a note on an overview of aliasing errors in discrete time formulations of time frequency representations various realizations asserting to produce the alias free discrete time wigner distribution have been reviewed and analyzed by costa and boudreaux bartels see ibid vol 47 no 5 p 1463 74 may 1999 here a simple alias free form of the pseudo wigner distribution is proposed it is obtained from the fact that the sampled signal can formally be considered as a multicomponent signal

soliton like phenomena in one dimensional cross diffusion systems a predator prey pursuit and evasion example abstract we have studied properties of non linear waves in a mathematical model of a predator prey system with pursuit and evasion we demonstrate a new type of propagating wave in this system the mechanism of propagation of these waves essentially depends on the taxis represented by non linear cross diffusion terms in the mathematical formulation we have shown that the dependence of the velocity of wave propagation on the taxis has two distinct forms parabolic and linear transition from one form to the other correlates with changes in the shape of the wave profile dependence of the propagation velocity on diffusion in this system differs from the square root dependence typical of reaction diffusion waves we also demonstrate that for systems with negative and positive taxis for example pursuit and evasion there typically exists a large region in the parameter space where the waves demonstrate quasi soliton interaction colliding waves can penetrate through each other and waves can also reflect from impermeable boundaries

cone kernel representation versus instantaneous power spectrum the cone kernel representation ckr and the instantaneous power spectrum ifs are two time frequency representations tfrs where the cross terms are localized in the region of auto terms exploring their relationship for discrete sequences we show that the ifs kernel is only two extreme terms of the ckr kernel further comparing other properties of these two tfrs viz invertibility aliasing and noise robustness we show that there is aliasing in some transform domains for signals sampled at nyquist rate and that the ckr has better noise robustness than the ifs

hypermeander of spirals local bifurcations and statistical properties in both experimental studies and numerical simulations of waves in excitable media rigidly rotating spiral waves are observed to undergo transitions to complicated spatial dynamics with long term brownian like motion of the spiral tip this phenomenon is known as hypermeander in this paper we review a number of recent results on dynamics with noncompact group symmetries and make the case that hypermeander may occur at a codimension two bifurcation from a rigidly rotating spiral wave our predictions are based on center bundle reduction sandstede scheel and wulff and on central limit theorems and invariance principles for group extensions of hyperbolic dynamical systems these predictions are confirmed by numerical simulations of the center bundle equations

technical allocative and overall efficiency estimation and inference abstract nonparametric data envelopment analysis and free disposal hull estimators are frequently used to estimate cost revenue and profit efficiency as well as the corresponding allocative efficiencies papers in the literature often report sample means of such estimates along with sample standard deviations inviting readers to make inference about means of these efficiencies using classical methods based on the standard lindeberg feller central limit theorem clt a number of papers explicitly make inference using the classical methods however the statistical properties of these estimators are until now unknown this paper establishes rates of convergence and existence of limiting distributions for the various estimators these properties are needed in order to make inference about individual producers using subsampling methods in addition properties of the first two moments of the estimators are derived and these results are subsequently used to establish new clts for the estimators providing formal justification for inference making the results reveal that the classical clts and methods do not provide valid inference when fdh estimators are used and provide valid inference when dea estimators only in a few restrictive special cases

spontaneous formation of dynamical patterns with fractal fronts in the cyclic lattice lotka volterra model dynamical patterns in the form of consecutive moving stripes or rings are shown to develop spontaneously in the cyclic lattice lotka volterra model when realized on square lattice at the reaction limited regime each stripe consists of different particles species and the borderlines between consecutive stripes are fractal the interface width w between the different species scales as w l t ensuremath sim l ensuremath alpha f t l z where l is the linear size of the interface t is the time and ensuremath alpha and z are the static and dynamical critical exponents respectively the critical exponents were computed as ensuremath alpha 0 49 ifmmode pm else textpm fi 0 03 and z 1 53 ifmmode pm else textpm fi 0 13 and the propagating fronts show dynamical characteristics similar to those of the eden growth models

