high precision estimate of g4 in the 2d ising model we compute the renormalized four point coupling in the 2d ising model using transfer matrix techniques we greatly reduce the systematic uncertainties which usually affect this type of calculation by using the exact knowledge of several terms in the scaling function of the free energy our final result is g4 14 697 35 3

a note on n estimators for the binomial distribution abstract consider k success counts from a binomial distribution with unknown n and success probability p we examine the problem of estimating n by integrating the likelihood for n and p over a beta density for p we obtain the beta binomial distribution resulting in stable and reasonably efficient estimators of n which compare favorably with and are often better than the estimates introduced by olkin et al 1981

the quartic oscillator a non perturbative study by continuous unitary transformations the quantum quartic oscillator is investigated in order to test the many body technique of the continuous unitary transformations the quartic oscillator is sufficiently simple to allow a detailed study and comparison of various approximation schemes due to its simplicity it can be used as a pedagogical introduction to the unitary transformations both the spectrum and the spectral weights are discussed

exponentially small corrections in the asymptotic expansion of the eigenvalues of the cubic anharmonic oscillator the asymptotic expansion of the eigenvalues of the cubic anharmonic oscillator is studied in a region of the coupling constant plane in which there is a sequence of exponentially small subseries beyond the standard rayleigh schrodinger perturbation theory rspt power series we give a simple algorithm for the calculation of these subseries to any desired order in terms of the rspt coefficients expressed as polynomials in the quantum number and illustrate our results with numerical borel pade summations of the expansion up to third exponentially small order

generalized quantum anharmonic oscillator using an operator ordering approach we construct a generalized expression for the normal ordering of a a m for integral values of m and use the result to study the quantum anharmonic oscillator problem in the heisenberg approach in particular we derive generalized expressions for energy eigenvalues and frequency shifts for the hamiltonian h x2 2 2 2 m xm we also derive a closed form first order multiscale perturbation theoretic operator solution of this hamiltonian with a view to generalize some recent results of bender and bettencourt 1996 phys rev lett 77 4114 1996 phys rev d 54 1710

the three dimensional ising model revisited numerically several basic universal amplitude ratios are studied afresh for three dimensional nearest neighbor ising models in revising earlier work modern estimates of the critical temperature and exponents are used in conjunction with biased inhomogeneous differential approximants to extrapolate the longest available series expansions to find the critical amplitudes c for the susceptibility 1 for the correlation length 1 a for the specific heat c t and b for the spontaneous magnetization m0 we find c c 4 95 0 15 1 1 1 960 0 01 a a 0 523 0 009 a c b 0 0581 0 0010 while a 1 3 verifies hyperuniversality to within 0 8 a method for calculating amplitude ratios which allows for corrections to scaling yields estimates for c c and 1 1 in excellent agreement with those derived from the individual amplitudes finally explicit formulae are given for the numerical evaluation of t 1 t c t and m0 t over the full temperature range from criticality to t 0 and corresponding plots and convenient near critical representations are also presented

on the singularity structure of the 2d ising model susceptibility some simplifications of the integrals 2n 1 derived by wu et al 1976 13 316 that contribute to the zero field susceptibility of the 2d square lattice ising model are reported in particular several alternate expressions for the integrands in 2n 1 are determined which greatly facilitate both the generation of high temperature series and analytical analysis one can show that as series 2n 1 22n s 2 4n n 1 1 o s where s is the high temperature variable sin 2k with k the conventional normalized inverse temperature analysis of the integrals near symmetry points of the integrands shows that 2n 1 s is singular on the unit circle at sk exp ik where 2cos k cos 2 k 2n 1 cos 2 2n 1 n k n the singularities k 0 excepted are logarithmic branch points of order 2n n 1 1ln with 1 s sk there is numerical evidence from series that these van hove points in addition to the known points at s 1 and i exhaust the singularities on the unit circle barring cancellation from extra unobserved singularities one can conclude that s 1 is a natural boundary for the susceptibility

ridge regression biased estimation for nonorthogonal problems in multiple regression it is shown that parameter estimates based on minimum residual sum of squares have a high probability of being unsatisfactory if not incorrect if the prediction vectors are not orthogonal proposed is an estimation procedure based on adding small positive quantities to the diagonal of x x introduced is the ridge trace a method for showing in two dimensions the effects of nonorthogonality it is then shown how to augment x x to obtain biased estimates with smaller mean square error

anharmonic oscillator discontinuity formulae up to second exponentially small order the eigenvalues of the quartic anharmonic oscillator as functions of the anharmonicity constant satisfy a once subtracted dispersion relation in turn this dispersion relation is driven by the purely imaginary discontinuity of the eigenvalues across the negative real axis in this paper we calculate explicitly the asymptotic expansion of this discontinuity up to second exponentially small order

mean field stochastic theory for species rich assembled communities a dynamical model of an ecological community is analyzed within a mean field approximation in which one of the species interacts with the combination of all of the other species in the community within this approximation the model may be formulated as a master equation describing a one step stochastic process the stationary distribution is obtained in closed form and is shown to reduce to a log series or log normal distribution depending on the values that the parameters describing the model take on a hyperbolic relationship between the connectance of the matrix of interspecies interactions and the average number of species exists for a range of parameter values the time evolution of the model at short and intermediate times is analyzed using van kampen s approximation which is valid when the number of individuals in the community is large good agreement with numerical simulations is found the large time behavior and the approach to the stationary state is obtained by solving the equation for the generating function of the probability distribution the analytical results which follow from the analysis are also in good agreement with direct simulations of the model

