s with s in 0 1 2 as defined in fourier space in the singular limit varepsilon to 0 we show that arbitrary solutions with uniformly bounded energy converge both in the energetic and geometric sense to surfaces of prescribed nonlocal mean curvature in whenever the chemical potential remains bounded in suitable sobolev spaces with no chemical potential the notion of surface of prescribed nonlocal mean curvature reduces to the stationary version of the nonlocal minimal surfaces introduced by caffarelli et al commun pure appl math 63 1111 1144 2010 under the same sobolev regularity assumption on the chemical potential we also prove that surfaces of prescribed nonlocal mean curvature have a minkowski codimension equal to one and that the associated sets have a locally finite fractional 2s prime perimeter in for every s prime in 0 1 2

entire solutions of semilinear elliptic equations in r 3 and a conjecture of de giorgi this paper is concerned with the study of bounded solutions of semilinear elliptic equations u f u in the whole space r under the assumption that u is monotone in one direction say nu in r n the goal is to establish the one dimensional character or symmetry of u namely that u only depends on one variable or equivalently that the level sets of u are hyperplanes this type of symmetry question was raised by de giorgi in who made the following conjecture we quote literally page of dg

on de giorgi s conjecture in dimension n 9 a celebrated conjecture due to de giorgi states that any bounded solution of the equation u 1 u 2 u 0 in r n with ynu 0 must be such that its level setsfu g are all hyperplanes at least for dimension n 8 a counterexample for n 9 has long been believed to exist starting from a minimal graph which is not a hyperplane found by bombieri de giorgi and giusti in r n n 9 we prove that for any small 0 there is a bounded solution u y with yn u 0 which resembles tanh a t p 2 a where t t y denotes a choice of signed distance to the blown up minimal graph 1 this solution is a counterexample to de giorgi s conjecture for n 9

an improved estimator of finite population mean when using two auxiliary attributes in this paper we propose an improved estimator of finite population mean using information on two auxiliary attributes under simple random sampling srs and two phase sampling schemes the bias and mean squared error mse expressions of the proposed estimators are obtained up to first order of approximation it is shown theoretically that the proposed estimator is more efficient than the ratio product type estimator regression estimator difference type estimator and malik and singh 2013 13 estimator in both srs and two phase sampling an empirical study using two data sets is also conducted to support the theoretical findings

a new estimator using two auxiliary variables utilizing the estimator in abu dayyeh et al appl math comput 139 2003 287 we suggest an estimator using two auxiliary variables in simple random sampling we obtain mean square error mse equation of the proposed estimator and theoretically compare it with the mse of the traditional estimator using two auxiliary variables by this comparison we show the condition that the proposed estimator is more efficient than the traditional one in addition we support this theoretical result by an application with original data

quantum strategies win in a defector dominated population a b s t r a c t quantum strategies are introduced into evolutionary games the agents using quantum strategies are regarded as invaders whose fraction generally is 1 of a population in contrast to the 50 of the population that are defectors in this paper the evolution of strategies on networks is investigated in a defector dominated population when three networks square lattice newman watts small world network and scale free network are constructed and three games prisoners dilemma snowdrift and stag hunt are employed as far as these three games are concerned the results show that quantum strategies can always invade the population successfully comparing the three networks we find that the square lattice is most easily invaded by agents that adopt quantum strategies however a scale free network can be invaded by agents adopting quantum strategies only if a hub is occupied by an agent with a quantum strategy or if the fraction of agents with quantum strategies in the population is significant

ratio estimators in simple random sampling this study proposes ratio estimators by adapting the estimators type of ray and singh j ind stat assoc 19 1981 147 to traditional and the other ratio type estimators in simple random sampling in literature theoretically mean square error mse equations of all proposed ratio estimators are obtained and compared with each other by these comparisons the conditions which make each proposed estimator more efficient than the others are found the theoretical results are supported by a numerical illustration

