age related alterations of relaxation processes and non markov effects in stochastic dynamics of r r intervals variability from human ecgs in this paper we consider the age related alterations of heart rate variability on the basis of the study of non markovian effects the age dynamics of relaxation processes is quantitatively described by means of local relaxation parameters calculated by the specific localization procedure we offer a quantitative informational measure of non markovity to evaluate the change of statistical effects of memory local relaxation parameters for young and elderly people differ by 3 3 times and quantitative measures of non markovity differ by 4 2 times the comparison of quantitative parameters allows to draw conclusions about the reduction of relaxation rate with ageing and the higher degree of the markovity of heart rate variability of elderly people

some nodal properties for a quasilinear differential equation involving the p laplacian abstract in this paper we study a quasilinear differential equation u x p 2 u x w x u x q 2 u x 0 in 0 b where q p 1 a theorem related to some oscillation properties depending on the initial parameters is developed on the basis of this result we also show that the identical zero set of solutions will determine the function w x uniquely under some minor assumption essentially the main methods using in this work are the scaling argument and prufer type substitutions

scaling relations in food webs in the last three decades researchers have tried to identify universal patterns in the structure of food webs it was recently proposed that the exponent characterizing the efficiency of the transport of energy in large and small food webs might have a universal value 1 13 in this work we establish lower and upper bounds for this exponent in a general spanning tree with a fixed number of trophic species and levels when the number of species is large the lower and upper bounds are equal to 1 implying that the result 1 13 is due to finite size effects and that the value of this exponent depends on the size of the web we also evaluate analytically and numerically the exponent for hierarchical and random networks in all cases the exponent depends on the number of trophic species k and when k is large we have that 1 moreover this result holds for any fixed number m of trophic levels

monotonicity properties and inequalities for the generalized elliptic integral of the first kind abstract the authors obtain some monotonicity and concavity properties and asymptotically sharp bounds for the generalized elliptic integral k a r of the first kind and its special case k r the complete elliptic integral of the first kind by studying the monotonicity and concavity properties of certain combinations defined in terms of the gaussian hypergeometric function f a 1 a 1 x and elementary functions thus improving some well known results

intensity approximation of random fluctuation in complex systems abstract the markov and non markov processes in complex systems are examined with the help of dynamical information shannon entropy method here we consider the essential role of two mutually independent channels of entropy involving creation of correlation and annihilation of correlation the developed method has been used to analyze the intensity fluctuation of the complex systems of various nature in psychology to analyze numerical and pattern short time human memory to study the effect of stress on the parameters of the dynamical taping test and in cardiology to analyze the random dynamics of rr intervals in human ecg s and to diagnose various diseases of human cardiovascular systems the received results show that the application of intensity approximation allows to improve essentially the diagnostics of parameters in the evolution of human dynamic states

epidemic dynamics in finite size scale free networks many real networks present a bounded scale free behavior with a connectivity cutoff due to physical constraints or a finite network size we study epidemic dynamics in bounded scale free networks with soft and hard connectivity cutoffs the finite size effects introduced by the cutoff induce an epidemic threshold that approaches zero at increasing sizes the induced epidemic threshold is very small even at a relatively small cutoff showing that the neglection of connectivity fluctuations in bounded scale free networks leads to a strong overestimation of the epidemic threshold we provide the expression for the infection prevalence and discuss its finite size corrections the present paper shows that the highly heterogeneous nature of scale free networks does not allow the use of homogeneous approximations even for systems of a relatively small number of nodes

quantification of heart rate variability by discrete nonstationary non markov stochastic processes we develop the statistical theory of discrete nonstationary non markov random processes in complex systems the objective of this paper is to find the chain of finite difference non markov kinetic equations for time correlation functions tcf in terms of nonstationary effects the developed theory starts from careful analysis of time correlation through nonstationary dynamics of vectors of initial and final states and nonstationary normalized tcf using the projection operators technique we find the chain of finite difference non markov kinetic equations for discrete nonstationary tcf and for the set of nonstationary discrete memory functions mf s the last one contains supplementary information about nonstationary properties of the complex system on the whole another relevant result of our theory is the construction of the set of dynamic parameters of nonstationarity which contains some information of the nonstationarity effects the full set of dynamic spectral and kinetic parameters and kinetic functions tcf short mf s statistical spectra of non markovity parameter and statistical spectra of nonstationarity parameter has made it possible to acquire the in depth information about discreteness non markov effects long range memory and nonstationarity of the underlying processes the developed theory is applied to analyze the long time holter series of rr intervals of human ecg s we had two groups of patients the healthy ones and the patients after myocardial infarction in both groups we observed effects of fractality standard and restricted self organized criticality and also a certain specific arrangement of spectral lines the received results demonstrate that the power spectra of all orders n 1 2 mf m n t exhibit the neatly expressed fractal feat ures we have found out that the full sets of non markov discrete and nonstationary parameters can serve as reliable and powerful means of diagnosis of the cardiovascular system states and can he used to distinguish healthy data from pathologic data

