parametric forcing of scroll wave patterns in three dimensional excitable media abstract the dynamics of axisymmetric and twisted scroll rings under homogeneous periodic forcing is studied numerically the collapse of axisymmetric rings can be enhanced or retarded significantly with resonant forcing twisted scroll rings exhibit the phenomenon of resonant drift in a direction normal to the axis of the central filament the scaling of mean and fluctuating axial drift due to forcing is determined evidence is provided showing that the appropriate symmetry group for the dynamics of the unforced twisted scroll ring is se 2 r ordinary differential equations based on symmetry considerations explain the dynamics without resorting to laws of filament motion and the local geometry hypothesis

stable particle like solutions to the nonlinear wave equations of three dimensional excitable media so called excitable media support nonlinear waves that propagate as pulses e g the action potential in nerve fibers and heart muscle and the oxidation pulse in certain chemical reactions in two dimensional media the right stimulus will also create rotating vortices which radiate such pulses periodically in every direction their investigation in diverse excitable media has dramatically expanded in the usa and ussr since their discovery in both countries in 1970 in three dimensional media the pivot of the rotating structure is not a point but a curved line generically a closed ring rings linked together and knotted constitute topologically distinctive organizing centers for periodic activity throughout the medium it is of interest to understand how stimuli create organizing centers and how organizing centers persist or decay the numerically discovered stable organizing centers exhibit enough symmetries to encourage mathematical attention this paper illustrates organizing centers by computer g

limited and full information estimation and goodness of fit testing in 2n contingency tables high dimensional contingency tables tend to be sparse and standard goodness of fit statistics such as x2 cannot be used without pooling categories as an improvement on arbitrary pooling for goodness of fit of large 2n contingency tables we propose classes of quadratic form statistics based on the residuals of margins or multivariate moments up to order r these classes of test statistics are asymptotically chi squared distributed under the null hypothesis further the marginal residuals are useful for diagnosing lack of fit of parametric models we show that when r is small r 2 3 the proposed statistics have better small sample properties and are asymptotically more powerful than x2 for some useful multivariate binary models related to these test statistics is a class of limited information estimators based on low dimensional margins we show that these estimators have high efficiency for one commonly used latent trait model for binary data

characterizing the manifest probabilities of latent trait models the problem of characterizing the manifest probabilities of a latent trait model is considered the item characteristic curve is transformed to the item passing odds curve and a corresponding transformation is made on the distribution of ability this results in a useful expression for the manifest probabilities of any latent trait model the result is then applied to give a characterization of the rasch model as a log linear model for a 2 j contingency table partial results are also obtained for other models the question of the identifiability of guessing parameters is also discussed

entropic lattice boltzmann method for microflows abstract a new method for the computation of flows at the micrometer scale is presented it is based on the recently introduced minimal entropic kinetic models both the thermal and isothermal families of minimal models are presented and the simplest isothermal entropic lattice bhatnagar gross krook elbgk is studied in detail in order to quantify its relevance for microflow simulations elbgk is equipped with boundary conditions which are derived from molecular models diffusive wall a map of three dimensional kinetic equations onto two dimensional models is established which enables two dimensional simulations of quasi two dimensional flows the elbgk model is studied extensively in the simulation of the two dimensional poiseuille channel flow results are compared to known analytical and numerical studies of this flow in the setting of the bhatnagar gross krook model the elbgk is in quantitative agreement with analytical results in the domain of weak rarefaction characterized by knudsen number kn the ratio of mean free path to the hydrodynamic scale up to kn 0 01 which is the domain of many practical microflows moreover the results qualitatively agree throughout the entire knudsen number range demonstrating knudsen s minimum for the mass flow rate at moderate values of kn as well as the logarithmic scaling at large kn the present results indicate that elbm can complement or even replace computationally expensive microscopic simulation techniques such as kinetic monte carlo and or molecular dynamics for low mach and low knudsen number hydrodynamics pertinent to microflows

spiral waves in reaction diffusion equations we consider the reaction diffusion system begin gathered r t nabla 2 r r left 1 r 2 vec nabla theta cdot vec nabla theta right hfill r theta t r nabla 2 theta 2 vec nabla r cdot vec nabla theta qr 3 hfill end gathered this system governs the solutions of reaction diffusion systems near a hopf bifurcation point in two spatial dimensions we use formal asymptotic expansions to contruct one armed and multi armed archimedean spiral waves for small values of the parameter q we then show that the one armed spiral waves are probably stable and the multi armed ones are unstable for q small next by numerical continuation methods we construct spiral waves for all q these calculations show that the one armed spiral waves are unstable when q 1 397 cdots we also find the explicit one dimensional analogues of spiral waves for all q and show that they are unstable for q small