intrinsic chaos and external noise in population dynamics abstract we address the problem of the relative importance of the intrinsic chaos and the external noise in determining the complexity of population dynamics we use a recently proposed method for studying the complexity of nonlinear random dynamical systems the new measure of complexity is defined in terms of the average number of bits per time unit necessary to specify the sequence generated by the system this measure coincides with the rate of divergence of nearby trajectories under two different realizations of the noise in particular we show that the complexity of a nonlinear time series model constructed from sheep populations comes completely from the environmental variations however in other situations intrinsic chaos can be the crucial factor this method can be applied to many other systems in biology and physics

phase transitions and spatio temporal fluctuations in stochastic lattice lotka volterra models we study the general properties of stochastic two species models for predator prey competition and coexistence with lotka volterra type interactions defined on a d dimensional lattice introducing spatial degrees of freedom and allowing for stochastic fluctuations generically invalidates the classical deterministic mean field picture already within mean field theory however spatial constraints modeling locally limited resources lead to the emergence of a continuous active to absorbing state phase transition field theoretic arguments supported by monte carlo simulation results indicate that this transition which represents an extinction threshold for the predator population is governed by the directed percolation universality class in the active state where predators and prey coexist the classical center singularities with associated population cycles are replaced by either nodes or foci in the vicinity of the stable nodes the system is characterized by essentially stationary localized clusters of predators in a sea of prey near the stable foci however the stochastic lattice lotka volterra system displays complex correlated spatio temporal patterns of competing activity fronts correspondingly the population densities in our numerical simulations turn out to oscillate irregularly in time with amplitudes that tend to zero in the thermodynamic limit yet in finite systems these oscillatory fluctuations are quite persistent and their features are determined by the intrinsic interaction rates rather than the initial conditions we emphasize the robustness of this scenario with respect to various model perturbations

on aggregate farrell efficiencies in this paper we establish the fact that an industry maximal revenue is the sum of its firms maximal revenues this fact enables us to discover conditions for aggregation of farrell efficiencies

pattern formation of a spatial predator prey system abstract there are random and directed movements of predator and prey populations in many natural systems which are strongly influenced and modified by spatial factors to investigate how these migration directed movement and diffusion random movement affect predator prey systems we have studied the spatiotemporal complexity in a predator prey system with holling tanner form a theoretical analysis of emerging spatial pattern is presented and wavelength and pattern speed are calculated at the same time we present the properties of pattern solutions the results of numerical simulations show that migration has prominent effect on the pattern formation of the population i e changing turing pattern into traveling pattern this study suggests that modelling by migration and diffusion in predator prey systems can account for the dynamical complexity of ecosystems

classification of coupled systems with two component nonlinear diffusion equations by the invariant subspace method the invariant subspace method is developed to perform classification of systems with two component nonlinear diffusion equations which was carried out with respect to the invariant subspaces defined by linear ordinary differential equations as a result the corresponding exact solutions generated by invariant subspaces to the resulting systems are obtained in most cases two components of these exact solutions belong to different scalar subspaces behaviour to several exact solutions of the systems is described

cross terms analysis in the modified instantaneous power spectrum this correspondence examines cross terms in the modified version of the instantaneous power spectrum mips which is a smoothed form of the real part of the rihaczek distribution mips was reported recently to be less sensitive to the poor resolution of spectro gram and the cross terms in the pseudo wigner ville distribution pwvd however in this correspondence we will show that like pwvd the mips possesses cross terms too the only differences be tween them are the location and the oscillating frequency of the cross terms we deduce that the cross terms of the mips are located in about the same region of the autoterms while the cross terms of the wvd are located midway between the autoterms the undesirable cross terms and artifact between different spectral components are much less se vere and interfere less with each other in mips than in pwvd cases i introduction page originally defined the instantaneous power specturm ips as the derivative of the running energy spectrum i which satis fied many of the properties of time frequency distribution how ever its ringing effect blocks its application hippenstiel and de oliveira 2 advocated the use of the fourier transform of an av eraged correlation function estimate this estimate is further mod ified by applying a sliding window after forming the correlation estimate the result a smoothed version of the real part of the rihaczek distribution 3 is a modified version of ips hippenstiel shows that the mips can be less sensitive to the time frequency resolution tradeoff problem occurring in the spectrogram 141 and the cross term interference problem occurring in wigner ville dis tribution wvd 5 7 moreover the modified ips mips can avoid the ringing effect which is a major problem in page s ips method however in this correspondence we will show that like pwvd the mips possesses cross terms too compared with wvd the only differences between them are the location and the oscil lating frequency of the cross terms this correspondence will also show why the modified ips reduces the ringing effect