fluctuations and correlations in an individual based model of biological coevolution we extend our study of a simple model of biological coevolution to its statistical properties starting with a complete description in terms of a master equation we provide its relation to the deterministic evolution equations used in previous investigations the stationary states of the mutationless model are generally well approximated by gaussian distributions so that the fluctuations and correlations of the populations can be computed analytically several specific cases are studied by monte carlo simulations and there is an excellent agreement between the data and the theoretical predictions

network growth with preferential attachment for high indegree and low outdegree abstract we study the growth of a directed transportation network such as a food web in which links carry resources we propose a growth process in which new nodes or species preferentially attach to existing nodes with high indegree in food web language number of prey and low outdegree or number of predators this scheme which we call inverse preferential attachment is intended to maximize the amount of resources available to each new node we show that the outdegree predator distribution decays at least exponentially fast for large outdegree and is continuously tunable between an exponential distribution and a delta function the indegree prey distribution is poissonian in the large network limit

multiple angle formulas of generalized trigonometric functions with two parameters abstract generalized trigonometric functions with two parameters were introduced by drabek and manasevich to study an inhomogeneous eigenvalue problem of the p laplacian concerning these functions no multiple angle formula has been known except for the classical cases and a special case discovered by edmunds gurka and lang not to mention addition theorems in this paper we will present new multiple angle formulas which are established between two kinds of the generalized trigonometric functions and apply the formulas to generalize classical topics related to the trigonometric functions and the lemniscate function

stochastic model for the species abundance problem in an ecological community we propose a model based on coupled multiplicative stochastic processes to understand the dynamics of competing species in an ecosystem this process can be conveniently described by a fokker planck equation we provide an analytical expression for the marginalized stationary distribution our solution is found in excellent agreement with numerical simulations and compares rather well with observational data from tropical forests

functional inequalities for generalized inverse trigonometric and hyperbolic functions abstract various miscellaneous functional inequalities are deduced for the so called generalized inverse trigonometric and hyperbolic functions for instance functional inequalities for sums difference and quotient of generalized inverse trigonometric and hyperbolic functions are given as well as some grunbaum inequalities with the aid of the classical bernoulli inequality moreover by means of certain already derived bounds bilateral bounding inequalities are obtained for the generalized hypergeometric f 2 3 clausen function

mixing patterns in networks we study assortative mixing in networks the tendency for vertices in networks to be connected to other vertices that are like or unlike them in some way we consider mixing according to discrete characteristics such as language or race in social networks and scalar characteristics such as age as a special example of the latter we consider mixing according to vertex degree i e according to the number of connections vertices have to other vertices do gregarious people tend to associate with other gregarious people we propose a number of measures of assortative mixing appropriate to the various mixing types and apply them to a variety of real world networks showing that assortative mixing is a pervasive phenomenon found in many networks we also propose several models of assortatively mixed networks both analytic ones based on generating function methods and numerical ones based on monte carlo graph generation techniques we use these models to probe the properties of networks as their level of assortativity is varied in the particular case of mixing by degree we find strong variation with assortativity in the connectivity of the network and in the resilience of the network to the removal of vertices

long range memory and non markov statistical effects in human sensorimotor coordination in this paper the non markov statistical processes and long range memory e ects in human sensorimotor coordination are investigated the theoretical basis of this study is the statistical theory of non stationary discrete non markov processes in complex systems phys rev e 62 6178 2000 the human sensorimotor coordination was experimentally studied by means of standard dynamical tappingtest on the g roup of 32 youngpeoples with tap numbers up to 400 this test was carried out separately for the right and the left hand according to the degree of domination of each brain hemisphere the numerical analysis of the experimental results was made with the help of power spectra of the initial time correlation function the memory functions of low orders and the 7rst three points of the statistical spectrum of non markovity parameter our observations demonstrate that with the regard to results of the standard dynamic tapping test it is possible to divide all examinees into 7ve di erent dynamic types we have introduced the con ict coe cient to estimate quantitatively the order disorder e ects underlying life systems the last one re ects the existence of disbalance between the nervous and the motor human coordination the suggested classi7cation of the neurophysiological activity represents the dynamic generalization of the well known neuropsychological types and provides the new approach in a modern neuropsychology c