classification of steady solutions of the full kinematic model abstract the geometric type of kinematic model governs any moving plane curve which propagates in the normal direction in the medium there have appeared some results in the literature via this model however these results are all based upon some simplification on the model or prior phenomenological assumptions on the solutions in this paper we use really full kinematic model to classify steady solutions i e curvature is independent of time with positive or negative curvature various type of solutions have been obtained such as rotating and translating waves especially for the rotating spiral waves spiral waves arise in many biological chemical and physiological systems the kinematical model can be used to describe the motion of the spiral arms approximated as curves in the plane in fact using our results theorem 3 8 we can answer the following questions is there any steadily rotating wave for a given weakly excitable medium if yes what kind of information we can know about these rotating waves e g the tip s curvature the tip s tangential velocity and the rotating frequency comparing our results with previous ones in the literature there are some differences between them the only evolving plane curves with positive or negative curvature must have monotonous curvatures via simplified model but full model admits solutions with any given oscillating number of the curvatures

a cellular automaton model of excitable media ii curvature dispersion rotating waves and meandering waves abstract a cellular automaton model of excitable media recently introduced by the authors is examined in more detail here we show that i the model is consistent with a linear dependence of wave speed on wave front curvature in two dimensional space ii the model exhibits a stepwise increasing relation between wave speed and temporal period the dispersion relation whose precise shape can be controlled by parameter settings iii the model generates rigidly rotating spiral waves whose frequency speed and core size are consistent with theoretical expectations and iv spiral waves rotate non rigidly showing short term flowerlet meandering which seems to arise by bifurcation from the rigidly rotating solution and long term irregular wandering over large distances these observations are consistent with many known features of wave propagation in two dimensional continuous excitable media governed by reaction diffusion equations suggesting that our cellular automaton model is not only a fast but also a reliable method for investigating the behavior of excitable media

oscillation and pattern formation in a system of self regulating cells abstract in this paper a model of a system of n 2 asymmetrically and nondiffusibly coupled self regulating cells is proposed intended to formally represent well known basic features of biological systems organization the model is discussed in terms of the activation desensitization dynamics in dictyostelium it is shown that the cells in the ensemble are capable of stable oscillations provided the intercellular coupling is strong enough otherwise their stationary values remain asymptotically stable the emergence of oscillations in the one dimensional ring shaped ensemble of size n 2 is due to a bifurcation of naimark sacker type which is proven to exist under rather mild conditions it is shown that a supercritical as well as a subcritical bifurcation branch exist at different parameter values moreover due to the dihedral symmetry of the system the parity of n is shown to determine the multiplicity of the critical pair of eigenvalues crossing the unit circle the model proposed does not represent a reaction diffusion system it is not excitable but exhibits pattern formation under conditions under which a stable limit cycle exists

spatial pattern dynamics due to the fitness gradient flux in evolutionary games we introduce a nondiffusive spatial coupling term into the replicator equation of evolutionary game theory the spatial flux is based on motion due to local gradients in the relative fitness of each strategy providing a game dependent alternative to diffusive coupling we study numerically the development of patterns in one dimension 1d for two strategy games including the coordination game and the prisoner s dilemma and in two dimensions 2d for the rock paper scissors game in 1d we observe modified traveling wave solutions in the presence of diffusion and asymptotic attracting states under a frozen strategy assumption without diffusion in 2d we observe spiral formation and breakup in the frozen strategy rock paper scissors game without diffusion a change of variables appropriate to replicator dynamics is shown to correctly capture the 1d asymptotic steady state via a nonlinear diffusion equation

analysis of residuals for the multinomial item response model using the item response model as developed on the multinomial distribution asymptotic variances are obtained for residuals associated with response patterns and first and second order marginal frequencies of manifest variables when the model does not fit well an examination of these residuals may reveal the source of the poor fit finally a limited information test of fit for the model is developed by using residuals defined for the first and second order marginals model evaluation based on residuals for these marginals is particularly useful when the response pattern frequencies are sparse

periodic travelling waves in a family of deterministic cellular automata abstract reaction diffusion equations whose kinetics contain a stable limit cycle are an established class of models for a range of biological and chemical systems in this paper i construct a family of deterministic cellular automata with nine states which are qualitatively similar to oscillatory reaction diffusion equations in that their rules reflect both local oscillations and spatial diffusion the automata can be crudely interpreted as models of predator prey interactions and i show that the behaviour following local perturbation of the prey only state in one space dimension is very similar in the automata and in standard reaction diffusion models for predator prey systems in particular in many cases invasion of prey by predators leaves behind periodic travelling waves in the wake of invasion i study in detail these periodic plane waves in the automaton by explicitly investigating periodic solutions of the difference equation governing travelling waves i show that the automaton has many different periodic wave solutions and i compare their properties with those of periodic wave solutions of reaction diffusion systems the basic conclusion is that included amongst the periodic waves in the automaton are a family of solutions which mimic quite closely the properties of reaction diffusion periodic waves

