approximate probabilistic cellular automata for the dynamics of single species populations under discrete logisticlike growth with and without weak allee effects we investigate one dimensional elementary probabilistic cellular automata pca whose dynamics in first order mean field approximation yields discrete logisticlike growth models for a single species unstructured population with nonoverlapping generations beginning with a general six parameter model we find constraints on the transition probabilities of the pca that guarantee that the ensuing approximations make sense in terms of population dynamics and classify the valid combinations thereof several possible models display a negative cubic term that can be interpreted as a weak allee factor we also investigate the conditions under which a one parameter pca derived from the more general six parameter model can generate valid population growth dynamics numerical simulations illustrate the behavior of some of the pca found

properties of symmetric matrices abstract we find the extreme points and the smooth points of the unit ball of the banach space n of all real symmetric n n matrices

relatively weakly open subsets of the unit ball in functions spaces for an infinite hausdorff compact set k and for any banach space x we show that every nonempty weak open subset relative to the unit ball of the space of x valued functions that are continuous when x is equipped with the weak respectively norm weak topology has diameter 2 as consequence we improve known results about nonexistence of denting points in these spaces also we characterize when every nonempty weak open subset relative to the unit ball has diameter 2 for the spaces of bochner integrable and essentially bounded measurable x valued functions

predator prey quasicycles from a path integral formalism the existence of beyond mean field quasicycle oscillations in a simple spatial model of predator prey interactions is derived from a path integral formalism the results agree substantially with those obtained from analysis of similar models using system size expansions of the master equation in all of these analyses the discrete nature of predator prey populations and finite size effects lead to persistent oscillations in time but spatial patterns fail to form the path integral formalism goes beyond mean field theory and provides a focus on individual realizations of the stochastic time evolution of population not captured in the standard master equation approach

on the extremal structure of the unit balls of banach spaces of weakly continuous functions and their duals a sufficient and then a necessary condition are given for a function to be an extreme point of the unit ball of the banach space c k x w of continuous functions under the supremum norm from a compact hausdorff topological space k into a banach space x equipped with its weak topology w strongly extreme points of the unit ball of c k x w are characterized as the norm one functions that are uniformly strongly extreme point valued on a dense subset of k it is shown that a variety of stronger types of extreme points e g denting points never exist in the unit ball of c k x w lastly some naturally arising and previously known extreme points of the unit ball of c k x w are shown to actually be strongly exposed points

rotundity properties in banach spaces via sublinear operators abstract conditions for extreme points strongly extreme points lur points su points points in direction of which the space is uniformly rotund and points with the kadec klee property with respect to the convergence almost everywhere for the space d e s generated by a kothe space e and a sublinear operator s defined on a linear space x and with values in l 0 are given as corollaries conditions for rotundity midpoint local uniform rotundity local uniform rotundity uniform rotundity in every direction and the kadec klee property for the convergence locally in measure of these spaces are deduced interpretations of the results in cases of kothe bochner spaces cesaro orlicz spaces and k interpolation spaces are presented

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

a new class of automata networks a new class of automata networks is defined their evolution rules are determined by a probability measure p on the set of all integers z and an indicator function ia on the interval 0 1 it is shown that any cellular automaton rule can be represented by a nonunique rule formulated in terms of a pair p ia this new class of automata networks contains discrete systems which are not cellular automata for a given p a metric can be defined on the space of all rules which induces a metric on the space of all cellular automata rules

quantitative assessment of the toner and tu theory of polar flocks we present a quantitative assessment of the toner and tu theory describing the universal scaling of fluctuations in polar phases of dry active matter using large scale simulations of the vicsek model in two and three dimensions we find the overall phenomenology and generic algebraic scaling predicted by toner and tu but our data on density correlations reveal some qualitative discrepancies the values of the associated scaling exponents we estimate differ significantly from those conjectured in 1995 in particular we identify a large crossover scale beyond which flocks are only weakly anisotropic we discuss the meaning and consequences of these results

