prisoner s dilemma on a stochastic nongrowth network evolution model we investigate the evolution of cooperation on a nongrowth dynamic network model with a death birth dynamics based on tournament selection in the limit of large population size the equilibrium cooperator density is well described by our mean field approximations and inversely related to the average degree in the system small populations are also examined and found to deviate considerably from their expected mean field behavior an expanded replicator equation incorporating gaussian fluctuations in the strategy densities is then constructed with its output agreeing well with our simulation data for all sizes we also briefly comment on the role of strategy mutation in sustaining polymorphic populations in small systems

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

similarity based cooperation and spatial segregation we analyze a cooperative game where the cooperative act is not based on the previous behavior of the coplayer but on the similarity between the players this system has been studied in a mean field description recently phys rev e 68 046129 2003 here the spatial extension to a two dimensional lattice is studied where each player interacts with eight players in a moore neighborhood the system shows a strong segregation independent of parameters the introduction of a local conversion mechanism towards tolerance allows for four state cycles and the emergence of spiral waves in the spatial game in the case of asymmetric costs of cooperation a rich variety of complex behavior is observed depending on both cooperation costs finally we study the stabilization of a cooperative fixed point of a forecast rule in the symmetric game which corresponds to cooperation across segregation borders this fixed point becomes unstable for high cooperation costs but can be stabilized by a linear feedback mechanism

weighted scale free networks with variable power law exponents abstract we present a weighted scale free network model in which the power law exponents can be controlled by the model parameters the network is generated through the weight driven preferential attachment of new nodes to existing nodes and the growth of the weights of existing links the simplicity of the model enables us to derive analytically the various statistical properties such as the distributions of degree strength and weight the degree strength and degree weight relationship and the dependencies of these power law exponents on the model parameters finally we demonstrate that networks of words coauthorship of researchers and collaboration of actor actresses are quantitatively well described by this model

prisoners dilemma in real world acquaintance networks spikes and quasiequilibria induced by the interplay between structure and dynamics we study nowak and may s spatial prisoners dilemma game driven by mutations random choices of suboptimal strategies on empirical social networks the time evolution of the cooperation level is highly complex containing spikes and steps between quasistable levels a statistical characterization of the quasistable states and a study of the mechanisms behind the steps are given we argue that the crucial structural ingredients causing the observed behavior is an inhomogeneous degree distribution and that the connections within vertices of highest degree are rather sparse based on these observations we construct model networks with a similar complex time evolution of the cooperation level

dynamics morphogenesis and convergence of evolutionary quantum prisoner s dilemma games on networks the authors proposed a quantum prisoner s dilemma pd game as a natural extension of the classic pd game to resolve the dilemma here we establish a new nash equilibrium principle of the game propose the notion of convergence and discover the convergence and phase transition phenomena of the evolutionary games on networks we investigate the many body extension of the game or evolutionary games in networks for homogeneous networks we show that entanglement guarantees a quick convergence of super cooperation that there is a phase transition from the convergence of defection to the convergence of super cooperation and that the threshold for the phase transitions is principally determined by the nash equilibrium principle of the game with an accompanying perturbation by the variations of structures of networks for heterogeneous networks we show that the equilibrium frequencies of super cooperators are divergent that entanglement guarantees emergence of super cooperation and that there is a phase transition of the emergence with the threshold determined by the nash equilibrium principle accompanied by a perturbation by the variations of structures of networks our results explore systematically for the first time the dynamics morphogenesis and convergence of evolutionary games in interacting and competing systems

pseudo reductive and quasi reductive groups over non archimedean local fields abstract among connected linear algebraic groups quasi reductive groups generalize pseudo reductive groups which in turn form a useful relaxation of the notion of reductivity we study quasi reductive groups over non archimedean local fields focusing on aspects involving their locally compact topology for such groups we construct valuated root data in the sense of bruhat tits and we make them act nicely on affine buildings we prove that they admit iwasawa and cartan decompositions and we construct small compact open subgroups with an iwahori decomposition we also initiate the smooth representation theory of quasi reductive groups among others we show that their irreducible smooth representations are uniformly admissible and that all these groups are of type i finally we discuss how much of these results remains valid if we omit the connectedness assumption on our linear algebraic groups