implementation of diffuse reflection boundary conditions in a thermal lattice boltzmann model with flux limiters we discuss three new implementation versions of diffuse reflection boundary conditions in a thermal lattice boltzmann model their accuracy is investigated in the case of couette flow by considering the slip regime the best results are recovered with versions 2 and 3 which rely on outgoing fluxes to express the particle distribution functions in the ghost nodes outside the flow domain version 2 is found to be more economical since it involves no interpolation procedure this version was thereafter used to investigate the temperature profile in couette flow for various values of prandtl number as well as the capability of the thermal lb model to capture the knudsen minimum in poiseuille flow

the dynamics of scroll waves in excitable media an overview is given of the attempts to understand the behavior of scroll waves in three dimensional excitable media using analytical methods and these results are compared with recent numerical and experimental results the behavior of untwisted planar scroll rings twisted rings and helices and knotted scroll wave filaments is discussed

minimum distance estimators for location and goodness of fit abstract a weighted cramer von mises distance between the empirical distribution function and the assumed model f0 x is minimized to produce estimators n that are asymptotically normal if the weight function is taken proportional to ln f 0 f 0 then n is asymptotically efficient and the minimized distance has the appropriate loss of one degree of freedom special attention is focused on the limiting distribution of this latter goodness of fit statistic in both null and alternative situations

renormalization of the lattice boltzmann hierarchy is it possible to solve boltzmann type kinetic equations using only a small number of particle velocities we introduce a technique of solving kinetic equations with a arbitrarily large number of particle velocities using only a lattice boltzmann method on standard low symmetry lattices the renormalized kinetic equation is validated with an exact solution of the planar couette flow at moderate knudsen numbers

the role of curvature and wavefront interactions in spiral wave dynamics abstract a theory of rotating spiral waves in excitable media is presented that allows the study of dynamical aspects such as nonsteady rotation an approximate spiral wave solution is proposed in the form of a superposition of curved solitary wavefronts parallel to each other this form is used by means of singular perturbation theory to derive an evolution equation for the spiral arm numerical solutions of that equation are found that describe one and two frequency rotations the transition to two frequency dynamics tip meandering is attributed to a destabilizing curvature effect

spiral waves in the belousov zhabotinskii reaction abstract the beautiful spiral waves of oxidation in the belousov zhabotinskii reaction are the source of many interesting and important questions about periods structures in excitable media it has long been known that these spirals are similar to involutes of circles at least some distance from the center but until now no way has been known to determine the correct wavelength and frequency in this paper we show that the parameters of a spiral wave can be viwed s eigenvalues of a problem with unique solution the critical ingredients of the theory are the effects of curvature on the propagation of wavefronts in two dimensional media and the dispersion of plane waves our analytical results are shown to be in good agreement with experimental data for the belousov zhabotinskii reagent

high order lattice boltzmann models for wall bounded flows at finite knudsen numbers we analyze a large number of high order discrete velocity models for solving the boltzmann bhatnagar gross krook equation for finite knudsen number flows using the chapman enskog formalism we prove for isothermal flows a relation identifying the resolved flow regimes for low mach numbers although high order lattice boltzmann models recover flow regimes beyond the navier stokes level we observe for several models significant deviations from reference results we found this to be caused by their inability to recover the maxwell boundary condition exactly by using supplementary conditions for the gas surface interaction it is shown how to systematically generate discrete velocity models of any order with the inherent ability to fulfill the diffuse maxwell boundary condition accurately both high order quadratures and an exact representation of the boundary condition turn out to be crucial for achieving reliable results for poiseuille flow we can reproduce the mass flow and slip velocity up to the knudsen number of 1 moreover for small knudsen numbers the knudsen layer behavior is recovered

extensions of the partial credit model the partial credit model developed by masters 1982 is a unidimensional latent trait model for responses scored in two or more ordered categories in the present paper some extensions of the model are presented first a marginal maximum likelihood estimation procedure is developed which allows for incomplete data and linear restrictions on both the item and the population parameters secondly two statistical tests for evaluating model fit are presented the former test has power against violation of the assumption about the ability distribution the latter test offers the possibility of identifying specific items that do not fit the model

singular filaments organize chemical waves in three dimensions iv wave taxonomy abstract this is the last of four papers on the anatomy of three dimensional organizing centers in excitable media these organizing centers are made of scroll ring waves with twists and knots in them diversely linked together each such aggregate of linked rings is characterized by a handful of topological quantum numbers which partition the family of organizing centers into discrete classes or atoms we derive the rules which govern nuclear structure in this periodic table as well as the selection rules for transmutation

diversity of three dimensional chemical waves abstract the propagation of spiral waves in the belousov zhabotinsky bz reaction has been extensively investigated the aim of this paper is to show the diversity of phenomenon in the three dimensional bz reagent with the aid of photographs of the evolving structures not all of which have been studied mathematically the most frequent observed wave forms are simple scrolls and toroidal scrolls a brief discussion of the existence of toroidal scroll solution to the eikonal equation in three dimensions is presented