fattening and nonfattening phenomena for planar nonlocal curvature flows we discuss fattening phenomenon for the evolution of sets according to their nonlocal curvature more precisely we consider a class of generalized curvatures which correspond to the first variation of suitable nonlocal perimeter functionals defined in terms of an interaction kernel k which is symmetric nonnegative possibly singular at the origin and satisfies appropriate integrability conditions we prove a general result about uniqueness of the geometric evolutions starting from regular sets with positive k curvature in mathbb r n and we discuss the fattening phenomenon in mathbb r 2 for the evolution starting from the cross showing that this phenomenon is very sensitive to the strength of the interactions as a matter of fact we show that the fattening of the cross occurs for kernels with sufficiently large mass near the origin while for kernels that are sufficiently weak near the origin such a fattening phenomenon does not occur we also provide some further results in the case of the fractional mean curvature flow showing that strictly starshaped sets in mathbb r n have a unique geometric evolution moreover we exhibit two illustrative examples in mathbb r 2 of closed nonregular curves the first with a lipschitz type singularity and the second with a cusp type singularity given by two tangent circles of equal radius whose evolution develops fattening in the first case and is uniquely defined in the second thus remarking the high sensitivity of the fattening phenomenon in terms of the regularity of the initial datum the latter example is in striking contrast to the classical case of the local curvature flow where two tangent circles always develop fattening as a byproduct of our analysis we provide also a simple proof of the fact that the cross in mathbb r 2 is not a k minimal set for the nonlocal perimeter functional associated to k

new alternatives to ratio estimators of population variance in sample surveys in this paper we propose alternative estimators to ratio estimators given by kadilar and cingi 2006 and a class of estimators for population variance using the same approach adopted by srivenkataramana 1980 conditions under which the proposed estimators are more efficient than usual unbiased estimator isaki 1983 estimator biradar and singh 1994 estimator and the estimators given by kadilar and cingi 2006 are obtained the exact expressions for biases and mean squared errors of the proposed estimators are obtained an empirical study has been carried out to demonstrate the performance of the suggested estimators also following searls 1964 generalized version of the proposed class of estimators is also studied with its properties

uncovering cooperative behaviors with sparse historical behavior data in the spatial games for past decades the main attention of the evolutionary games has been focused on cooperation mechanism with the assumption that the strategy information of all players are known however it is difficult for observers to obtain the global information of players strategies in the real world and some players even hide their strategy information to confuse their opponents here we try to solve the problem to predicate the hidden strategies with sparse historical behavior data in the evolutionary games to quantify the similarity of strategies among the players in our method the euclidean distance of players is defined from the strategies of the players in the few past rounds then the hidden strategy of a player will be determined from the tendency that players with minimum euclidean distance will adopt similar strategies the method has good performance on determining hidden strategy of human beings in both the prisoner s dilemma game and the public goods game where strategies of twenty five percent players are hidden and the success rate to determine hidden strategy reaches up to 0 9 it is also found that the success rate to determine hidden strategy depends on both length of historical behavior data and tempting payoff b the prisoner s dilemma game or multiple factor r the public goods game

transmission of information and herd behavior an application to financial markets we propose a model for stochastic formation of opinion clusters modeled by an evolving network and herd behavior to account for the observed fat tail distribution in returns of financial price data the only parameter of the model is h the rate of information dispersion per trade which is a measure of herding behavior for h below a critical h the system displays a power law distribution of the returns with exponential cutoff however for hg h an increase in the probability of large returns is found and may be associated with the occurrence of large crashes

calibration estimators in survey sampling abstract this article investigates estimation of finite population totals in the presence of univariate or multivariate auxiliary information estimation is equivalent to attaching weights to the survey data we focus attention on the several weighting systems that can be associated with a given amount of auxiliary information and derive a weighting system with the aid of a distance measure and a set of calibration equations we briefly mention an application to the case in which the information consists of known marginal counts in a two or multi way table known as generalized raking the general regression estimator greg was conceived with multivariate auxiliary information in mind ordinarily this estimator is justified by a regression relationship between the study variable y and the auxiliary vector x but we note that the greg can be derived by a different route by focusing instead on the weights the ordinary sampling weights of the kth observation is 1 k where k is the inclusion probabilit

preferential selection promotes cooperation in a spatial public goods game abstract we introduce a preferential selection mechanism into a spatial public goods game where players are located on a square lattice each individual chooses one of its neighbors as a reference with a probability proportional to exp p y a where p y is the neighbor s payoff and a 0 is a tunable parameter it is shown that the introduction of such a preferential selection can remarkably promote the emergence of cooperation over a wide range of the multiplication factor we find that the mean payoffs of cooperators along the boundary are higher than that of defectors and cooperators form larger clusters as a increases the extinction thresholds of cooperators and defectors for different values of noise are also investigated

