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

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

diversity of neighborhoods promotes cooperation in evolutionary social dilemmas abstract explaining the evolution of cooperative behavior is one of the most important and interesting problems in a myriad of disciplines such as evolutionary biology mathematics statistical physics social science and economics up to now there have been a great number of works aiming to this issue with the help of evolutionary game theory however vast majority of existing literatures simply assume that the interaction neighborhood and replacement neighborhood are symmetric which seems inconsistent with real world cases in this paper we consider the asymmetrical neighborhood player of type a whose factor is controlled by a parameter has four interaction neighbors and four replacement neighbors while player of type b whose factor is controlled by a parameter 1 possess eight interaction neighbors and four replacement neighbors by means of numerous monte carlo simulations we found that middle can make the cooperation reach the highest level while for this finding its robustness can be further validated in more games

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

promotion of cooperation by payoff noise in a 2 2 game a series of numerical simulations of a 2 ifmmode times else texttimes fi 2 symmetric game on a network examined whether payoff matrix noise promotes cooperation as reported initially by perc new j phys 8 22 2006 agents have no memory they offer cooperation c or defection d we assume that the network is time invariable the effect of payoff matrix noise pmn is measured by a simulated payoff difference between a normal network game and a network game with pmn the effect of pmn appears only when a local strategy adaptation is implemented for example a network game with imitation dynamics the influence of pmn becomes more significant with a larger stochastic deviation and less significant in a larger degree network one reason for pmn s effectiveness is the local strategy adaptation mechanism which helps both the preservation and fixation of c agents and not that the payoff matrix noise makes a dilemma game into a trivial dilemma free game

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

evolutionary dynamics on degree heterogeneous graphs the evolution of two species with different fitness is investigated on degree heterogeneous graphs the population evolves either by one individual dying and being replaced by the offspring of a random neighbor voter model dynamics or by an individual giving birth to an offspring that takes over a random neighbor node invasion process dynamics the fixation probability for one species to take over a population of n individuals depends crucially on the dynamics and on the local environment starting with a single fitter mutant at a node of degree k the fixation probability is proportional to k for voter model dynamics and to 1 k for invasion process dynamics

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

theoretical challenges towards cutting plane selection while many classes of cutting planes are at the disposal of integer programming solvers our scientific understanding is far from complete with regards to cutting plane selection i e the task of selecting a portfolio of cutting planes to be added to the lp relaxation at a given node of the branch and bound tree in this paper we review the different classes of cutting planes available known theoretical results about their relative strength important issues pertaining to cut selection and discuss some possible new directions to be pursued in order to accomplish cutting plane selection in a more principled manner finally we review some lines of work that we undertook to provide a preliminary theoretical underpinning for some of the issues related to cut selection

cooperation in aspiration based n person prisoner s dilemmas we propose a mathematical model of the n person prisoner s dilemma game played by a continuous population of agents with a time dependent aspiration level the model a system of differential equations takes into account the evolution of the aspiration level and of the mean frequency of the cooperators in the population the dependence of the asymptotic level of cooperation on the individual payoffs and on the transition rates determining the agent s reaction to the received payoffs is studied in general the existence and the magnitude of the asymptotic level of cooperation depends on n the payoffs and the transition rates and decreases with increasing n

cooperation and age structure in spatial games we study the evolution of cooperation in evolutionary spatial games when the payoff correlates with the increasing age of players the level of correlation is set through a single parameter ensuremath alpha the demographic heterogeneous age distribution directly affecting the outcome of the game is thus shown to be responsible for enhancing the cooperative behavior in the population in particular moderate values of ensuremath alpha allow cooperators not only to survive but to outcompete defectors even when the temptation to defect is large and the ageless standard ensuremath alpha 0 model does not sustain cooperation the interplay between age structure and noise is also considered and we obtain the conditions for optimal levels of cooperation