quasilinearization method and its verification on exactly solvable models in quantum mechanics the proof of the convergence of the quasilinearization method of bellman and kalaba whose origin lies in the theory of linear programming is extended to large and infinite domains and to singular functionals in order to enable the application of the method to physical problems this powerful method approximates solution of nonlinear differential equations by treating the nonlinear terms as a perturbation about the linear ones and is not based unlike perturbation theories on existence of some kind of small parameter the general properties of the method particularly its uniform and quadratic convergence which often also is monotonic are analyzed and verified on exactly solvable models in quantum mechanics namely application of the method to scattering length calculations in the variable phase method shows that each approximation of the method sums many orders of the perturbation theory and that the method reproduces properly the singular structure of the exact solutions the method provides final and reasonable answers for infinite values of the coupling constant and is able to handle even super singular potentials for which each term of the perturbation theory is infinite and the perturbation expansion does not exist

the likelihood ratio test for poisson versus binomial distributions abstract the estimation of n in the binomial b n p distribution is a considerably harder problem than the estimation of p we approach it as a boundary value estimation and testing problem where the boundary n corresponds to a poisson distribution for the data whereas n corresponds to a binomial distribution the asymptotic distribution of the deviance statistic for testing the hypothesis that the true value of n is infinite is shown to be a 50 50 mixture between a point mass at zero and a chi squared distribution we show also that the asymptotic distribution is not a good approximation for small samples discuss the application of the method and compare it to alternative approaches

models for estimating abundance from repeated counts of an open metapopulation summary using only spatially and temporally replicated point counts royle 2004b biometrics 60 108 115 developed an n mixture model to estimate the abundance of an animal population when individual animal detection probability is unknown one assumption inherent in this model is that the animal populations at each sampled location are closed with respect to migration births and deaths throughout the study in the past this has been verified solely by biological arguments related to the study design as no statistical verification was available in this article we propose a generalization of the n mixture model that can be used to formally test the closure assumption additionally when applied to an open metapopulation the generalized model provides estimates of population dynamics parameters and yields abundance estimates that account for imperfect detection probability and do not require the closure assumption a simulation study shows these abundance estimates are less biased than the abundance estimate obtained from the original n mixture model the proposed model is then applied to two data sets of avian point counts the first example demonstrates the closure test on a single season study of mallards anas platyrhynchos and the second uses the proposed model to estimate the population dynamics parameters and yearly abundance of american robins turdus migratorius from a multi year study

universal surface tension and critical isotherm amplitude ratios in three dimensions the universal surface tension and critical isotherm amplitude ratios are studied numerically for three dimensional ising models modern estimates of the critical temperature and exponents allow reliable evaluation of the critical surface tension amplitude k using recent monte carlo data for the simple cubic lattice likewise the amplitudes cc for the susceptibility and 1c for the second moment correlation length on the critical isotherm have been re estimated using existing series expansions the method of inhomogeneous differential approximants also yields a direct estimate of the correction to scaling exponent c on the critical isotherm which via scaling corresponds to the thermal correction exponent 0 55 5 this supports previous estimates and the stronger conclusion 0 54 3 for the universal ratios we estimate k 1 2 0 0965 2 cc b 1c 1 0 93 25 and c cc 1c 1 2 1 17 2 where b 1 and c are the amplitudes of the spontaneous magnetization and second moment correlation length and of the susceptibility above tc

analytical calculation of two leading exponents of the dilute potts model a potts model on a square lattice with two and four spin interaction and site and bond dilution is shown to be dual to itself the model is mapped onto a vertex problem which in turn is equivalent to a solid on solid model by means of these mappings the dilute potts model can be written as a gaussian like model with staggered and direct periodic fields the leading and next to leading exponents of the potts model are calculated subject to the validity of certain assumptions

bayesian analyses for a multiple capture recapture model summary in multiple capture recapture surveys the probability of capture can vary between sampling occasions the model accounting for this variation is known as at bayes empirical bayes and bayes empirical bayes solutions are given to the problems of interval estimation decision making and point estimation of the population size n when the number of sampling occasions is small to moderate and the number of recaptured units observed on each sampling occasion is moderate estimates obtained from empirical bayes and bayes empirical bayes methods compare closely to bayesian methods using a reference prior distribution for the capture probabilities however when the number of sampling occasions is large and the number of recaptured units observed on each sampling occasion is small inferences obtained using different reference priors can differ considerably

inference for exponential order statistic models based on an integrated likelihood function abstract methods of statistical inference are developed for the exponential order statistic eos model where only a subset of order statistics from a collection of n iid exponential random detection times is observable when the rate parameter for detections is unknown the maximum likelihood estimator mle of the unknown integer parameter n can be infinite with substantial probability inference for n is developed using a pseudolikelihood function obtained by integrating out the rate parameter the estimator that maximizes this function called the integrated likelihood estimator ile is shown to be finite and to have better sampling properties than the mle parameter based asymptotics are developed for the case where n is large application of the methodology is illustrated using two datasets

critical exponents hyperscaling and universal amplitude ratios for two and three dimensional self avoiding walks we make a high precision monte carlo study of two and three dimensional self avoiding walks saws of length up to 80 000 steps using the pivot algorithm and the karp luby algorithm we study the critical exponents v and 2 triangle sub 4 gamma as well as several universal amplitude ratios in particular we make an extremely sensitive test of the hyperscaling relation dv 2 triangle sub 4 gamma in two dimensions we confirm the predicted exponent v 3 4 and the hyperscaling relation we estimate the universal ratios 0 14026 0 00007 0 43961 0 00034 and psi 0 66296 0 00043 68 confidence limits in three dimensions we estimate v 0 5877 0 0006 with a correction to scaling exponent triangle sub 1 0 56 0 03 subjective 68 confidence limits this value for v agrees excellently with the field theoretic renormalization group prediction but there is some discrepancy for triangle 1 earlier monte carlo estimates of v which were approximately 0 592 are now seen to be biased by corrections to scaling we estimate the universal ratios 0 1599 0 0002 and psi 0 2471 0 0003 since psi 0 hyperscaling holds the approach to psi is from above contrary to the prediction of the two parameter renormalization group theory we critically reexamine this theory and explain where the error lies in an appendix we prove rigorously modulo some standard scalingmore assumptions the hyperscaling relation dv 2 triangle sub 4 gamma for two dimensional saws less