extinction risk and structure of a food web model we investigate in detail the model of a trophic web proposed by amaral and meyer phys rev lett 82 652 1999 we focus on small size systems that are relevant for real biological food webs and for which the fluctuations play an important role we show using monte carlo simulations that such webs can be nonviable leading to extinction of all species in small and or weakly coupled systems estimations of the extinction times and survival chances are also given we show that before the extinction the fraction of highly connected species omnivores is increasing viable food webs exhibit a pyramidal structure where the density of occupied niches is higher at lower trophic levels and moreover the occupations of adjacent levels are closely correlated we also demonstrate that the distribution of the lengths of food chains has an exponential character and changes weakly with the parameters of the model on the contrary the distribution of avalanche sizes of the extinct species depends strongly on the connectedness of the web for rather loosely connected systems we recover the power law type of behavior with the same exponent as found in earlier studies while for densely connected webs the distribution is not of a power law type

functional inequalities for the ratio of complete p elliptic integrals abstract in this paper we show monotonicity and convexity properties of a function involving the ratio of complete p elliptic integrals which reduces to the modulus of the grotzsch ring as applications we obtain several sharp functional inequalities

monotonicity and functional inequalities for the complete p elliptic integrals abstract takeuchi s generalized complete elliptic integrals related to generalized trigonometric functions are of importance in the computation of the generalized pi and in the elementary proof of ramanujan s cubic transformation in this paper we generalize some well known results of the classical complete elliptic integrals to the case of takeuchi s generalized complete elliptic integrals we obtain sharp monotonicity and convexity results for combinations of these functions as well as functional inequalities

regular and stochastic behavior of parkinsonian pathological tremor signals abstract regular and stochastic behavior in the time series of parkinsonian pathological tremor velocity is studied on the basis of the statistical theory of discrete non markov stochastic processes and flicker noise spectroscopy we have developed a new method of analyzing and diagnosing parkinson s disease pd by taking into consideration discreteness fluctuations long and short range correlations regular and stochastic behavior markov and non markov effects and dynamic alternation of relaxation modes in the initial time signals the spectrum of the statistical non markovity parameter reflects markovity and non markovity in the initial time series of tremor the relaxation and kinetic parameters used in the method allow us to estimate the relaxation scales of diverse scenarios of the time signals produced by the patient in various dynamic states the local time behavior of the initial time correlation function and the first point of the non markovity parameter give detailed information about the variation of pathological tremor in the local regions of the time series the obtained results can be used to find the most effective method of reducing or suppressing pathological tremor in each individual case of a pd patient generally the method allows one to assess the efficacy of the medical treatment for a group of pd patients

extinction dynamics of lotka volterra ecosystems on evolving networks lotka volterra models of interacting populations are typically used on a time scale that is shorter than the lifetime of species such long term behaviour of ecosystems is very often studied but using models that operate at the level of species rather than individuals such an approach usually refers to the notion of fitness that is not commonly accepted in the present paper we show that a lotka volterra model can be used to describe long term behaviour of multi species ecosystems interactions among species in our model form a network whose evolution is determined by the dynamics of the model numerical simulations show a power law for the distribution of intervals between extinctions but only for ecosystems with a sufficient variability of species and with networks of connectivity above a certain threshold that is very close to the percolation threshold of the network effect of slow environmental changes on extinction dynamics degree distribution of the network of interspecies interactions and some emergent properties of our model are also examined

stability of a model food web we investigate numerically the stability of a model food web introduced by nunes amaral and meyer phys rev lett 82 652 1999 the model describes a system of species located in niches at several levels upper level species are predating on those from a lower level we show that the model web is more stable when it is larger although the number of niches is more important than the number of levels the food web is self organizing itself trying to reach a certain degree of complexity i e number of species and links among them if the system cannot achieve this state it will go extinct we demonstrate that the average number of links per species and the reduced number of species depend in the same way on the number of niches we also determine how the stability of the food web depends on another parameter of the model the killing probability despite keeping the ratio of the creation and killing probabilities constant increasing the latter reduces significantly the stability of the model food web we show that connectance dependence on the number of niches has a power type character which agrees with the field data and that it decreases with the number of species also as a power type function