boundary conditions for the upwind finite difference lattice boltzmann model evidence of slip velocity in micro channel flow we conduct a systematic study of the effect of various boundary conditions bounce back and three versions of diffuse reflection for the two dimensional first order upwind finite difference lattice boltzmann model simulation of couette flow in a micro channel using the diffuse reflection boundary condition reveals the existence of a slip velocity that depends on the knudsen number e l l where l is the mean free path and l is the channel width for walls moving in opposite directions with speeds u w the slip velocity satisfies u s l i p 2 eu w a l l 1 2 e in the case of poiseuille flow in a micro channel the slip velocity is found to depend on the lattice spacing ds and knudsen number e to both first and second order the best results are obtained for diffuse reflection boundary conditions that allow thermal mixing at a wall located at half lattice spacing outside the boundary nodes

simulation of micro and nano scale flows via the lattice boltzmann method abstract we use the lattice boltzmann method lbm for analysis of high and moderate knudsen number phenomena simulation results are presented for microscale couette and poiseuille flows the slip velocity nonlinear pressure drop and mass flow rate are compared with previous numerical results and or experimental data the knudsen minimum is successfully predicted for the first time within the lbm framework these results validate the usage of the lbm based commercial arbitrary geometry code powerflow for simulating nanoscale problems

coupled double distribution function lattice boltzmann method for the compressible navier stokes equations a coupled double distribution function lattice boltzmann method is developed for the compressible navier stokes equations different from existing thermal lattice boltzmann methods this method can recover the compressible navier stokes equations with a flexible specific heat ratio and prandtl number in the method a density distribution function based on a multispeed lattice is used to recover the compressible continuity and momentum equations while the compressible energy equation is recovered by an energy distribution function the energy distribution function is then coupled to the density distribution function via the thermal equation of state in order to obtain an adjustable specific heat ratio a constant related to the specific heat ratio is introduced into the equilibrium energy distribution function two different coupled double distribution function lattice boltzmann models are also proposed in the paper numerical simulations are performed for the riemann problem the double mach reflection problem and the couette flow with a range of specific heat ratios and prandtl numbers the numerical results are found to be in excellent agreement with analytical and or other solutions

lattice boltzmann models based on half range gauss hermite quadratures we discuss general features of thermal lattice boltzmann models based on half range gauss quadratures specialising to the half range gauss hermite and gauss laguerre cases the main focus of the paper is on the construction of high order half range hermite lattice boltzmann hhlb models the performance of the hhlb models is compared with that of laguerre lattice boltzmann llb and full range hermite lattice boltzmann hlb models by conducting convergence tests with respect to the quadrature order on stationary profiles of the particle number density macroscopic velocity temperature and heat fluxes in the two dimensional couette flow the bhatnagar gross krook bgk collision term is used throughout the paper to reduce the computational costs of the numerical simulations we use mixed lattice boltzmann models constructed using different quadrature methods on each cartesian axis for kn 0 01 the hlb models require the least number of velocities to satisfy our convergence test when kn 0 05 the hlb models are outperformed in terms of number of velocities employed by both the llb and the hhlb models moreover we find that the hhlb models require less quadrature points than the llb models at all tested values of kn which we attribute to the maxwellian form of the weight function for the half range hermite polynomials

testing goodness of fit with multinomial data abstract several new test procedures are proposed for assessing the goodness of fit of a postulated multinomial distribution the new tests are neyman smooth type tests with orders selected adaptively from the data they are shown through fourier and large sample analyses to provide potential improvements over classical methods in terms of their ability to detect certain types of alternatives simulation results and a real example illustrate the finite sample validity of the large sample theory and the practical utility of the proposed methods

helical and circular scroll wave filaments abstract we present a formal theory of the motion of circular and helical scroll wave filaments with uniform twist some implications of the theory are derived and compared to numerical computations of scroll wave evolution

singular filaments organize chemical waves in three dimensions iii knotted waves abstract this is the third of a series of papers on the anatomy of three dimensional organizing centers in excitable media we here ask whether all self consistent waves in excitable media are topologically equivalent to the experimentally verified scroll ring whose axis lies in a plane as a test case we examine a scroll ring whose axis contains a knot it proves to be incompatible with the requirements of physical chemistry unless simultaneously twisted by an amount equal to the writhing number of its axis which is zero for planar closed curves appropriate initial conditions are suggested for experimentally creating a wave whose source is a scroll ring knotted and twisted in this way

knotted and linked phase singularities in monochromatic waves exact solutions of the helmholtz equation are constructed possessing wavefront dislocation lines phase singularities in the form of knots or links where the wave function vanishes knotted nothings the construction proceeds by making a nongeneric structure with a strength n dislocation loop threaded by a strength m dislocation line and then perturbing this in the resulting unfolded stable structure the dislocation loop becomes an m n torus knot if m and n are coprime and n linked rings or knots if m and n have a common factor n the loop or rings are threaded by an m stranded helix in our explicit implementation the wave is a superposition of bessel beams accessible to experiment paraxially the construction fails