on the critical polynomial of the simple cubic ising model in 1985 rosengren conjectured that the critical point of the symmetric simple cubic sc ising model is given by nu c identical to tanh j kbtc nu r identical to square root 5 2 cos pi 8 this guess is examined in the context of attempting to construct the fully critical polynomial p3 nu x nu y nu z with a root nu c jx jy jz for the anisotropic sc ising model with couplings jx jy and jz it transpires that nu r is a surd which satisfies r nu r2 0 where r x is a quartic polynomial with integral coefficients but r nu 2 is a poor candidate for p3 nu nu nu since it does not display various nice properties embodied in the critical polynomial p2 nu x nu y for the square 2d ising lattices methods for constructing nice polynomials qk nu x nu y nu z that provide excellent approximations for nu c and for nu r are demonstrated however scaling arguments etc for the dimensional crossover induced when say jz to 0 cast doubt on the existence and nature of the sought for critical polynomial p3

dose finding using the biased coin up and down design and isotonic regression we are interested in finding a dose that has a prespecified toxicity rate in the target population in this article we investigate five estimators of the target dose to be used with the up and down biased coin design bcd introduced by durham and flournoy 1994 statistical decision theory and related topics these estimators are derived using maximum likelihood weighted least squares sample averages and isotonic regression a linearly interpolated isotonic regression estimate is shown to be simple to derive and to perform as well as or better than the other target dose estimators in terms of mean square error and average number of subjects needed for convergence in most scenarios studied

the susceptibility of the square lattice ising model new developments we have made substantial advances in elucidating the properties of the susceptibility of the square lattice ising model we discuss its analyticity properties certain closed form expressions for subsets of the coefficients and give an algorithm of complexity o n6 to determine its first n coefficients as a result we have generated and analyzed series with more than 300 terms in both the high and low temperature regime we quantify the effect of irrelevant variables to the scaling amplitude functions in particular we find and quantify the breakdown of simple scaling in the absence of irrelevant scaling fields arising first at order t tc 9 4 though high low temperature symmetry is still preserved at terms of order t tc 17 4 and beyond this symmetry is no longer present the short distance terms are shown to have the form t tc p log t tc q with p q2 conjectured exact expressions for some correlation functions and series coefficients in terms of elliptic theta functions also foreshadow future developments

inadmissibility of the maximum likelihood estimator in the sequential estimation of the size of a population summary for the sequential estimation of the size of a finite population the maximum likelihood estimator is a commonly used estimator but has no explicit expression in this paper it is shown that the maximum likelihood estimator is inadmissible an estimator which is simple in form and dominates the maximum likelihood estimator asymptotically is proposed to study the optimality property of the estimator for the stopping rule sb from a decision theoretical approach we investigate the admissibility of the estimator under a general weighted squared error loss function although the maximum likelihood estimator and its risk have no closed form expression the estimator will be shown to be inadmissible by means of a general theorem that we establish later as theorem 2 1 in this paper we only consider the simple capture capture model discussed by samuel 1968 more complex and realistic capture recapture models have been developed subsequently pollack otto 1983 pickands raghavachari 1987 bonett woodward bentler 1987 cormack 1989 huggins 1989 we conjecture that many of the

quantum states of a sextic potential hidden symmetry and quantum monodromy a known terminating polynomial ansatz for a finite sub set of states of the sextic central potential v a b c r ar2 br4 cr6 c 0 subject to integer related parameter constraints is confirmed to apply in two as well as three dimensions a hidden symmetry relating the eigenstates of v a b c r to those of v a b c r is used to establish the boundary between the ansatz sub set and the infinite set of higher states connections between the radial wavefunctions rn a b c r and rn a b c r also provide semiclassical insight into the origin of the parameter constraint finally the ansatz eigenvalue dispositions are related to the phenomenon of quantum monodromy

a monte carlo study of leading order scaling corrections of phi 4 theory on a three dimensional lattice we present a monte carlo study of the one component 4 model on a cubic lattice in three dimensions leading order scaling corrections are studied using the finite size scaling method we compute the corrections to scaling exponent with high precision we determine the value of the coupling at which leading order corrections to scaling vanish using this result we obtain estimates for critical exponents that are more precise than those obtained with field theoretic methods

inference for the binomial n parameter a hierarchical bayes approach summary a hierarchical bayes approach to the problem of estimating n in the binomial distribution is presented this provides a simple and flexible way of specifying prior information and also allows a convenient representation of vague prior knowledge it yields solutions to the problems of interval estimation prediction and decision making as well as that of point estimation the bayes estimator compares favourably with the best previously proposed point estimators in the literature unknown parameters n and 0 most of the literature about statistical analysis of this model has focused on point estimation of n while interval estimation prediction and decision making have been little considered see 2 i adopt a hierarchical bayes approach this provides a simple way of specifying prior information and also allows a convenient representation of vague prior knowledge using limiting improper prior forms it leads to solutions of the problems of interval estimation prediction and decision making as well as that of point estimation a difficulty with bayesian analysis of this problem has been the absence of a sufficiently flexible and tractable family of prior distributions mainly due to the fact that n is an integer the present approach gets around this by first assuming that n has a poisson distribution the resulting hyperparameters are then continuous valued and one may use existing results about conjugate and vague priors in better understood settings

comparison of monte carlo results for the 3d ising interface tension and interface energy with extrapolated series expansions abstract we compare monte carlo results for the interface tension and interface energy of the 3 dimensional ising model with pade and inhomogeneous differential approximants of the low temperature series that was recently extended by arisue to 17th order in u exp 4 the series is expected to suffer from the roughening singularity at u 0 196 the comparison with the monte carlo data shows that the pade and inhomogeneous differential approximants fail to improve the truncated series result of the interface tension and the interface energy in the region around the roughening transition the monte carlo data show that the specific heat displays a peak in the smooth phase neither the truncated series nor the pade approximants find this peak we also compared monte carlo data for the energy of the asos model with the corresponding low temperatures series that we extended to order u12

