connexions affines et projectives sur les surfaces complexes compactes soit s une surface complexe compacte connexe munie d une connexion affine holomorphe sans torsion nous demontrons que est localement modelee sur une connexion affine invariante par translations sur c2 en particulier est localement homogene sauf si s est un fibre elliptique principal au dessus d une surface de genre g 2 de premier nombre de betti impair et est une connexion affine holomorphe sans torsion generique sur s auquel cas l algebre de lie des champs de killing locaux est de dimension un engendree par le champ fondamental de la fibration principale nous en deduisons que toute connexion projective holomorphe normale sur une surface complexe compacte est plate

random perturbations of heteroclinic attractors estimates are derived for the mean recurrence time of orbits in the neighborhood of an attracting homoclinic orbit or heteroclinic cycle in an ordinary differential equation subject to small additive random noise the theory presented is illustrated with numerical simulations of several systems including ones invariant under symmetry groups for which such heteroclinic attractors are structurally stable the physical implications of the work presented are briefly discussed

volatility clustering and scaling for financial time series due to attractor bubbling a microscopic model of financial markets is considered consisting of many interacting agents spins with global coupling and discrete time heat bath dynamics similar to random ising systems the interactions between agents change randomly in time in the thermodynamic limit the obtained time series of price returns show chaotic bursts resulting from the emergence of attractor bubbling or on off intermittency resembling the empirical financial time series with volatility clustering for a proper choice of the model parameters the probability distributions of returns exhibit power law tails with scaling exponents close to the empirical ones

equivalent continuous and discrete realizations of levy flights a model of one dimensional motion of an inertial particle abstract the paper is devoted to the relationship between the continuous markovian description of levy flights developed previously see e g i a lubashevsky truncated levy flights and generalized cauchy processes eur phys j b 82 2011 189 195 and references therein and their equivalent representation in terms of discrete steps of a wandering particle a certain generalization of continuous time random walks to simplify understanding the key points of the technique to be created our consideration is confined to the one dimensional model for continuous random motion of a particle with inertia its dynamics governed by stochastic self acceleration is described as motion on the phase plane x v comprising the position x and velocity v d x d t of the given particle a notion of random walks inside a certain neighborhood l of the line v 0 the x axis and outside it is developed it enables us to represent a continuous trajectory of particle motion on the plane x v as a collection of the corresponding discrete steps each of these steps matches one complete fragment of the velocity fluctuations originating and terminating at the boundary of l as demonstrated the characteristic length of particle spatial displacement is mainly determined by velocity fluctuations with large amplitude which endows the derived random walks along the x axis with the characteristic properties of levy flights using the developed classification of random trajectories a certain parameter free core stochastic process is constructed its peculiarity is that all the characteristics of levy flights similar to the exponent of the levy scaling law are no more than the parameters of the corresponding transformation from the particle velocity v to the related variable of the core process in this way the previously found validity of the continuous markovian model for all the regimes of levy flights is explained based on the obtained results an efficient single peak approximation is constructed in particular it enables us to calculate the basic characteristics of levy flights using the probabilistic properties of extreme velocity fluctuations and the shape of the most probable trajectory of particle motion within such extreme fluctuations

analog study of the first passage time problem driven by power law distributed noise abstract in this work we develop an analog circuit to generate a stochastic signal with stationary distribution exhibiting a tunable power law tail the proposed circuit design is a variant of a recently introduced one based on a differential equation with both multiplicative and additive noises here the circuit is carefully designed in order to ensure that all components operate within their specific regimes we provide a detailed characterization of the output signal including the power law exponent dependence on the tunable component we apply the present circuit to study the first passage time problem in a simple integrate fire model of neural dynamics driven by a non gaussian noise

harmonic oscillator with multiplicative noise nonmonotonic dependence on the strength and the rate of dichotomous noise the output signal of a undamped linear oscillator with a random frequency subject to a periodic force shows nonmonotonic dependence on the strength and the rate of color noise stochastic resonance the effect is absent for white noise

a microscopic model of triangular arbitrage we introduce a microscopic model which describes the dynamics of each dealer in multiple foreign exchange markets taking account of the triangular arbitrage transaction the model reproduces the interaction among the markets well we explore the relation between the parameters of the present microscopic model and the spring constant of a macroscopic model that we proposed previously

statistical analysis of 5 s index data of the budapest stock exchange abstract a statistical analysis of the budapest stock index bux is presented the high time resolution 5 s sampling makes it possible to extract information on market functioning which does not emerge from daily data the main results are as follows from a statistical point of view the large drop in october 1997 was a normal event strong autocorrelation has been detected in the volatility and market activity data detrended fluctuation analysis reveals superdiffusive scaling without persistence finally we report on a simple method for mapping local trends to represent sequences in order to obtain pattern statistics