deterministic brownian motion in the hypermeander of spiral waves abstract we explain the phenomenon of hypermeander of spiral waves observed in numerical with various models of excitable media as a chaotic attractor in the quotient system with respect to the euclidean group such an attractor should lead to a motion of the spiral wave tip analogous to that of a brownian particle with mean square of displacement of the tip growing linearly at large times this prediction is confirmed by numerical experiments with hypermeandering spiral waves

self organized packs selection in predator prey ecosystems received 19 july 2005 revised manuscript received 3 october 2005 published 23 february 2006we present a lattice model of a system of predators of ve kinds competing for prey the predators aregrouped in packs and characterized by two parameters the energy spent on hunting and energy gained by thekill the success of hunting depends on the actual competition among predators found near a prey wedetermine via monte carlo simulations the numbers of predators of each kind as a function of time and thedistribution of the size of their packs we show that the ratio of the energy spent by the competing predatorsdetermines their fate the energy gain plays only a secondary role we show also that the system self organizesitself into groups of predators living in well de ned packs which size depends on the energy spent the mostpreferred size dependence on the energy spent follows a very simple power law we present also a mean eld type approach to the problem and we discuss the differences in the results obtained by the two methods showing in particular that the simulation approach produces more reliable results doi 10 1103 physreve 73 021913 pacs number s 87 23 cc 87 23 kg 05 10 ln 87 23 n

wavefront propagation in a competition equation with a new motility term modelling contact inhibition between cell populations linear diffusion is an established model for spatial spread in biological systems including movement of cell populations however for interacting closely packed cell populations simple diffusion is inappropriate because different cell populations will not move through one another rather a cell will stop moving when it encounters another cell in this paper i introduce a nonlinear diffusion term that reflects this phenomenon known as contact inhibition of migration i study this term in the context of two competing cell populations one of which has a proliferative advantage over the other this is motivated by the very early stages of solid tumour growth i focus in particular on travelling wave solutions corresponding to moving interfaces between the two cell populations numerical simulations indicate that there are wavefront solutions for wave speeds above a critical minimum value and i present linear analysis that explains the selection of wave speeds by initial conditions i obtain an approximation to the shape of these waves for high speeds and show that the minimum speed arises via quite new behaviour in the travelling wave equations with the proportion of cells of each type approaching a step function as the wave speed decreases towards the minimum exploiting this structure i use singular perturbation theory to investigate the wave shape for speeds close to the minimum

nonstationary spectral analysis based on time frequency operator symbols and underspread approximations we present a unified framework for time varying or time frequency tf spectra of nonstationary random processes in terms of tf operator symbols we provide axiomatic definitions and tf operator symbol formulations for two broad classes of tf spectra one of which is new these classes contain all major existing tf spectra such as the wigner ville evolutionary instantaneous power and physical spectrum our subsequent analysis focuses on the practically important case of nonstationary processes with negligible high lag tf correlations so called underspread processes we demonstrate that for underspread processes all tf spectra yield effectively identical results and satisfy several desirable properties at least approximately we also show that gabor frames provide approximate karhunen loeve kl functions of underspread processes and tf spectra provide a corresponding approximate kl spectrum finally we formulate simple approximate input output relations for the tf spectra of underspread processes that are passed through underspread linear time varying systems all approximations are substantiated mathematically by upper bounds on the associated approximation errors our results establish a tf calculus for the second order analysis and time varying filtering of underspread processes that is as simple as the conventional spectral calculus for stationary processes

a unified definition for the discrete time discrete frequency and discrete time frequency wigner distributions various discrete definitions of the wigner distribution wd for discrete time signals have been proposed in previous works the formulation developed in this paper leads to natural and unified definitions of discrete versions of the wd they are directly related to the continuous and preserve most of its properties the discretization is first considered in the time domain dtwd in the frequency domain dfwd and then in both domains simultaneously dtfwd in each case the aliasing problem is studied and generalized interpolation formulas allowing the reconstruction of the continuous wd are derived the dtfwd is particulary relevant for computer implementation of the wd