possibility between earthquake and explosion seismogram differentiation by discrete stochastic non markov processes and local hurst exponent analysis the basic scientific point of this paper is to draw the attention of researchers to new possibilities of differentiation of similar signals having different nature one example of such kinds of signals is presented by seismograms containing recordings of earthquakes eq s and technogenic explosions te s eq s are among the most dramatic phenomena in nature we propose here a discrete stochastic model for possible solution of a problem of strong eq forecasting and differentiation of te s from the weak eq s theoretical analysis is performed by two independent methods by using statistical theory of discrete non markov stochastic processes phys rev e 62 6178 2000 and the local hurst exponent the following earth states have been considered among them before ib and during i strong eq during weak eq ii and during te iii and in a calm state of earth s core iv the estimation of states i ii and iii has been made on the particular examples of turkey 1999 eq s state iv has been taken as an example of earth s state before underground te time recordings of seismic signals of the first four dynamic orthogonal collective variables six various planes of phase portrait of four dimensional phase space of orthogonal variables and the local hurst exponent have been calculated for the dynamic analysis of states of systems i char21 iv the analysis of statistical properties of seismic time series i char21 iv has been realized with the help of a set of discrete time dependent functions time correlation function and first three memory functions their power spectra and the first three points in the statistical spectrum of non markovity parameters in all systems studied we have found a bizarre combination of the following spectral characteristics the fractal frequency spectra adjustable by phenomena of usual and restricted self organized criticality spectra of white and color noises and unusual alternation of markov and non markov effects of long range memory detected earlier j phys a 27 5363 1994 only for hydrodynamic systems our research demonstrates that discrete non markov stochastic processes and long range memory effects play a crucial role in the behavior of seismic systems i char21 iv the approaches permitting us to obtain an algorithm of strong eq forecasting and to differentiate te s from weak eq s have been developed

stochastic dynamics of time correlation in complex systems with discrete time in this paper we present the concept of description of random processes in complex systems with discrete time it involves the description of kinetics of discrete processes by means of the chain of finite difference non markov equations for time correlation functions tcfs we have introduced the dynamic time dependent information shannon entropy s i t where i 0 1 2 3 ellipsis as an information measure of stochastic dynamics of time correlation i 0 and time memory i 1 2 3 ellipsis the set of functions s i t constitute the quantitative measure of time correlation disorder i 0 and time memory disorder i 1 2 3 ellipsis in complex system the theory developed started from the careful analysis of time correlation involving dynamics of vectors set of various chaotic states we examine two stochastic processes involving the creation and annihilation of time correlation or time memory in details we carry out the analysis of vectors dynamics employing finite difference equations for random variables and the evolution operator describing their natural motion the existence of tcf results in the construction of the set of projection operators by the usage of scalar product operation harnessing the infinite set of orthogonal dynamic random variables on a basis of gram shmidt orthogonalization procedure tends to creation of infinite chain of finite difference non markov kinetic equations for discrete tcfs and memory functions mfs the solution of the equations above thereof brings to the recurrence relations between the tcf and mf of senior and junior orders this offers new opportunities for detecting the frequency spectra of power of entropy function s i t for time correlation i 0 and time memory i 1 2 3 ellipsis the results obtained offer considerable scope for attack on stochastic dynamics of discrete random processes in a complex systems application of this technique on the analysis of stochastic dynamics of rr intervals from human ecg s shows convincing evidence for a non markovian phenomemena associated with a peculiarities in short and long range scaling this method may be of use in distinguishing healthy from pathologic data sets based in differences in these non markovian properties