multiplicative stochastic differential equations with noise induced transitions the author investigates a class of linear multiplicative stochastic differential equations and demonstrates the existence of a striking noise induced transition in the structure of the resulting asymptotic stationary probability distribution for the dependent variable the transition amounts to a change from a bounded distribution to an unbounded one with only a finite number of convergent moments it occurs when the range of fluctuation of one of the variables driven by the underlying stochastic process increases sufficiently to permit changes of sign for the variable it seems likely that the phenomenon is a general one and occurs in a wider class of models than that discussed in this paper he obtains explicit results for simple cases which he confirms by appropriate numerical simulations this gives him the opportunity of assessing the applicability of perturbation theory which is one of the few calculational methods employed on these models up until now

statistical properties of deterministic threshold elements the case of market price abstract we analyze statistical properties of a set of deterministic threshold elements which is introduced as a model for the stock market the macroscopic variable of the stock market price shows seemingly stochastic fluctuation with a f 2 power spectrum consistent with real economic fluctuations the maximum lyapunov exponent is estimated to be zero indicating that the system is at the edge of chaos

fractal distribution of floaters on a fluid surface and the transition to chaos for random maps abstract the long time spatial distribution of particles floating on the surface of a confined fluid whose flow velocity has complicated time dependence is considered it is shown that this distribution can be either a fractal or else can clump at several or one discrete points the transition from the latter type of distribution to the former occurs when the lyapunov exponent characterizing the particle motion passes through zero from negative values to positive values the characteristic features of this type of transition are investigated using random maps it is shown that near the transition there are extremely intermittent temporal fluctuations in the particle cloud and their scaling with a parameter is elucidated

projective uniformization extremal chern classes and quaternionic shimura curves projective structures on compact real manifolds are classical objects in real differential geometry complex manifolds with a holomorphic projective structure on the other hand form a special class as soon as the dimension is greater than one in the kahler einstein case mathbb p m tori and ball quotients are essentially the only examples they can be described purely in terms of chern class conditions we give a complete classification of all projective manifolds carrying a projective structure the only additional examples are modular abelian families over quaternionic shimura curves they can also be described purely in terms of chern class conditions

dynamic numerical models of stock market price from microscopic determinism to macroscopic randomness abstract a variant of threshold dynamics is introduced to model the behaviors of a large assembly of dealers in a stock market although the microscopic evolution dynamics is deterministic the collective behaviors such as market prices show seemingly stochastic fluctuations the statistical properties of market price change can be well approximated by a simple discrete langevin type equation with random amplification the macroscopic stochastic equation is solved both numerically and analytically showing that the market price change generally follow power law distributions in the steady state the reason for the appearance of rapid decay in the distribution tails are discussed

stock market dynamics and turbulence parallel analysis of fluctuation phenomena abstract we report analogies and differences between the fluctuations in an economic index and the fluctuations in velocity of a fluid in a fully turbulent state specifically we systematically compare i the statistical properties of the s p 500 cash index recorded during the period january 84 december 89 with ii the statistical properties of the velocity of turbulent air measured in the atmospheric surface layer about 6 m above a wheat canopy in the connecticut agricultural research station we find non gaussian statistics and intermittency for both processes i and ii but the deviation from a gaussian probability density function are different for stock market dynamics and turbulence

a hierarchical model of financial crashes abstract we follow up our previous conjecture that large stock market crashes are analogous to critical points in statistical physics the term critical refers to regimes of cooperative behavior such as magnetism at the curie temperature and liquid gas transitions and is characterized by the singular mathematical behavior of relevant observables to illustrate the concept of criticality we present a simple hierarchical model of traders exhibiting crowd behavior and show that it has a well defined critical point whose mathematical signature is a power law dependence of the price modulated by log periodic structures as recently found in market data by several independent groups

sampling based approaches to calculating marginal densities abstract stochastic substitution the gibbs sampler and the sampling importance resampling algorithm can be viewed as three alternative sampling or monte carlo based approaches to the calculation of numerical estimates of marginal probability distributions the three approaches will be reviewed compared and contrasted in relation to various joint probability structures frequently encountered in applications in particular the relevance of the approaches to calculating bayesian posterior densities for a variety of structured models will be discussed and illustrated

