strong allee effect in a diffusive predator prey system with a protection zone article history a reaction diffusion predator prey system with strong allee effect and a protection zone for the prey is considered dynamics and steady state solutions of the system are analyzed in particular it is shown that the overexploitation phenomenon can be avoided if the allee effect threshold is low and the protection zone is large

harmonics to noise ratio as an index of the degree of hoarseness degree of hoarseness can be evaluated by judging the extent to which noise replaces the harmonic structure in the spectrogram of a sustained vowel however this visual method is subjective the present study was undertaken to develop the harmonics to noise h n ratio as an objective and quantitative evaluation of the degree of hoarseness the computation is conceptually straightforward 50 consecutive pitch periods of a sustained vowel a are averaged h is the energy of the averaged waveform while n is the mean energy of the differences between the individual periods and the averaged waveform recordings of 42 normal voices and 41 samples with varying degrees of hoarseness were analyzed two experts rated the spectrogram of each voice sample based on the amount of noise relative to that of the harmonic component the results showed a highly significant agreement the rank correlation coefficient 0 849 between h n calculations and the subjective evaluations of the spectrograms the h n ratio also proved useful in quantitatively assessing the results of treatment for hoarseness

particle representations for measure valued population models models of populations in which a type or location represented by a point in a metric space e is associated with each individual in the population are considered a population process is neutral if the chances of an individual replicating or dying do not depend on its type measurevalued processes are obtained as infinite population limits for a large class of neutral population models and it is shown that these measure valued processes can be represented in terms of the total mass of the population and the de finetti measures associated with an e valued particle model

quasi invariance and reversibility in the fleming viot process fleming viot processes with mutation selection and recombination are studied their reversible distributions are shown to be characterized as quasi invariant measures with a cocycle given in terms of the mutation operator the selection intensity and the recombination kernel by using this we derive not only a necessary and sufficient condition for the fleming viot process to be reversible but also identify the reversible distributions in the reversible case

perturbation free measurement of the harmonics to noise ratio in voice signals using pitch synchronous harmonic analysis the measurement of the harmonics to noise ratio hnr in speech signals gives an indication of the aperiodicity of the speech waveform this may be due to the presence of jitter shimmer additive noise waveshape change or some unknown combination of these factors in order to estimate the hnr as a measure of the additive noise component only the contaminating effects of the other contributory components must first be removed a pitch synchronous harmonic analysis is proposed to overcome this problem the procedure takes advantage of the time scale compression frequency expansion property of the fourier series in order to eliminate jitter and shimmer successive spectra are added by harmonic number as opposed to frequency location and perturbation is removed due to the fact that the relative heights of the harmonic components remain the same for scaled signals the technique is examined on synthetically generated voice signals a discussion of the results is given in terms of human voice signals characterization of jitter vocal tract filtering effects perturbation mechanisms nonlinear dynamics and the possibility of developing the method for use with inverse filtering strategies

stochastic flows associated to coalescent processes we study a class of stochastic flows connected to the coalescent processes that have been studied recently by mohle pitman sagitov and schweinsberg in connection with asymptotic models for the genealogy of populations with a large fixed size we define a bridge to be a right continuous process b r r 0 1 with nondecreasing paths and exchangeable increments such that b 0 0 and b 1 1 we show that flows of bridges are in one to one correspondence with the so called exchangeable coalescents this yields an infinite dimensional version of the classical kingman representation for exchangeable partitions of we then propose a poissonian construction of a general class of flows of bridges and identify the associated coalescents we also discuss an important auxiliary measure valued process which is closely related to the genealogical structure coded by the coalescent and can be viewed as a generalized fleming viot process

configurational transition in a fleming viot type model and probabilistic interpretation of laplacian eigenfunctions we analyse and simulate a two dimensional brownian multi type particle system with death and branching birth depending on the position of particles of different types the system is confined in a two dimensional box whose boundaries act as the sink of brownian particles the branching rate matches the death rate so that the total number of particles is kept constant in the case of m types of particle in a rectangular box of size and elongated shape we observe that the stationary distribution of particles corresponds to the mth laplacian eigenfunction for smaller elongations a b we find a configurational transition to a new limiting distribution the ratio a b for which the transition occurs is related to the value of the mth eigenvalue of the laplacian with rectangular boundaries

regular transition functions and regular superprocesses the class of regular markov processes is very close to the class of right processes studied by meyer getoor and others we say that a transition function p is regular if it is the transition function of a well defined regular markov process a characterization of regular transition functions is given which implies that if p is regular then the dawson watanabe and the flemingviot supertransition functions over p belong to the same class