boundary effects on population dynamics in stochastic lattice lotka volterra models abstract we investigate spatially inhomogeneous versions of the stochastic lotka volterra model for predator prey competition and coexistence by means of monte carlo simulations on a two dimensional lattice with periodic boundary conditions to study boundary effects for this paradigmatic population dynamics system we employ a simulation domain split into two patches upon setting the predation rates at two distinct values one half of the system resides in an absorbing state where only the prey survives while the other half attains a stable coexistence state wherein both species remain active at the domain boundary we observe a marked enhancement of the predator population density the predator correlation length displays a minimum at the boundary before reaching its asymptotic constant value deep in the active region the frequency of the population oscillations appears only very weakly affected by the existence of two distinct domains in contrast to their attenuation rate which assumes its largest value there we also observe that boundary effects become less prominent as the system is successively divided into subdomains in a checkerboard pattern with two different reaction rates assigned to neighboring patches when the domain size becomes reduced to the scale of the correlation length the mean population densities attain values that are very similar to those in a disordered system with randomly assigned reaction rates drawn from a bimodal distribution

improving the readability of time frequency and time scale representations by the reassignment method in this paper the use of the reassignment method first applied by kodera gendrin and de villedary 1976 to the spectrogram is generalized to any bilinear time frequency or time scale distribution this method creates a modified version of a representation by moving its values away from where they are computed so as to produce a better localization of the signal components we first propose a new formulation of this method followed by a thorough theoretical study of its characteristics its practical use for a large variety of known time frequency and time scale distributions is then addressed finally some experimental results are reported to demonstrate the performance of this method

a huygens principle for diffusion and anomalous diffusion in spatially extended systems we present a universal view on diffusive behavior in chaotic spatially extended systems for anisotropic and isotropic media for anisotropic systems strong chaos leads to diffusive behavior brownian motion with drift and weak chaos leads to superdiffusive behavior levy processes with drift for isotropic systems the drift term vanishes and strong chaos again leads to brownian motion we establish the existence of a nonlinear huygens principle for weakly chaotic systems in isotropic media whereby the dynamics behaves diffusively in even space dimension and exhibits superdiffusive behavior in odd space dimensions

positive time frequency distribution functions we demonstrate the existence of positive joint distributions of time and frequency for arbitrary signals a method is given to readily generate an infinite number of them for any signal general properties of these distribution functions are derived and specific examples for some common signals are presented

a model for fast computer simulation of waves in excitable media abstract starting from a two variable system of reaction diffusion equations an algorithm is devised for efficient simulation of waves in excitable media the spatio temporal resolution of the simulation can be varied continuously for fine resolutions the algorithm provides accurate solution of the underlying reaction diffusion equations for coarse resolutions the algorithm provides qualitative simulations at small computational cost

solitary waves in excitable systems with cross diffusion we consider a fitzhughnagumo system of equations where the traditional diffusion terms are replaced with linear cross diffusion of components this system describes solitary waves that have unusual

semianalytical approach to criteria for ignition of excitation waves we consider the problem of ignition of propagating waves in one dimensional bistable or excitable systems by an instantaneous spatially extended stimulus earlier we proposed a method i idris and v n biktashev phys rev lett 101 244101 2008 for analytical description of the threshold conditions based on an approximation of the center stable manifold of a certain critical solution here we generalize this method to address a wider class of excitable systems such as multicomponent reaction diffusion systems and systems with non self adjoint linearized operators including systems with moving critical fronts and pulses we also explore an extension of this method from a linear to a quadratic approximation of the center stable manifold resulting in some cases in a significant increase in accuracy the applicability of the approach is demonstrated on five test problems ranging from archetypal examples such as the zeldovich frank kamenetsky equation to near realistic examples such as the beeler reuter model of cardiac excitation while the method is analytical in nature it is recognized that essential ingredients of the theory can be calculated explicitly only in exceptional cases so we also describe methods suitable for calculating these ingredients numerically

