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

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

on proving the extended minimax disparity owa problem determining associated weights in the theory of ordered weighted averaging owa operators is an important issue wang and parkan information sciences 175 2005 20 29 proposed a minimax disparity approach for obtaining owa operator weights which is based on the solution of a linear program lp model for a given degree of orness recently amin and emrouznejad computers industrial engineering 50 2006 proposed an extended minimax disparity model and improved their proposed lp to obtain weights that would be as close as possible they also left an open problem related to the extended model for an even number of arguments there would be an interval for the degree of orness such that the optimal solution of the extended model could be obtained by a compact mathematical form in this paper we completely prove this open problem mathematically for all orness levels whatever the number of arguments

combining multiple comparisons and modeling techniques in dose response studies the analysis of data from dose response studies has long been divided according to two major strategies multiple comparison procedures and model based approaches model based approaches assume a functional relationship between the response and the dose taken as a quantitative factor according to a prespecified parametric model the fitted model is then used to estimate an adequate dose to achieve a desired response but the validity of its conclusions will highly depend on the correct choice of the a priori unknown dose response model multiple comparison procedures regard the dose as a qualitative factor and make very few if any assumptions about the underlying dose response model the primary goal is often to identify the minimum effective dose that is statistically significant and produces a relevant biological effect one approach is to evaluate the significance of contrasts between different dose levels while preserving the family wise error rate such procedures are relatively robust but inference is confined to the selection of the target dose among the dose levels under investigation we describe a unified strategy to the analysis of data from dose response studies which combines multiple comparison and modeling techniques we assume the existence of several candidate parametric models and use multiple comparison techniques to choose the one most likely to represent the true underlying dose response curve while preserving the family wise error rate the selected model is then used to provide inference on adequate doses

on the issue of obtaining owa operator weights we first investigate the issue of obtaining the weights associated with the owa aggregation in the situation when we have observed data on the arguments and the aggregated value we next introduce a family of owa operators called exponential owa operators finally we look at a simple procedure for generating the weights given a required degree of orness

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 obtaining minimal variability owa operator weights one important issue in the theory of ordered weighted averaging owa operators is the determination of the associated weights one of the first approaches suggested by o hagan determines a special class of owa operators having maximal entropy of the owa weights for a given level of orness algorithmically it is based on the solution of a constrained optimization problem another consideration that may be of interest to a decision maker involves the variability associated with a weighting vector in particular a decision maker may desire low variability associated with a chosen weighting vector in this paper using the kuhn tucker second order sufficiency conditions for optimality we shall analytically derive the minimal variability weighting vector for any level of orness

confidence curves in nonlinear regression abstract standard wald confidence regions for parameters in a normal nonlinear regression model often fail to capture accurately the uncertainty of estimation as reflected by the corresponding profile log likelihood we present a graphical method along with a stable computational algorithm for inference on scalar parameters in a nonlinear regression model

owa operators in regression problems we consider an application of fuzzy logic connectives to statistical regression we replace the standard least squares least absolute deviation and maximum likelihood criteria with an ordered weighted averaging owa function of the residuals depending on the choice of the weights we obtain the standard regression problems high breakdown robust methods least median least trimmed squares and trimmed likelihood methods as well as new formulations we present various approaches to numerical solution of such regression problems owa based regression is particularly useful in the presence of outliers and we illustrate the performance of the new methods on several instances of linear regression problems with multiple outliers

a transformation weighting model for estimating michaelis menten parameters abstract there has been considerable disagreement about how best to estimate the parameters in michaelis menten models this document points out that many fitting methods are based on different stochastic models being weighted least squares estimates after appropriate transformation the authors propose a flexible model which can be used to help determine the proper transformation and choice of weights the method is illustrated by examples keywords nonlinear regression lineweaver burke transformation