fundamental conditions for n th order accurate lattice boltzmann models in this paper we theoretically prove a set of fundamental conditions pertaining to discrete velocity sets and corresponding weights these conditions provide sufficient conditions for a priori formulation of lattice boltzmann models that automatically admit correct hydrodynamic moments up to any given n th order

mean and covariance structure analysis theoretical and practical improvements abstract the most widely used multivariate statistical models in the social and behavioral sciences involve linear structural relations among observed and latent variables in practice these variables are generally nonnormally distributed hence classical multivariate analysis based on multinomial error free variables having no simultaneous interrelations is not adequate to deal with such data a promising alternative based on asymptotically distribution free adf covariance structure analysis has been found to be virtually useless in practical model evaluation at finite sample sizes with nonnormal data we take a new look at the basic statistical theory of structural models under arbitrary distributions using the methodology of nonlinear regression and generalized least squares estimation for example we adopt the use of residual weight matrices from regression theory we develop a series of estimators and tests based on arbitrary distribution theory we obtain a type of probabilistic bartlett co

two dimensional thermal model of the finite difference lattice boltzmann method with high spatial isotropy the existing lattice boltzmann method multispeed thermal models show a limited accuracy this paper proposes a two dimensional multispeed thermal model for the finite difference lattice boltzmann method fdlbm to recover correct fluid equations up to fourth orders of local flow velocity should be retained in the local equilibrium distribution function and tensors of particle velocities should have up to seventh rank isotropy in the fdlbm particle velocities can be selected independently from the lattice configuration therefore particle velocities of octagonal directions which have up to seventh rank isotropic tensors are adopted the proposed model was verified by two simulations the model showed excellent numerical stability in addition to strict accuracy

existence and uniqueness of stabilized propagating wave segments in wave front interaction model abstract recent experimental studies of photosensitive belousov zhabotinskii reaction have revealed the existence of propagating wave segments the propagating wave segments are unstable but can be stabilized by using a feedback control to continually adjust the excitability of the medium experimental studies also indicate that the locus of the size of a stabilized wave segment as a function of the excitability of the medium gives the excitability boundary for the existence of 2d wave patterns with free ends in excitable media to study the properties of this boundary curve we use the wave front interaction model proposed by zykov and showalter this is equivalent to study a first order system of three ordinary differential equations which includes a singular nonlinearity using two different reduced first order systems of two ordinary differential equations we first show the existence of wave segments for any given propagating velocity then the wave profiles can be classified into two types namely convex and non convex types more precisely when the normalized propagating velocity is small we show that the wave profile is of convex type while the wave profile is of non convex type when the normalized velocity is close to 1

an integral invariant for scroll rings in a reaction diffusion system abstract the evolution of scroll rings with filaments of arbitrary shape has been studied analytically for reaction diffusion systems with all the state variables having the same diffusion coefficients belonging to this class of systems are in particular models of the belousov zhabotinskii bz chemical reaction it has been found that the speed of decrease of an area bounded by the planar scroll filament is given by s 2 d d is the diffusion coefficient and is independent of the kind of model used to describe an active medium time and filament shape i e the integral d s 2 d where d s is the differential of the filament length and is the drift velocity always remains valid using this integral invariant a number of problems on the drift of closed and unclosed three dimensional vortices have been solved the theoretical predictions have been verified in experiments with the bz reaction

a general family of limited information goodness of fit statistics for multinomial data maydeu olivares and joe j am stat assoc 100 1009 1020 2005 psychometrika 71 713 732 2006 introduced classes of chi square tests for sparse multidimensional multinomial data based on low order marginal proportions our extension provides general conditions under which quadratic forms in linear functions of cell residuals are asymptotically chi square the new statistics need not be based on margins and can be used for one dimensional multinomials we also provide theory that explains why limited information statistics have good power regardless of sparseness we show how quadratic form statistics can be constructed that are more powerful than x2 and yet have approximate chi square null distribution in finite samples with large models examples with models for truncated count data and binary item response data are used to illustrate the theory

a cellular automation model of excitable media iv untwisted scroll rings abstract we study the motion of untwisted circular scroll rings in an excitable medium modeled by a cellular automation that includes the effects of curvature and dispersion on wave propagation we find that scroll rings either shrink or expand with a velocity that is a function of the curvature of the ring and they drift along their axis of symmetry

