locating a changed segment in a sequence of bernoulli variables the theory underlying inferences about a single change point in a sequence of independent bernoulli variables is extended to the two change points problem where the distance between the two change points is known namely a changed segment both null and nonnull distributions of the log likelihood ratio for testing the hypothesis that there is no changed segment against the alternative that there is one of specified length are derived using recurrence equations the distribution of the maximum likelihood estimator of the location of the changed segment is derived

three state cyclic voter model extended with potts energy the cyclically dominated voter model on a square is extended by taking into consideration the variation of potts energy during the nearest neighbor invasions we have investigated the effect of surface tension on the self organizing patterns maintained by the cyclic invasions a geometrical analysis is also developed to study the three color patterns these investigations clearly indicate that in the voter model limit the pattern evolution is governed by the loop creation due to the overhanging during the interfacial roughening conversely in the presence of surface tension the evolution is governed by spiral formation whose geometrical parameters depend on the strength of cyclic dominance

evolutionary dynamics of spatial games abstract a lattice model of coevolution of strategies for two person 2 2 matrix games is introduced the model allows evolution in an unbounded space of strategies in particular we explore the region of parameter space corresponding to the prisoner s dilemma and classify the types of dynamical and evolutionary behavior that appear for certain restricted strategy spaces we explore the complete space of lattice games

four classes of interactions for evolutionary games the symmetric four strategy games are decomposed into a linear combination of 16 basis games represented by orthogonal matrices among these basis games four classes can be distinguished as it is already found for the three strategy games the games with self dependent cross dependent payoffs are characterized by matrices consisting of uniform rows columns six of 16 basis games describe coordination type interactions among the strategy pairs and three basis games span the parameter space of the cyclic components that are analogous to the rock paper scissors games in the absence of cyclic components the game is a potential game and the potential matrix is evaluated the main features of the four classes of games are discussed separately and we illustrate some characteristic strategy distributions on a square lattice in the low noise limit if logit rule controls the strategy evolution analysis of the general properties indicates similar types of interactions at larger number of strategies for the symmetric matrix games

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

an improved bonferroni inequality and applications summary we present an improved bonferroni inequality which gives an upper bound for the probability of the union of an arbitrary sequence of events the bound is constructed in terms of the joint probability of pairs of events which are represented by edges on a graph examples of applications to periodicity location shift detection kolmogorovsmirnov tests and outlier detection are given

branching annihilating random walk on random regular graphs the branching annihilating random walk is studied on a random graph whose sites have a uniform number of neighbors z the monte carlo simulations in agreement with the generalized mean field analysis indicate that the concentration decreases linearly with the branching rate for z 4 while the coefficient of the linear term becomes zero if z 3 these properties are described by a modified mean field theory taking explicitly into consideration the probability of mutual annihilation of the parent and its offspring particles using the returning features of a single walker on the same graph

on the distributions of scan statistics abstract this article considers the distribution of the scan statistic over some interval of the real line both for a fixed number of independent uniform points and for a poisson process it provides a new series method of calculating this distribution in the poisson case and a simple self contained recursive approximation in the fixed case these results work best at low densities which is precisely the case when the closed formulas are computationally impractical the results are compared with values tabulated by neff and naus 1980 and with a recent approximation due to naus 1982 there is also an explanation of why naus s approximation is good in the poisson case and a derivation of recursive bounds in the fixed case

emergence of cooperation among interacting individuals we study the evolution of interacting individuals located on the sites of a regular lattice the individuals play a two action game in which the players either cooperate or defect with respect to a certain issue the main rule of the game is that a player does not change his action when he and his opponent have held the same action in the previous round numerical simulations performed on a square lattice show a stationary state in which the lattice has a finite number of cooperators and defectors and two frozen states one full of cooperators and the other full of defectors

approximations for the tail probabilities and moments of the scan statistic the scan statistic is used to test the hypothesis that the observed events occur at random uniformly distributed in time or space versus the hypothesis that they cluster within a moving window of size w to implement the testing procedure based on the scan statistic its tail probabilities have to be effectively evaluated in this article a survey of results on the approximations of the distribution of the scan statistic and its moments is presented numerical results comparing these approximations are also given numerous references with applications in epidemiological studies using the scan statistics are mentioned related scan statistics that have been used in many other interesting applications are listed in the reference section the article concludes with the presentation of unsolved problems related to the scan statistic

meixner pollaczek polynomials and the heisenberg algebra an alternative proof is given for the connection between a system of continuous hahn polynomials and identities for symmetric elements in the heisenberg algebra which was first observed by bender mead and pinsky phys rev lett 56 2445 1986 j math phys 28 509 1987 the continuous hahn polynomials turn out to be meixner pollaczek polynomials use is made of the connection between laguerre polynomials and meixner pollaczek polynomials the rodrigues formula for laguerre polynomials an operational formula involving meixner pollaczek polynomials and the schrodinger model for the irreducible unitary representations of the three dimensional heisenberg group