non extensive random walks stochastic variables whose addition leads to q gaussian distributions gq x 1 q 1 bx 2 1 1 q with b40 1pqo3 and where f x maxff x 0g as limit law for a large number of terms are investigated random walk sequences related to this problem possess a simple additive multiplicative structure commonly found in several contexts thus justifying the ubiquity of those distributions a characterization of the statistical properties of the random walk step lengths is performed moreover a connection with non linear stochastic processes is exhibited q gaussian distributions have special relevance within the framework of non extensive statistical mechanics a generalization of the standard boltzmann gibbs formalism introduced by tsallis over one decade ago therefore the present findings may give insights on the domain of applicability of such generalization r 2005 elsevier b v all rights reserved

scaling characteristics in the taiwan stock market some statistical tools including histogram spectral analysis and fractal theory were used on the daily taiwan stock price index tspi from 1987 to 2002 to examine the possible scale invariant behavior and the clustering characteristics in taiwan stock market it was found that the tspi data exhibited the characteristic of right skewed frequency distribution the long term memory and the possibility of scale invariance were roughly identified through the analysis of autocorrelation and power spectrum respectively the monofractal analysis was then performed by the box counting method scale invariance was clearly found in the time series and the box dimension was shown to be a decreasing function of the threshold index level implying multifractal characteristics i e the low and high regions scale differently to test this hypothesis the time series were transferred into a useful compact form through the multifractal formalism namely the q q and f plots the analysis confirmed the existence of multifractal characteristics in the investigated time series the origin of multifractal phenomena in taiwan stock market might be interpreted in terms of the multiplicative cascade process of stock market information

fluctuation controlled transient below the on off intermittency transition on off intermittency is an ubiliquitous phenomenon observed beyond the instability of a particular chaotic motion the system below the instability reveals a typical transient chaos it is found that near the instability point the inverse characteristic first passage time satisfies the scaling law with the transverse lyapunov exponent tle and being respectively an initial condition dependent characteristic tle and the fluctuation intensity of local transverse expansion rate numerical simulation for several systems suggests that the scaling function g z is a universal function

physiological pharmacokinetic analysis using population modeling and informative prior distributions abstract we describe a general approach using bayesian analysis for the estimation of parameters in physiological pharmacokinetic models the chief statistical difficulty in estimation with these models is that any physiological model that is even approximately realistic will have a large number of parameters often comparable to the number of observations in a typical pharmacokinetic experiment e g 28 measurements and 15 parameters for each subject in addition the parameters are generally poorly identified akin to the well known ill conditioned problem of estimating a mixture of declining exponentials our modeling includes a hierarchical population modeling which allows partial pooling of information among different experimental subjects b a pharmacokinetic model including compartments for well perfused tissues poorly perfused tissues fat and the liver and c informative prior distributions for population parameters which is possible because the parameters represent real physiological

statistical analysis of the overnight and daytime return we investigate the two components of the total daily return close to close the overnight return close to open and the daytime return open to close as well as the corresponding volatilities of the 2215 new york stock exchange stocks for the 20 year period from 1988 to 2007 the tail distribution of the volatility the long term memory in the sequence and the cross correlation between different returns are analyzed our results suggest that i the two component returns and volatilities have features similar to that of the total return and volatility the tail distribution follows a power law for all volatilities and long term correlations exist in the volatility sequences but not in the return sequences ii the daytime return contributes more to the total return both the tail distribution and the long term memory of the daytime volatility are more similar to that of the total volatility compared to the overnight records in addition the cross correlation between the daytime return and the total return is also stronger iii the two component returns tend to be anticorrelated moreover we find that the cross correlations between the three different returns total overnight and daytime are quite stable over the entire 20 year period

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

the order of a linearly invariant family in cn abstract we study the trace order of the linearly invariant family in the ball b n defined by s f where f b n c n is locally biholomorphic and s f is the schwarzian operator by adapting pommerenke s approach we establish a characteristic equation for the extremal mapping that yields an upper bound for the order of the family in terms of and the dimension n lower bounds for the order are established in similar terms by means of examples

models and estimation methods for clinical hiv 1 data clinical hiv 1 data include many individual factors such as compliance to treatment pharmacokinetics variability in respect to viral dynamics race sex income etc which might directly influence or be associated with clinical outcome these factors need to be taken into account to achieve a better understanding of clinical outcome and mathematical models can provide a unifying framework to do so the first objective of this paper is to demonstrate the development of comprehensive hiv 1 dynamics models that describe viral dynamics and also incorporate different factors influencing such dynamics the second objective of this paper is to describe alternative estimation methods that can be applied to the analysis of data with such models in particular we consider i simple but effective two stage estimation methods in which data from each patient are analyzed separately and summary statistics derived from the results ii more complex nonlinear mixed effect models used to pool all the patient data in a single analysis bayesian estimation methods are also considered in particular iii maximum posterior approximations map and iv markov chain monte carlo mcmc bayesian methods incorporate prior knowledge into the models thus avoiding some of the model simplifications introduced when the data are analyzed using two stage methods or a nonlinear mixed effect framework we demonstrate the development of the models and the different estimation methods using real aids clinical trial data involving patients receiving multiple drugs regimens