robustness of spiral waves in two dimensional reactive diffusive media the effects of the reaction terms diffusion coefficients and size of the computational domain on the dynamics of the two equation oregonator model in two dimensional reactive diffusive media is studied numerically and it is shown that spiral waves are robust under truncation or expansion of the computational domain it is also shown that large diffusion coefficients for the inhibitor may result on either annihilation of the wave or unbounded growth whereas large diffusion coefficients for the activator concentration may result in unbounded decay of both the activator s and inhibitor s concentrations small diffusion coefficients of the inhibitor may result in stationary tongue like shapes whereas small diffusion coefficients of the activator may result in narrow ring shapes where the activator s concentration is high a decrease in the parameter which controls the stiffness of the activator s reaction rate is found to result in unbounded growth of the activator s concentration whereas an increase in the parameter that couples the activator and inhibitor is found to result in either annihilation of the spiral wave or unbounded growth of the concentrations of both the activator and the inhibitor

flocks herds and schools a quantitative theory of flocking we present a quantitative continuum theory of flocking the collective coherent motion of large numbers of self propelled organisms in agreement with everyday experience our model predicts the existence of an ordered phase of flocks in which all members of even an arbitrarily large flock move together with the same mean velocity stackrel ensuremath rightarrow v ensuremath ne 0 this coherent motion of the flock is an example of spontaneously broken symmetry no preferred direction for the motion is picked out a priori in the model rather each flock is allowed to and does spontaneously pick out some completely arbitrary direction to move in by analyzing our model we can make detailed quantitative predictions for the long distance long time behavior of this broken symmetry state the goldstone modes associated with this spontaneously broken rotational symmetry are fluctuations in the direction of motion of a large part of the flock away from the mean direction of motion of the flock as a whole these goldstone modes mix with modes associated with conservation of bird number to produce propagating sound modes these sound modes lead to enormous fluctuations of the density of the flock far larger at long wavelengths than those in e g an equilibrium gas our model is similar in many ways to the navier stokes equations for a simple compressible fluid in other ways it resembles a relaxational time dependent ginsburg landau theory for an n d component isotropic ferromagnet in spatial dimensions dg4 the long distance behavior is correctly described by a linearized theory and is equivalent to that of an unusual but nonetheless equilibrium model for spin systems for dl4 nonlinear fluctuation effects radically alter the long distance behavior making it different from that of any known equilibrium model in particular we find that in d 2 where we can calculate the scaling exponents exactly flocks exhibit a true long range ordered spontaneously broken symmetry state in contrast to equilibrium systems which cannot spontaneously break a continuous symmetry in d 2 the mermin wagner theorem we make detailed predictions for various correlation functions that could be measured either in simulations or by quantitative imaging of real flocks we also consider an anisotropic model in which the birds move preferentially in an easy e g horizontal plane and make analogous but quantitatively different predictions for that model as well for this anisotropic model we obtain exact scaling exponents for all spatial dimensions including the physically relevant case d 3

effects of cross diffusion on turing bifurcations in two species reaction transport systems we study the turing bifurcation in general two species reaction transport systems where particle dispersal is governed by diffusion including cross diffusion by performing a linear stability analysis we find conditions for the turing instability and compare the results with the standard turing conditions we apply our results to two model systems the lengyel epstein model and the brusselator and find strong effects of cross diffusion on the turing bifurcation

time varying spectral estimation using the instantaneous power spectrum ips the spectral content of time varying signals is examined using a modified version of the instantaneous power spectrum ips the short duration periodogram and the pseudo wigner ville distribution pwd have been used extensively to display the time varying spectral information a disadvantage of the periodogram is its inherently poor resolution due to the requirement of matching the resolution width to the spectral dynamics of the signal potential problems associated with pwd are spectral cross terms and an inability to resolve spectral components at the endpoints of the analysis segment a modified version of ips is shown to be less sensitive to these types of problems in addition ips can work with real valued signals sampled at the traditional nyquist rate

a new test for chaos in deterministic systems we describe a new test for determining whether a given deterministic dynamical system is chaotic or nonchaotic in contrast to the usual method of computing the maximal lyapunov exponent our metho

fluctuations and correlations in lattice models for predator prey interaction including spatial structure and stochastic noise invalidates the classical lotka volterra picture of stable regular population cycles emerging in models for predator prey interactions growth limiting terms for the prey induce a continuous extinction threshold for the predator population whose critical properties are in the directed percolation universality class we discuss the robustness of this scenario by considering an ecologically inspired stochastic lattice predator prey model variant where the predation process includes next nearest neighbor interactions we find that the corresponding stochastic model reproduces the above scenario in dimensions 1 d or 4 in contrast with the mean field theory which predicts a first order phase transition however the mean field features are recovered upon allowing for nearest neighbor particle exchange processes provided these are sufficiently fast