non markov stochastic dynamics of real epidemic process of respiratory infections abstract the study of social networks and especially of stochastic dynamics of diseases spread in human population has recently attracted considerable attention in statistical physics in this work we present a new statistical method of analyzing the spread of epidemic processes of grippe and acute respiratory track infections arti by means of the theory of discrete non markov stochastic processes we use the results of our last theory phys rev e 65 2002 046107 to study statistical memory effects long range correlation and discreteness in real data series describing the epidemic dynamics of human arti infections and grippe we have carried out the comparative analysis of the data of the two infections grippe and arti in one of the industrial districts of kazan one of the largest cities of russia the experimental data are analyzed by the power spectra of the initial time correlation function and the memory functions of junior orders the phase portraits of the four first dynamic variables the three first points of the statistical non markov parameter and the locally averaged kinetic and relaxation parameters the received results give an opportunity to provide a strict quantitative description of regular and stochastic components in epidemic dynamics of social networks taking into account their time discreteness and effects of statistical memory they also allow to reveal the degree of randomness and predictability of the real epidemic process in the specific social network

a homotopic deformation along p of a leray schauder degree result and existence for u p 2u ƒ t u 0 u 0 u t 0 p 1 soit f 0 1 r r une fonction continue et soit o p r r definie par o p s s p 2 s pour p fixe 1 on considere le probleme de dirichlet suivant o p u f t u 0 u 0 u t 0 ou t est un nombre reel positif

solution of epidemic models with quenched transients we consider a model for single season disease epidemics with a delay latent period in the onset of infectivity and a decay quenching in host susceptibility described by time varying rates of primary and secondary infections the classical susceptible exposed infected sei model of epidemiology is a special case with constant rates the decaying rates force the epidemics to slow down and eventually stop in a quenched transient state that depends on the full history of the epidemic including its initial state this equilibrium state is neutrally stable i e has zero value eigenvalues and cannot be studied using standard equilibrium analysis we introduce a method that gives an approximate analytical solution for the quenched state the method uses an interpolation between two exactly solvable limits and applies to the whole five dimensional parameter space of the model some applications of the solutions for analysis of epidemics are given

transform estimation of parameters for stage frequency data we consider multistage development models that occur in the maturation of biological organisms disease progressions and industrial processes the situations that we address are distinguished by the essentially destructive sampling required to assess the stage reached by each individual we develop robust estimators of stage dependent maturation rates and overall death rates using method of moments based on laplace transforms for which we develop variance estimates under different sampling schemes we apply these methods to studies of cattle parasite and grasshopper life cycles and show that the laplace methods compare well with maximum likelihood methods

generalized jacobian elliptic functions and their application to bifurcation problems associated with p laplacian abstract the jacobian elliptic functions are generalized and applied to bifurcation problems associated with p laplacian the values of bifurcation parameter and the corresponding solutions are represented in terms of common parameters and a complete description of the bifurcation diagram and a closed form representation of the corresponding solutions are obtained as a by product of the representation it turns out that a kind of solution is also a solution of an eigenvalue problem of p 2 laplacian

shape of ecological networks we study the statistics of ecosystems with a variable number of coevolving species the species interact in two ways by prey predator relationships and by direct competition with similar kinds the interaction coefficients change slowly through successful adaptations and speciations they are treated as quenched random variables these interactions determine long term topological features of the species network which are found to agree with those of biological systems

individual based predator prey model for biological coevolution fluctuations stability and community structure we study an individual based predator prey model of biological coevolution using linear stability analysis and large scale kinetic monte carlo simulations the model exhibits approximate 1 f noise in diversity and population size fluctuations and it generates a sequence of quasisteady communities in the form of simple food webs these communities are quite resilient toward the loss of one or a few species which is reflected in different power law exponents for the durations of communities and the lifetimes of species the exponent for the former is near ensuremath 1 while the latter is close to ensuremath 2 statistical characteristics of the evolving communities including degree predator and prey distributions and proportions of basal intermediate and top species compare reasonably with data for real food webs

organization of growing random networks the organizational development of growing random networks is investigated these growing networks are built by adding nodes successively and linking each to an earlier node of degree k with an attachment probability a k when a k grows more slowly than linearly with k the number of nodes with k links n k t decays faster than a power law in k while for a k growing faster than linearly in k a single node emerges which connects to nearly all other nodes when a k is asymptotically linear n k t ensuremath sim mathrm tk ensuremath ensuremath nu with ensuremath nu dependent on details of the attachment probability but in the range 2l ensuremath nu l ensuremath infty the combined age and degree distribution of nodes shows that old nodes typically have a large degree there is also a significant correlation in the degrees of neighboring nodes so that nodes of similar degree are more likely to be connected the size distributions of the in and out components of the network with respect to a given node namely its descendants and ancestors are also determined the in component exhibits a robust s ensuremath 2 power law tail where s is the component size the out component has a typical size of order mathrm ln t and it provides basic insights into the genealogy of the network