probability distributions for one component equations with multiplicative noise abstract systems described by equations involving both multiplicative and additive noise are common in nature examples include convection of a passive scalar field polymers in turbulent flow and noise in dye lasers in this paper the one component version of this problem is studied the steady state probability distribution is classified into two different types of behavior one class has power law tails and the other is of the form of an exponential to a power law the value of the power law exponent is determined analytically for models having colored gaussian noise it is found to only depend on the power spectrum of the noise at zero frequency when non gaussian noise is considered it is shown that stretched exponential tails are possible an intuitive understanding of the results is found and makes use of the lyapunov exponents for these systems

frequency analysis of tick quotes on foreign currency markets and the double threshold agent model abstract power spectrum densities for the number of tick quotes per minute market activity on three currency markets usd jpy eur usd and jpy eur are analyzed for periods from january 2000 to december 2000 we find some peaks on the power spectrum densities at a few minutes we develop the double threshold agent model and confirm that the corresponding periodicity can be observed for the activity of this model even though market participants perceive common weaker periodic information than threshold for decision making of them this model is numerically performed and theoretically investigated by utilizing the mean field approximation we propose a hypothesis that the periodicities found on the power spectrum densities can be observed due to nonlinearity and diversity of market participants

symmetry breaking bifurcation for coupled chaotic attractors the authors consider transitions from synchronous to asynchronous chaotic motion in two identical dissipatively coupled one dimensional mappings they show that the probability density of the asymmetric component satisfies a scaling law the exponent in this scaling law varies continuously with the distance from the bifurcation point and is determined by the spectrum of local lyapunov exponents of the uncoupled map finally they show that the topology of the invariant set is rather unusual though the attractor for supercritical coupling is a line it is surrounded by a strange invariant set which is dense in a two dimensional neighbourhood of the attractor

levy walks and enhanced diffusion in milan stock exchange abstract we perform statistical analyses of the general and sectorial historical m i b indices of the milan stock exchange our analyses show that the price indices have statistical properties which are compatible with a levy random walk the time evolution of the daily variations of indices is intermittent on a time scale of years and the variance of almost all indices displays a superdiffusive behavior by using the theory of enhanced diffusion in levy walks as theoretical framework we ascribe the superdiffusive behavior to a nonlocal memory coupling price and time

schwarps locally projective image warps based on 2d schwarzian derivatives image warps or just warps capture the geometric deformation existing between two images of a deforming surface the current approach to enforce a warp s smoothness is to penalize its second order partial derivatives bookstein in ieee trans pattern anal mach intell 11 567 585 1989 rueckert et al in ieee trans med imaging 18 712 721 1999 because this favors locally affine warps this fails to capture the local projective component of the image deformation this may have a negative impact on applications such as image registration and deformable 3d reconstruction we propose a novel penalty designed to smooth the warp while capturing the deformation s local projective structure our penalty is based on equivalents to the schwarzian derivatives which are projective differential invariants exactly preserved by homographies we propose a methodology to derive a set of partial differential equations with only homographies as solutions we call this system the schwarzian equations and we explicitly derive them for 2d functions using differential properties of homographies we name as schwarp a warp which is estimated by penalizing the residual of schwarzian equations experimental evaluation shows that schwarps outperform existing warps in modeling and extrapolation power and lead to better results in three deformable reconstruction methods namely shape reconstruction in shape from template camera calibration in shape from template and non rigid structure from motion

periodic orbit theory of the blowout bifurcation this paper presents a theory for characterization of the blowout bifurcation by periodic orbits blowout bifurcation in chaotic systems occurs when a chaotic attractor lying in some symmetric invariant subspace becomes transversely unstable we present an analysis and numerical results that indicate that the bifurcation is mediated by changes in the transverse stability of an infinite number of unstable periodic orbits embedded in the chaotic attractor there are two distinct groups of periodic orbits one transversely stable and another transversely unstable the bifurcation occurs when some properly weighted transverse eigenvalues of these two groups are balanced our results thus categorize the blowout bifurcation as a unique type of bifurcation that involves an infinite number of periodic orbits in contrast to most previously known bifurcations that are mediated by only a finite number of periodic orbits