effects of dynamical grouping on cooperation in n person evolutionary snowdrift game a population typically consists of agents that continually distribute themselves into different groups at different times this dynamic grouping has recently been shown to be essential in explaining many features observed in human activities including social economic and military activities we study the effects of dynamic grouping on the level of cooperation in a modified evolutionary n person snowdrift game due to the formation of dynamical groups the competition takes place in groups of different sizes at different times and players of different strategies are mixed by the grouping dynamics it is found that the level of cooperation is greatly enhanced by the dynamic grouping of agents when compared with a static population of the same size as a parameter ensuremath beta which characterizes the relative importance of the reward and cost increases the fraction of cooperative players f c increases and it is possible to achieve a fully cooperative state analytically we present a dynamical equation that incorporates the effects of the competing game and group size distribution the distribution of cooperators in different groups is assumed to be a binomial distribution which is confirmed by simulations results from the analytic equation are in good agreement with numerical results from simulations we also present detailed simulation results of f c over the parameter space spanned by the probabilities of group coalescence ensuremath nu m and group fragmentation ensuremath nu p in the grouping dynamics a high ensuremath nu m and low ensuremath nu p promotes cooperation and a favorable reward characterized by a high ensuremath beta would lead to a fully cooperative state

evolutionary prisoner s dilemma game on weighted scale free networks this paper investigates the evolutionary prisoner s dilemma on weighted scale free networks the weighted networks are generated by adopting barabscale free network and assigning link weight with wij ki kj simulation results show thatthe cooperationfrequency hasa strongdependence on the value of which isassociated withthe maximalcooperation frequency has been sought out moreover gini coefficient and pareto exponent of the system s wealth distribution are investigated the inequality of wealth distribution is minimized at 1

an improved family of estimators of finite population mean based on the auxiliary attribute abstract recently koyuncu 2012 3 proposed an efficient family of estimators for estimation of finite population mean using information on the auxiliary attribute in this paper we propose two improved estimators of finite population mean the biases and mean squared errors of the proposed estimators are derived up to the first order of approximation it is observed that the first proposed estimator is always better than the first family of estimators adapted by koyuncu 2012 3 an empirical study is carried out to demonstrate the performance of the proposed estimators

estimation of population mean using information on auxiliary attribute in two phase sampling in this paper we have proposed an estimator for finite population mean using auxiliary information in form of attributes under double sampling we have also derived the expression of mean squared error of the proposed estimator the proposed estimator is compared with the simple mean per unit usual double sampling ratio and product estimators an empirical study is carried out to judge the merit of the proposed estimator

networking effects on evolutionary snowdrift game in networks with fixed degrees abstract we study the effects of spatial structures other than the degree distribution on the extent of the emergence of cooperation in an evolutionary snowdrift game by swapping the links in three different types of regular lattices with a fixed degree k we study how the frequency of cooperator f c changes as the clustering coefficient cc which signifies how the nearest neighbors of a vertex are connected and the sharing coefficient sc which signifies how the next nearest neighbors of a vertex are shared by the nearest neighbors are varied for small k a non vanishing cc tends to suppress f c a non vanishing sc also leads to a suppressed f c for the networks studied as the degree increases the sensitivity of f c to the network properties is found to become increasingly weak the result is discussed within the context of the ranking patterns of average payoffs as k changes an approximation for f c which is based on the idea of a finite fully connected network and gives results in good agreement with numerical results is derived in the limit of large k

evolutionary snowdrift game incorporating costly punishment in structured populations abstract the role of punishment and the effects of a structured population in promoting cooperation are important issues within a recent model of snowdrift game sg incorporating a costly punishing strategy p we study the effects of a population connected through a square lattice the punishers who carry basically a cooperative c character are willing to pay a cost so as to punish a non cooperative d opponent by depending on the cost to benefit ratio r in sg and the initial conditions the system evolves into different phases that could be homogeneous or inhomogeneous the spatial structure imposes geometrical constraint on how one agent is affected by neighboring agents results of extensive numerical simulations both for the steady state and the dynamics are presented possible phases are identified and discussed and isolated phases in the r space are identified as special local structures of strategies that are stable due to the lattice structure in contrast to a well mixed population where punishers are suppressed due to the cost of punishment the altruistic punishing strategy can flourish and prevail for appropriate values of the parameters implying an enhancement in cooperation by imposing punishments in a structured population the system could evolve to a phase corresponding to the coexistence of c d and p strategies at some particular payoff parameters and such a phase is absent in a well mixed population the pair approximation a commonly used analytic approach is extended from a two strategy system to a three strategy system we show that the pair approximation can at best capture the numerical results only qualitatively due to the improper way of including spatial correlation imposed by the lattice structure the approximation does not give the frequencies of c d and p accurately and fails to give the homogeneous alld and allp phases