cooperation in spatial prisoner s dilemma with two types of players for increasing number of neighbors we study a spatial two strategy cooperation and defection prisoner s dilemma game with two types a and b of players located on the sites of a square lattice the evolution of strategy distribution is governed by iterated strategy adoption from a randomly selected neighbor with a probability depending on the payoff difference and also on the type of the neighbor the strategy adoption probability is reduced by a prefactor w 1 from the players of type b we consider the competition between two opposite effects when increasing the number of neighbors k 4 8 and 24 within a range of the portion of influential players type a the inhomogeneous activity in strategy transfer yields a relevant increase dependent on w in the density of cooperators the noise dependence of this phenomenon is also discussed by evaluating phase diagrams

effects of inhomogeneous activity of players and noise on cooperation in spatial public goods games we study the public goods game in the noisy case by considering the players with inhomogeneous activity of teaching on a square lattice it is shown that the introduction of the inhomogeneous activity of teaching the players can remarkably promote cooperation by investigating the effects of noise on cooperative behavior in detail we find that the variation of cooperator density c with the noise parameter displays several different behaviors c monotonically increases decreases with c first increases decreases with and then it decreases increases monotonically after reaching its maximum minimum value which depends on the amount of the multiplication factor r on whether the system is homogeneous or inhomogeneous and on whether the adopted updating is synchronous or asynchronous these results imply that the noise plays an important and nontrivial role in the evolution of cooperation

stochasticity and evolutionary stability in stochastic dynamical systems different concepts of stability can be obtained in different limits a particularly interesting example is evolutionary game theory which is traditionally based on infinite populations where strict nash equilibria correspond to stable fixed points that are always evolutionarily stable however in finite populations stochastic effects can drive the system away from strict nash equilibria which gives rise to a new concept for evolutionary stability the conventional and the new stability concepts may apparently contradict each other leading to conflicting predictions in large yet finite populations we show that the two concepts can be derived from the frequency dependent moran process in different limits our results help to determine the appropriate stability concept in large finite populations the general validity of our findings is demonstrated showing that the same results are valid employing vastly different co evolutionary processes

on neron raynaud class groups of tori and the capitulation problem we discuss the capitulation problem for neron raynaud class groups of tori over global fields f and obtain generalizations of the main results of 10 we also show that short exact sequences of f tori induce long exact sequences involving the corresponding neronraynaud class groups for example we show that the neron raynaud class group of any f torus which is split by a metacyclic extension of f can be resolved in terms of classical ideal class groups of global fields

computing discrete logarithms in high genus hyperelliptic jacobians in provably subexponential time we provide a subexponential algorithm for solving the discrete logarithm problem in jacobians of high genus hyperelliptic curves over finite fields its expected running time for instances with genus g and underlying finite field fq satisfying g log q for a positive constant is given by o e f 1 3 2 3 2 o 1 g log q log g log q the algorithm works over any finite field and its running time does not rely on any unproven assumptions

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

on the local langlands conejcture mathrm gl n the cyclic case let f be a locally compact nonarchimedean field and p its residue characteristic let f be a separable algebraic closure of f wf the weil group of f over f e a character of fx of order n and e the corresponding character of wf then there exists a canonical map from the set of equivalence classes a of irreducible degree n representations of wf such that e a a to the set of equivalence classes 7r of admissible irreducible supercuspidal representations of gl n f verifying odet x 7t this map is shown to be bijective and to preserve e factors for pairs

computing hermite and smith normal forms of triangular integer matrices abstract this paper considers the problem of transforming a triangular integer input matrix to canonical hermite and smith normal form we provide algorithms and prove deterministic running times for both transformation problems that are optimal in the matrix dimension the algorithms are easily implemented assume standard integer arithmetic and admit excellent performance in practice the results presented here lead to a faster algorithm for computing the smith normal form of an arbitrary i e non triangular input matrix