scaling laws for noise induced temporal riddling in chaotic systems recent work has considered the situation of riddling where when a chaotic attractor lying in an invariant subspace is transversely stable the basin of the attractor can be riddled with holes that belong to the basin of another attractor the existence of invariant subspace often relies on certain symmetry of the system which is however a nongeneric property as system defects and small random noise can destroy the symmetry this paper addresses the influence of noise on riddling we show that riddling can actually be induced by arbitrarily small noise even in parameter regimes where one expects no riddling in the absence of noise specifically we argue that when there are attractors located off the invariant subspace the basins of these attractors can be temporally riddled even when the chaotic attractor in the invariant subspace is transversely unstable w e investigate universal scaling laws for noise induced temporal riddling our results imply that the phenomenon of riddling is robust and it can be more prevalent than expected before as noise is practically inevitable in physical systems s1063 651x 97 01410 4

synchronization threshold in coupled logistic map lattices abstract we consider regular lattices of coupled chaotic maps whose local dynamics is ruled by the logistic map x 4 x 1 x a usual paradigm of chaotic systems through finite time exponents we scrutinize the lattice dynamics in the vicinity of the threshold of complete synchronization we connect dynamical features such as relaxation to the coherent state and intermittency with the statistics of finite time exponents focusing on the implications of the particular statistics related to the logistic map although numerical examples are given for lattice couplings decaying with distance as a power law our results are expected to be valid for a wider class of schemes coupling logistic maps

the transition to chaotic attractors with riddled basins abstract recently it has been shown that there are chaotic attractors whose basins are such that any point in the basin has pieces of another attractor basin arbitrarily nearby the basin is riddled with holes here we consider the dynamics near the transition to this situation as a parameter is varied using a simple analyzable model we obtain the characteristic behaviors near this transition numerical tests on a more typical system are consistent with the conjecture that these results are universal for the class of systems considered

phase coherence in an ensemble of uncoupled limit cycle oscillators receiving common poisson impulses an ensemble of uncoupled limit cycle oscillators receiving common poisson impulses shows a range of nontrivial behavior from synchronization desynchronization to clustering the group behavior that arises in the ensemble can be predicted from the phase response of a single oscillator to a given impulsive perturbation we present a theory based on phase reduction of a jump stochastic process describing a poisson driven limit cycle oscillator and verify the results through numerical simulations and electric circuit experiments we also give a geometrical interpretation of the synchronizing mechanism a perturbative expansion to the stationary phase distribution and the diffusion limit of our jump stochastic model

volatility cluster and herding stock markets can be characterized by fat tails in the volatility distribution clustering of volatilities and slow decay of their time correlations for an explanation models with several mechanisms and consequently many parameters as the lux marchesi model have been used we show that a simple herding model with only four parameters leads to a quantitative description of the data as a new type of data we describe the volatility cluster by the waiting time distribution which can be used successfully to distinguish between different models

kinetic theory for financial brownian motion from microscopic dynamics recent technological development has enabled researchers to study social phenomena scientifically in detail and financial markets has particularly attracted physicists since the brownian motion has played the key role as in physics in our previous report arxiv 1703 06739 to appear in phys rev lett we have presented a microscopic model of trend following high frequency traders hfts and its theoretical relation to the dynamics of financial brownian motion directly supported by a data analysis of tracking trajectories of individual hfts in a financial market here we show the mathematical foundation for the hft model paralleling to the traditional kinetic theory in statistical physics we first derive the time evolution equation for the phase space distribution for the hft model exactly which corresponds to the liouville equation in conventional analytical mechanics by a systematic reduction of the liouville equation for the hft model the bogoliubov born green kirkwood yvon hierarchal equations are derived for financial brownian motion we then derive the boltzmann like and langevin like equations for the order book and the price dynamics by making the assumption of molecular chaos the qualitative behavior of the model is asymptotically studied by solving the boltzmann like and langevin like equations for the large number of hfts which is numerically validated through the monte carlo simulation our kinetic description highlights the parallel mathematical structure between the financial brownian motion and the physical brownian motion

noise induced unstable dimension variability and transition to chaos in random dynamical systems results are reported concerning the transition to chaos in random dynamical systems in particular situations are considered where a periodic attractor coexists with a nonattracting chaotic saddle which can be expected in any periodic window of a nonlinear dynamical system under noise the asymptotic attractor of the system can become chaotic as characterized by the appearance of a positive lyapunov exponent generic features of the transition include the following 1 the noisy chaotic attractor is necessarily nonhyperbolic as there are periodic orbits embedded in it with distinct numbers of unstable directions unstable dimension variability and this nonhyperbolicity develops as soon as the attractor becomes chaotic 2 for systems described by differential equations the unstable dimension variability destroys the neutral direction of the flow in the sense that there is no longer a zero lyapunov exponent after the noisy attractor becomes chaotic and 3 the largest lyapunov exponent becomes positive from zero in a continuous manner and its scaling with the variation of the noise amplitude is algebraic formulas for the scaling exponent are derived in all dimensions numerical support using both low and high dimensional systems is provided