incorporating the auxiliary information available in variance estimation a difference estimator using an auxiliary variable x is defined to estimate the finite population variance s y 2 of the study character y classical difference type estimators use auxiliary information based on a single auxiliary parameter specifically the parameter of interest associated with the auxiliary variable in practice however several parameters for auxiliary variables are available this paper discusses how such estimators can be modified to improve the usual methods if information related to other parameters associated with an auxiliary variable is known a simulation study is carried out to demonstrate the superiority of the suggested estimator over the others

cooperative behavior in n person evolutionary snowdrift games with punishment abstract we generalize the n person evolutionary snowdrift game to incorporate the effects of costly punishment in a well mixed population a set of dynamical equations that account for the evolution of the frequencies of the three strategies under replicator dynamics is formulated at long time the system evolves into one of two phases with different properties consisting only of two strategies and three strategy coexistence is not allowed small cost to benefit ratio big competing group size and severe punishment tend to suppress non cooperators and lead to a cooperative system with a mixture of cooperators and punishers the resulting composition depends on the initial conditions as the dynamics is frozen once non cooperators extinct large cost to benefit ratio small competing group size and light punishment tend to be self destructive for the punishers and lead to a mixture of cooperators and non cooperators with composition independent of initial conditions and a continual dynamics the frozen phase and dynamical phase correspond to a line of fixed points and a single fixed point on different axes in the phase space respectively a simulation algorithm that mimics the replicator dynamics exactly is proposed results of the dynamical equations and numerical simulations are found to be in exact agreement

cooperation in n person evolutionary snowdrift game in scale free barabasi albert networks abstract cooperation in the n person evolutionary snowdrift game nesg is studied in scale free barabasi albert ba networks due to the inhomogeneity of the network two versions of nesg are proposed and studied in a model where the size of the competing group varies from agent to agent the fraction of cooperators drops as a function of the payoff parameter the networking effect is studied via the fraction of cooperative agents for nodes with a particular degree for small payoff parameters it is found that the small k agents are dominantly cooperators while large k agents are of non cooperators studying the spatial correlation reveals that cooperative agents will avoid to be nearest neighbors and the correlation disappears beyond the next nearest neighbors the behavior can be explained in terms of the networking effect and payoffs in another model with a fixed size of competing groups the fraction of cooperators could show a non monotonic behavior in the regime of small payoff parameters this non trivial behavior is found to be a combined effect of the many agents with the smallest degree in the ba network and the increasing fraction of cooperators among these agents with the payoff for small payoffs

evolutionary mixed games in structured populations cooperation and the benefits of heterogeneity evolutionary games on networks traditionally involve the same game at each interaction here we depart from this assumption by considering mixed games where the game played at each interaction is drawn uniformly at random from a set of two different games while in well mixed populations the random mixture of the two games is always equivalent to the average single game in structured populations this is not always the case we show that the outcome is in fact strongly dependent on the distance of separation of the two games in the parameter space effectively this distance introduces payoff heterogeneity and the average game is returned only if the heterogeneity is small for higher levels of heterogeneity the distance to the average game grows which often involves the promotion of cooperation the presented results support preceding research that highlights the favorable role of heterogeneity regardless of its origin and they also emphasize the importance of the population structure in amplifying facilitators of cooperation

nonlocal minimal graphs in the plane are generically sticky we prove that nonlocal minimal graphs in the plane exhibit generically stickiness effects and boundary discontinuities more precisely we show that if a nonlocal minimal graph in a slab is continuous up to the boundary then arbitrarily small perturbations of the far away data produce boundary discontinuities hence either a nonlocal minimal graph is discontinuous at the boundary or a small perturbation of the prescribed conditions produces boundary discontinuities the proof relies on a sliding method combined with a fine boundary regularity analysis based on a discontinuity smoothness alternative namely we establish that nonlocal minimal graphs are either discontinuous at the boundary or their derivative is holder continuous up to the boundary in this spirit we prove that the boundary regularity of nonlocal minimal graphs in the plane jumps from discontinuous to c 1 gamma with no intermediate possibilities allowed in particular we deduce that the nonlocal curvature equation is always satisfied up to the boundary as an interesting byproduct of our analysis one obtains a detailed understanding of the switch between the regime of continuous and hence differentiable nonlocal minimal graphs to that of discontinuous and hence with differentiable inverse ones