addendum to on the singularity structure of the 2d ising model susceptibility a remarkable product formula first derived by palmer and tracy 1981 adv appl math 2 329 for the integrand of the two dimensional ising model susceptibility expansion coefficients 2n for temperatures t less than the critical t c is shown to apply equally for 2n 1 for t t c and agrees with formulae derived by yamada 1984 prog theor phys 71 1416 this new representation simplifies the derivation of the results in the original paper of this title 1999 j phys a math gen 32 3889 to the extent that the leading series behaviour and the singularity structure can be deduced almost by inspection the derivation of series is also simplified and i show using extended series and knowledge of the singularity structure that there is now unambiguous evidence for correction to scaling terms in the susceptibility beyond those inferred from a nonlinear scaling field analysis

master singular behavior for the sugden factor of one component fluids near their gas liquid critical point we present the master i e unique behavior of the squared capillary length the so called sugden factor as a function of the temperaturelike field along the critical isochore asymptotically close to the gas liquid critical point of about twenty one component fluids this master behavior is obtained using the scale dilatation of the relevant physical fields of the one component fluids the scale dilatation method introduces the fluid dependent scale factors in a manner analog to the linear relations between physical fields and scaling fields needed by the renormalization theory applied to any physical system belonging to the ising like universality class the master behavior for the sugden factor satisfies hyperscaling it can be asymptotically fitted by the leading terms of the theoretical crossover functions for the correlation length and the susceptibility in the homogeneous domain recently obtained from massive renormalization in field theory in the absence of corresponding estimation of the theoretical crossover functions for the interfacial tension we define the range of the temperaturelike field where the master leading power law can be practically used to predict the singular behavior of the sugden factor in conformity with the theoretical description provided by the massive renormalization scheme within the extended asymptotic domain of the one component fluid subclass

improved high temperature expansion and critical equation of state of three dimensional ising like systems high temperature series are computed for a generalized three dimensional ising model with arbitrary potential three specific improved potentials suppressing leading scaling corrections are selected by monte carlo computation critical exponents are extracted from high temperature series specialized to improved potentials achieving high accuracy our best estimates are gamma 1 2371 4 nu 0 630 02 23 alpha 0 1099 7 eta 0 0364 4 beta 0 326 48 18 by the same technique the coefficients of the small field expansion for the effective potential helmholtz free energy are computed these results are applied to the construction of parametric representations of the critical equation of state a systematic approximation scheme based on a global stationarity condition is introduced the lowest order approximation reproduces the linear parametric model this scheme is used for an accurate determination of universal ratios of amplitudes a comparison with other theoretical and experimental determinations of universal quantities is presented

duality symmetry strong coupling expansion and universal critical amplitudes in two dimensional phi 4 field models we show that the exact beta function g in the continuous two dimensional g4 model possesses the kramers wannier duality symmetry the duality symmetry transformation d g such that d g d g g is constructed and the approximate values of g computed from the duality equation d g g are shown to agree with the available numerical results the calculation of the beta function g for the 2d scalar g4 field theory based on the strong coupling expansion is developed and the expansion of g in powers of g 1 is obtained up to order g 8 the numerical values calculated for the renormalized coupling constant g are in reasonably good agreement with the best modern estimates recently obtained from the high temperature series expansion and with those known from the perturbative four loop renormalization group calculations the application of cardy s theorem for calculating the renormalized isothermal coupling constant gc of the 2d ising model and the related universal critical amplitudes is also discussed

borel summable solutions to one dimensional schrodinger equation it is shown that so called fundamental solutions the semiclassical expansions of which have been established earlier to be borel summable to the solutions themselves appear also to be the unique solutions to the one dimensional 1d schrodinger equation having this property namely it is shown in this paper that for the polynomial potentials the borel function defined by the fundamental solutions can be considered as the canonical one the latter means that any borel summable solution can be obtained by the borel transformation of this unique canonical borel function multiplied by some dependent and borel summable constant this justifies the exceptional role the fundamental solutions play in 1d quantum mechanics and completes the relevant semiclassical theory relied on the borel resummation technique and developed in our other papers

dispersive hyperasymptotics and the anharmonic oscillator hyperasymptotic summation of steepest descent asymptotic expansions of integrals is extended to functions that satisfy a dispersion relation we apply the method to energy eigenvalues of the anharmonic oscillator for which there is no known integral representation but for which there is a dispersion relation hyperasymptotic summation exploits the rich analytic structure underlying the asymptotics and is a practical alternative to borel summation of the rayleigh schrodinger perturbation series

a new method for the solution of the schrodinger equation we present a new method for the solution of the schrodinger equation applicable to problems of a non perturbative nature the method works by identifying three different scales in the problem which then are treated independently an asymptotic scale which depends uniquely on the form of the potential at large distances an intermediate scale still characterized by an exponential decay of the wavefunction and finally a short distance scale in which the wavefunction is sizable the notion of optimized perturbation is then used in the last two regimes we apply the method to the quantum anharmonic oscillator and find it suitable to treat both energy eigenvalues and wavefunctions even for strong couplings

uniform asymptotic and jwkb expansions for anharmonic oscillators we show explicitly the relation between the uniform asymptotic and the jeffreys wentzel kramers brillouin jwkb wavefunctions and between the matching of uniform asymptotic expansions and the complete jwkb connection formulae written in terms of stokes multipliers and loop integrals as an application we give a unified derivation of the asymptotic behaviour of the imaginary part of the resonances in anharmonic oscillators and via dispersion relations the corresponding asymptotic behaviour of the rayleigh schrodinger perturbation theory coefficients