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

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

a useful upper bound for the tail probabilities of the scan statistic when the sample size is large abstract although a number of approximations to the distribution under uniformity of the scan statistic are known they are when the sample size is large either difficult to compute or numerically unstable a simple upper bound for the upper tail of the distribution based on a result of hunter 1976 is derived it is found that for large sample sizes and a reasonably wide range of window widths this bound gives a numerically stable approximation that is sufficiently accurate for hypothesis testing purposes

evolutionary prisoner s dilemma in random graphs abstract we study an evolutionary version of the spatial prisoner s dilemma game spd where the agents are placed in a random graph for graphs with fixed connectivity we show that for low values of the final density of cooperating agents c depends on the initial conditions however if the graphs have large connectivities c is independent of the initial conditions we characterize the phase diagram of the system using both extensive numerical simulations and analytical computations it is shown that two well defined behaviors are present a nash equilibrium where the final density of cooperating agents c is constant and a non stationary region where c fluctuates in time moreover we study the spd in poisson random graphs and find that the phase diagram previously developed looses its meaning in fact only one regime may be defined this regime is characterized by a non stationary final state where the density of cooperating agents varies in time

role separating ordering in social dilemmas controlled by topological frustration three is a crowd is an old proverb that applies as much to social interactions as it does to frustrated configurations in statistical physics models accordingly social relations within a triangle deserve special attention with this motivation we explore the impact of topological frustration on the evolutionary dynamics of the snowdrift game on a triangular lattice this topology provides an irreconcilable frustration which prevents anticoordination of competing strategies that would be needed for an optimal outcome of the game by using different strategy updating protocols we observe complex spatial patterns in dependence on payoff values that are reminiscent to a honeycomb like organization which helps to minimize the negative consequence of the topological frustration we relate the emergence of these patterns to the microscopic dynamics of the evolutionary process both by means of mean field approximations and monte carlo simulations for comparison we also consider the same evolutionary dynamics on the square lattice where of course the topological frustration is absent however with the deletion of diagonal links of the triangular lattice we can gradually bridge the gap to the square lattice interestingly in this case the level of cooperation in the system is a direct indicator of the level of topological frustration thus providing a method to determine frustration levels in an arbitrary interaction network

ising model versus normal form game abstract the 2 spin ising model in statistical mechanics and the 2 2 normal form game in game theory are compared all configurations allowed by the second are recovered by the first when the only concern is about nash equilibria but it holds no longer when pareto optimum considerations are introduced as in the prisoner s dilemma this gap can nevertheless be filled by adding a new coupling term to the ising model even if that term has up to now no physical meaning an individual complete bilinear objective function is thus found to be sufficient to reproduce all possible configurations of a 2 2 game using this one to one mapping new perspectives for future research in both fields can be envisioned

solution of the hausdorff moment problem by the use of pollaczek polynomials abstract we present a new method for solving the hausdorff moment problem which makes use of pollaczek polynomials this problem is ill posed in the sense of hadamard and therefore it is unstable from a numerical viewpoint we shall prove that the expansion which we obtain is asymptotically convergent in the l2 norm when the data i e the moments are perturbed by noise and finite in number this result is largely used in the numerical analysis of the problem

nonoverlapping clusters approximate distribution and application to molecular biology summary an approach is developed for the screening of genomic sequence data to identify gene regulatory regions this approach is based on deciding if putative transcription factor binding sites are clustered together to a greater extent than one would expect by chance given n events occurring on an interval of width l l base pairs an r w cluster is defined as r 1 consecutive events all contained within a window of length wl accurate and easily computable approximations are derived for the distribution of the number of nonoverlapping r w clusters under the model that the positions of the n events have a uniform distribution simulations demonstrate that these approximations have greater accuracy than existing methods the approximation is applied to detect erythroid specific regulatory regions in genomic dna sequences first in an artificial case where r is specified a priori and then as part of an exploratory approach