effect of the spatial autocorrelation of empty sites on the evolution of cooperation abstract an evolutionary game model is constructed to investigate the spatial autocorrelation of empty sites on the evolution of cooperation each individual is assumed to imitate the strategy of the one who scores the highest in its neighborhood including itself simulation results illustrate that the evolutionary dynamics based on the prisoner s dilemma game pd depends severely on the initial conditions while the snowdrift game sd is hardly affected by that a high degree of autocorrelation of empty sites is beneficial for the evolution of cooperation in the pd whereas it shows diversification effects depending on the parameter of temptation to defect in the sd moreover for the repeated game with three strategies always defect alld tit for tat tft and always cooperate allc simulations reveal that an amazing evolutionary diversity appears for varying of parameters of the temptation to defect and the probability of playing in the next round of the game the spatial autocorrelation of empty sites can have profound effects on evolutionary dynamics equilibrium and oscillation and spatial distribution

on some haar measures on reductive groups we give a characteristic free proof of a theorem of b h gross comparing two haar measures on a reductive group over a local field as a consequence of this theorem we obtain an integration formula for adele groups over global function fields

on galois cohomology of semisimple groups over local and global fields of positive characteristic ii we show that the recent results of prasad and rapinchuk adv math 207 2 646 660 2006 on the existence and uniqueness of certain global forms of semisimple algebraic groups with given local behaviour in the case of number fields still hold in the case of global function fields

computing discrete logarithms in real quadratic congruence function fields of large genus the discrete logarithm problem in various finite abelian groups is the basis for some well known public key cryptosystems recently real quadratic congruence function fields were used to construct a public key distribution system the security of this public key system is based on the difficulty of a discrete logarithm problem in these fields in this paper we present a probabilistic algorithm with subexponential running time that computes such discrete logarithms in real quadratic congruence function fields of sufficiently large genus this algorithm is a generalization of similar algorithms for real quadratic number fields

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

computing the sign or the value of the determinant of an integer matrix a complexity survey computation of the sign of the determinant of a matrix and the determinant itself is a challenge for both numerical and exact methods we survey the complexity of existing methods to solve these problems when the input is an n n matrix a with integer entries we study the bit complexities of the algorithms asymptotically in n and the norm of a existing approaches rely on numerical approximate computations on exact computations or on both types of arithmetic in combination

evolutionary prisoner s dilemma game with dynamic preferential selection we study a modified prisoner s dilemma game taking place on two dimensional disordered square lattices the players are pure strategists and can either cooperate or defect with their immediate neighbors in the generations each player updates its strategy by following one of the neighboring strategies with a probability dependent on the payoff difference the neighbor selection obeys a dynamic preferential rule i e the more frequently a neighbor s strategy was adopted by the focal player in the previous rounds the larger probability it will be chosen to refer to in the subsequent rounds it is found that cooperation is substantially promoted due to this simple selection mechanism corresponding analysis is provided by the investigation of the distribution of the players impact weights persistence and correlation function

on the topology of relative and geometric orbits for actions of algebraic groups over complete fields abstract in this paper we investigate the problem of closedness of relative orbits for the action of algebraic groups on affine varieties defined over complete fields in its relation with the problem of equipping a topology on cohomology groups sets and give some applications

on weil restriction of reductive groups and a theorem of prasad let g be a connected simple semisimple algebraic group over a local field f of arbitrary characteristic in a previous article by the author the zariski dense compact subgroups of g f were classified in the present paper this information is used to give another proof of a theorem of prasad 8 also proved by margulis 3 which asserts that if g is isotropic every non discrete closed subgroup of finite covolume contains the image of open image in new window where open image in new window denotes the universal covering of g this result played a central role in prasad s proof of strong approximation the present proof relies on some basic properties of weil restrictions over possibly inseparable field extensions which are also proved here

anti affine algebraic groups abstract we say that an algebraic group g over a field is anti affine if every regular function on g is constant we obtain a classification of these groups with applications to the structure of algebraic groups in positive characteristics and to the construction of many counterexamples to hilbert s fourteenth problem

hermite and smith normal form algorithms over dedekind domains we show how the usual algorithms valid over euclidean domains such as the hermite normal form the modular hermite normal form and the smith normal form can be extended to dedekind rings in a sequel to this paper we will explain the use of these algorithms for computing in relative extensions of number fields

the constraints of the group of an integral monoid abstract a z module group of integral vectors can be constrained by subspace and integrality constraints we show how to extract these constraints from the chvatal constraints of an integral monoid