symmetric phase only matched filtering of fourier mellin transforms for image registration and recognition presents a new method to match a 2d image to a translated rotated and scaled reference image the approach consists of two steps the calculation of a fourier mellin invariant fmi descriptor for each image to be matched and the matching of the fmi descriptors the fmi descriptor is translation invariant and represents rotation and scaling as translations in parameter space the matching of the fmi descriptors is achieved using symmetric phase only matched filtering spomf the performance of the fmi spomf algorithm is the same or similar to that of phase only matched filtering when dealing with image translations the significant advantage of the new technique is its capability to match rotated and scaled images accurately and efficiently the innovation is the application of spomf to the fmi descriptors which guarantees high discriminating power and excellent robustness in the presence of noise this paper describes the principle of the new method and its discrete implementation for either image detection problems or image registration problems practical results are presented for various applications in medical imaging remote sensing fingerprint recognition and multiobject identification

monotonicity characteristic of kothe bochner spaces abstract estimates of the characteristic of monotonicity in kothe bochner function spaces e x with some consequences are given characterizations of strict and uniform monotonicity of the sequence lattice e x n n 1 are obtained

role of the noise on the transient dynamics of an ecosystem of interacting species abstract we analyze the transient dynamics of an ecosystem described by generalized lotka volterra equations in the presence of a multiplicative noise and a random interaction parameter between the species we consider specifically three cases i two competing species ii three interacting species one predator two preys iii n interacting species the interaction parameter in case i is a stochastic process which obeys a stochastic differential equation we find noise delayed extinction of one of two species which is akin to the noise enhanced stability phenomenon other two noise induced effects found are temporal oscillations and spatial patterns of the two competing species in case ii the noise induces correlated spatial patterns of the predator and of the two preys concentrations finally in case iii we find the asymptotic behavior of the time average of the ith population when the ecosystem is composed of a great number of interacting species

correlation filters with controlled scale response correlation filtering methods are becoming increasingly popular for image recognition and location the recent introduction of optimal tradeoff circular harmonic function filters allowed the user to specify the response of a correlation filter to in plane rotation distortion in this paper we introduce a new correlation filter design that can provide a user specified response to in plane scale distortion the design is based on the mellin radial harmonic mrh transform and incorporates multiple harmonics into the correlation filter for improved discrimination capability additionally the filter design minimizes the average correlation energy in order to achieve sharp correlation peaks and thus we refer to these filters as minimum average correlation energy mellin radial harmonic mace mrh filters we present underlying theory a mace mrh filter design method and numerical simulation results

extremity in kothe bochner function spaces abstract letebe a kothe function space over a complete measurable space andxa banach space recall an elementhineis said to beorder continuousif for any decreasing sequence gn inse ngn 0 andgn h implies limn gn 0 we show that every denting point of the unit ball ofeis order continuous using this result we prove thatfis a denting point of the unit ball ofe x if and only if is a denting point of the unit ball of for almost all supp is a denting point of the unit ball of suppose thateis order continuous we also prove that for any unit vectorfine x if f xis a strongly exposed point of the unit ball ofeand for almost allt supp f f t f t xis a strongly exposed point of the unit ball ofx thenfis a strongly exposed point of the unit ball ofe x

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

critical and oscillatory behavior of a system of smart preys and predators it is shown that a system of smart preys and predators exhibits irreversible phase transitions between a regime of prey predator coexistence and an state where predator extinction is observed within the coexistence regime the system exhibits a transition between a regime where the densities of species remain constant and another with self sustained oscillations respectively this transition is located by means of a combined treatment involving finite size scaling and fourier transforms furthermore it is shown that the transition can be rationalized in terms of the standard percolation theory the existence of an oscillatory regime in the thermodynamic limit which is in contrast to previous findings of boccara et al phys rev e 50 4531 1994 may be due to subtle differences between the studied models