testing for a pulse in seasonal event data most tests for seasonal clustering are sensitive to the peak in incidence in some season 90 day interval followed by a trough 6 months later we present two statistics sensitive to a relatively sharp increase in disease incidence for a season superimposed on a constant incidence over the entire year the ratchet scan based on the maximum number of events in k consecutive months and the continuous circular scan the maximum number of events in d consecutive days we tabulate the tail distribution of the ratchet scan for n less than or equal to 35 and k 2 and 3 and find the asymptotic distribution which is applicable for n greater than or equal to 50 when k 2 or 3 we evaluate an approximation for the distribution of the continuous scan the statistics are applied to investigate seasonal clustering of adolescent suicide in the united states an illustration is given of the application of the circular scan and a small simulation study and the example are used to compare the statistics with others proposed in the literature language en

extension of a spatial evolutionary coordination game with neutral options the multiagent evolutionary games on a lattice are equivalent to a kinetic ising model if the uniform pair interactions are defined by a two strategy coordination game and the logit rule controls the strategy updates now we extend this model by allowing the players to use additional neutral strategies that provide zero payoffs for both players if one of them selects one of the neutral strategies in the resulting n strategy evolutionary games the analytical methods and numerical simulations indicate continuous order disorder phase transitions when increasing the noise level if n does not exceed a threshold value for larger n the system exhibits a first order phase transition at a critical noise level decreasing asymptotically as 2 ln n

spatial coherence resonance in excitable media we study the phenomenon of spatial coherence resonance in a two dimensional model of excitable media with fitzhugh nagumo local dynamics in particular we show that there exists an optimal level of additive noise for which an inherent spatial scale of the excitable media is best pronounced we argue that the observed phenomenon occurs due to the existence of a noise robust excursion time that is characteristic for the local dynamics whereby the diffusion constant representing the rate of diffusive spread determines the actual resonant spatial frequency additionally biological implications of presented results in the field of neuroscience are outlined

clique percolation in random networks the notion of k clique percolation in random graphs is introduced where k is the size of the complete subgraphs whose large scale organizations are analytically and numerically investigated for the erdos renyi graph of n vertices we obtain that the percolation transition of k cliques takes place when the probability of two vertices being connected by an edge reaches the threshold p c k k 1 n 1 k 1 at the transition point the scaling of the giant component with n is highly nontrivial and depends on k we discuss why clique percolation is a novel and efficient approach to the identification of overlapping communities in large real networks

promoting cooperation by local contribution under stochastic win stay lose shift mechanism a b s t r a c t we introduce a stochastic win stay lose shift wsls mechanism into evolutionary prisoner s dilemma on small world networks at each time step after playing with all its immediate neighbors each individual gets a score to evaluate its performance in the game the score is a linear combination of an individual s total payoff i e individual gain from the group and local contribution to its neighbors i e individual donation to the group if one s actual score is not larger than its desired score aspiration it switches current strategy to the opposite one with the probability depending on the difference between the two scores under this stochastic wsls regime we assume that each focal individual gains its fixed score aspiration under the condition of full cooperation in its neighborhood and find that cooperation is significantly enhanced under some certain parameters of the model by studying the evolution of cooperation we also explore the influences of different values of learning rate and intensity of deterministic switch on the evolution of cooperation simulation results show that cooperation level monotonically increases with the relative weight of the local contribution to the score for much low intensity of deterministic switch cooperation is to a large extent independent of learning rate and full cooperation can be reached when relative weight is not less than 0 5 otherwise cooperation level is affected by the value of learning rate besides we find that the cooperation level is not sensitive to the topological parameters to explain these simulation results we provide corresponding analytical results based on mean field approximation and find out that simulationresultsareincloseagreementwiththeanalyticalones ourworkmaybehelpful in understanding the cooperative behavior in social systems based on this stochastic wsls mechanism

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

phase diagrams for an evolutionary prisoner s dilemma game on two dimensional lattices the effects of payoffs and noise on the maintenance of cooperative behavior are studied in an evolutionary prisoner s dilemma game with players located on the sites of different two dimensional lattices this system exhibits a phase transition from a mixed state of cooperators and defectors to a homogeneous one where only the defectors remain alive using monte carlo simulations and the generalized mean field approximations we have determined the phase boundaries critical points separating the two phases on the plane of the temperature noise and temptation to choose defection in the zero temperature limit the cooperation can be sustained only for those connectivity structures where three site clique percolation occurs