study of interacting particle systems the transition to the oscillatory behavior of a prey predator model abstract a prey predator system with intelligent pursuit and evasion is studied by means of computer simulations it is found that the model exhibits a coexistence state between prey and predators in this state and depending on the parameters the system may evolve toward two different regimes characterized by the behavior of the prey predator population whitin the oscillatory fixed point regime the specie s density changes periodically remains constant respectively the transition between such regimes is rationalized in terms of a dynamic percolation process

instantaneous power spectra conventional spectral analysis methods do not describe the distribution of signal power in both time and frequency simultaneously time dependent fourier transforms are defined to extend the conventional theory to include instantaneous energy and power spectra for the past and future signal these spectra are combined to define an instantaneous power spectrum ips of the entire signal the ips is a noncausal mathematical property of the signal from which observable properties can be derived e g the lagged window fourier transform estimate of the time frequency variations of the signal the ips for a nonstationary process is shown to be given by the fourier transform of loeve s generalized power spectrum of the process and to be a generalization of the wiener kintchine theorem it is also shown to represent the special cases of the stationary process the locally stationary process and the deterministic process

front propagation and segregation in a reaction diffusion model with cross diffusion abstract a study of front propagation and segregation in a system of reaction diffusion equations with cross diffusion is presented the reaction models predator prey dynamics involving two fields the diffusive part is nonlinear in the sense that the diffusion coefficient instead of being a constant as in the well studied case depends on one of the fields a key element of the model is a cross diffusion term according to which the flux of one of the fields is driven by gradients of the other field the original motivation of the model was the study of the turbulence shear flow interaction in plasmas the model also bears some similarities with models used in the study of spatial segregation of interacting biological species the system has three nontrivial fixed points and a study of traveling fronts solutions joining these states is presented depending on the stability properties of the fixed points the fronts are uniform or have spatial structure in the latter case a cross diffusion driven pattern forming k 0 instability leads to segregation in the wake of the front the segregated state consists of layered structures a ginzburg landau amplitude equation is used to describe the dynamics near marginal stability

spatio temporal patterns in two dimensional excitable media subject to robin boundary conditions a numerical study of spiral wave propagation in two dimensional excitable media subject to homogeneous robin boundary conditions is presented and it is shown that depending on the magnitude of the transfer coefficient periodic almost periodic and nonperiodic dynamics may be observed for transfer coefficients equal to or smaller than one spiral waves almost identical to those obtained with homogeneous neumann boundary conditions are observed whereas arms of spiral waves layers along the boundaries of the domain break up attachment to and detachment from boundaries islands and complex spatio temporal patterns result when the transfer coefficients for both the activator and inhibitor are larger than one along either the top and bottom boundaries or the left and right boundaries when the transfer coefficients are larger than one along all the boundaries of the domain it has been found that there is a layer of high activator s concentration along the boundaries and an arm of spiral waves may appear and interact with the boundary layers and the dynamics of the excitable medium is complex and nonperiodic

improving finite sample approximation by central limit theorems for estimates from data envelopment analysis abstract we propose an improvement of the finite sample approximation of the central limit theorems clts that were recently derived for statistics involving production efficiency scores estimated via data envelopment analysis dea or free disposal hull fdh approaches the improvement is very easy to implement since it involves a simple correction of the variance estimator with an estimate of the bias of the already employed statistics without any additional computational burden and reserves the original asymptotic results such as consistency and asymptotic normality the proposed approach persistently showed improvement in all the scenarios that we tried in various monte carlo experiments especially for relatively small samples or relatively large dimensions measured by total number of inputs and outputs of the underlying production model this approach therefore is expected to produce more accurate estimates of confidence intervals of aggregates of individual efficiency scores in empirical research using dea or fdh approaches and so must be valuable for practitioners we also illustrate this method using a popular real data set to confirm that the difference in the estimated confidence intervals can be substantial a step by step implementation algorithm of the proposed approach is included in the appendix