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

radon nikodym property for the projective tensor product of kothe function spaces abstract let e be an order continuous kothe function space or an order continuous banach lattice and x be a dual banach space then e x the projective tensor product of e and x has the radon nikodym property if and only if both e and x do

extreme polynomials and multilinear forms onl1 abstract given a 2 homogeneous polynomialp x y ax2 by2 cxywith real coefficients let p rand p cdenote the norms ofpon the real and complex banach spacel21 respectively we show p r p c and obtain a sufficient and necessary condition on the coefficientsa b andcforpto have norm 1 applying these results we characterize extreme points of the unit ball of p 2l1 for the real banach spacel21and examine them for the complex banach spacel21 we apply them to find extreme points and strongly extreme points of the unit ball of p 2l1 and get an extremal 2 homogeneous polynomial onl1that is not an extreme point we also characterize extreme points and strongly extreme points of the unit ball of l ml1 or l ml1 0 1

stable oscillations of a predator prey probabilistic cellular automaton a mean field approach we analyze a probabilistic cellular automaton describing the dynamics of coexistence of a predator prey system the individuals of each species are localized over the sites of a lattice and the local stochastic updating rules are inspired by the processes of the lotka volterra model two levels of mean field approximations are set up the simple approximation is equivalent to an extended patch model a simple metapopulation model with patches colonized by prey patches colonized by predators and empty patches this approximation is capable of describing the limited available space for species occupancy the pair approximation is moreover able to describe two types of coexistence of prey and predators one where population densities are constant in time and another displaying self sustained time oscillations of the population densities the oscillations are associated with limit cycles and arise through a hopf bifurcation they are stable against changes in the initial conditions and in this sense they differ from the lotka volterra cycles which depend on initial conditions in this respect the present model is biologically more realistic than the lotka volterra model

on the oscillatory dynamical behaviour of epidemic spreading in fractal media we present numerical evidence that dynamical physical processes that develop a time dependent characteristic length and take place in fractal media exhibiting spatial discrete scale invariance dsi with fundamental scaling ratio b may become coupled to the topology of the fractal leading to the observation of time dsi the hallmark of time dsi is the observation of a log periodic modulation of the dynamic or kinetic observables which is characterized by a well defined fundamental time scaling ratio both fundamental scaling ratios are linked according to b 1 z where z is the dynamic exponent characteristic of the physical process specifically we have studied the epidemic behaviour of the contact process cp in sierpinski carpets the cp exhibits second order irreversible phase transitions between an active regime and an absorbing state where the system is trapped without any escape possibility we observed that relevant dynamic observables such as the number of active sites the survival probability of the epidemics and the mean square displacement of the epidemic from the origin r2 t exhibit log periodic modulations by fitting the data we evaluate the fundamental time scaling ratio for various fractals and the corresponding dynamic exponents since at criticality one has that r2 t t2 z an independent estimation of the dynamic exponent can be performed in excellent agreement with results obtained by using the conjectured relationship for the fundamental scaling ratios b and

advanced in plane rotation invariant correlation filters advanced correlation filter synthesis algorithms to achieve rotation invariance are described we use a specified form for the filter as the rotation invariance constraint and derive a general closed form solution for a multiclass rotation invariant filter that can recognize a number of different objects by requiring the filter to minimize the average correlation plane energy we produce a multiclass rotation invariant ri ri mace filter which controls correlation plane sidelobes and improves discrimination against false targets to improve noise performance we require the filter to minimize a weighted sum of correlation plane signal and noise energy initial test results of all filters are provided

the threshold of coexistence and critical behaviour of a predator prey cellular automaton we study a probabilistic cellular automaton to describe two population biology problems the threshold of species coexistence in a predator prey system and the spreading of an epidemic in a population by carrying out mean field approximations and numerical simulations we obtain the phase boundaries thresholds related to the transition between an active state where prey and predators present a stable coexistence and a prey absorbing state the numerical estimates for the critical exponents show that the transition belongs to the directed percolation universality class in the limit where the cellular automaton maps into a model for the spreading of an epidemic with immunization we observe a crossover from directed percolation class to the dynamic percolation class patterns of growing clusters related to species coexistence and spreading of epidemic are shown and discussed