embedding problems over large fields in this paper we study galois theoretic properties of a large class of fields a class which includes all fields satisfying a universal local global principle for the existence of rational points on varieties as applications we give a positive answer to a long standing conjecture which originates in an unpublished note of roquette and asserts that the absolute galois group of a countable hilbertian pac field is profinite free see f j problem 24 41 secondly we give new evidence for the conjecture of shafarevich which asserts that the absolute galois group of qab is profinite free finally one of the most interesting applications of the theory we develop here is the insight in the galois structure of the totally eg adic numbers

influence of the variance of degree distributions on the evolution of cooperation in complex networks abstract we study how initial network structure affects the evolution of cooperation in a spatial prisoner s dilemma game the network structure is characterized by various statistical properties among those properties we focus on the variance of the degree distribution and inquire how it affects the evolution of cooperation by three methods of imitation for every method it was found that a scale free network does not always promote the evolution of cooperation and that there exists an appropriate value of the variance at which cooperation is optimal

on galois cohomology of unipotent algebraic groups over local fields abstract in this paper we give a necessary and sufficient condition for the finiteness of galois cohomology of unipotent groups over local fields of positive characteristic

on the computation of unit groups and class groups of totally complex quartic fields in this paper we describe the computation of a system of fundamental units and of the class group for each totally real quartic field y of discriminant less than 106 generating equations integral bases and the galois groups for all those fields were recently given by buchmann and ford

weil restriction and support varieties this paper extends the comparison results for cohomological support varieties for chevalley groups of the form g fp established by j carlson z lin and d nakano to chevalley groups of the form g fpd other topics considered are complexity and non maximal support varieties for modules techniques developed by j pevtsova and the author together with the use of weil restriction functors are employed

recognizing badly presented z modules finitely generated z modules have canonical decompositions when such modules are given in a finitely presented form there is a classical algorithm for computing a canonical decomposition this is the algorithm for computing the smith normal form of an integer matrix we discuss algorithms for smith normal form computation and present practical algorithms which give excellent performance for modules arising from badly presented abelian groups we investigate such issues as congruential techniques sparsity considerations pivoting strategies for gauss jordan elimination lattice basis reduction and computational complexity our results which are primarily empirical show dramatically improved performance on previous methods

evolutionary prisoner s dilemma game on a square lattice a simplified prisoner s game is studied on a square lattice when the players interacting with their neighbors can follow two strategies to cooperate c or to defect d unconditionally the players updated in random sequence have a chance to adopt one of the neighboring strategies with a probability depending on the payoff difference using monte carlo simulations and dynamical cluster techniques we study the density c of cooperators in the stationary state this system exhibits a continuous transition between the two absorbing states when varying the value of temptation to defect in the limits stackrel ensuremath rightarrow c 0 and 1 we have observed critical transitions belonging to the universality class of directed percolation

hermite normal form computation using modulo determinant arithmetic this paper describes a new class of hermite normal form solution procedures which perform modulo determinant arithmetic throughout the computation this class of procedures is shown to possess a polynomial time complexity bound which is a function of the length of the input string computational results are also given

algorithms for computing a hermite reduction of a matrix with polynomial coefficients resume nous etudions dans cet article des algorithmes de calcul de la reduction de hermite d une matrice a coefficients polynomiaux qui evitent l explosion de la taille des objets intermediaires et ont une bonne complexite sequentielle le deuxieme et le troisieme algorithmes generalisent la methode des sous resultants pour le calcul du pgcd de deux polynomes le dernier de ces algorithmes semble optimal en ce sens qu il calcule une reduction de hermite avec une matrice de passage de degre minimal en utilisant une methode progressive et economique nous ramenons le calcul de la reduite de hermite a un probleme de triangulation progressive des matrices dont les tailles sont bien controlees et dont les entrees sont des coefficients de polynomes donnes en entree l algorithme est donc faisable des qu on dispose d une methode de triangulation en temps polynomial pour les matrices dans le corps des coefficients il revient au meme de dire que le calcul des determinants est en temps polynomial dans le corps en question pour le codage choisi les resultats theorqiues sont meilleurs que pour les algorithmes connus precedemment et les resultats partiques sont encourageants

