dilemma solving by the coevolution of networks and strategy in a 2 2 game a 2 ifmmode times else texttimes fi 2 game model implemented by a coevolution mechanism of both networks and strategy inspired by the work of zimmermann and eguiluz phys rev e72 056118 2005 is established network adaptation is the manner in which an existing link between two agents is destroyed and how a new one is established to replace it the strategy is defined as whether an agent offers cooperation c or defection d both the networks and strategy are synchronously renovated in a simulation time step a series of numerical experiments considering various 2 ifmmode times else texttimes fi 2 game structures reveals that the proposed coevolution mechanism can solve dilemmas in several game classes the effect of solving a dilemma means mutual cooperation reciprocity r reciprocity which is brought about by emerging several cooperative hub agents who have plenty of links this effect can be primarily observed in game classes of the prisoner s dilemma and stag hunt the coevolution mechanism however seems counterproductive for game classes of leader and hero where the alternating reciprocity st reciprocity is meaningful

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

ends of maps ii versions of the finiteness obstruction and simple homotopy theory within e overx are developed this provides a setting for obstructions to the map analogs of the end ands cobordism theorems for manifolds these are applied to study equivariant mapping cylinder neighborhoods in topological group actions triangulations of locally triangulable spaces and block bundle structures on approximate fibrations

critical exponent for evolution equations in modulation spaces abstract in this paper we propose a method to find the critical exponent for certain evolution equations in modulation spaces we define an index s q and use it to determine the critical exponent of the fractional heat equation as an example we prove that when s q is greater than the critical exponent this equation is locally well posed in the space c 0 t m p q s and when s q is less than the critical exponent this equation is ill posed in the space c 0 t m 2 q s our method may further be applied to some other evolution equations

mixing protocols in the public goods game if interaction partners in social dilemma games are not selected randomly from the population but are instead determined by a network of contacts it has far reaching consequences for the evolutionary dynamics selecting partners randomly leads to a well mixed population where pattern formation is essentially impossible this rules out important mechanisms that can facilitate cooperation most notably network reciprocity in contrast if interactions are determined by a lattice or a network then the population is said to be structured where cooperators can form compact clusters that protect them from invading defectors between these two extremes however there is ample middle ground that can be brought about by the consideration of temporal networks mobility or other coevolutionary processes the question that we here seek to answer is when does mixing on a lattice actually lead to well mixed conditions to that effect we use the public goods game on a square lattice and we consider nearest neighbor and random mixing with different frequencies as well as a mix of both mixing protocols not surprisingly we find that nearest neighbor mixing requires a higher frequency than random mixing to arrive at the well mixed limit the differences between the two mixing protocols are most expressed at intermediate mixing frequencies whilst at very low and very high mixing frequencies the two almost converge we also find a near universal exponential growth of the average size of cooperator clusters as their fraction increases from zero to one regardless of whether this increase is due to increasing the multiplication factor of the public goods decreasing the frequency of mixing or gradually shifting the mixing from random to nearest neighbors

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 the regularity of the flow map for the gravity capillary equations abstract we prove via explicitly constructed initial data that solutions to the gravity capillary wave system in r 3 representing a 2 d air water interface immediately fail to be c 3 with respect to the initial data if the initial data h 0 0 h s 1 2 h s for s 3 similar results hold in r 2 domains with a 1 d interface furthermore we discuss the related threshold for the pure gravity water wave system

local well posedness for the sixth order boussinesq equation abstract in this work we study the local well posedness of the initial value problem for the nonlinear sixth order boussinesq equation u t t u x x u x x x x u x x x x x x u 2 x x where 1 we prove the local well posedness with initial data in non homogeneous sobolev spaces h s r for negative indices of s r

enhancement of cooperation in highly clustered scale free networks we study the effect of clustering on the organization of cooperation by analyzing the evolutionary dynamics of the prisoner s dilemma on scale free networks with a tunable value of clustering we find on the one hand that a high value of the clustering coefficient produces an overall enhancement of cooperation in the network even for a very high temptation to defect on the other hand high clustering homogenizes the process of invasion of degree classes by defectors decreasing the chances of survival of low densities of cooperators in the network

the cauchy problem for the schrodinger kdv system abstract in this paper we prove that in the general case i e not necessarily vanishing the cauchy problem for the schrodinger korteweg de vries system is locally well posed in l 2 h 3 4 and if 0 then it is locally well posed in h s h 3 4 with 3 16 s 1 4 these results improve the corresponding results of corcho and linares 2007 5 idea of the proof is to establish some bilinear and trilinear estimates in the space g s f s where g s and f s are dyadic bourgain type spaces related to the schrodinger operator i t x 2 and the airy operator t x 3 respectively but with a modification on f s in low frequency part of functions with a weaker structure related to the maximal function estimate of the airy operator