insight into the so called spatial reciprocity up to now there have been a great number of studies that demonstrate the effect of spatial topology on the promotion of cooperation dynamics namely the so called spatial reciprocity however most researchers probably attribute it to the positive assortment of strategies supported by spatial arrangement in this paper we analyze the time course of cooperation evolution under different evolution rules interestingly a typical evolution process can be divided into two evident periods the enduring end period and the expanding exp period where the former features that cooperators try to endure defectors invasion and the latter shows that perfect c clusters fast expand their area we find that the final cooperation level relies on two key factors the formation of the perfect c cluster at the end of the end period and the expanding fashion of the perfect c cluster during the exp period for deterministic rule the smooth expansion of c cluster boundaries enables cooperators to reach a dominant state whereas the rough boundaries for stochastic rule cannot provide a sufficient beneficial environment for the evolution of cooperation moreover we show that expansion of the perfect c cluster is closely related to the cluster coefficient of interaction topology to some extent we present a viable method for understanding the spatial reciprocity mechanism in nature and hope that it will inspire further studies to resolve social dilemmas

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

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

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

design and verify a new scheme for generating cutting planes a cutting plane procedure for integer programming ip problems usually involves invoking a black box procedure such as the gomory chvatal procedure to compute a cutting plane in this paper we describe an alternative paradigm of using the same cutting plane black box this involves two steps in the first step we design an inequality cx le d where c and d are integral independent of the cutting plane black box in the second step we verify that the designed inequality is a valid inequality by verifying that the set p cap x in mathbb r n mid cx ge d 1 cap mathbb z n is empty using cutting planes from the black box here p is the feasible region of the linear programming relaxation of the ip we refer to the closure of all cutting planes that can be verified to be valid using a specific cutting plane black box as the verification closure of the considered cutting plane black box this paper undertakes a systematic study of properties of verification closures of various cutting plane black box procedures

cutting plane proofs in polynomial space following chvatal cutting planes may be viewed as a proof system for establishing that a given system of linear inequalities has no integral solution we show that such proofs may be carried out in polynomial workspace

learning mutation and long run equilibria in games an evolutionary model with a finite number of players and with stochastic mutations is analyzed the expansion and contraction of strategies is linked to their current relative success but mutuation perturbing the system from its deterministic evolution are present as well the focus is on the long run implications of ongoing mutations which drastically reduce the set of equilibria for 2 by 2 symmetric games with two symmetric strict nash equilibria the risk dominant equilibrium is selected in particular if both strategies have equal security levels the pareto dominant nash equilibrium is selected in particular if both strategies have equal security levels the pareto dominant nash equilibrium is selected even though there is another strict nash equilibrium copyright 1993 by the econometric society

simple calibration algorithm for high distortion lens camera a simple and useful calibration method for a tv camera with a high distortion lens is presented the parameters to be calibrated are effective focal length one pixel width on an image plane image distortion center and distortion coefficient a simple pattern calibration chart composed of parallel straight lines is introduced as a reference for calibration an ordinary 2d model fitting is decomposed into two 1d model fittings on the column and row of a frame buffer across the image distortion center by ingeniously utilizing the point symmetry characteristic of image distortion some parameters with a calibration chart are eliminated by setting up a calibration chart precisely and by utilizing negligibly low distortion near the image distortion center thus the number of unknown parameters to be calibrated is drastically decreased enabling simple and useful calibration the effectiveness of the proposed calibration method is confirmed by experimentation

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

correction of distortion in endoscope images images formed with endoscopes suffer from a spatial distortion due to the wide angle nature of the endoscope s objective lens this change in the size of objects with position precludes quantitative measurement of the area of the objects which is important in endoscopy for accurately measuring ulcer and lesion sizes over time a method for correcting the distortion characteristic of endoscope images is presented a polynomial correction formula was developed for the endoscope lens and validated by comparing quantitative test areas before and after the distortion correction the distortion correction has been incorporated into a computer program that could readily be applied to electronic images obtained at endoscopy using a desk top computer the research presented here is a key step towards the quantitative determination of the area of regions of interest in endoscopy