traveling wave solutions for a continuous and discrete diffusive predator prey model abstract we study a diffusive predator prey model of lotka volterra type functional response in which both species obey the logistic growth such that the carrying capacity of the predator is proportional to the prey population and the one for prey is a constant both continuous and discrete diffusion are addressed our aim is to see whether both species can survive eventually if an alien invading predator is introduced to the habitat of an existing prey the answer to this question is positive under certain restriction on the parameter applying schauder s fixed point theory with the help of suitable upper and lower solutions the existence of traveling wave solutions for this model is proven furthermore by deriving the non existence of traveling wave solutions we also determine the minimal speed of traveling waves for this model this provides an estimation of the invasion speed

dynamics of prey threshold harvesting and refuge the dynamics of a predator prey model with continuous threshold prey harvesting and prey refuge is studied one central question is how harvesting and refuge could directly affect the dynamics of the ecosystem such as the stability properties of some coexistence equilibria and periodic solutions theoretical and numerical methods are used to investigate boundedness of solutions existence of bionomic equilibria as well as the existence and stability properties of equilibrium points and periodic solutions several bifurcations are also studied

smaller population size at the mrca time for stationary branching processes we consider an elementary model of random size varying population governed by a stationary continuous state branching process we compute the distributions of various variables related to the most recent common ancestor mrca the time to the mrca the size of the current population and the size of the population just before the mrca in particular we observe a natural mild bottleneck effect as the size of the population just before the mrca is stochastically smaller than the size of the current population we also compute the number of individuals involved in the last coalescent event of the genealogical tree that is the number of individuals at the time of the mrca who have descendants in the current population by studying more precisely the genealogical structure of the population we get asymptotics for the number of ancestors just before the current time we give explicit computations in the case of the quadratic branching mechanism in this case the size of the population at the mrca is in mean 2 3 of the size of the current population we also provide in this case the fluctuations for the renormalized number of ancestors

functional inequalities for the two parameter extension of the infinitely many neutral alleles diffusion abstract by explicitly identifying the transition density function we derived the super poincare and super log sobolev inequalities for the two parameter extension of the infinitely many neutral alleles diffusion which in particular implies the gross log sobolev inequality

dynamics and patterns of a diffusive leslie gower prey predator model with strong allee effect in prey abstract this paper is devoted to study the dynamical properties and stationary patterns of a diffusive leslie gower prey predator model with strong allee effect in the prey population we first analyze the nonnegative constant equilibrium solutions and their stabilities and then study the dynamical properties of time dependent solutions moreover we investigate the stationary patterns induced by diffusions turing pattern our results show that the impact of the strong allee effect essentially increases the system spatiotemporal complexity

a predator prey disease model with immune response in infected prey abstract in this paper a predator prey disease model with immune response in the infected prey is formulated the basic reproduction number of the within host model is defined and it is found that there are three equilibria extinction equilibrium infection free equilibrium and infection persistent equilibrium the stabilities of these equilibria are completely determined by the reproduction number of the within host model furthermore we define a basic reproduction number of the between host model and two predator invasion numbers predator invasion number in the absence of disease and predator invasion number in the presence of disease we have predator and infection free equilibrium infection free equilibrium predator free equilibrium and a co existence equilibrium we determine the local stabilities of these equilibria with conditions on the reproduction and invasion reproduction numbers finally we show that the predator free equilibrium is globally stable

correcting the use of ensemble averages in the calculation of harmonics to noise ratios in voice signals a correcting formula for the estimation of harmonics to noise ratios hnr based on ensemble averaging techniques is derived the original method yields a biased approximation which is more accurate as the number of averaged pulses n increases however the method treats gradual waveform changes incorrectly as noise which is worsened for large values of n the obtained formula allows the use of as few averaged pulses as desired while allowing the complete removal of the bias from the estimate of hnr

spectral properties for a class of continuous state branching processes with immigration abstract we explicitly construct nontrivial invariant probability measures for a class of continuous state branching processes with immigration the class of these measures include random gamma measures and path space measures of levy subordinators as particular examples using the explicit construction we study long time behaviour and hypercontractivity of the transition semigroups in corresponding l 2 spaces

bifurcation and spatiotemporal patterns in a homogeneous diffusive predator prey system abstract a diffusive predator prey system with holling type ii predator functional response subject to neumann boundary conditions is considered hopf and steady state bifurcation analysis are carried out in details in particular we show the existence of multiple spatially non homogeneous periodic orbits while the system parameters are all spatially homogeneous our results and global bifurcation theory also suggest the existence of loops of spatially non homogeneous periodic orbits and steady state solutions these results provide theoretical evidences to the complex spatiotemporal dynamics found by numerical simulation