the origin of fat tailed distributions in financial time series abstract a classic problem in physics is the origin of fat tailed distributions generated by complex systems we study the distributions of stock returns measured over different time lags we find that destroying all correlations without changing the 1 d distribution by shuffling the order of the daily returns causes the fat tails to almost vanish for 1 d we argue that the fat tails are caused by the well known long range volatility correlations that have already been systematically studied previously indeed destroying only sign correlations by shuffling the order of only the signs but not the absolute values of the daily returns allows the fat tails to persist for 1 d

scaling and memory of intraday volatility return intervals in stock markets we study the return interval tau between price volatilities that are above a certain threshold q for 31 intraday data sets including the standard and poor s 500 index and the 30 stocks that form the dow jones industrial index for different threshold q the probability density function pq tau scales with the mean interval tau as formula see text similar to that found in daily volatilities since the intraday records have significantly more data points compared to the daily records we could probe for much higher thresholds and still obtain good statistics we find that the scaling function f x is consistent for all 31 intraday data sets in various time resolutions and the function is well approximated by the stretched exponential f x similar to e ax gamma with gamma 0 38 0 05 and a 3 9 0 5 which indicates the existence of correlations we analyze the conditional probability distribution pq tau tau0 for tau following a certain interval tau0 and find pq tau tau0 depends on tau0 which demonstrates memory in intraday return intervals also we find that the mean conditional interval tau tau0 increases with tau0 consistent with the memory found for pq tau tau0 moreover we find that return interval records in addition to having short term correlations as demonstrated by pq tau tau0 have long term correlations with correlation exponents similar to that of volatility records

the schwarzian derivative for maps between manifolds with complex projective connections in this paper we define in two equivalent ways the schwarzian derivative of a map between complex manifolds equipped with complex projective connections also a new coordinate free definition of complex projective connections is given we show how the schwarzian derivative is related to the projective structure of the manifolds to projective linear transformations and to complex geodesics

classical harmonic oscillator with multiplicative noise abstract the first two moments of an underdamped harmonic oscillator were found for additive and multiplicative noises a detailed analysis is performed of the case of a random damping which supplements the case of a random frequency which has received the most study in both cases the second moments are unstable for the sufficient large noise strength the difference appears in the stability conditions of the first moments which can diverge already for white noise for the random damping and only for color noise for the random frequency the difference between these two types of multiplicative noises shows up also in the response to an external periodic force namely white noise influences the first moment only in the case of a random damping however the second moments in both cases show the non monotonic dependence on the noise strength and correlation rate stochastic resonance in linear systems

statistical properties of the noisy on off intermittency the dependence of the escape time on the deviation from the critical point is investigated for the noisy on off intermittency the power law scaling behaviour is destroyed by the noise in a wide region above the critical point in the general case the width of the region decreases logarithmically with the decrease in the noise amplitude below the critical point the noise induced escape time is sensitive to the statistical properties of the chaotic driving signal universal exponential dependence holds only for the gaussian approximation

accurate approximations for posterior moments and marginal densities abstract this article describes approximations to the posterior means and variances of positive functions of a real or vector valued parameter and to the marginal posterior densities of arbitrary i e not necessarily positive parameters these approximations can also be used to compute approximate predictive densities to apply the proposed method one only needs to be able to maximize slightly modified likelihood functions and to evaluate the observed information at the maxima nevertheless the resulting approximations are generally as accurate and in some cases more accurate than approximations based on third order expansions of the likelihood and requiring the evaluation of third derivatives the approximate marginal posterior densities behave very much like saddle point approximations for sampling distributions the principal regularity condition required is that the likelihood times prior be unimodal

on off intermittency in oscillatory media abstract on off intermittency observed in three types of spatially extended dynamical systems is reported this is done by examining the linear stability of spatially synchronized state under a spatially inhomogeneous fluctuation when the system size slightly exceeds the critical size and a single inhomogeneous mode becomes unstable systems exhibit typical on off intermittency whose statistical characteristics such as distribution of burst amplitude fourier spectrum and distribution of laminar duration turn out to be in agreement with those known in the on off intermittency for small degrees of freedom system

invariant manifolds and collective coordinates we introduce suitable coordinate systems for interacting many body systems with invariant manifolds these are cartesian in coordinate and momentum space and chosen such that several components are identically zero for motion on the invariant manifold in this sense these coordinates are collective we make a connection to zickendraht s collective coordinates and present certain configurations of few body systems where rotations and vibrations decouple from single particle motion these configurations do not depend on details of the interaction