traveling excitable waves successively generated in a nonlinear proliferation system we study the dynamics of spatiotemporal pattern formation in a nonlinear proliferation system e g cell division supported on a field of nutrition in which the mechanism of activation and its self suppression is simultaneously implemented this dynamical model has been numerically realized with coupled cellular automata ca and various long standing spatiotemporal patterns have been observed among others a successive generation of traveling waves by implanting a spot of cells onto the field consisting of nutrition and activator is particularly interesting this takes place despite the fact that the present reaction network has a stable fixed point and therefore autonomous temporal oscillatory does not exist in the mean field indeed the reaction diffusion equation method rd applied to this network reproduces only a single excitable wave and soon falls into a steady state a fixed point without the following propagating waves this system having a stable fixed point is an excitable system of different kind from the fitzhugh nagumo model in that it can generate a pulse propagating outwards by adding only a single cell onto it from outside the system the present excitation upon dropping a cell is amplified to macroscopic level by a hidden dynamics of oscillation between the activation and its self suppression a pulse thus generated is propagated in space time with the help of diffusion through a precise comparison between ca and rd it is found that a very small amount of residue of the cells and activators which are left unburned in the stochastic treatment of reactions by the ca becomes a seed to excite the system and generate the next pulse wave this newly born wave can leave another seed of reaction in the field after its propagation based on this analysis we account for the appearance of other patterns observed a possible control of these patterns by varying the spatial distribution of initial concentration of the relevant agents such as the activator is also discussed

a composite likelihood inference in latent variable models for ordinal longitudinal responses the paper proposes a composite likelihood estimation approach that uses bivariate instead of multivariate marginal probabilities for ordinal longitudinal responses using a latent variable model the model considers time dependent latent variables and item specific random effects to be accountable for the interdependencies of the multivariate ordinal items time dependent latent variables are linked with an autoregressive model simulation results have shown composite likelihood estimators to have a small amount of bias and mean square error and as such they are feasible alternatives to full maximum likelihood model selection criteria developed for composite likelihood estimation are used in the applications furthermore lower order residuals are used as measures of fit for the selected models

an inar 1 negative multinomial regression model for longitudinal count data this paper discusses a regression model for the analysis of longitudinal count data observed in a panel study an integer valued first order autoregressive inar 1 poisson process is adapted to represent time dependent correlations among the counts by combining the inar 1 representation with a random effects approach a new negative multinomial distribution is derived that includes the bivariate negative binomial distribution proposed by edwards and gurland 1961 and subrahmaniam 1966 as a special case a detailed analysis of the relationship between personality factors and daily emotion experiences illustrates the approach

limited information goodness of fit testing in multidimensional contingency tables we introduce a family of goodness of fit statistics for testing composite null hypotheses in multidimensional contingency tables these statistics are quadratic forms in marginal residuals up to order r they are asymptotically chi square under the null hypothesis when parameters are estimated using any asymptotically normal consistent estimator for a widely used item response model when r is small and multidimensional tables are sparse the proposed statistics have accurate empirical type i errors unlike pearson s x2 for this model in nonsparse situations the proposed statistics are also more powerful than x2 in addition the proposed statistics are asymptotically chi square when applied to subtables and can be used for a piecewise goodness of fit assessment to determine the source of misfit in poorly fitting models

diffuse reflection boundary condition for high order lattice boltzmann models with streaming collision mechanism for lattice boltzmann lb models their particle feature is ensured by the streaming collision mechanism however this mechanism is often discarded for high order lb models due to multi speed lattices here we propose a new way of implementing the diffuse reflection boundary condition that can maintain the characteristic streaming collision mechanism for high order models it is then tested on four lattice models namely d2q16 d2q17 d2q37 and d3q121 for isothermal and thermal couette flows and lid driven cavity flows our implementation is shown to be able to achieve second order accuracy globally

kinetic boundary conditions in the lattice boltzmann method derivation of the lattice boltzmann method from the continuous kinetic theory x he and l s luo phys rev e 55 r6333 1997 x shan and x he phys rev lett 80 65 1998 is extended in order to obtain boundary conditions for the method for the model of a diffusively reflecting moving solid wall the boundary condition for the discrete set of velocities is derived and the error of the discretization is estimated numerical results are presented which demonstrate convergence to the hydrodynamic limit in particular the knudsen layer in the kramers problem is reproduced correctly for small knudsen numbers

how should we assess the fit of rasch type models approximating the power of goodness of fit statistics in categorical data analysis we investigate the performance of three statistics r 1 r 2 glas in psychometrika 53 525 546 1988 and m 2 maydeu olivares joe in j am stat assoc 100 1009 1020 2005 psychometrika 71 713 732 2006 to assess the overall fit of a one parameter logistic model 1pl estimated by marginal maximum likelihood ml r 1 and r 2 were specifically designed to target specific assumptions of rasch models whereas m 2 is a general purpose test statistic we report asymptotic power rates under some interesting violations of model assumptions different item discrimination presence of guessing and multidimensionality as well as empirical rejection rates for correctly specified models and some misspecified models all three statistics were found to be more powerful than pearson s x 2 against two and three parameter logistic alternatives 2pl and 3pl and against multidimensional 1pl models the results suggest that there is no clear advantage in using goodness of fit statistics specifically designed for rasch type models to test these models when marginal ml estimation is used

symmetric spirals in media with relaxation kinetics and two diffusing species abstract we find an approximate solution for the shape and rotation frequency of spirals in excitable media with anti symmetric kinetics and diffusion in both species using singular perturbation theory we approximate the governing diffusion reaction system with a free boundary problem and then map this free boundary problem onto a fixed domain problem the resulting fixed domain problem is viewed as a nonlinear eigenvalue problem which can be solved iteratively using a numerical shooting algorithm solutions of the approximate free boundary problem are compared with numerical solutions of the full system of diffusion reaction equations and shown to be in good agreement