a polynomial time algorithm to compute generalized hermite normal forms of matrices over z x abstract in this paper we give the first polynomial time algorithm to compute the generalized hermite normal form for a matrix f over z x or equivalently the reduced grobner basis of the z x module generated by the column vectors of f the algorithm has polynomial bit size computational complexities and is also shown to be practically more efficient than existing algorithms the algorithm is based on three key ingredients first an f4 style algorithm to compute the grobner basis is adopted where a novel prolongation is designed such that the sizes of coefficient matrices under consideration are nicely controlled second the complexity bound of the algorithm is achieved by a nice estimation for the degree and height bounds of the polynomials in the generalized hermite normal form third fast algorithms to compute hermite normal forms of matrices over z are used as the computational tool

on some local global principles for linear algebraic groups over infinite algebraic extensions of global fields abstract in this paper we develop an arithmetic theory of quadratic and hermitian forms over infinite algebraic extensions of local and global fields in particular we prove that the cohomological hasse principle for h 1 holds for all semisimple simply connected algebraic groups defined over any infinite algebraic extension of any global field and we also show the validity of some local global principles for skew hermitian forms defined over such infinite extension fields as applications we deduce some analogs of well known results such as landherr s and kneser s strong hasse principle hasse maass schilling norm theorem albert brauer hasse noether theorem and hasse norm theorem over such fields

hasse principles for multinorm equations abstract a classical result of hasse states that the norm principle holds for finite cyclic extensions of global fields in other words local norms are global norms we investigate the norm principle for finite dimensional commutative etale algebras over global fields since such an algebra is a product of separable extensions this is often called the multinorm principle under the assumption that the etale algebra contains a cyclic factor we give a necessary and sufficient condition for the hasse principle to hold in terms of an explicitly constructed element of a finite abelian group this can be seen as an explicit description of the brauer manin obstruction to the hasse principle

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

a fast las vegas algorithm for computing the smith normal form of a polynomial matrix abstract a las vegas probabilistic algorithm is presented that finds the smith normal form s q x n n of a nonsingular input matrix a z x n n the algorithm requires an expected number of o n 3 d d n 2 log a bit operations where a bounds the magnitude of all integer coefficients appearing in a and d bounds the degrees of entries of a in practice the main cost of the computation is obtaining a nonunimodular triangularization of a polynomial matrix of the same dimension and with similar size entries to those of the input matrix we show how to accomplish this in o n 5 d d log a log a bit operations using standard integer polynomial and matrix arithmetic these complexity results improve significantly on previous algorithms in both a theoretical and a practical sense

a rigorous subexponential algorithm for computation of class groups let c d denote the gauss class group of quadratic forms of a negative discriminant d or equivalently the class group of the imaginary quadratic field q a we give a rigorous proof that there exists a las ve gas algorithm that will compute the structure of c d with an expected running time of l d vf2 1 bit operations where l d exp vlog d log log d thus of course also includes the computation of the class number h d the cardinality of c d ibm research division almaden research center k53 802 650 harry road san jose california 95 120 6099 current address k mccurley organization 1423 sandia national laboratories albuquerque new mexico 87185 this content downloaded from 207 46 13 180 on thu 08 sep 2016 05 47 29 utc all use subject to http about jstor org terms

reachability and steering of rolling polyhedra a case study in discrete nonholonomy rolling a ball on a plane is a standard example of nonholonomy reported in many textbooks and the problem is also well understood for any smooth deformation of the surfaces for nonsmoothly deformed surfaces however much less is known although it may seem intuitive that nonholonomy is conserved think e g to polyhedral approximations of smooth surfaces current definitions of nonholonomy are inherently referred to systems described by ordinary differential equations and are thus inapplicable to such systems in this paper we study the set of positions and orientations that a polyhedral part can reach by rolling on a plane through sequences of adjacent faces we provide a description of such reachable set discuss conditions under which the set is dense or discrete or has a compound structure and provide a method for steering the system to a desired reachable configuration robustly with respect to model uncertainties based on ideas and concepts encountered in this case study and in some other examples we provide we turn back to the most general aspects of the problem and investigate the possible generalization of the notion of kinematic nonholonomy to nonsmooth discrete and hybrid dynamical systems to capture the essence of phenomena commonly regarded as nonholonomic at least two irreducible concepts are to be defined of internal and external nonholonomy which may coexist in the same system these definitions are instantiated by examples