probabilistically weighted owa aggregation in decision making under uncertainty we have a collection of alternatives from which we must choose one associated with each alternative is an uncertainty profile consisting of the set of possible outcomes that can occur if we choose this alternative along with some indication of the uncertainty associated with the outcomes since it is difficult to compare these uncertainty profiles one commonly used approach is to obtain a representative value an aggregation of the information in the uncertainty profile and use these to compare the alternatives the method that we use to aggregate the information in the uncertainty profile must reflect aspects of the decision attitude of the decision maker here we look at the role that the ordered weighted averaging owa can play in the aggregation process used to obtain these representative values since an uncertainty profile can involve a discrete set of possible outcomes or an interval of possible outcomes we provide the owa operator with the capability to perform aggregations in either of these environments in addition we provide the owa operator with the ability to perform aggregations in situations where the arguments being aggregated the potential outcomes have an associated uncertainty probability of occurrence particularly notable is the extension the owa operator to perform aggregation with arguments consisting of a continuum of values with an associated probability density function we also look at the cases where the uncertainty is modeled with a belief structure as well a possibility distribution

transformations to symmetry and homoscedasticity abstract this article considers transformations in regression to eliminate skewness and heteroscedasticity of the response we work with the transform both sides model where the relationship between the median response and the independent variables has been identified at least tentatively to preserve this relationship the response and the regression model are transformed in the same way extending the work of others for the location parameter case we propose an estimator that eliminates skewness we also develop an estimator to eliminate heteroscedasticity and an estimator that attempts to induce both symmetry and homoscedasticity both and appear new by comparing and we develop a test of the null hypothesis that there exists a transformation to both symmetry and homoscedasticity we study the question when does the estimator of behave in terms of asymptotic variance as if the regression parameter were known and vice versa the results are of use for telling when the optimal estimator of do

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

owa operators with maximal renyi entropy this paper lays bare a parametric class of ordered weighted averaging owa operators with maximal renyi entropy owa weights for any level of orness in particular we shall formulate an extended approach to decision making with owa operators by introducing considerations of maximizing information content in the aggregation according to a general parametric class of dispersion measures

confidence bounds for nonlinear dose response relationships an important aim of drug trials is to characterize the dose response relationship of a new compound such a relationship can often be described by a parametric nonlinear function that is monotone in dose if such a model is fitted it is useful to know the uncertainty of the fitted curve it is well known that wald confidence intervals are based on linear approximations and are often unsatisfactory in nonlinear models apart from incorrect coverage rates they can be unreasonable in the sense that the lower confidence limit of the difference to placebo can be negative even when an overall test shows a significant positive effect bootstrap confidence intervals solve many of the problems of the wald confidence intervals but are computationally intensive and prone to undercoverage for small sample sizes in this work we propose a profile likelihood approach to compute confidence intervals for the dose response curve these confidence bounds have better coverage than wald intervals and are more precise and generally faster than bootstrap methods moreover if monotonicity is assumed the profile likelihood approach takes this automatically into account the approach is illustrated using a public dataset and simulations based on the emax and sigmoid emax models

diagnostics and robust estimation when tranforming the regression model and the response in regression analysis the response is often transformed to remove heteroscedasticity and or skewness when a model already exists for the untransformed response then it can be preserved by applying the same transform to both the model and the response this methodology which we call transform both sides has been applied in several recent papers and appears highly useful in practice when a parametric transformation family such as the power transformations is used then the transformation can be estimated by maximum likelihood the maximum likelihood estimator however is very sensitive to outliers in this article we propose diagnostics to indicate cases influential for the transformation or regression parameters we also propose a robust bounded influence estimator similar to the krasker welsch regression estimator

a minimax disparity approach for obtaining owa operator weights one of the key issues in the theory of ordered weighted averaging owa operators is the determination of owa operator weights in this paper a minimax disparity approach for obtaining owa operator weights is proposed this involves the formulation and solution of a linear programming lp model for a given degree of orness the proposed approach generates the owa operator weights by minimizing the maximum difference between any two adjacent weights a numerical example is provided to illustrate the application of the proposed approach in generating viable owa operator weights in a simple and effective way