cooperation for volunteering and partially random partnerships competition among cooperative defective and loner strategies is studied by considering an evolutionary prisoner s dilemma game for different partnerships in this game each player can adopt one of its coplayer s strategy with a probability depending on the difference of payoffs coming from games with the corresponding coplayers our attention is focused on the effects of annealed and quenched randomness in the partnership for fixed number of coplayers it is shown that only the loners survive if the four coplayers are chosen randomly mean field limit on the contrary on the square lattice all the three strategies are maintained by the cyclic invasions resulting in a self organizing spatial pattern if the fixed partnership is described by a regular small world structure then a homogeneous oscillation occurs in the population dynamics when the measure of quenched randomness exceeds a threshold value similar behavior with higher sensitivity to the randomness is found if temporary partners are substituted for the standard ones with some probability at each step of iteration

adaptive networks coevolution of disease and topology d epartement de physique de g enie physique et d optique universit e laval qu ebec qu ebec canada g1v 0a6 dated september 13 2010 adaptive networks have been recently introduced in the context of disease propagation on complexnetworks they account for the mutual interaction between the network topology and the states ofthe nodes until now existing models have been analyzed using low complexity analytic formalisms revealing nevertheless some novel dynamical features however current methods have failed toreproduce with accuracy the simultaneous time evolution of the disease and the underlying networktopology in the framework of the adaptive sis model of gross et al phys rev lett 96 208701 2006 we introduce an improved compartmental formalism able to handle this coevolutionarytask successfully with this approach we analyze the interplay and outcomes of both dynamicalelements process and structure on adaptive networks featuring di erent degree distributions at theinitial stage

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

evolutionary prisoner s dilemma game on newman watts networks maintenance of cooperation was studied for a two strategy evolutionary prisoner s dilemma game where the players are located on a one dimensional chain and their payoff comes from games with the nearest and next nearest neighbor interactions the applied host geometry makes it possible to study the impacts of two conflicting topological features the evolutionary rule involves some noise affecting the strategy adoptions between the interacting players using monte carlo simulations and the extended versions of dynamical mean field theory we determined the phase diagram as a function of noise level and a payoff parameter the peculiar feature of the diagram is changed significantly when the connectivity structure is extended by extra links as suggested by newman and watts

remarks on the cauchy problem for the one dimensional quadratic fractional heat equation abstract we prove that the cauchy problem associated with the one dimensional quadratic fractional heat equation u t u u 2 t 0 t x r or t with 0 1 is well posed in h s for s max 1 2 2 except in the case 1 2 where it is shown to be well posed for s 1 2 and ill posed for s 1 2 as a by product we improve the known well posedness results for the heat equation 1 by reaching the end point sobolev index s 1 finally in the case 1 2 1 we also prove optimal results in the besov spaces b 2 s q

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

well posedness of the good boussinesq equation in analytic gevrey spaces and time regularity abstract the cauchy problem for the good boussinesq equation with data in analytic gevrey spaces on the line and the circle is considered and its local well posedness in these spaces is proved the proof is based on bilinear estimates in bourgain type spaces incorporating the symbol of the linear part of the equation and an exponential weight expressing the analytic gevrey regularity of the solution in the spatial variable also gevrey regularity of the solution in time variable is provided

hawks and doves on small world networks we explore the hawk dove game on networks with topologies ranging from regular lattices to random graphs with small world networks in between this is done by means of computer simulations using several update rules for the population evolutionary dynamics we find the overall result that cooperation is sometimes inhibited and sometimes enhanced in those network structures with respect to the mixing population case the differences are due to different update rules and depend on the gain to cost ratio we analyze and qualitatively explain this behavior by using local topological arguments

degree mixing in multilayer networks impedes the evolution of cooperation traditionally the evolution of cooperation has been studied on single isolated networks yet a player especially in human societies will typically be a member of many different networks and those networks will play different roles in the evolutionary process multilayer networks are therefore rapidly gaining on popularity as the more apt description of a networked society with this motivation we here consider two layer scale free networks with all possible combinations of degree mixing wherein one network layer is used for the accumulation of payoffs and the other is used for strategy updating we find that breaking the symmetry through assortative mixing in one layer and or disassortative mixing in the other layer as well as preserving the symmetry by means of assortative mixing in both layers impedes the evolution of cooperation we use degree dependent distributions of strategies and cluster size analysis to explain these results which highlight the importance of hubs and the preservation of symmetry between multilayer networks for the successful resolution of social dilemmas

norm inflation for the generalized boussinesq and kawahara equations abstract we consider ill posedness of the cauchy problem for the generalized boussinesq and kawahara equations we prove norm inflation with general initial data an improvement over the ill posedness results by geba et al 2014 for the generalized boussinesq equations and by kato 2011 for the kawahara equation