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

finite size scaling analysis of the critical behavior of a general epidemic process in 2d abstract we investigate the critical behavior of a stochastic lattice model describing a general epidemic process by means of a monte carlo procedure we simulate the model on a regular square lattice and follow the spreading of an epidemic process with immunization a finite size scaling analysis is employed to determine the critical point as well as some critical exponents we show that the usual scaling analysis of the order parameter moment ratio does not provide an accurate estimate of the critical point precise estimates of the critical quantities are obtained from data of the order parameter variation rate and its fluctuations our numerical results corroborate that this model belongs to the dynamic isotropic percolation universality class we also check the validity of the hyperscaling relation and present data collapse curves which reinforce the accuracy of the estimated critical parameters

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

monotonicity properties in banach spaces via sublinear operators and corrigendum to rotundity properties in banach spaces via sublinear operators nonlinear analysis 64 2006 1171 1188 abstract various kinds of monotone points namely lower and upper strictly monotone lower and upper locally uniformly monotone points are studied in the space d e s generated by a kothe space e and a sublinear operator s defined on a banach lattice x and with values in e some results on global monotonicity properties are easily deduced from those results interpretations of the result in three different classes of the space d e s are given at the end a small corrigendum to our paper rotundity properties in banach spaces via sublinear operators published in nonlinear analysis 64 2006 1171 1188 is given

optimal tradeoff circular harmonic function correlation filter methods providing controlled in plane rotation response correlation methods are becoming increasingly attractive tools for image recognition and location this renewed interest in correlation methods is spurred by the availability of high speed image processors and the emergence of correlation filter designs that can optimize relevant figures of merit in this paper a new correlation filter design method is presented that allows one to optimally tradeoff among potentially conflicting correlation output performance criteria while achieving desired correlation peak value behavior in response to in plane rotation of input images such controlled in plane rotation response is useful in image analysis and pattern recognition applications where the sensor follows a pre arranged trajectory while imaging an object since this new correlation filter design is based on circular harmonic function chf theory we refer to the resulting filters as optimal tradeoff circular harmonic function otchf filters underlying theory otchf filter design method and illustrative numerical results are presented

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

directed percolation in 2 1 dimensions the author presents results of monte carlo simulations for directed percolation in 2 1 dimensions very close to the percolation threshold his values for pc for bond and site percolation on the bcc and simple cubic lattices are more precise than previous estimates by one to two orders of magnitude the improvement on the critical exponents describing the behaviour at pc is less impressive but they are also substantially more precise than previous ones

risk perception in epidemic modeling we investigate the effects of risk perception in a simple model of epidemic spreading we assume that the perception of the risk of being infected depends on the fraction of neighbors that are ill the effect of this factor is to decrease the infectivity that therefore becomes a dynamical component of the model we study the problem in the mean field approximation and by numerical simulations for regular random and scale free networks we show that for homogeneous and random networks there is always a value of perception that stops the epidemics in the worst case scenario of a scale free network with diverging input connectivity a linear perception cannot stop the epidemics however we show that a nonlinear increase of the perception risk may lead to the extinction of the disease this transition is discontinuous and is not predicted by the mean field analysis

consensus analysis of switching multi agent systems with fixed topology and time delay abstract this paper investigates the average consensus problems of the discrete time markov switching linear multi agent systems lmas with fixed topology and time delay firstly we introduce a concept of the average consensus to adapt the stochastic systems secondly a time delay switching consensus protocol is proposed by developing a new signal mode the switching signal of the systems and the time delay signal of the controller can be merged into one signal thirdly by lyapunov technique two lmis criteria of average consensus are provided and they reveal that the consensus of the multi agent systems relates to the spectral radius of the laplacian matrix furthermore by our results and ccl type algorithms we can get the gain matrices finally a numerical example is given to illustrate the efficiency of our results