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

promotion of cooperation by payoff driven migration abstract migration plays an important role in the evolution of cooperation previous studies concerning mobile population often assumed that all agents move with the identical velocity in this paper we propose a payoff driven migration in which the velocity of an agent depends on his her payoff a parameter is introduced to adjust the influence of payoff when 0 means that agents all move with the identical velocity while 0 means that the lower the payoff is the faster the moving speed is and vice versa for the prisoner s dilemma game we find that in comparison with the case that agents all move with the same speed cooperation could be promoted strongly when payoff dependent velocity is considered remarkably the cooperation level is not a monotonic function of and there exists an optimal value of which can lead to the maximum cooperation level for the snowdrift game the cooperation level increases with

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

cutting planes and the elementary closure in fixed dimension the elementary closurep of a polyhedronp is the intersection ofp with all its gomory chvatal cutting planes p is a rational polyhedron provided thatp is rational the known bounds for the number of inequalities definingp are exponential even in fixed dimension we show that the number of inequalities needed to describe the elementary closure of a rational polyhedron is polynomially bounded in fixed dimension ifp is a simplicial cone we construct a polytopeq whose integral elements correspond to cutting planes ofp the vertices of the integer hullq iinclude the facets ofp a polynomial upper bound on their number can be obtained by applying a result of cook et al 1992 finally we present a polynomial algorithm in varying dimension which computes cutting planes for a simplicial cone that correspond to vertices ofq i

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

valid linear inequalities for fixed charge problems many problems in the operations research management science literature can be formulated with both zero one and continuous variables however the exact optimization of such mixed zero one models remains a computational challenge in this paper we propose to study mixed problems from a mathematical point of view that is similar in spirit to recent research on purely combinatorial problems that has investigated systems of defining linear inequalities or facets of the underlying polytope at least two numerical studies have validated this line of research computationally and the advances in the problem solving capabilities are considerable we expect that similar gains are possible for the mixed zero one problem more precisely we consider the mixed integer programs whose feasible region x is composed of i a simple additive constraint in the continuous variables xj for j 1 2 n and ii constraints 0 xj mjyj defined by binary variables yj for j 1 2 n this type of feasible region arises in a variety of mixed integer problems and particularly in network problems with fixed charges on the arcs we derive two classes of facet defining linear inequalities of the convex hull of x and show that the second of these classes gives a complete description of the convex hull when mj m for all j we also develop methods to detect violated inequalities from these classes so that these facets can be used as cutting planes to strengthen the formulations of certain mixed integer problems

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

improvement of depth position in 2 d 3 d registration of knee implants using single plane fluoroscopy two dimensional 2 d three dimensional 3 d registration techniques using single plane fluoroscopy are highly important for analyzing 3 d kinematics in applications such as total knee arthroplasty tka implants the accuracy of single plane fluoroscopy based techniques in the determination of translation perpendicular to the image plane depth position however is relatively poor because a change in the depth position causes only small changes in the 2 d silhouette accuracies achieved in depth position using conventional 2 d 3 d registration techniques are insufficient for clinical applications therefore we propose a technique for improving the accuracy of depth position determination in order to develop a system for analyzing knee kinematics over the full six degrees of freedom 6 dof using single plane fluoroscopy in preliminary experiments the behaviors of errors for each free variable were quantified as evaluation curves by examining changes in cost function with variations in the free variable the evaluation curve for depth position was more jagged and the curve peak less pointy compared to the evaluation curves of the other five variables and the curve was found to behave differently depth position is therefore optimized independently of the other variables using an approximate evaluation curve of depth position prepared after initial registration accuracy of the proposed technique was evaluated by computer simulation and in vitro tests with validation of absolute position and orientation performed for each knee component in computer simulation tests root mean square error rmse in depth position was improved from 2 6 mm conventional to 0 9 mm proposed whereas for in vitro tests rmse improved from 3 2 mm to 1 4 mm accuracy of the estimation of the remaining two translational and three rotational variables was found to be almost the same as that obtained by conventional techniques results of in vivo tests are also described in which the possibility of full 6 dof kinematic analysis of tka implants is shown