multifractal features of financial markets abstract we study the tick dynamical behavior of three assets in financial markets the kospi the won dollar and yen dollar exchange rates using the rescaled range r s analysis the multifractal hurst exponents with long run memory effect can be obtained from those assets and we discuss whether there exists the crossover or not for the hurst exponents at characteristic time scales particularly we find that the probability distribution of returns approaches to a lorentz distribution different from gaussian properties

newton raphson and em algorithms for linear mixed effects models for repeated measures data abstract we develop an efficient and effective implementation of the newton raphson nr algorithm for estimating the parameters in mixed effects models for repeated measures data we formulate the derivatives for both maximum likelihood and restricted maximum likelihood estimation and propose improvements to the algorithm discussed by jennrich and schluchter 1986 to speed convergence and ensure a positive definite covariance matrix for the random effects at each iteration we use matrix decompositions to develop efficient and computationally stable implementations of both the nr algorithm and an em algorithm laird and ware 1982 for this model we compare the two methods em vs nr in terms of computational order and performance on two sample data sets and conclude that in most situations a well implemented nr algorithm is preferable to the em algorithm or em algorithm with aitken s acceleration the term repeated measures refers to experimental designs where there are several individuals and several

scaling characteristics in aftershock sequence of earthquake abstract the possible scale invariant behavior and the clustering characteristics in aftershock sequence of chi chi taiwan main earthquake asccme that occurred in 1999 9 20 17 47 were investigated by means of some statistical tools histogram spectral analysis and fractal theory the examined data were constructed from the aftershocks that occurred at the locations defined at longitude 120 1 121 3 and latitude 23 3 24 5 during the 1999 9 20 17 47 1999 9 24 08 13 period it was found that the aftershock sequence exhibited the characteristic right skewed frequency distribution and could be well described with the lognormal distribution long term memory and the possibility of scale invariance were first roughly identified through the analysis of autocorrelation and power spectrum respectively scale invariance was clearly revealed with the aid of box counting method and the box dimension was shown to be a decreasing function of the threshold magnitude level i e the weak and intense regions scaled differently to verify the existence of multifractal characteristics the aftershock sequence was transferred into a useful compact form through the multifractal formalism namely the q q and f plots the analysis confirmed the existence of multifractal characteristics in the examined aftershock sequence the origin of both the pronounced right skewness and multifractal phenomena in aftershock sequence might be interpreted in terms of the multiplicative cascade process of the stress in the earth s crust a simple two scale cantor set with unequal scales and weights was then used to fit the calculated q q plot this model fitted remarkably well the entire spectrum of scaling exponents of the examined asccme

distribution of the first return time in fractional brownian motion and its application to the study of on off intermittency herein the term fractional brownian motion is used to refer to a class of random walks with long range correlated steps where the mean square displacement of the walker at large time t is proportional to mathit t 2 mathit h with 0h1 for ordinary brownian motion we obtain h 1 2 let t denote the time at which the random walker starting at the origin first returns to the origin the purpose of this paper is to show that the probability distribution of t scales with t as p t ensuremath sim mathit t mathit h mathrm ensuremath 2 theoretical arguments and numerical simulations are presented to support the result additional issues explored include modification to the power law distribution when the random walk is biased and the application of the result to the characterization of on off intermittency a recently proposed mechanism for bursting

influence of noise near blowout bifurcation we consider effects of zero mean additive noise on systems that are undergoing supercritical blowout bifurcation i e where a chaotic attractor in an invariant subspace loses transverse stability to a nearby on off intermittent attractor we concentrate on the low noise limit and two statistical properties of the trajectories the variance of the normal component and the mean first crossing time of the invariant subspace before blowout we find that the asymptotic variance scales algebraically with the noise level and exponentially with the lyapunov exponent after blowout it is limited to the nonzero variance of the associated on off intermittent state surprisingly for a large enough lyapunov exponent the effect of added noise can be to decrease rather than increase the variance the mean crossing time becomes infinite at and after the blowout in the limit of small noise after the blowout there is exponential dependence on the lyapunov exponent and algebraic dependence on the noise level the results are obtained using a drift diffusion model of venkataramani et al the results are confirmed in numerical experiments on a smooth mapping we observe that although there are qualitative similarities between bubbling noise driven and on off intermittency dynamics driven these can be differentiated using the statistical properties of the variance of the normal dynamics and the mean crossing time of the invariant subspace in the limit of low noise

time interval between successive trading in foreign currency market from microscopic to macroscopic abstract recently it has been shown that inter transaction interval iti distribution of foreign currency rates has a fat tail in order to understand the statistical property of the iti dealer model with n interactive agents is proposed from numerical simulations it is confirmed that the iti distribution of the dealer model has a power law tail the random multiplicative process rmp can be approximately derived from the iti of the dealer model consequently we conclude that the power law tail of the iti distribution of the dealer model is a result of the rmp