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

separation of cyclic and starlike hierarchical dominance in evolutionary matrix games we study antisymmetric components of matrices characterizing pair interactions in multistrategy evolutionary games based on the dyadic decomposition of matrices we distinguish cyclic and starlike hierarchical dominance in the appropriate components in the symmetric matrix games the strengths of these elementary components are determined the general features and intrinsic symmetries of these interactions are represented by directed graphs it is found that the variation of a single matrix component modifies simultaneously the strengths of two starlike hierarchical basis games and many other independent rock paper scissors type cyclic basis games the application of the related concepts is illustrated by discussing the three strategy voluntary prisoner s dilemma

evolutionary games combining two or three pair coordinations on a square lattice we study multiagent logit rule driven evolutionary games on a square lattice whose pair interactions are composed of a maximal number of nonoverlapping elementary coordination games describing ising type interactions between just two of the available strategies using monte carlo simulations we investigate the macroscopic noise level dependent behavior of the two and three pair games and the critical properties of the continuous phase transtitions these systems exhibit the four strategy game is shown to be equivalent to a system that consists of two independent and identical ising models

hausdorff moments hardy spaces and power series in this paper we consider power and trigonometric series whose coefficients are supposed to satisfy the hausdorff conditions which play a relevant role in the moment problem theory we prove that these series converge to functions analytic in cut domains we are then able to reconstruct the jump functions across the cuts from the coefficients of the series expansions by the use of the pollaczek polynomials we can thus furnish a solution for a class of cauchy integral equations

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

volterra algebra and the bethe salpeter equation the diagonalization of the bethe salpeter equation for the absorptive part of the amplitude is reconsidered in particular the mathematical tools required by the diagonalization like the volterra algebra and the related spherical laplace transform are investigated in detail

fourier decomposition of payoff matrix for symmetric three strategy games in spatial evolutionary games the payoff matrices are used to describe pair interactions among neighboring players located on a lattice now we introduce a way how the payoff matrices can be built up as a sum of payoff components reflecting basic symmetries for the two strategy games this decomposition reproduces interactions characteristic to the ising model for the three strategy symmetric games the fourier components can be classified into four types representing games with self dependent and cross dependent payoffs variants of three strategy coordinations and the rock scissors paper rsp game in the absence of the rsp component the game is a potential game the resultant potential matrix has been evaluated the general features of these systems are analyzed when the game is expressed by the linear combinations of these components

on the solution of a class of cauchy integral equations in a previous paper we have presented a new method for solving a class of cauchy integral equations in this work we discuss in detail how to manage this method numerically when only a finite and noisy data set is available particular attention is focused on the question of the numerical stability

the role of mixed strategies in spatial evolutionary games abstract we study three strategy evolutionary games on a square lattice when the third strategy is a mixed strategy of the first and second ones it is shown that the resultant three strategy game is a potential game as well as its two strategy version evaluating the potential we derive a phase diagram on a two dimensional plane of rescaled payoff parameters that is valid in the zero noise limit of the logit dynamical rule the mixed strategy is missing in this phase diagram the effects of two different dynamical rules are analyzed by monte carlo simulations and the results of imitation dynamics indicate the dominance of the mixed strategy within the region of the hawk dove game where it is an evolutionarily stable strategy the effects and consequences of the different dynamical rules on the final stationary states and phase transitions are discussed

evolutionary matching pennies game on bipartite regular networks evolutionary games are studied here with two types of players located on a chessboard or on a bipartite random regular graph each player s income comes from matching pennies games played with the four neighbors the players can modify their own strategies according to a myopic strategy update resembling the glauber dynamics for the kinetic ising model this dynamical rule drives the system into a stationary state where the two strategies are present with the same probability without correlations between the nearest neighbors while a weak correlation is induced between the second and the third neighbors in stationary states the deviation from the detailed balance is quantified by the evaluation of entropy production finally our analysis is extended to evolutionary games where the uniform pair interactions are composed of an anticoordination game and a weak matching pennies game this system preserves the ising type order disorder transitions at a critical noise level decreasing with the strength of the matching pennies component for both networks