stochastic win stay lose shift strategy with dynamic aspirations in evolutionary social dilemmas in times of plenty expectations rise just as in times of crisis they fall this can be mathematically described as a win stay lose shift strategy with dynamic aspiration levels where individuals aspire to be as wealthy as their average neighbor here we investigate this model in the realm of evolutionary social dilemmas on the square lattice and scale free networks by using the master equation and monte carlo simulations we find that cooperators coexist with defectors in the whole phase diagram even at high temptations to defect we study the microscopic mechanism that is responsible for the striking persistence of cooperative behavior and find that cooperation spreads through second order neighbors rather than by means of network reciprocity that dominates in imitation based models for the square lattice the master equation can be solved analytically in the large temperature limit of the fermi function while for other cases the resulting differential equations must be solved numerically either way we find good qualitative agreement with the monte carlo simulation results our analysis also reveals that the evolutionary outcomes are to a large degree independent of the network topology including the number of neighbors that are considered for payoff determination on lattices which further corroborates the local character of the microscopic dynamics unlike large scale spatial patterns that typically emerge due to network reciprocity here local checkerboard like patterns remain virtually unaffected by differences in the macroscopic properties of the interaction network

variance function estimation abstract heteroscedastic regression models are used in fields including economics engineering and the biological and physical sciences often the heteroscedasticity is modeled as a function of the covariates or the regression and other structural parameters standard asymptotic theory implies that how one estimates the variance function in particular the structural parameters has no effect on the first order properties of the regression parameter estimates there is evidence however both in practice and higher order theory to suggest that how one estimates the variance function does matter further in some settings estimation of the variance function is of independent interest or plays an important role in estimation of other quantities in this article we study variance function estimation in a unified way focusing on common methods proposed in the statistical and other literature to make both general observations and compare different estimation schemes we show that there are significant di

random effect models in nonlinear regression with applications to bioassay summary transformation and weighting techniques are applied to dose response curve models in particular weighting methods derived from a controlled variable random effect model and a closely related random coefficient model are studied these two models correspond to additive and multiplicative effects of variations in the dose and both lead to variance components proportional to the square of the derivative of the response function with respect to dose when the dose response curve is nonlinear in dose the variance components are typically identifiable even without replicate measurements of dose in a bioassay example the fit of a logistic model is studied the transform both sides technique with a power transformation is shown to give a vast improvement in fit compared to the analysis with no transformation and no weighting and it also gives considerably better estimates of the parameters in the logistic function for the data set studied a significant further improvement in the fit is possible by use of the random effect models

testing effect of a drug using multiple nested models for the dose response summary during development of a drug typically the choice of dose is based on a phase ii dose finding trial where selected doses are included with placebo two common statistical dose finding methods to analyze such trials are separate comparisons of each dose to placebo using a multiple comparison procedure or a model based strategy where a dose response model is fitted to all data the first approach works best when patients are concentrated on few doses but cannot conclude on doses not tested model based methods allow for interpolation between doses but the validity depends on the correctness of the assumed dose response model bretz et al 2005 biometrics 61 738 748 suggested a combined approach which selects one or more suitable models from a set of candidate models using a multiple comparison procedure the method initially requires a priori estimates of any non linear parameters of the candidate models such that there is still a degree of model misspecification possible and one can only evaluate one or a few special cases of a general model we propose an alternative multiple testing procedure which evaluates a candidate set of plausible dose response models against each other to select one final model the method does not require any a priori parameter estimates and controls the type i error rate of selecting a too complex model

a note on the fuzzy weighted additive rule abstract the characteristic or attribute of a fuzzy weighted additive rule fwar is presented fwar has provided a method of assessing weights for criteria based on the fuzzy opinions of experts the method is to elicit weights for aggregating the fuzzy sets of type 1 and type 2 by using quadratic programming but fwar has not expressed a specific description on the information of experts overall evaluations for alternatives if the style of experts overall evaluations is characterized as linear additive weighting of the performances of alternative for criterion then the optimal aggregated value of the given performances of alternative is given by the arithmetic mean of the experts overall evaluations without solving time consuming quadratic programming in fwar