modelling and analysis of a harvested prey predator system incorporating a prey refuge the present paper deals with a prey predator model incorporating a prey refuge and independent harvesting in either species our study shows that using the harvesting efforts as controls it is possible to break the cyclic behaviour of the system and drive it to a required state the possibility of existence of bionomic equilibria has been considered the problem of optimal harvest policy is then solved by using pontryagin s maximal principle

long time behaviour and regularity properties of transition semigroups of fleming viot processes let a be a feller generator on a compact space and l be the corresponding fleming viot fv operator with no selection and no recombination in this paper we give conditions on a implying that the semigroup t t generated by l i converges towards equilibrium with exponential rate moreover we determine explicit bounds on the rate of convergence in terms of a ii is hypercontractive iii is strong feller and iv is compact we give applications of the last result to the existence of invariant measures for fv operators with interactive selection

turing instability and pattern induced by cross diffusion in a predator prey system with allee effect to have spatial patterns form small allee effect admits relatively large range of predator mortality rate found cross diffusion is the key mechanism of spatial pattern formation obtained amplitude equations suggest both supercritical and subcritical bifurcation may occur weak allee effect admits supercritical bifurcation while strong one allows subcritical bifurcation in this paper we first propose a mathematical model for a spatial predator prey system with allee effect and then by using the proposed model we investigate the turing instability and the phenomena of pattern formation we show how cross diffusion destabilizes the spatially uniform steady state the method of multiple time scales is employed to derive the amplitude equations which is the cubic stuart landau equation in the supercritical case and the quintic in the subcritical case based on the amplitude equations we obtain the asymptotic solutions of the model close to the onset of instability

geometric aspects of fleming viot and dawson watanabe processes this paper is concerned with the intrinsic metrics of the two main classes of superprocesses for the fleming viot process we identify it as the bhattacharya distance and for dawson watanabe processes we find the kakutani hellinger metric the corresponding geometries are studied in some detail in particular representation formulas for geodesics and arc length functionals are obtained the relations between the two metrics yield a geometric interpretation of the identification of the fleming viot process as a dawson watanabe superprocess conditioned to have total mass 1 as an application a functional limit theorem for super brownian motion conditioned on local extinction is proved

on the validity of the log sobolev inequality for symmetric fleming viot operators we prove that fleming viot operators with parent independent mutation satisfy a logarithmic sobolev inequality if and only if the set of types is finite

fleming viot processes in population genetics fleming and viot indiana univ math j 28 1979 pp 817 843 introduced a class of probability measure valued diffusion processes that has attracted the interest of both pure and applied probabilists this paper surveys the subject of fleming viot processes as it relates to population genetics topics include 1 introduction 2 some measure valued markov chains 2 1 a diploid model 2 2 the wright fisher model 2 3 a moran model 3 the fleming viot process characterization 4 convergence 5 ergodicity 6 an infinite particle system 7 bounded mutation operators 8 reversibility 9 examples 9 1 continuous state stepwise mutation model 9 2 infinitely many neutral alleles model 9 3 infinitely many neutral alleles model with ages 9 4 two locus model with recombination 9 5 n locus model with gene conversion 9 6 infinitely many sites model without recombination 9 7 infinitely many neutral alleles model with allelic genealogies

distribution functions of means of a dirichlet process let be a random probability measure chosen by a dirichlet process on r b with parameter and such that x dx turns out to be a finite random variable the main concern of this paper is the statement of a suitable expression for the distribution function of that random variable such an expression is deduced through an extension of a procedure based on the use of generalized stieltjes transforms

a note on superprocesses subject to a mild restriction ona generator of the one particle motion we show thea fleming viot superprocess can be obtained from thea dawson watanabe superprocess by conditioning the latter to have constant total mass

complex dynamics of a diffusive predator prey model with strong allee effect and threshold harvesting abstract in this paper complex dynamics of a diffusive predator prey model is investigated where the prey is subject to strong allee effect and threshold harvesting the existence and stability of nonnegative constant steady state solutions are discussed the existence and nonexistence of nonconstant positive steady state solutions are analyzed to identify the ranges of parameters of pattern formation spatially homogeneous and nonhomogeneous hopf bifurcation and discontinuous hopf bifurcation are proved these results show that the introduction of strong allee effect and threshold harvesting increases the system spatiotemporal complexity finally numerical simulations are presented to validate the theoretical results