sur certaines identites endoscopiques entre transformees de fourier the main geometric terms of the arthur selberg trace formula are the weighted orbital integrals an important problem is to express these distributions as images by transfer of analogous distributions on endoscopic groups arthur has given a solution but under the hypothesis of the fundamental lemma of langlands in this paper we prove some relations between the fourier transforms of weighted orbital integrals on the lie alge bras of groups which are inner forms of each other these relations hold unconditionnally and they provide some evidence for arthur s solution besides they should enable us to prove new results of transfer in the context of the non invariant trace formula

cooperation enhanced by the difference between interaction and learning neighborhoods for evolutionary spatial prisoner s dilemma games we study an evolutionary prisoner s dilemma game with two layered graphs where the lower layer is the physical infrastructure on which the interactions are taking place and the upper layer represents the connections for the strategy adoption learning mechanism this system is investigated by means of monte carlo simulations and an extended pair approximation method we consider the average density of cooperators in the stationary state for a fixed interaction graph while varying the number of edges in the learning graph according to the monte carlo simulations the cooperation is modified substantially in a way resembling a coherence resonance like behavior when the number of learning edges is increased this behavior is reproduced by the analytical results

decomposing finitely generated integral monoids by elimination abstract a finitely generated integral monoid can always be decomposed into a finite although generally exponential number of integral monoids having special structure in that their related integer programming feasibility problems can be solved in polynomial time the decomposition can be constructed using an elimination scheme due to presburger and williams that generalizes fourier motzkin elimination

an application of the hermite normal form in integer programming abstract a new algorithm for solving integer programming problems is developed it is based on cuts which are generated from the hermite normal form of the basis matrix at a continuous extreme point

local global principles for torsors over arithmetic curves we consider local global principles for torsors under linear algebraic groups over function fields of curves over complete discretely valued fields the obstruction to such a principle is a version of the tate shafarevich group and for groups with rational components we compute it explicitly and show that it is finite this yields necessary and sufficient conditions for local global principles to hold our results rely on first obtaining a mayer vietoris sequence for galois cohomology and then showing that torsors can be patched we also give new applications to quadratic forms and central simple algebras

motif structure and cooperation in real world complex networks abstract networks of dynamical nodes serve as generic models for real world systems in many branches of science ranging from mathematics to physics technology sociology and biology collective behavior of agents interacting over complex networks is important in many applications the cooperation between selfish individuals is one of the most interesting collective phenomena in this paper we address the interplay between the motifs cooperation properties and their abundance in a number of real world networks including yeast protein protein interaction human brain protein structure email communication dolphins social interaction zachary karate club and net science coauthorship networks first the amount of cooperativity for all possible undirected subgraphs with three to six nodes is calculated to this end the evolutionary dynamics of the prisoner s dilemma game is considered and the cooperativity of each subgraph is calculated as the percentage of cooperating agents at the end of the simulation time then the three to six node motifs are extracted for each network the significance of the abundance of a motif represented by a z value is obtained by comparing them with some properly randomized versions of the original network we found that there is always a group of motifs showing a significant inverse correlation between their cooperativity amount and z value i e the more the z value the less the amount of cooperativity this suggests that networks composed of well structured units do not have good cooperativity properties

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

on the topology on group cohomology of algebraic groups over complete valued fields abstract we introduce some topologies on the group cohomology of algebraic groups over complete valued fields and consider some applications

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

on the galois and flat cohomology of unipotent algebraic groups over local and global function fields i abstract we discuss some results on the triviality and finiteness for galois cohomology of connected unipotent groups over non perfect and especially local and global function fields and their relation with the closedness of orbits which extend some well known results of serre raynaud and oesterle as one of the applications we show that a separable additive polynomial over a global field k of characteristic p 0 in two variables is universal over k if and only if it is so over all completions k v of k

counting maximal arithmetic subgroups we study the growth rate of the number of maximal arithmetic subgroups of bounded covolumes in a semisimple lie group using an extension of the method developed by borel and prasad

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