a new method for distortion correction of electronic endoscope images a new method to correct the barrel distortion of an electronic endoscope image is presented a correction model assuming circularly symmetric distortion is introduced with the following model parameters the center of distortion and the coefficients of polynomials representing the distortion correction in the radial direction if the imaging system is distortion free straight lines in the object space should be imaged as straight lines based on this criterion a distorted image of a standard pattern consisting of a grid of several straight lines is recorded and the model parameters are then estimated as a basis for straightening distorted lines this method has the advantage of not needing a careful placement of the standard pattern for calibration correction results are presented for the grid pattern chart to verify a sufficient degree of correction examples of distortion correction of real intestinal images and physicians comments are also presented

integer programming with a fixed number of variables it is shown that the integer linear programming problem with a fixed number of variables is polynomially solvable the proof depends on methods from geometry of numbers

a new approach for nonlinear distortion correction in endoscopic images based on least squares estimation images captured with a typical endoscope show spatial distortion which necessitates distortion correction for subsequent analysis here a new methodology based on least squares estimation is proposed to correct the nonlinear distortion in the endoscopic images a mathematical model based on polynomial mapping is used to map the images from distorted image space onto the corrected image space the model parameters include the polynomial coefficients distortion center and corrected center the proposed method utilizes a line search approach of global convergence for the iterative procedure to obtain the optimum expansion coefficients a new technique to find the distortion center of the image based on curvature criterion is presented a dual step approach comprising token matching and integrated neighborhood search is also proposed for accurate extraction of the centers of the dots contained in a rectangular grid used for the model parameter estimation the model parameters were verified with different grid patterns the distortion correction model is applied to several gastrointestinal images and the results are presented the proposed technique provides high speed response and forms a key step toward online camera calibration which is required for accurate quantitative analysis of the images

automatic correction of barrel distorted images using a cascaded evolutionary estimator all optical systems are to some extent burdened by one or more aberrations barrel distortion of an image is also an aberration in this paper we used an innovative method to solve the problem of the centric radial distortion of a static image which serves for biometric identification of persons using 2d contour of a human hand the method proposed uses a cascaded arrangement of two algorithms the classic meta heuristic referred to as jde differential evolution and an algorithm called covariance matrix adaptation evolution strategy optimizers use methods of inverse engineering and numerical mathematics to resolve the question of how to determine the correct parameters of the algebraic polynomial equation of the nth degree by the application of which it is possible to obtain an image free of barrel distortion from an image affected by this distortion the proposed method provides a high quality and time acceptable method of optimization and the option of choosing the approximation accuracy with the use of the coefficients obtained it is then possible to use a method called back mapping to permanently correct the centric radial distortion aberration in the biometric scanner extensive experiments presented in this paper enable a better understanding of relationships the accuracy obtained and options of using evolutionary optimizers in a larger sense

exponential lower bounds on the lengths of some classes of branch and cut proofs we examine the complexity of branch and cut proofs in the context of 0 1 integer programs we establish an exponential lower bound on the length of branch and cut proofs that use 0 1 branching and lift and project cuts called simple disjunctive cuts by some authors gomory chvatal cuts and cuts arising from the n0 matrix cut operator of lovasz and schrijver a consequence of the lower bound result in this paper is that branch and cut methods of the type described above have exponential running time in the worst case

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

minkowski s convex body theorem and integer programming the paper presents an algorithm for solving integer programming problems whose running time depends on the number n of variables as non this is done by reducing an n variable problem to 2n5i 2 problems in n i variables for some i greater than zero chosen by the algorithm the factor of on5 2 per variable improves the best previously known factor which is exponential in n minkowski s convex body theorem and other results from geometry of numbers play a crucial role in the algorithm several related algorithms for lattice problems are presented the complexity of these problems with respect to polynomial time reducibilities is studied

the intractability of resolution abstract we prove that for infinitely many disjunctive normal form propositional calculus tautologies the length of the shortest resolution proof of cannot be bounded by any polynomial of the length of the tautologies we use were introduced by cook and reckhow 1979 and encode the pigeonhole principle extended resolution can furnish polynomial length proofs of these formulas