an approximation for the distribution of the scan statistic the scan statistic evaluates whether an apparent cluster of disease in time is due to chance the statistic employs a moving window of length w and finds the maximum number of cases revealed through the window as it scans or slides over the entire time period t computation of the probability of observing a certain size cluster under the hypothesis of a uniform distribution is infeasible when n the total number of events is large and w is of moderate or small size relative to t we give an approximation that is an asymptotic upper bound easy to compute and for the purposes of hypothesis testing more accurate than other approximations presented in the literature the approximation applies both when n is fixed and when n has a poisson distribution we illustrate the procedure on a data set of trisomic spontaneous abortions observed in a two year period in new york city

approximations for distributions of scan statistics abstract certain statistical applications deal with the extremal distributions of the number of points in a moving interval or window of fixed length this article gives an approximation that is highly accurate for several of these distributions applications include the maximum cluster of points on a line or circle multiple coverage by subintervals or subarcs of fixed size the length of the longest success run in bernoulli trials and the generalized birthday problem

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

power of the scan statistic for detection of clustering the scan statistic is the maximum number of events in an interval of fixed length w as the subinterval moves over the entire time frame previous research derived the null distribution of the scan statistic under the conditional model which assumed that the total number of events was fixed and under the unconditional model which let the total number of events be a random variable this paper derives approximations for the power of the scan test for a pulse alternative under this alternative the relative risk of disease on a subinterval tau tau w tau unknown is theta fold as high as it is for other subintervals of length w two sets of approximations are given for each model the first approximation gives highly accurate results but requires use of a personal computer the second procedure can be performed on a hand held calculator and appears very accurate for the cases examined

payoff components and their effects in a spatial three strategy evolutionary social dilemma we study a three strategy spatial evolutionary prisoner s dilemma game with imitation and logit update rules players can follow the always cooperating always defecting or the win stay lose shift wsls strategies and gain their payoff from games with their direct neighbors on a square lattice the friendliness parameter of the wsls strategy characterizing its cooperation probability in the first round tunes the cyclic component of the game determining whether the game can be characterized by a potential we measured and calculated the phase diagrams of the system for a wide range of parameters when the game is a potential game and the logit rule is applied the theoretically predicted phase diagram agrees very well with the simulation results surprisingly this phase diagram can be accurate even in the nonpotential case if there are only two surviving strategies in the stationary state this result harmonizes with the fact that all 2 2 games are potential games for the imitation dynamics we found that the effects of spatiality combined with the presence of two cooperative strategies are so strong that they suppress even substantial changes in the payoff matrix thus the phase diagrams are independent of the cyclic component s intensity at the same time this type of strategy update mechanism supports the formation of cooperative clusters that results in a cooperative society in a wider parameter range compared to the logit dynamics

approximations and bounds for the distribution of the scan statistic abstract the scan statistic is used in many areas of science to test the null hypothesis of uniformity against a clustering alternative this article derives approximations and bounds for the distribution of scan statistics an extensive simulation study is carried out to compare the approximations and the bounds derived in this article with other known approximations and bounds the new lower and upper bounds that have been derived are very useful in evaluating the approximations and the simulation a quantity of average number of points in the scanning interval of length d d is introduced to study the approximations for the distribution of the scan statistic for low values of d the approximation derived in this article is the most accurate one the importance of the scan statistics arises from their applications in many areas including nuclear physics geology radio optics photography and epidemiology

analysis of quasi dynamic ordinary differential equations and the quasi dynamic replicator abstract we study the mathematical properties of the quasi dynamic ordinary differential equations defined empirically in chen et al 2019 in particular we show how the allometric scaling mentioned in that work emerges naturally from the generalized lotka volterra model under the quasi dynamic ordinary differential equations paradigm we then define and study the proportional quasi dynamic ordinary differential equations and discuss the relationship of this equation system to both the classical and discrete time replicator dynamics we prove asymptotic properties of these systems for large and small populations and show that there exist populations for which the proportion of the population varies cyclically as a function of total logarithmic population size

social dilemmas in multistrategy evolutionary potential games the nature of social dilemmas is studied in n strategy evolutionary potential games on a square lattice with nearest neighbor interactions and the logit rule for symmetric games with symmetric payoff matrices there are no dilemmas because of the coincidence of individual and common interests the dilemmas are caused by the antisymmetric parts of the self and cross dependent payoff components if it modifies the preferred nash equilibrium the contentment of players and the emergence of dilemmas in the preferred nash equilibria are illustrated on some two dimensional cross sections of the parameter space