extended rayleigh schrodinger perturbation theory for the quartic anharmonic oscillator this paper follows the ideas of the author s earlier works that there is a possible metastable process passing from unperturbed to perturbed as a perturbation potential evolves furthermore we extend the balance condition which was fully described in earlier works from the total wave to each corresponding sth order component wave n s s 0 1 therefore to our great benefit an infinite set of coupled balance conditions can be gained we add this new idea to perturbation theory and hence present the so called extended rayleigh schrodinger perturbation theory as is well known earlier applications in pfskb principles of the first and second kind of balance theory seldom went beyond the first to at most second order in the eigenvalue because of computational difficulties in evaluating the minimization of the total energy of infinite summations which appear in the equations for the higher order terms fortunately these difficulties can be overcome by individually balancing the conditions of the corresponding sth order component waves n s however it seems reasonable to hope that a better understanding of extended rayleigh schrodinger perturbation theory may be gained in many cases of interest the quartic anharmonic oscillator is chosen as an example for the demonstration of extended rayleigh schrodinger perturbation theory because of its divergent rayleigh schrodinger perturbation expansions and wide applications

critical exponents of the n vector model recently the series for two renormalization group functions corresponding to the anomalous dimensions of the fields and of the three dimensional field theory have been extended to next order seven loops by murray and nickel we examine the influence of these additional terms on the estimates of critical exponents of the n vector model using some new ideas in the context of the borel summation techniques the estimates have slightly changed but remain within the errors of the previous evaluation exponents such as related to the field anomalous dimension which were poorly determined in the previous evaluation of le guillou zinn justin have seen their apparent errors significantly decrease more importantly perhaps summation errors are better determined the change in exponents affects the recently determined ratios of amplitudes and we report the corresponding new values finally because an error has been discovered in the last order of the published expansions order we have also re analysed the determination of exponents from the expansion the conclusion is that the general agreement between expansion and three dimensional series has improved with respect to le guillou zinn justin

colored noise induced discontinuous transitions in symbiotic ecosystems a symbiotic ecosystem is studied by means of the lotka volterra stochastic model using the generalized verhulst self regulation the effect of fluctuating environment on the carrying capacity of a population is taken into account as dichotomous noise the study is a follow up of our investigation of symbiotic ecosystems subjected to three level trichotomous noise r mankin a ainsaar a haljas and e reiter phys rev e 65 051108 2002 relying on the mean field theory an exact self consistency equation for stationary states is derived in some cases the mean field exhibits hysteresis as a function of noise parameters it is established that random interactions with the environment can cause discontinuous transitions the dependence of the critical coupling strengths on the noise parameters is found and illustrated by phase diagrams predictions from the mean field theory are compared with the results of numerical simulations our results provide a possible scenario for catastrophic shifts of population sizes observed in nature

rank frequency distribution of natural languages a difference of probabilities approach abstract in this paper we investigate the time variation of the rank k of words for six indo european languages using the google books n gram dataset based on numerical evidence we regard k as a random variable whose dynamics may be described by a fokker planck equation which we solve analytically for low ranks the distinct languages behave differently maybe due to the syntax rules whereas for k 50 the law of large numbers predominates we analyze the frequency distribution of words using the data and their adjustment in terms of time dependent probability density distributions we find small differences between the data and the fits due to conflicting dynamic mechanisms but the data show a consistent behavior with our general approach for the lower ranks the behavior of the data changes among languages presumably again due to distinct dynamic mechanisms we discuss a possible origin of these differences and assess the novel features and limitations of our work

estimating the binomial parameter n abstract estimating the parameter n of the binomial distribution on the basis of r independent observations has been considered sporadically over the years many questions regarding asymptotic and small sample properties of moment maximum likelihood and related estimators either have been ignored or have received inadequate treatment a unified and comprehensive study of these topics is given here we also consider the problem of zero truncated observations

unimodality of likelihood functions for the binomial distribution abstract a maximum likelihood estimate exists for both parameters of the binomial distribution if and only if the sample mean exceeds the sample variance the derivative of the log likelihood function has at most one finite root consequently the likelihood function is unimodular

admissible estimation of the binomial parameter n suppose that x has a binomial distribution b n p with known p in 0 1 and unknown n in 1 2 cdots a natural estimator for n is given by t 0 1 t x x p x 1 2 cdots this estimator is shown to be inadmissible under quadratic loss it is shown that modifying t 0 to t 0 1 p p ln p results in an admissible estimator for p geq frac 1 2 it is further shown that this is the only admissible modification of t 0 a partial result is also obtained for p frac 1 2

on the erratic behavior of estimators of n in the binomial n p distribution abstract the problem of estimating the number of trials in a binomial distribution is known to be particularly difficult in certain circumstances both the maximum likelihood and method of moments estimators can produce very erratic results being extremely sensitive to minor fluctuations in the data but existing asymptotic theory for these estimators does not provide any insight into this peculiar behavior as the theory typically produces asymptotic normal distributions with respectable means and variances likewise the limiting distributions of other estimators do not convey much information about why those estimators might perform better than their more classical counterparts in this article we develop an alternative asymptotic theory that clearly and vividly depicts not only the erratic performance of the maximum likelihood and method of moments estimators but also the more regular robust properties of alternative estimators proposed by carroll and lombard we note that the parameter configurati

non analyticity of the callan symanzik β function of two dimensional o n models we discuss the analytic properties of the callan symanzik function g associated with the zero momentum four point coupling g in the two dimensional 4 model with o n symmetry using renormalization group arguments we derive the asymptotic behaviour of g at the fixed point g we argue that g g o g g 1 7 for n 1 and g g o 1 log g g for n 3 our claim is supported by an explicit calculation in the ising lattice model and by a 1 n calculation for the two dimensional 4 theory we discuss how these non analytic corrections may give rise to a slow convergence of the perturbative expansion in powers of g

chain binomial models and binomial autoregressive processes we establish a connection between a class of chain binomial models of use in ecology and epidemiology and binomial autoregressive ar processes new results are obtained for the latter including expressions for the lag inline image conditional distribution and related quantities we focus on two types of chain binomial model extinction colonization and colonization extinction models and present two approaches to parameter estimation the asymptotic distributions of the resulting estimators are studied as well as their finite sample performance and we give an application to real data a connection is made with standard ar models which also has implications for parameter estimation