bayesian approach to the analysis of nonlinear models implementation and evaluation a traditional approach to parameter estimation and hypothesis testing in nonlinear models is based on least squares procedures error analysis depends on large sample theory bayesian analysis is an alternative approach that avoids substantial errors which could result frorn this dependence this communication is concerned with the implementation of the bayesian approach as an alternative to least squares nonlinear regression special attention is given to the numerical evaluation of multiple integrals and to the behavior of the parameter estimators and their estimated covariances the bayesian approach is evaluated in the light of practical as well as theoretical considerations 1 inttoduction the traditional approach to the statistical analysis of nonlinear models is first to use some numerical method to minimize the sum of squares objective function in order to obtain least squares estimators of the parameters draper and smith 1966 pp 267 275 nelder and mead 1965 and then to apply linear regression theory to the linear part of the taylor series approximation of the model expanded about these estimators in order to obtain the asymptotic covariance matrix bard 1974 pp 176 179 the distributions of the estimators obtained in this manner are known only in the limit as the sample size approaches infinity jennrich 1969 hence analyses based on these statistics may be inappropriate for small sample problems such as those arising in pharmacokinetics wagner 1975 an alternative approach to the statistical analysis of nonlinear models is to utilize methods based on bayes s theorem box and tiao 1973 pp 1 73 parameters are regarded as random variables rather than as unknown constants if a nonlinear model with known error distribution is assumed a correct probability analysis follows and asymptotic theory is not involved in this communication a bayesian approach to nonlinear regression is implemented and evaluated particular attention is given to numerical integration methods and the calculation of confidence regions using the posterior distributions

power law distributions in random multiplicative processes with non gaussian colored multipliers abstract one class of universal mechanisms that generate power law probability distributions is that of random multiplicative processes in this paper we consider a multiplicative langevin equation driven by non gaussian colored multipliers we analytically derive a formula that relates the power law exponent to the statistics of the multipliers and numerically confirm its validity using multiplicative noise generated by chaotic dynamical systems and by a two valued markov process we also investigate the relationship between our treatment and the large deviation analysis of time series and demonstrate the appearance of log periodic fluctuations superimposed on the power law distribution due to the non gaussian nature of the multipliers

on off intermittency power spectrum and fractal properties of time series abstract some dynamical systems possess invariant submanifolds such that the dynamics restricted to the invariant submanifold is chaotic this situation arises in systems with a spatial symmetry or in the synchronization of chaotic oscillators the invariant submanifold could become unstable to perturbations in the transverse directions when a parameter of the system is changed through a critical blow out value this could result in an extreme form of temporally intermittent bursting called on off intermittency we propose a model that incorporates the universal features of systems that display on off intermittency we study this model both with and without additive noise and we derive scaling results for the power spectral density of the on off intermittent process and for the box counting dimension for the set of time intervals when the process takes on values above a given threshold we then present numerical simulations realizing these results

maximum likelihood estimators for generalized cauchy processes maximum likelihood estimator mle for a generalized cauchy process gcp is studied with the aid of the method of information geometry in statistics our gcp is described by the langevin equation with multiplicative and additive noises the exact expressions of mles are given for the two cases that the two types of noises are uncorrelated and mutually correlated it is shown that the mles for these two gcps are free from divergence even in the parameter region wherein the ordinary moments diverge the mle relations can be regarded as a generalized fluctuation dissipation theorem for the present langevin equation availability of them and of some other higher order statistics is demonstrated theoretically and numerically

the interacting gaps model reconciling theoretical and numerical approaches to limit order models we consider the emergence of power law tails in the returns distribution of limit order driven markets we explain a previously observed clash between the theoretical and numerical studies of such models we introduce a solvable model that interpolates between the previous studies and agrees with each of them in the relevant limit c

a reactive lattice gas approach to economic cycles abstract a microscopic approach to macroeconomic features is intended a model for macroeconomic behavior under heterogeneous spatial economic conditions is reviewed a birth death lattice gas model taking into account the influence of an economic environment on the fitness and concentration evolution of economic entities is numerically and analytically examined the reaction diffusion model can also be mapped onto a high order logistic map the role of the selection pressure along various dynamics with entity diffusion on a square symmetry lattice has been studied by monte carlo simulation the model leads to a sort of phase transition for the fitness gap as a function of the selection pressure and to cycles the control parameter is a scalar business plan the business plan s allows for spin offs or merging and enterprise survival evolution law s whence bifurcations cycles and chaotic behavior