camera calibration with distortion models and accuracy evaluation a camera model that accounts for major sources of camera distortion namely radial decentering and thin prism distortions is presented the proposed calibration procedure consists of two steps 1 the calibration parameters are estimated using a closed form solution based on a distribution free camera model and 2 the parameters estimated in the first step are improved iteratively through a nonlinear optimization taking into account camera distortions according to minimum variance estimation the objective function to be minimized is the mean square discrepancy between the observed image points and their inferred image projections computed with the estimated calibration parameters the authors introduce a type of measure that can be used to directly evaluate the performance of calibration and compare calibrations among different systems the validity and performance of the calibration procedure are tested with both synthetic data and real images taken by tele and wide angle lenses

evolutionary prisoner s dilemma game on barabasi albert scale free networks an evolutionary prisoner s dilemma game pdg with players located on barabasi albert scale free networks basfn with average connectivity 8 is studied in detail the players are pure strategists and can adopt two strategies either defect or cooperate several alternative update rules determining the evolution of each player s strategy are considered using monte carlo mc simulations we implemented both synchronous and asynchronous update dynamics to calculate the average density of cooperators pc as a function of the temptation to defect b in the equilibrium state for the sake of comparison evolution of cooperative behavior on random regular graphs rrg and regular lattices rl with the same total size and average connectivity as basfn are also investigated we find the overall result that cooperation is sometimes inhibited and sometimes enhanced on the basfn with respect to the cases on the rrg and rl the differences depend on the detailed evaluation function of the players success average payoffs of the players in the present case the different update rules that determine a player s future strategy the synchronous and asynchronous events of strategy updating and also on the temptation to defect c 2007 elsevier b v all rights reserved

impact of separation of interaction and replacement neighborhoods on spatial reciprocity elucidating the evolution of cooperation is one of the greatest challenges in both evolutionary biology and social science however vast majority of existing studies simply assume that the interaction neighborhood and replacement neighborhood are symmetric irrespective of the size of both neighborhoods in this paper we consider the asymmetrical setup namely the separation of interaction neighborhood and replacement neighborhood into the prisoner s dilemma game in detail it is assumed that there exist two types of players player a possessing moore interaction neighborhood and von neumann replacement neighborhood and player b having von neumann interaction neighborhood and moore replacement neighborhood importantly the fraction of former player is the latter is 1 and this ration keeps constant during the whole process by means of monte carlo simulations it is unveiled that cooperation can be promoted to the highest level at middle which is related to the formation of giant cluster moreover we also inspect the impact of uncertainty on the phase diagrams and find that middle completely changes the evolution trend of low or middle value it is thus suggested the separation of interaction and replacement neighborhoods may shed new light into the solution of social dilemmas

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

voter models on heterogeneous networks we study simple interacting particle systems on heterogeneous networks including the voter model and the invasion process these are both two state models in which in an update event an individual changes state to agree with a neighbor for the voter model an individual imports its state from a randomly chosen neighbor here the average time t n to reach consensus for a network of n nodes with an uncorrelated degree distribution scales as n ensuremath mu 1 2 ensuremath mu 2 where ensuremath mu k is the k text th moment of the degree distribution quick consensus thus arises on networks with broad degree distributions we also identify the conservation law that characterizes the route by which consensus is reached parallel results are derived for the invasion process in which the state of an agent is exported to a random neighbor we further generalize to biased dynamics in which one state is favored the probability for a single fitter mutant located at a node of degree k to overspread the population char22 the fixation probability char22 is proportional to k for the voter model and to 1 k for the invasion process

a cutting plane algorithm for the linear ordering problem the linear ordering problem is an np hard combinatorial optimization problem with a large number of applications including triangulation of input output matrices archaeological senation minimizing total weighted completion time in one machine scheduling and aggregation of individual preferences in a former paper we have investigated the facet structure of the 0 1 polytope associated with the linear ordering problem here we report on a new algorithm that is based on these theoretical results the main part of the algorithm is a cutting plane procedure using facet defining inequalities this procedure is combined with various heuristics and branch and bound techniques our computational results compare favorably with the results of existing codes in particular we could triangulate all input output matrices of size up to 60 60 available to us within acceptable time bounds

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

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