continuous probabilistic approach to species dynamics in hubbell s zero sum local community in this paper a continuous probabilistic approach formulated using kolmogorov fokker planck forward and backward models is applied to hubbell s zero sum neutral theory for species dynamics in local community using this technique the probability density of species abundance distribution of the first passage time to extinction or fixation and probability of extinction are defined the resulting values for the distribution of the first passage time to extinction are verified by the simulation study of hubbell s zero sum neutral model for the local community based on the sensitivity analysis for the continuous probabilistic models the realistic classification of local communities subject to their diversity and species dynamics is proposed with respect to the immigration probability the species metacommunity relative abundance and the size of local community doi 10 1103 physreve 74 021902 pacs numbers 87 23 cc 02 50 r the main goals of biodiversity study are to explain and quantify the distribution abundance and dynamics of living organisms in ecological communities these questions are also of central theoretical and practical importance in conservation biology and ecosystem management 1 2 since understanding the mechanisms of species abundance dynamics is of high concern in viability analysis species abundance relationships have long been studied by ecologists who defined them as species commonness and rarity in ecological communities 1 3 4 these relationships are usually described by species abundance distributions which show the number of species as the functions of their observed abundances early studies on species abundance relationships were focused on finding distributions that could fit well empirical data among the proposed distributions were the log series 5 and the log normal 6 later the preference was given to modeling species abundance relationships using one or another ecological theory of community organization using this approach the broken stick model was proposed by macarthur 7 8 the log normal patterns of species abundances were explained using the niche preemption model 9 11 and using the dynamic population model with gompertz density dependence 12 the gamma type of abundance distribution including fisher s log series the extended gamma distribution and macarthur s broken stick model was elucidated using the dynamic approach with logistic density dependence 13

confluent singularities in 3d continuum φ4 theory resolving critical point discrepancies a new analysis of the three dimensional 4 continuum model series for critical exponents and amplitude ratios is presented by explicitly allowing for a second correction to scaling term with exponent 2 and 2 1 2 0 a revision is found of previous critical point estimates that are all in the direction of resolving the remaining discrepancies between the 3d and 4 analyses the new estimates are also consistent with those obtained from high temperature series analyses of 3d lattice ising models for example the exponents 1 238 0 630 0 0355 and correction to scaling amplitude ratio 0 77 are easily accommodated and possibly even preferred detailed verification will require further terms both in the low order perturbation theory and the high order asymptotic expansions

colored noise induced hopf bifurcations in predator prey communities a broad class of n 1 species ratio dependent predator prey stochastic models which consist of one predator population and n prey populations is considered the effect of a fluctuating environment on the carrying capacities of prey populations is taken into account as colored noise in the framework of the mean field theory approximate self consistency equations for prey populations mean density and for predator population density are derived to the first order in the noise variance in some cases the mean field exhibits hopf bifurcations as a function of noise correlation time the corresponding transitions are found to be reentrant e g the periodic orbit appears above a critical value of the noise correlation time but disappears again at a higher value of the noise correlation time the nonmonotonous dependence of the critical control parameter on the noise correlation time is found and the conditions for the occurrence of hopf bifurcations are presented our results provide a possible scenario for environmental fluctuations induced transitions between the oscillatory regime and equilibrium state of population sizes observed in nature

semiclassical spectrum using secular perturbation theory the quartic oscillator we analyse the quartic oscillator using the technique of removal of resonances in a region of parameter space where the system exhibits soft chaos we obtain analytic expressions for all primary resonances and thus obtain a semiclassical spectrum a criterion relating to overlapping resonances gives an estimate about the break down of the removal of resonance method

rank abundance relations in evolutionary dynamics of random replicators we present a nonequilibrium statistical mechanics description of rank abundance relations rar in random community models of ecology specifically we study a multispecies replicator system with quenched random interaction matrices we here consider symmetric interactions as well as asymmetric and antisymmetric cases rars are obtained analytically via a generating functional analysis describing fixed point states of the system in terms of a small set of order parameters and in dependence on the symmetry or otherwise of interactions and on the productivity of the community our work is an extension of tokita phys rev lett 93 178102 2004 where the case of symmetric interactions was considered within an equilibrium setup the species abundance distribution in our model come out as truncated normal distributions or transformations thereof and in some case are similar to left skewed distributions observed in ecology we also discuss the interaction structure of the resulting food web of stable species at stationarity cases of heterogeneous cooperation pressures as well as effects of finite system size and of higher order interactions

on bayesian estimation of group size summary in estimating the size of a group of animals it is commonly the case that the sighting probability for individuals is less than one if each individual in the group is independently sighted with equal probability the problem is one of estimating the number of trials from the number of successes in one or more binomial experiments in many cases some individuals in the group have unit sighting probability whereas others do not this note describes the bayesian estimation of group size for this case

estimating the number of faults in a system abstract we consider a reliability system with an unknown number of faults which is observed for a fixed length of time failures are assumed to follow an exponential distribution with an unknown mean and we concentrate on estimation of the number of faults v the likelihood function considered as a function of v has its maximum at one of the boundary points the observed number of faults or infinity with substantial probability likelihood interval estimates and improved point estimates are discussed the harmonic mean of the endpoints of the likelihood interval turns out to be a reasonable point estimate we comment on some extensions of this problem suggested in the software reliability literature

the shape of the van der waals loop and universal critical amplitude ratios assuming that a van der waals loop for a fluid ferromagnet etc can be defined its shape is analysed on the basis of universal critical amplitude ratios for three dimensional ising type systems selected estimates for these ratios are tabulated near criticality the loop attains a universal scaled form given optimally by a new parametric extended sine model for the bulk asymptotic equation of state but a particular low order interpolating pade approximant provides a reasonable fit among other universal features the reduced spinodal magnetization density and conjugate field are found to be in contrast to the van der waals values thus the spinodal lies appreciably closer to the binodal or coexistence curve than predicted classically