norms induced from owa operators we describe the basic properties of a norm and introduce the minkowski norm we then show that the owa aggregation operator can be used to provide norms to enable this we require that the owa weights satisfy the buoyancy property w j w k for j k we consider a number of different classes of owa norms it is shown that the functional generation of the weights of an owa norm requires the weight generating function have a non positive second derivative we discuss the use of the generalized owa operator to provide norms finally we describe the use of owa operators to induce similarity measures

programming based owa operator weights with quadratic objective function yager s ordered weighted averaging owa operators are extensively employed to perform mean type aggregations their success heavily depends on proper determination of the associated weights that characterize the operators several methods have been established to determine the weights and thereby to support successful owa aggregation in this study the least square method which is one of the nonlinear programs with a quadratic objective function is reformulated by using the extreme points that correspond to its constraints and then solved by a few steps of matrix operations finally we present a new weighting method called the minimizing distances from the extreme points mdp wherein the owa operator weights that minimize the expected quadratic distance with respect to the set of extreme points are chosen a different attitudinal character leads to different extreme points and thus the mdp seeks to find the owa operator weights that are dynamically adjusted to be at the center of attitude dependent polytope

improving minimax disparity model to determine the owa operator weights determining the ordered weighted averaging owa operator weights is important in decision making applications several approaches have been proposed in the literature to obtain the associated weights this paper provides an alternative disparity model to identify the owa operator weights the proposed mathematical model extends the existing disparity approaches by minimizing the sum of the deviation between two distinct owa weights the proposed disparity model can be used for a preference ranking aggregation a numerical example in preference ranking and an application in search engines prove the usefulness of the generated owa weights

polymorphism in rapidly changing cyclic environment selection in a time periodic environment is modeled via the continuous time two player replicator dynamics which for symmetric payoffs reduces to the fisher equation of mathematical genetics for a sufficiently rapid and cyclic fine grained environment the time averaged population frequencies are shown to obey a replicator dynamics with a nonlinear fitness that is induced by environmental changes the nonlinear terms in the fitness emerge due to populations tracking their time dependent environment these terms can induce a stable polymorphism though they do not spoil the polymorphism that exists already without them in this sense polymorphic populations are more robust with respect to their time dependent environments the overall fitness of the problem is still given by its time averaged value but the emergence of polymorphism during genetic selection can be accompanied by decreasing mean fitness of the population the impact of the uncovered polymorphism scenario on the models of diversity is exemplified via the rock paper scissors dynamics and also via the prisoner s dilemma in a time periodic environment

analytic properties of maximum entropy owa operators we discuss the maximum entropy approach to obtaining the weights associated with the ordered weighted averaging owa aggregation operator the resulting weights are called the meowa weights using the method of lagrange multipliers we obtain an analytic form for these weights and describe some of their properties the concept of immediate probabilities is introduced as being a transformation of a probability distribution based on a decision maker s degree of optimism this transformation which is affected by an owa operator is shown to result in a relationship between the transformed expected value and the degree of optimism that is monotone when the weights used are the meowa weights

stancu owa operator a critical issue when selecting an ordered weighted aggregation owa operator is the determination of the associated weights for this reason numerous weight generating methods have appeared in the literature in this paper a generalization of the binomial owa operator on the basis of the stancu polynomial is proposed and analyzed we propose a weight function in the parametric form using the stancu polynomial by which the weights of owa operators can be generated easily the proposed stancu owa operator provides infinitely many sets of weight vectors for a given level of the orness value an important property of this kind of owa operator is its orness which remains constant irrespective of the number of objectives aggregated and always equal to one of its parameters this approach provides a significant advantage for generating the owa operators weights over existing methods one can choose a set of weight vectors based on his her own preference this class of owa operators can utilize a prejudiced preference to determine the corresponding weight vector the maximum entropy shannon owa operator s weights for a given level of orness is calculated by the purposed weight function and compared with the existing maximum entropy owa operator

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