coupling and ergodic theorems for fleming viot processes fleming viot processes are probability measure valued diffusion processes that can be used as stochastic models in population genetics here we use duality methods to prove ergodic theorems for fleming viot processes including those with recombination coupling methods are also used to establish ergodicity of fleming viot processes first without and then with selection a special type of selection known as symmetric overdominance is treated by other methods

dynamics and pattern formation in a diffusive predator prey system with strong allee effect in prey abstract the dynamics of a reaction diffusion predator prey system with strong allee effect in the prey population is considered nonexistence of nonconstant positive steady state solutions are shown to identify the ranges of parameters of spatial pattern formation bifurcations of spatially homogeneous and nonhomogeneous periodic solutions as well as nonconstant steady state solutions are studied these results show that the impact of the allee effect essentially increases the system spatiotemporal complexity

minimizing the effect of period determination on the computation of amplitude perturbation in voice current methods of computing amplitude perturbation present in human voices depend upon being able to accurately determine fundamental period in this paper two methods of estimating the amplitude perturbation present in human voices which do not depend on accurate determination of the boundaries between fundamental periods are described in both of these methods amplitude perturbation is computed as the variance of an ensemble of periods calculated after these periods have been aligned in time in one method time alignment is accomplished using zero phase transformation in the second method an unconstrained dynamic programming procedure is used the accuracy of estimating amplitude perturbation by these two methods is evaluated using synthetic and natural voice signals and is also compared with an estimation using zero padding based time alignment the unconstrained dynamic programming method is shown to provide accurate estimation of voice amplitude perturbation over a variety of signal conditions

dynamics in a ratio dependent predator prey model with predator harvesting abstract the objective of this paper is to study systematically the dynamical properties of a ratio dependent predator prey model with nonzero constant rate predator harvesting it is shown that the model has at most two equilibria in the first quadrant and can exhibit numerous kinds of bifurcation phenomena including the bifurcation of cusp type of codimension 2 i e bogdanov takens bifurcation the subcritical and supercritical hopf bifurcations these results reveal far richer dynamics compared to the model with no harvesting and different dynamics compared to the model with nonzero constant rate prey harvesting in d xiao l jennings bifurcations of a ratio dependent predator prey system with constant rate harvesting siam appl math 65 2005 737 753 biologically it is shown that nonzero constant rate predator harvesting can prevent mutual extinction as a possible outcome of the predator prey interaction and remove the singularity of the origin which was regarded as pathological behavior for a ratio dependent predator prey model in p yodzis predator prey theory and management of multispecies fisheries ecological applications 4 2004 51 58

global bifurcation analysis and pattern formation in homogeneous diffusive predator prey systems abstract the dynamics of a general diffusive predator prey system is considered existence and nonexistence of non constant positive steady state solutions are shown to identify the ranges of parameters of spatial pattern formation bifurcations of spatially homogeneous and nonhomogeneous periodic solutions as well as non constant steady state solutions are studied

stationary distributions for a class of generalized fleming viot processes we identify stationary distributions of generalized fleming viot processes with jump mechanisms specified by certain beta laws together with a parameter measure each of these distributions is obtained from normalized stable random measures after a suitable biased transformation followed by mixing by the law of a dirichlet random measure with the same parameter measure the calculations are based primarily on the well known relationship to measure valued branching processes with immigration

time normalization of voice signals using functional data analysis the harmonics to noise ratio hnr has been used to quantify the waveform irregularity of voice signals yumoto et al j acoust soc am 71 1544 1550 1982 this measure assumes that the signal consists of two components a harmonic component which is the common pattern that repeats from cycle to cycle and an additive noise component which produces the cycle to cycle irregularity it has been shown j qi j acoust soc am 92 2569 2576 1992 that a valid computation of the hnr requires a nonlinear time normalization of the cycle wavelets to remove phase differences between them this paper shows the application of functional data analysis to perform an optimal nonlinear normalization and compute the hnr of voice signals results obtained for the same signals using zero padding linear normalization and dynamic programming algorithms are presented for comparison functional data analysis offers certain advantages over other approaches it preserves meaningful features of signal shape produces differentiable results and allows flexibility in selecting the optimization criteria for the wavelet alignment an extension of the technique for the time normalization of simultaneous voice signals such as acoustic egg and airflow signals is also shown the general purpose of this article is to illustrate the potential of functional data analysis as a powerful analytical tool for studying aspects of the voice production process

on transition semigroups of a ψ superprocesses with immigration we study the global properties of transition semigroups p at of a superprocesses over compact type spaces with possibly nonzero immigration in various function spaces in particular we compare the different rates of convergence of p at to equilibrium our analysis is based on an explicit formula for the gateaux derivative of p atf