the dynamics of three dimensional scroll waves in excitable media abstract we investigate the motion of the central filament of a scroll wave in excitable medium we assume that two dimensional spiral solutions are known and use these solutions to produce slowly varying scroll waves in three dimensional space using standard ideas from perturbation theory multiscale techniques we find equations governing the motion of the central filament of the scroll and the twist of the scroll wave these equations are specialized to the case of a circular filament with uniformly distributed twist to determine the collapse or expansion and vertical drift of the spiral filament and to a helical filament with drift the predictions of these equations are in good qualitative agreement with the numerical experiments

power robustification of approximately linear tests abstract we present a general method of improving the power of linear and approximately linear tests when deviations from a translation family of distributions must be taken into account this method involves the combination of a linear statistic measuring location and a quadratic statistic measuring change of shape of the underlying distribution the tests funnel tests are constructed as certain bayes tests in general they gain a sizeable amount of power over the linear tests adapted to the translation family when a change of shape of the underlying distribution occurs while losing little for translation alternatives power robustification we introduce the concept of funnel tests in an gaussian framework first the effect of power robustification is studied by means of a power function expansion which applies to a large class of tests sharing a certain invariance property the funnel tests are characterized by a maximin property over a region defined by a rotational cone the idea of the const

efficient kinetic method for fluid simulation beyond the navier stokes equation we present a further theoretical extension to the kinetic theory based formulation of the lattice boltzmann method of shan j fluid mech 550 413 2006 in addition to the higher order projection of the equilibrium distribution function and a sufficiently accurate gauss hermite quadrature in the original formulation a regularization procedure is introduced in this paper this procedure ensures a consistent order of accuracy control over the nonequilibrium contributions in the galerkin sense using this formulation we construct a specific lattice boltzmann model that accurately incorporates up to third order hydrodynamic moments numerical evidence demonstrates that the extended model overcomes some major defects existing in conventionally known lattice boltzmann models so that fluid flows at finite knudsen number kn can be more quantitatively simulated results from force driven poiseuille flow simulations predict the knudsen s minimum and the asymptotic behavior of flow flux at large kn

the derivation of some tests for the rasch model from the multinomial distribution the present paper is concerned with testing the fit of the rasch model it is shown that this can be achieved by constructing functions of the data on which model tests can be based that have power against specific model violations it is shown that the asymptotic distribution of these tests can be derived by using the theoretical framework of testing model fit in general multinomial and product multinomial models the model tests are presented in two versions one that can be used in the context of marginal maximum likelihood estimation and one that can be applied in the context of conditional maximum likelihood estimation

minimum distance estimation and components of goodness of fit statistics summary the relationship of minimum distance md estimation to components of goodness of fit statistics is considered m estimation is viewed as a special case with interesting interpretations in terms of the defining function as related to linear combinations of the components and modified fourier approximations to the efficient score the essence of the competition between efficiency and robustness is the determination of the magnitudes of the coefficients of the high frequency components applications to the composite and simple goodness of fit problems are indicated

knotted scroll wave filaments in excitable media abstract it is shown that certain general systems of diffusion reaction equations can have invariant knotted scroll wave solutions the theory is based on the assumption that the system of equations supports permanently rotating spiral solutions and from this assumptions equations governing the motion of the scroll wave filament can be derived then bifurcatilon theory is used to show that the equations of motion have torus knots as invariant solutions analytical methods are used to determine qualitative and quantitative features of these knotted solutions

limited information estimation and testing of discretized multivariate normal structural models discretized multivariate normal structural models are often estimated using multistage estimation procedures the asymptotic properties of parameter estimates standard errors and tests of structural restrictions on thresholds and polychoric correlations are well known it was not clear how to assess the overall discrepancy between the contingency table and the model for these estimators it is shown that the overall discrepancy can be decomposed into a distributional discrepancy and a structural discrepancy a test of the overall model specification is proposed as well as a test of the distributional specification i e discretized multivariate normality also the small sample performance of overall distributional and structural tests as well as of parameter estimates and standard errors is investigated under conditions of correct model specification and also under mild structural and or distributional misspecification it is found that relatively small samples are needed for parameter estimates standard errors and structural tests larger samples are needed for the distributional and overall tests furthermore parameter estimates standard errors and structural tests are surprisingly robust to distributional misspecification

a cellular automaton describing the formation of spatially ordered structures in chemical systems abstract a cellular automaton describing a certain heterogeneous catalytic reaction is introduced as a theoretical approach towards the investigation of pattern formation in chemical systems the numerically obtained results demonstrate that the time evolution of this cellular automaton leads to a self sustained organization of circular and spiral wave like structures even starting from random initial states