well posedness for a quadratic derivative nonlinear schrodinger system at the critical regularity abstract we consider the cauchy problem for a quadratic derivative nonlinear schrodinger system in sobolev space h s in this paper under the null condition and the mass resonance relation we prove large data local well posedness if the space dimension d 3 and s s c d 2 and s s c or d 1 and s 0 where s c is the scaling critical regularity moreover under the same assumptions we also prove small data global well posedness and scattering in h s if d 3 and s s c our proof is based on a contraction argument using the u p and v p type function spaces

phase transitions in a coevolving snowdrift game with costly rewiring we propose and study a dissatisfied adaptive snowdrift game with a payoff parameter r that incorporates a cost for rewiring a connection an agent facing adverse local environment may switch action without a cost or rewire an existing link with a cost a so as to attain a better competing environment detailed numerical simulations reveal nontrivial and nonmonotonic dependence of the frequency of cooperation and the densities of different types of links on a and r a theory that treats the cooperative and noncooperative agents separately and accounts for spatial correlation up to neighboring agents is formulated the theory gives results that are in good agreement with simulations the frequency of cooperation f c is enhanced suppressed at high rewiring cost relative to that at low rewiring cost when r is small large for a given value of r there exists a critical value of the rewiring cost below which the system evolves into a phase of frozen dynamics with isolated noncooperative agents segregated from a cluster of cooperative agents and above which the system evolves into a connected population of mixed actions with continual dynamics the phase boundary on the a text ensuremath r phase space that separates the two phases with distinct structural population and dynamical properties is mapped out the phase diagram reveals that as a general feature for small r small a the disconnected and segregated phase can survive over a wider range of a r

evolutionary prisoner s dilemma game on hierarchical lattices an evolutionary prisoner s dilemma pd game is studied with players located on a hierarchical structure of layered square lattices the players can follow two strategies d defector and c cooperator and their income comes from pd games with the neighbors the adoption of one of the neighboring strategies is allowed with a probability dependent on the payoff difference monte carlo simulations are performed to study how the measure of cooperation is affected by the number of hierarchical levels q and by the temptation to defect according to the simulations the highest frequency of cooperation can be observed at the top level if the number of hierarchical levels is low q 4 for larger q however the highest frequency of cooperators occurs in the middle layers the four level hierarchical structure provides the highest average total income for the whole community

sharp well posedness and ill posedness results for a quadratic non linear schrodinger equation abstract we establish that the quadratic non linear schrodinger equation iu t u xx u 2 where u r r c is locally well posed in h s r when s 1 and ill posed when s 1 previous work in c kenig g ponce l vega quadratic forms for the 1 d semilinear schrodinger equation trans amer math soc 346 1996 3323 3353 had established local well posedness for s 3 4 the local well posedness is achieved by an iteration using a modification of the standard x s b spaces the ill posedness uses an abstract and general argument relying on the high to low frequency cascade present in the non linearity and a computation of the first non linear iterate

cooperation in the noisy case prisoner s dilemma game on two types of regular random graphs we have studied an evolutionary prisoner s dilemma game with players located on two types of random regular graphs with a degree of 4 the analysis is focused on the effects of payoffs and noise temperature on the maintenance of cooperation when varying the noise level and or the highest payoff the system exhibits a second order phase transition from a mixed state of cooperators and defectors to an absorbing state where only defectors remain alive for the random regular graph and bethe lattice the behavior of the system is similar to those found previously on the square lattice with nearest neighbor interactions although the measure of cooperation is enhanced by the absence of loops in the connectivity structure for low noise the optimal connectivity structure is built up from randomly connected triangles

spatial social dilemmas dilution mobility and grouping effects with imitation dynamics abstract we present an extensive systematic study of the prisoner s dilemma and snowdrift games on a square lattice under a synchronous noiseless imitation dynamics we show that for both the occupancy of the network and the random mobility of the agents there are intermediate values that may increase the amount of cooperators in the system and new phases appear we analytically determine the transition lines between these phases and compare with the mean field prediction and the observed behavior on a square lattice we point out which are the more relevant microscopic processes that entitle cooperators to invade a population of defectors in the presence of mobility and discuss the universality of these results

improved local well posedness for the periodic good boussinesq equation abstract we prove that the good boussinesq model is locally well posed in the space h h 2 3 8 in the proof we employ the method of normal forms which allows us to explicitly extract the rougher part of the solution while we show that the remainder is in the smoother space c 0 t h t min 1 3 1 2 thus we establish a smoothing effect of order min 1 2 1 2 for the nonlinear evolution this is new even in the previously considered cases 0 1 4

