the ratio of uniforms approach for generating discrete random variates abstract the most efficient algorithms for sampling from classical discrete distributions are based upon the acceptance rejection principle they are complicated and not easy to understand by adapting the ratio of uniforms method to unimodal discrete distributions sampling procedures can be established which are both simple and fast algorithms for the hypergeometric distribution are developed and compared with competing methods

evolution of a multimodal map induced by an equivariant vector field it has been shown that the topological characterization of an equivariant system should preferably be achieved by working in a fundamental domain generated by the symmetry properties appearing in the phase space in this paper we discuss the case when the equivariance of the studied system is taken into account to study the evolution of the population of periodic orbits when a control parameter is varied the burke shaw system is considered here as an example it is shown that the equivariance of this system may be used to reduce the multimodal first return map in a poincare section to a unimodal map a relationship between four symbol sequences and two symbol sequences is given the non trivial evolution of the orbit spectrum of a multimodal map is then predicted from the much simpler unimodal map to which the multimodal map reduces

the exact approximation method for generating random variables in a computer abstract a suitably chosen approximation to the inverse of a probability distribution can lead to exact and very fast methods for generating random variables if the approximation is made exact by adjusting the argument of the approximating function this article describes the basic method and extensions of it it gives four examples of which two are methods for generating gamma and t variates that while meant to illustrate the basic method show promise of being faster than the best current methods

non uniform random variate generation by the vertical strip method abstract in this paper a method called the vertical strip vs method is proposed for generating non uniform random variates with a given density it can be considered as an improvement of the grid method as the vs method avoids setting up a directory to store information on big rectangles unlike the horizontal strip method that is based on the riemann integral the vs method is based on the lebesgue integral and can be applied to unbounded densities or densities with infinite support applications of the vs method for generating random variates which follow the exponential distribution and normal density are also given

systematic template extraction from chaotic attractors i genus one attractors with an inversion symmetry describing the topological properties by a template is a powerful technique to classify chaotic attractors most of the time reduced templates are used but direct templates in which all mechanisms torsions branch permutation etc identified in the attractor are explicitly described without any simplification are of great interest for a better description of the subtleties of the dynamics we introduce here two additional conventions for representing in a unique way the reduced template from a given linking matrix we then propose an addition law for linking matrices which allows us to manipulate combine different mechanisms a direct template can thus be described by using a series of linking matrices on the other hand we show how to analytically build the linking matrix associated with an attractor which is the image under an inversion symmetry of an attractor whose linking matrix is known

crises sudden changes in chaotic attractors and transient chaos abstract the occurrence of sudden qualitative changes of chaotic dynamics as a parameter is varied is discussed and illustrated it is shown that such changes may result from the collision of an unstable periodic orbit and a coexisting chaotic attractor we call such collisions crises phenomena associated with crises include sudden changes in the size of chaotic attractors sudden appearances of chaotic attractors a possible route to chaos and sudden destructions of chaotic attractors and their basins this paper presents examples illustrating that crisis events are prevalent in many circumstances and systems and that just past a crisis certain characteristic statistical behavior whose type depends on the type of crisis occurs in particular the phenomenon of chaotic transients is investigated the examples discussed illustrate crises in progressively higher dimension and include the one dimensional quadratic map the two dimensional henon map systems of ordinary differential equations in three dimensions and a three dimensional map in the case of our study of the three dimensional map a new route to chaos is proposed which is possible only in invertible maps or flows of dimension at least three or four respectively based on the examples presented the following conjecture is proposed almost all sudden changes in the size of chaotic attractors and almost all sudden destruction or creations of chaotic attractors and their basins are due to crises

patchwork rejection algorithms abstract new methods for implementing rejection algorithms are suggested the objectives are to avoid the generation of unwanted envelope variates to use fewer pseudorandom uniform variates and to bypass as far as possible the need to decide whether to accept or to reject considerably fewer than two uniforms on average per attempted output of a target random variable can be achieved together with an increased acceptance rate the generation of tail variates from a normal distribution is used as illustration

systematic template extraction from chaotic attractors ii genus one attractors with multiple unimodal folding mechanisms asymmetric and symmetric chaotic attractors produced by the simplest jerk equivariant system are topologically characterized in the case of this system with an inversion symmetry it is shown that symmetric attractors bounded by genus one tori are conveniently analyzed using a two components poincare section resulting from a merging attractor crisis these attractors can be easily described as being made of two folding mechanisms here described as mixers one for each of the two attractors co existing before the crisis symmetric attractors are thus described by a template made of two mixers we thus developed a procedure for concatenating two mixers here associated with unimodal maps into a single one allowing the description of a reduced template that is a template simplified under an isotopy the so obtained reduced template is associated with a description of symmetric attractors based on one component poincare section as suggested by the corresponding genus one bounding torus it is shown that several reduced templates can be obtained depending on the choice of the retained one component poincare section

classification of strange attractors by integers we show how to characterize a strange attractor by a set of integers these are extracted from the chaotic time series data by first reconstructing the low period orbits and then determining the template or knot holder which supports all periodic orbits embedded in the strange attractor and the strange attractor itself the template is identified by a set of integers which therefore characterize the strange attractor this identification is explicitly demonstrated for the pirogon using a relatively small data set 5000 points