the core of the spiral the problem of finding the unique frequency and shape including the core of spirals in excitable media is studied a leading order approximation of the problem is formulated as a nonlinear eigenvalue problem involving only ordinary differential equations odes shooting and comparison arguments are used to show why solutions of the leading order approximate problem exist and some of their quantitative features are explored numerically because of inaccuracies of the results in certain parameter ranges an improved formulation of the problem is proposed when solved numerically as in the special case of symmetric spirals solutions of the improved formulation differ significantly from solutions of the leading order problem but agree closely with the numerical solution of the full partial differential equation pde system

testing equality of a large number of densities the problem of testing equality of a large number of densities is considered the classical k sample problem compares a small fixed number of distributions and allows the sample size from each distribution to increase without bound in our asymptotic analysis the number of distributions tends to infinity but the size of individual samples remains fixed the proposed test statistic is motivated by the simple idea of comparing kernel density estimators from the various samples to the average of all density estimators however a novel interpretation of this familiar type of statistic arises upon centring it the asymptotic distribution of the statistic under the null hypothesis of equal densities is derived and power against local alternatives is considered it is shown that a consistent test is attainable in many situations where all but a vanishingly small proportion of densities are equal to each other the test is studied via simulation and an illustration involving microarray data is provided

tailor made tests of goodness of fit summary we examine a large class of distributional tests equivalent to tests based on degenerate u statistics the factors which influence the performance of these tests are isolated an analysis of the factors leads us to suggest tests with improved power properties against certain types of alternatives one such test is based on a chi squared statistic which employs overlapping cells rather than disjoint cells it is shown that this test has power superior to that of the classical chi squared statistic

dynamical stability of untwisted scroll rings in excitable media abstract we report numerical simulations of the dynamical behavior of three dimensional untwisted scroll rings for three different models of excitable media the computations reveal for the first time the existence of a stable steadily rotating non drifting as well as non expanding shrinking scroll wave near a wall expansion of the scroll ring is observed for different choices of kinetic models along with contraction and drift numerical calculations also indicate aperiodic or meandering movement of the three dimensional scroll ring near the wall contrary to earlier observations some scroll rings do not drift noticeably at any value of the diffusion coefficient of the recovery variable

slip velocity and knudsen layer in the lattice boltzmann method for microscale flows we present mesoscopic fluid wall interaction models for lattice boltzmann lb model simulations of microscale flows the exact solution of the slip velocity for the lb equation with the bhatnagar gross krook collision operator is obtained for poiseuille flow at finite knudsen numbers with a consistent definition of the knudsen number the slip coefficients of the lb equation with the standard d2q9 scheme are found to be slightly larger than those of the boltzmann equation with the same boundary condition which makes the standard lb method remain quantitatively accurate only for small knudsen numbers by modifying the nonequilibrium energy flux or introducing the effective relaxation time the lb method is analytically shown to reproduce the slip phenomena up to second order in the knudsen number for the standard lb method the knudsen layer is captured only with modification of the relaxation dynamics such as in the effective relaxation time model

dispersion of traveling waves in the belousov zhabotinskii reaction abstract we use perturbation and numerical methods to calculate the dispersion relation for periodic wave train solutions of diffusion reaction equations modeling the belousov zhabotinskii reaction these results are compared with experimental data for the belousov zhabotinskii reagent and shown to be in good agreement

singular perturbation theory of traveling waves in excitable media a review abstract waves of chemical or electrical activity traveling through space have been observed in several contexts chemical reaction mixtures in non convecting liquid phase cell suspensions nerve axons and neuromuscular tissues typically wave supporting preparations are excitable that is they respond and sensitivity to perturbations are rapidly damped out but suprathreshold disturbances trigger an abrupt and substantial response the abruptness of the response can be exploited by the methods of singular perturbation theory to obtain a mathematical description of wave propagation in spatially distributed excitable media singular perturbation analysis of propagating waves in one spatial dimension is straightforward and uncontentious but the analysis of propagating waves in one spatial dimension is straightforward and several fundamentally different ways we compare and contrast the approaches taken by greenberg zykov fife krinskii and his collaborators and ourselves with particular emphasis on the case of rotating spiral waves our intention is to bring some order to the important but difficult theory of propagating waves in two dimensional excitable media in conclusion we discuss briefly some possible extensions of the singular perturbation approach to propagating wave surfaces in three dimensional space

alternative stable rotors in an excitable medium abstract a given excitable medium continuous uniform isotropic simply connected two or three dimensional may support alternative types of vortex like solution radiating from a rotor these have distinct periods wavelengths behaviors near interfaces and in rotationally symmetric vortex rings different contraction or expansion rates and drift rates initial conditions select among the discrete alternatives rotors of different types may coexist within one medium until the interface between their domains encroaches upon the rotor of longer period examples are given using the fitzhugh nagumo model they are interpreted in terms of the measured dispersion curve for one dimensional propagation and a hypothetical curvature relation with one undetermined parameter