separatrices between healthy and endemic states in an adaptive epidemic model abstract the separatrices between the healthy and endemic states in the bistable regime and issues related to determining the critical infected fraction i crit in a recently proposed epidemic model on an adaptive network are analyzed the epidemic follows the susceptible infected susceptible sis process and the network adapts by breaking connections between healthy and infected individuals and rewiring to other healthy individuals using a set of mean field equations the separatrix can be found for a given set of system parameters the unstable fixed point is shown to correspond to a highly atypical network configuration and thus using it as an estimate of i crit may be erroneous the characteristics of initial configurations leading to either a healthy or an endemic final state are investigated and how the configurations determine i crit is discussed results of numerical simulations confirm that the unstable fixed point does not in general give a good estimate of i crit while our discussion focuses on an adaptive sis model the approach in determining i crit and the conclusion are general and they can be applied to other co evolving dynamical systems

estimating population proportions in the presence of missing data this paper discusses the estimation of a population proportion in the presence of missing data and using auxiliary information at the estimation stage a general class of estimators which make efficient use of the available information are proposed some theoretical properties of the proposed estimators are analyzed and they allow us to find the optimal value for the proposed class in the sense of minimal variance the optimal estimator is thus more efficient than the customary estimator results derived from a simulation study indicate that the proposed optimal estimator gives desirable results in comparison to alternative estimators

evolution of cooperation in well mixed n person snowdrift games abstract we study the time evolution of cooperation in a recently proposed n person evolutionary snowdrift game by focusing on the details of the evolutionary dynamics it is found that the analytic solution for the equilibrium fraction of cooperators as given previously by the replicator dynamics stems from a balance between the terms the cost to contribute to a common task and the risk in refusing to participate in a common task analytic expressions for these two terms are given and their magnitudes are studied over the whole range of parameter space away from equilibrium it is the imbalance between these terms that drives the system to equilibrium a continuous time first order differential equation for the degree of cooperation is derived for arbitrary interacting group size n and cost to benefit ratio analytic solutions to the time evolution of cooperation for the cases of n 2 and n 3 are obtained with results in good agreement with those obtained by numerical simulations for arbitrary n numerical solutions to the equation give the time evolution of cooperation with the long time limit giving the equilibrium fraction of cooperators

properties of wealth distribution in multi agent systems of a complex network abstract we present a simple model for examining the wealth distribution with agents playing evolutionary games the prisoners dilemma and the snowdrift game on complex networks pareto s power law distribution of wealth from 1897 is reproduced on a scale free network and the gibbs or log normal distribution for a low income population is reproduced on a random graph the pareto exponents of a scale free network are in agreement with empirical observations the gini coefficient of an er random graph shows a sudden increment with game parameters we suggest that the social network of a high income group is scale free whereas it is more like a random graph for a low income group

cooperative behavior in evolutionary snowdrift game with bounded rationality abstract an evolutionary snowdrift game sg that incorporates bounded rationality and limited information in the evolutionary process is proposed and studied based on sg in a well mixed population and defining the winning action at a turn to be the one that gets a higher payoff the most recent m winning actions can be used as a public information based on which the competing agents decide their next actions this defines a strategy pool from which each agent picks a number of strategies as their tool in adapting to the competing environment the payoff parameter r in sg serves to set the maximum number of winners per turn due to the bounded rationality and limited information the cooperative frequency shows steps and plateaux as a function of r and these features tend to be smoothed out as m increases these features are results of an interplay between a restricted subset of m bit histories that the system can visit at a value of r and the limited capacity that agents can adapt the standard deviation in the number of agents taking the cooperative action is also studied for general values of r our model generates a realization of the binary agent resource model the idea of introducing bounded rationality into a two person game to realize the minority game or binary agent resource model could be a useful tool for future research

on higher dimensional singularities for the fractional yamabe problem a nonlocal mazzeo pacard program we consider the problem of constructing solutions to the fractional yamabe problem which are singular at a given smooth submanifold for which we establish the classical gluing method of mazzeo and pacard j differential geom 1996 for the scalar curvature in the fractional setting this proof is based on the analysis of the model linearized operator which amounts to the study of a fractional order ordinary differential equation ode thus our main contribution here is the development of new methods coming from conformal geometry and scattering theory for the study of nonlocal odes note however that no traditional phase plane analysis is available here instead we first provide a rigorous construction of radial fast decaying solutions by a blowup argument and a bifurcation method then second we use conformal geometry to rewrite this nonlocal ode giving a hint of what a nonlocal phase plane analysis should be third for the linear theory we use complex analysis and some non euclidean harmonic analysis to examine a fractional schrodinger equation with a hardy type critical potential we construct its green s function deduce fredholm properties and analyze its asymptotics at the singular points in the spirit of frobenius method surprisingly enough a fractional linear ode may still have a 2 dimensional kernel as in the second order case