performance analysis of hypothesis testing for sparse pairwise interaction point processes the sufficient statistic for performing the likelihood ratio test for pairwise interaction point processes is well known however the evaluation of its performance is a very difficult problem it is shown that the distribution of the sufficient statistic can be approximated by the distribution of a poisson driven shot noise random variable which can be readily computed

required criteria for recognizing new types of chaos application to the cord attractor after suggesting criteria to recognize a new system and a new attractor and to make a distinction between them the paper details the topological analysis of the cord attractor this attractor which resembles a cord between two leaves is produced by a three dimensional system that is obtained after a modification of the lorenz 84 model for the global atmospheric circulation l a aguirre and c letellier phys rev e 83 066209 2011 the nontrivial topology of the attractor is described in terms of a template that corresponds to a reverse horseshoe that is to a spiral rossler attractor with negative and positive global twists due to its particular structure and to the fact that such a system has two variables from which the dynamics is poorly observable this attractor qualifies as a challenging benchmark in nonlinear dynamics

templates and subtemplates of rossler attractors from a bifurcation diagram we study the bifurcation diagram of the rossler system it displays the various dynamical regimes of the system stable or chaotic when a parameter is varied we choose a diagram that exhibits coexisting attractors and banded chaos we use the topological characterization method to study these attractors then we detail how the templates of these attractors are subtemplates of a unique template our main result is that only one template describes the topological structure of eight attractors this leads to a topological partition of the bifurcation diagram that gives the symbolic dynamic of all bifurcation diagram attractors with a unique template

a nonparametric estimator for pairwise interaction point processes summary the paper develops a nonparametric estimator for the class of pairwise interaction point processes the estimator is based on an approximation in statistical physics due to percus and yevick which relates the interaction function of a pairwise interaction point process to its second order statistics via an integral equation the results of a simulation study are presented

some simple chaotic flows a systematic examination of general three dimensional autonomous ordinary differential equations with quadratic nonlinearities has uncovered 19 distinct simple examples of chaotic flows with either five terms and two nonlinearities or six terms and one nonlinearity the properties of these systems are described including their critical points lyapunov exponents and fractal dimensions

a numerical solution of open loop nash equilibrium in nonlinear differential games based on chebyshev pseudospectral method in general the applications of differential games for solving practical problems have been limited because all calculations had to be done analytically in this investigation a simple and efficient numerical method for solving nonlinear nonzero sum differential games with finite and infinite time horizon is presented in both cases derivation of open loop nash equilibria solutions usually leads to solving nonlinear boundary value problems for a system of odes the proposed numerical method is based on a combination of minimum principle of pontryagin and expanding the required approximate solutions as the elements of chebyshev polynomials applying chebyshev pseudospectral method two point boundary value problems in differential games are reduced to the solution of a system of algebraic equations finally several examples are given to demonstrate the accuracy and efficiency of the proposed method and a comparison is made with the results obtained by fourth order runge kutta method

unimodal order in the image of the simplest equivariant chaotic system the simplest equivariant chaotic dynamics is investigated in terms of its image i e under the 2 1 mapping allowing one to obtain a projection of the dynamics without any residual symmetry the inversion symmetry is therefore deleted the bifurcation diagram can thus be predicted from the unimodal order although the first return map computed in the original phase space exhibits three critical points this feature is the same as the one observed on the burke and shaw system although this latter system has a rotation symmetry

nash equilibrium approximation of some class of stochastic differential games a combined chebyshev spectral collocation method with policy iteration abstract this study relates to nonzero sum stochastic games with perfect information it proposes an efficient combined chebyshev spectral collocation method cscm with the policy iteration pi algorithm for solving nonlinear coupled hamilton jacobi hj equations the proposed approach is comprised of two steps first the pi algorithm is used to reduce the nonlinear coupled hj equations to a sequence of linear uncoupled pdes then these equations are approximated by the cscm the cscm pi is especially useful when the cscm fails due to the increasing number of collocation points for solving the associated system of nonlinear algebraic equations the main advantage of the resulting method is that it converts nonlinear coupled hj equations to the systems of linear algebraic equations which can be solved readily convergence analysis of this method is also provided in detail to confirm the accuracy and validity of the proposed computational algorithm several illustrative examples are presented

computation of shot noise probability distributions and densities the computation of the cumulative distribution cdf the complementary cdf ccdf and the density of certain shot noise random variables is discussed after subtracting off a few terms that can be computed in closed form what remains can be approximated by a general method for approximating samples of a cdf or ccdf by summing a fourier series whose coefficients are modulated samples of their characteristic function to approximate the density a spline is fit to the cdf samples and then differentiated when the density has corners it is important that the spline have coincident knots at these locations for shot noise densities these locations are easily identified

likelihood analysis of spatial point patterns summary the likelihood procedure for estimating the pairwise interaction potential function is developed for statistical analysis of homogeneous spatial point patterns approximation methods of the normalizing factor of gibbs canonical distribution are discussed both to estimate a scale parameter and to measure the softness or hardness of repulsive interactions the approximations are useful up to a considerably high density the validity of our procedure is demonstrated by some computer experi ments some real data are analysed