computational complexity arising from degree correlations in networks we apply a bethe peierls approach to statistical mechanics models defined on random networks of arbitrary degree distribution and arbitrary correlations between the degrees of neighboring vertices using the nondeterministic polynomial time hard optimization problem of finding minimal vertex covers on these graphs we show that such correlations may lead to a qualitatively different solution structure as compared to uncorrelated networks this results in a higher complexity of the network in a computational sense simple heuristic algorithms fail to find a minimal vertex cover in the highly correlated case whereas uncorrelated networks seem to be simple from the point of view of combinatorial optimization

a complete classification of bifurcation diagrams for a class of p q laplace equations abstract we study the bifurcation problem of positive solutions for the one dimensional p q laplace equation with nonlinear term u r 1 there are five types of order relations for p q r we investigate the exact shape of the bifurcation curve in each type of the order relation we prove that there are two types of bifurcation curves that are increasing two types that are decreasing and one that is not monotone and turns exactly once moreover we study the asymptotic profile of the normalized solution u x u as u 0 or u where u denotes the l norm of u

effects of preference for attachment to low degree nodes on the degree distributions of a growing directed network and a simple food web model we study the growth of a directed network in which the growth is constrained by the cost of adding links to the existing nodes we propose a preferential attachment scheme in which a new node attaches to an existing node i with probability ensuremath pi k i ensuremath propto k i ensuremath 1 where k i is the number of outgoing links at i we calculate the degree distribution for the outgoing links in the asymptotic regime t ensuremath rightarrow ensuremath infty n k both analytically and by monte carlo simulations the distribution decays like k ensuremath mu k ensuremath gamma k for large k where ensuremath mu is a constant we investigate the effect of this preferential attachment scheme by comparing the results to an equivalent growth model with a degree independent probability of attachment which gives an exponential outdegree distribution also we relate this mechanism to simple food web models by implementing it in the cascade model we show that the low degree preferential attachment mechanism breaks the symmetry between in and outdegree distributions in the cascade model it also causes a faster decay in the tails of the outdegree distributions for both our network growth model and the cascade model

evolutionary reconstruction of networks can a graph specifying the pattern of connections of a dynamical network be reconstructed from statistical properties of a signal generated by such a system in this model study we present a metropolis algorithm for reconstruction of graphs from their laplacian spectra through a stochastic process of mutations and selection evolving test networks converge to a reference graph applying the method to several examples of random graphs clustered graphs and small world networks we show that the proposed stochastic evolution allows exact reconstruction of relatively small networks and yields good approximations in the case of large sizes

bifurcation phenomena associated to the p laplace operator on determine la structure de l ensemble des solutions u de u x p 2 u x x f u u p 2 u sur 0 1 telles que u 0 u 1 0 ou p 1 et r on demontre que les solutions avec k zeros sont uniques quand 1 2

inequalities on generalized trigonometric and hyperbolic functions abstract in this paper we prove some inequalities involving the generalized trigonometric and hyperbolic functions

nonequilibrium transitions in complex networks a model of social interaction we analyze the nonequilibrium order disorder transition of axelrod s model of social interaction in several complex networks in a small world network we find a transition between an ordered homogeneous state and a disordered state the transition point is shifted by the degree of spatial disorder of the underlying network the network disorder favoring ordered configurations in random scale free networks the transition is only observed for finite size systems showing system size scaling while in the thermodynamic limit only ordered configurations are always obtained thus in the thermodynamic limit the transition disappears however in structured scale free networks the phase transition between an ordered and a disordered phase is restored

exact multiplicity results for boundary value problems with nonlinearities generalizing cubic using techniques of bifurcation theory we present two exact multiplicity results for boundary value problems of the type the first result concerns the case when the nonlinearity is independent of x and behaves like a cubic in u the second one deals with a class of nonlinearities with explicit x dependence