analytic calculation of energies and wave functions of the quartic and pure quartic oscillators ground state energies and wave functions of quartic and pure quartic oscillators are calculated by first casting the schrodinger equation into a nonlinear riccati form and then solving that nonlinear equation analytically in the first iteration of the quasilinearization method qlm in the qlm the nonlinear differential equation is solved by approximating the nonlinear terms by a sequence of linear expressions the qlm is iterative but not perturbative and gives stable solutions to nonlinear problems without depending on the existence of a smallness parameter our explicit analytic results are then compared with exact numerical and also with wkb solutions and it is found that our ground state wave functions using a range of small to large coupling constants yield a precision of between 0 1 and 1 percent and are more accurate than wkb solutions by two to three orders of magnitude in addition our qlm wave functions are devoid of unphysical turning point singularities and thus allow one to make analytic

critical endpoints interfaces and walls abstract the behavior of thermodynamic properties at critical endpoints is discussed and the first results of studies underway in collaboration with p j upton and with m c barbosa are sketched new universal aspects beyond normal bulk criticality appear in singularities of the phase boundary to the spectator phase and in the surface tensions of the corresponding noncritical interfaces mean field theory and more general local free energy functionals can be applied some quantitative estimates are presented for universal surface tension amplitude ratios for two distinct classes of endpoint symmetric and nonsymmetric a promising parametric trigonometric model for the scaled equation of state is mentioned and other approaches are touched upon

surface tension from finite volume vacuum tunneling in the 3d ising model we measure the surface tension in the broken phase of the 3d ising model at a temperaturet 0 955t c with two different methods which are taken from quantum field theory in finite volumes both methods rely on finite size effects close to the phase transition the first one measures from the size dependence of the vacuum tunneling energy which is determined by the decay of a correlation giving 0 030 the second one extracts from the size dependence of the rate of flip events and its corresponding correlation time it leads to 0 027 both values agree reasonably with other calculations

calculation of energy eigenvalues for the quantum anharmonic oscillator with a polynomial potential we choose the squeezed vacuum state as a one parameter trial wavefunction to minimize the energy of an anharmonic oscillator with a polynomial perturbation potential using the optimal vacuum state obtained we generate the optimal generalized number state basis and set up the hamiltonian in the normal ordered form then truncating the basis we produce finite dimensional matrices in a simple manner and find their eigenvalues by standard methods we will apply our method to the morse potential whose exact eigenvalues are known as a check on the accuracy of the results that we have derived two models of the double well and the quartic potential are considered as examples

origin of pareto like spatial distributions in ecosystems recent studies of cluster distribution in various ecosystems revealed pareto statistics for the size of spatial colonies these results were supported by cellular automata simulations that yield robust criticality for endogenous pattern formation based on positive feedback we show that this patch statistics is a manifestation of the law of proportionate effect mapping the stochastic model to a markov birth death process the transition rates are shown to scale linearly with cluster size this mapping provides a connection between patch statistics and the dynamics of the ecosystem the first passage time for different colonies emerges as a powerful tool that discriminates between endogenous and exogenous clustering mechanisms imminent catastrophic shifts such as desertification manifest themselves in a drastic change of the stability properties of spatial colonies

stabilizing binomial n estimators abstract the maximum likelihood estimator of the binomial parameter n can be highly unstable resulting in huge fluctuations in the estimate when the data are only slightly perturbed a method of assessing this sensitivity based on perturbing the log likelihood function is proposed and examined

a comparison of n estimators for the binomial distribution abstract estimating the number n of trials given a sequence of independent success counts obtained by replicating the n trial experiment is less studied and a considerably harder problem than estimating p for the binomial distribution both the method of moments and the maximum likelihood estimators of n are considered when p is unknown and small while n is large both estimators become highly unstable stabilized versions of these estimators are proposed and their performance is described in terms of results obtained by simulation

bulk surface and hull fractal dimension of critical ising clusters in d 2 the authors present accurate numerical calculations of the fractal dimension d and surface dimension ds of the critical ising cluster in d 2 the results clearly support the values d 187 96 ds 5 6 which are consistent with ising clusters being described by tricritical q 1 potts model exponents from this the hull dimension dh of critical ising clusters is found to be dh 11 8 consistent with numerical work of other authors

covariate measurement error in logistic regression abstract in a logistic regression model when covariates are subject to measurement error the naive estimator obtained by regressing on the observed covariates is asymptotically biased this document introduces a bias adjusted estimator and two estimators appropriate for normally distributed measurement errors a functional maximum likelihood estimator and an estimator which exploits the consequences of sufficiency the four proposals are studied asymptotically under conditions which are appropriate when the measurement error is small a small monte carlo study illustrates the superiority of the measurement error estimators in certain situations additional keywords mathematical models

birth and death master equation for the evolution of complex networks abstract master equations for the evolution of complex networks with positive birth and negative death transition probabilities per unit time are analyzed explicit equations for the time evolution of the total number of nodes and for the relative node frequencies are given it is shown that in the continuous limit the master equation reduces to a fokker planck equation fpe the basic dynamical function for its stationary solution is the ratio between its drift and diffusion coefficients when this ratio is approximated by partial fractions pade s approximants a hierarchy of stationary solutions of the fpe is obtained analytically which are expressed as an exponential times the product of powers of monomials and binomials it is also shown that if the difference between birth and death transition probabilities goes asymptotically to zero the exponential factor in the solution is absent fits to real complex network probability distribution functions are shown comparison with rank ordered data shows that in general the value of this exponential factor is close to unity evidencing crossovers among power law scale invariant regimes which might be associated to an underlying criticality and are related to a generalization of the beta distribution the time dependent solution is also obtained analytically in terms of hyper geometric functions it is also shown that the fpe has similarity solutions the limitations of the approach here presented are also discussed