conjugation spaces and 4 manifolds we show that 4 dimensional conjugation manifolds are all obtained from branched twofold coverings of knotted surfaces in mathbb z 2 homology 4 spheres

ill posedness results for generalized boussinesq equations abstract in this article we investigate both the periodic and non periodic initial value problems for generalized boussinesq equations we show that the associated flow map is not smooth for a range of sobolev indices thus providing a threshold for the regularity needed to perform a picard iteration for these problems

nonstable solitons and sharp criteria for wave collapse sharp sufficient criteria for collapse are found for the nonlinear schr odinger equation in the so called supercritical case as well as for the ginzburg landau equation in the case of the subcritical bifurcation it is demonstrated that nonstable solitons in these models under some additional assumptions play the role of a boundary saddle points between collapsing and noncollapsing solutions

well posedness and ill posedness of kdv equation with higher dispersion abstract first the cauchy problem for kdv equation with 2 n 1 order dispersion is studied and the local well posedness result for the initial data in sobolev spaces h s r with s n 1 4 is established via the fourier restriction norm method second we prove that the kdv equation with 2 n 1 order dispersion is ill posed for the initial data in h s r with s n 1 4 n 2 n n if the flow map is c 2 differentiable at zero form h s r to c 0 t h s r finally we obtain the sharp regularity requirement for the kdv equation with 2 n 1 order dispersion s n 1 4

coevolutionary games on networks we study agents on a network playing an iterated prisoner s dilemma against their neighbors the resulting spatially extended coevolutionary game exhibits stationary states which are nash equilibria after perturbation of these equilibria avalanches of mutations reestablish a stationary state scale free avalanche distributions are observed that are in accordance with calculations from the nash equilibria and a confined branching process the transition from subcritical to critical avalanche dynamics can be traced to a change in the degeneracy of the cooperative macrostate and is observed for many variants of this game

quadratic dispersive generalized benjamin ono equation abstract this paper is concerned with quadratic dispersive generalized benjamin ono equation 1 1 1 2 we prove sharp local well posedness in h s s 1 4 with a solution map that is analytic from h s r to c 0 t h s r and the ill posed result in h s r as soon as s s in the sense that the flow map u 0 u t cannot be continuous

graph fission in an evolving voter model we consider a simplified model of a social network in which individuals have one of two opinions called 0 and 1 and their opinions and the network connections coevolve edges are picked at random if the two connected individuals hold different opinions then with probability 1 one imitates the opinion of the other otherwise i e with probability the link between them is broken and one of them makes a new connection to an individual chosen at random i from those with the same opinion or ii from the network as a whole the evolution of the system stops when there are no longer any discordant edges connecting individuals with different opinions letting be the fraction of voters holding the minority opinion after the evolution stops we are interested in how depends on and the initial fraction u of voters with opinion 1 in case i there is a critical value c which does not depend on u with u for c and 0 for c u u but for c u we have u 1 2 using simulations and approximate calculations we explain why these two nearly identical models have such dramatically different phase transitions

towards effective payoffs in the prisoner s dilemma game on scale free networks we study the transition towards effective payoffs in the prisoner s dilemma game on scale free networks by introducing a normalization parameter guiding the system from accumulated payoffs to payoffs normalized with the connectivity of each agent we show that during this transition the heterogeneity based ability of scale free networks to facilitate cooperative behavior deteriorates continuously eventually collapsing with the results obtained on regular graphs the strategy donations and adaptation probabilities of agents with different connectivities are studied results reveal that strategies generally spread from agents with larger towards agents with smaller degree however this strategy adoption flow reverses sharply in the fully normalized payoff limit surprisingly cooperators occupy the hubs even if the averaged cooperation level due to partly normalized payoffs is moderate

quadratic forms for the 1 d semilinear schrodinger equation this paper is concerned with 1 d quadratic semilinear schr6dinger equations we study local well posedness in classical sobolev space hs of the associated initial value problem and periodic boundary value problem our main interest is to obtain the lowest value of s which guarantees the desired local well posedness result we prove that at least for the quadratic cases these values are negative and depend on the structure of the nonlinearity considered

global existence of smooth solutions and stability of solitary waves for a generalized boussinesq equation certain generalizations of one of the classical boussinesq type equations u tt u xx u 2 u xx xx are considered it is shown that the initial value problem for this type of equation is always locally well posed it is also determined that the special solitary wave solutions of these equations are nonlinearly stable for a range of their phase speeds these two facts lead to the conclusion that initial data lying relatively close to a stable solitary wave evolves into a global solution of these equations this contrasts with the results of blow up obtained recently by kalantarov and ladyzhenskaya for the same type of equation and casts additional light upon the results for the original version of this class of equations obtained via inverse scattering theory by deift tomei and trubowitz