effects of correlated interactions in a biological coevolution model with individual based dynamics models of biological coevolution have recently been proposed and studied in which a species is defined by a genome in the form of a finite bitstring and the interactions between species i and j are given by a fixed matrix with independent randomly distributed elements mij a consequence of the stochastic independence is that species whose genotypes differ even by a single bit may have completely different phenotypes as defined by their interactions with the other species this is clearly unrealistic as closely related species should be similar in their interactions with the rest of the ecosystem here we therefore study a model in which the mij are correlated to a controllable degree by means of a local averaging scheme we calculate both analytically and numerically the correlation function for matrix elements mij and mkl versus the hamming distance between the bitstrings representing the species the agreement between the analytical and numerical calculations is excellent for correlations of limited range but explainable differences arise for correlation ranges that are a significant fraction of the length of the bitstring we compare long kinetic monte carlo simulations of coevolution models with uncorrelated and correlated interactions respectively in particular we consider the probability density for the lifetimes of individual species the species lifetime distribution is close to a power law with an exponent near 2 over eight decades in time in both uncorrelated and correlated cases the durations of quasi steady states and power spectral densities for the diversity indices display noticeable differences however some qualitative features such as 1 f behaviour in power spectral densities for the diversity indices are not affected by the correlations in the interaction matrix

criticality and unpredictability in macroevolution a recently presented model of large scale evolution exhibiting self organized criticality is explored from the dynamical point of view it is shown that the system approaches the critical state in an anomalous way with a dynamical exponent z50 at the same time the complexity of the interactions among species increases leading to higher unpredictability the dynamic evolution is able to generate phylogenetic fractal trees with dimension close to the one obtained from real taxonomy some analytic results are presented and an interesting interpretation of the macroevolutionary process is suggested s1063 651x 97 15503 9

giant strongly connected component of directed networks we describe how to calculate the sizes of all giant connected components of a directed graph including the strongly connected one in particular the world wide web is a directed network the results are obtained for graphs with statistically uncorrelated vertices and an arbitrary joint in and out degree distribution p k i k o we show that if p k i k o does not factorize the relative size of the giant strongly connected component deviates from the product of the relative sizes of the giant in and out components the calculations of the relative sizes of all the giant components are demonstrated using the simplest examples we explain that the giant strongly connected component may be less resilient to random damage than the giant weakly connected one

the inverse hyperbolic tangent function and jacobian sine function abstract the holder convexity of the composition of inverse hyperbolic tangent function and jacobian sine function is investigated in this paper

on certain second order ordinary differential equations associated with sobolev poincare type inequalities on considere l equation e i 1 n u x i p 2 u x i x i u q 2 u 0 dans u x 0 sur on donne les proprietes des solutions de e pour le cas n 1 et a b mais pour p q 1 avec p q regularite existence et unicite de solutions positives

extinctions and taxonomy in a trophic model of coevolution we investigate the statistics of extinction sizes and the taxonomy in a trophic model of evolution recently proposed phys rev lett 82 652 1999 by further exploring the parameters of this model we find that the distribution of extinction sizes n s shows typically a characteristic maximum before developing the power law behavior n s approximately s alpha with alpha approximately 2 in agreement with empirical observations furthermore the derivation of the alpha 2 exponent given by drossel phys rev lett 81 5011 1998 for this model is completed the extinction sizes in each trophic level are also analyzed one finds that at the fourth level and up l or 4 the extinction size statistics is a power law with exponent alpha l approximately 1 4 and exponential like at the second level also in agreement with some empirical data not previously explained by current models on the other hand in contrast to the observed power law distribution of the number of species in genera numerical simulations yield an exponential law a modification of the model is presented that provides an approximate potential behavior for taxonomy and some consequences for future modeling are outlined

empirical transform estimation for indexed stochastic models we present a method for estimating the parameters in indexed stochastic models via a least squares approach based on empirical transforms asymptotic approximations are derived for the distribution of the resulting estimators an explicit expression for the mean squared error provides a natural way of selecting the transform variable and a numerical example illustrates the performance of the resulting method a common finding which we term diagonal optimization occurs when multiparameter models are fitted by using transforms diagonal optimization arises when optimal performance results from equating the elements of the transform vector and we provide a heuristic explanation of why this occurs