two point correlation function of three dimensional o n models the critical limit and anisotropy in three dimensional o n models we investigate the low momentum behavior of the two point green s function g x in the critical region of the symmetric phase we consider physical systems whose criticality is characterized by a rotationally invariant fixed point several approaches are exploited such as strong coupling expansion of lattice n vector model and 1 n expansion field theoretical methods within the ensuremath varphi 4 continuum formulation non gaussian corrections to the universal low momentum behavior of g x are evaluated and found to be very small in nonrotationally invariant physical systems with o n invariant interactions the vanishing of the spatial anisotropy approaching the rotationally invariant fixed point is described by a critical exponent ensuremath rho which is universal and is related to the leading irrelevant operator breaking rotational invariance at n ensuremath infty one finds ensuremath rho 2 we show that for all values of ng 0 ensuremath rho ensuremath simeq 2

high precision monte carlo study of the 3d xy universality class we present a monte carlo study of the two component 4 model on the simple cubic lattice in three dimensions by suitable tuning of the coupling constant we eliminate leading order corrections to scaling high statistics simulations using finite size scaling techniques yield 0 6723 3 8 and 0 0381 2 2 where the statistical and systematical errors are given in the first and second bracket respectively these results are more precise than any previous theoretical estimate of the critical exponents for the 3d xy universality class

n mixture models for estimating population size from spatially replicated counts spatial replication is a common theme in count surveys of animals such surveys often generate sparse count data from which it is difficult to estimate population size while formally accounting for detection probability in this article i describe a class of models n mixture models which allow for estimation of population size from such data the key idea is to view site specific population sizes n as independent random variables distributed according to some mixing distribution e g poisson prior parameters are estimated from the marginal likelihood of the data having integrated over the prior distribution for n carroll and lombard 1985 journal of american statistical association 80 423 426 proposed a class of estimators based on mixing over a prior distribution for detection probability their estimator can be applied in limited settings but is sensitive to prior parameter values that are fixed a priori spatial replication provides additional information regarding the parameters of the prior distribution on n that is exploited by the n mixture models and which leads to reasonable estimates of abundance from sparse data a simulation study demonstrates superior operating characteristics bias confidence interval coverage of the n mixture estimator compared to the caroll and lombard estimator both estimators are applied to point count data on six species of birds illustrating the sensitivity to choice of prior on p and substantially different estimates of abundance as a consequence

anharmonic oscillators and generalized squeezed states we present a new method to study the eigenvalues and eigenfunctions of anharmonic oscillators it involves a new class of bogoliubov transformations and leads to the introduction of k photon coherent states we consider the hamiltonians for the simple harmonic and anharmonic oscillators as the two generators of a lie algebra whose other generators may be found exactly or up to any desired order of the perturbation parameter involved an element of this lie group turning out to be the multi photon operator transforms the anharmonic hamiltonian to the harmonic one thus facilitating the calculation of the eigenvalues and eigenfunctions of the former the transformation of the ordinary annihilation and creation operators leads to generalized ones corresponding to generalized oscillation modes and also helps us out to introduce multi photon coherent states we specifically consider four photon coherent states in detail and study time dependent position and momentum uncertainties in these states

alternative to the diffusion equation in population genetics since its inception by kimura in 1955 m kimura proc natl acad sci u s a 41 144 1955 the diffusion equation has become a standard technique of population genetics the diffusion equation is however only an approximation valid in the limit of large populations and small selection moreover useful quantities such as the fixation probabilities are not easily extracted from it and need the concomitant use of a forward and backward equation we show here that the partial differential equation governing the probability generating function can be used as an alternative to the diffusion equation with none of its drawbacks it does not involve any approximation it has well defined initial and boundary conditions and its solutions are finite polynomials we apply this technique to derive analytical results for the moran process with selection which encompasses the kimura diffusion equation

crossover critical behavior in the three dimensional ising model the character of critical behavior in physical systems depends on the range of interactions in the limit of infinite range of the interactions systems will exhibit mean field critical behavior i e critical behavior not affected by fluctuations of the order parameter if the interaction range is finite the critical behavior asymptotically close to the critical point is determined by fluctuations and the actual critical behavior depends on the particular universality class a variety of systems including fluids and anisotropic ferromagnets belongs to the three dimensional ising universality class recent numerical studies of ising models with different interaction ranges have revealed a spectacular crossover between the asymptotic fluctuation induced critical behavior and mean field type critical behavior in this work we compare these numerical results with a crossover landau model based on renormalization group matching for this purpose we consider an application of the crossover landau model to the three dimensional ising model without fitting to any adjustable parameters the crossover behavior of the critical susceptibility and of the order parameter is analyzed over a broad range ten orders of the scaled distance to the critical temperature the dependence of the coupling constant on the interaction range governing the crossover critical behavior is discussed

a stabilized moment estimator for the beta binomial distribution the beta binomial distribution has been proposed as a model for the incorporation of historical control data in the analysis of rodent carcinogenesis bioassays low spontaneous tumor incidences along with the small number and sizes of historical control groups combine to make the moment and maximum likelihood estimates of the beta binomial parameters deficient we therefore propose a stabilized moment estimator for one of the parameters the stabilized moment estimator is similar to the ridge regression estimator and introduces a shrinkage parameter computer simulations were run to examine the behavior of the stabilized moment estimator the effect of the stabilized moment estimator on the score test for dose related trend is considered both on simulated data and on an example from the literature

stochastic models in population biology and their deterministic analogs we introduce a class of stochastic population models based on patch dynamics the size of the patch may be varied and this allows one to quantify the departures of these stochastic models from various mean field theories which are generally valid as the patch size becomes very large these models may be used to formulate a broad range of biological processes in both spatial and nonspatial contexts here we concentrate on two species competition we present both a mathematical analysis of the patch model in which we derive the precise form of the competition mean field equations and their first order corrections in the nonspatial case and simulation results these mean field equations differ in some important ways from those which are normally written down on phenomenological grounds our general conclusion is that mean field theory is more robust for spatial models than for a single isolated patch this is due to the dilution of stochastic effects in a spatial setting resulting from repeated rescue events mediated by interpatch diffusion however discrete effects due to modest patch sizes lead to striking deviations from mean field theory even in a spatial setting