effect of nonstationarities on detrended fluctuation analysis detrended fluctuation analysis dfa is a scaling analysis method used to quantify long range power law correlations in signals many physical and biological signals are noisy heterogeneous and exhibit different types of nonstationarities which can affect the correlation properties of these signals we systematically study the effects of three types of nonstationarities often encountered in real data specifically we consider nonstationary sequences formed in three ways i stitching together segments of data obtained from discontinuous experimental recordings or removing some noisy and unreliable parts from continuous recordings and stitching together the remaining parts a cutting procedure commonly used in preparing data prior to signal analysis ii adding to a signal with known correlations a tunable concentration of random outliers or spikes with different amplitudes and iii generating a signal comprised of segments with different properties e g different standard deviations or different correlation exponents we compare the difference between the scaling results obtained for stationary correlated signals and correlated signals with these three types of nonstationarities we find that introducing nonstationarities to stationary correlated signals leads to the appearance of crossovers in the scaling behavior and we study how the characteristics of these crossovers depend on a the fraction and size of the parts cut out from the signal b the concentration of spikes and their amplitudes c the proportion between segments with different standard deviations or different correlations and d the correlation properties of the stationary signal we show how to develop strategies for preprocessing raw data prior to analysis which will minimize the effects of nonstationarities on the scaling properties of the data and how to interpret the results of dfa for complex signals with different local characteristics

estimation of stage duration distributions and mortality under repeated cohort censuses many processes in nature can be viewed as arising from subjects progressing through sequential stages and may be described by multistage models examples include disease development and the physiological development of plants and animals we develop a multistage model for sampling designs where a small set of subjects is followed and the number of subjects in each stage is assessed repeatedly for a sequence of time points but for which the subjects cannot be identified the motivating problem is the laboratory study of developing arthropods through stage frequency data our model assumes that the same individuals are censused at each time introducing among sample dependencies this type of data often occur in laboratory studies of small arthropods but their detailed analysis has received little attention the likelihood of the model is derived from a stochastic model of the development and mortality of the individuals in the cohort we present an mcmc scheme targeting the posterior distribution of the times of development and times of death of individuals this is a novel type of mcmc that uses customized proposals to explore a posterior with disconnected support arising from the fact that individual identities are unknown the mcmc algorithm may be used for inference about parameters governing stage duration distributions and mortality rates the method is demonstrated by fitting the development model to stage frequency data of a mealybug cohort placed on a grape vine

bak sneppen model near zero dimension we consider the bak sneppen model near zero dimension where the avalanche exponent tau is close to 1 and the exponents m and sigma are close to 0 we demonstrate that tau 1 m sigma exp m 1 gamma small middle dot small middle dot small middle dot in this limit where gamma is euler s constant the avalanche hierarchy equation is rewritten in a form that makes it possible to find the relation between the critical exponents sigma and m with high accuracy we obtain precise values of the critical exponents for the one and two dimensional bak sneppen model and for the one dimensional anisotropic bak sneppen model

analytical solution of a model for complex food webs we investigate numerically and analytically a recently proposed model for food webs nature 404 180 2000 in the limit of large web sizes and sparse interaction matrices we obtain analytical expressions for several quantities with ecological interest in particular the probability distributions for the number of prey and the number of predators we find that these distributions have fast decaying exponential and gaussian tails respectively we also find that our analytical expressions are robust to changes in the details of the model

stochastic model for tumor growth with immunization we analyze a stochastic model for tumor cell growth with both multiplicative and additive colored noises as well as nonzero cross correlations in between whereas the death rate within the logistic model is altered by a deterministic term characterizing immunization the birth rate is assumed to be stochastically changed due to biological motivated growth processes leading to a multiplicative internal noise moreover the system is subjected to an external additive noise which mimics the influence of the environment of the tumor the stationary probability distribution p s is derived depending on the finite correlation time the immunization rate and the strength of the cross correlation p s offers a maximum which becomes more pronounced for increasing immunization rate the mean first passage time is also calculated in order to find out under which conditions the tumor can suffer extinction its characteristics are again controlled by the degree of immunization and the strength of the cross correlation the behavior observed can be interpreted in terms of a biological model of tumor evolution

inequalities for the generalized trigonometric and hyperbolic functions abstract the generalized trigonometric functions occur as an eigenfunction of the dirichlet problem for the one dimensional p laplacian the generalized hyperbolic functions are defined similarly some classical inequalities for trigonometric and hyperbolic functions such as mitrinovic adamovic s inequality lazarevic s inequality huygens type inequalities wilker type inequalities and cusa huygens type inequalities are generalized to the case of generalized functions

parameter convexity and concavity of generalized trigonometric functions abstract we study the convexity properties of the generalized trigonometric functions viewed as functions of the parameter we show that p sin p y and p cos p y are log concave on the appropriate intervals while p tan p y is log convex we also prove similar facts about the generalized hyperbolic functions in particular our results settle a major part of the conjecture recently put forward in 4