hurst entropy a method to determine predictability in a binary series based on a fractal related process shannon s concept of information is related to predictability in a binary series the value of information relies on the frequency of 0 s and 1 s or how it is expected to occur however information entropy does not consider the bias in randomness related to autocorrelation in fact it is possible for a binary temporal series to carry both short and long term memories related to the sequential distribution of 0 s and 1 s although the hurst exponent measures the range of autocorrelation there is a lack of mathematical connection between information entropy and autocorrelation present in the series to fill this important gap we combined numerical simulations and an analytical approach to determine how information entropy changes according to the frequency of 0 s and 1 s and the hurst exponent indeed we were able to determine how predictability depends on both parameters our findings are certainly useful to several fields when binary times series are applied such as neuroscience to econophysics

on special bessel periods and the gross prasad conjecture for mathrm so 2n 1 times mathrm so 2 in this paper we investigate one instance of the global gross prasad conjecture our main result proves that if an irreducible cuspidal automorphic representation pi of an odd dimensional special orthogonal group whose local component pi w at some finite place w is generic admits the special bessel model corresponding to a quadratic extension e over a base field f then the central l value l 1 2 pi l 1 2 pi times chi e does not vanish here chi e denotes the quadratic character of mathbb a f times corresponding to e as an application we obtain the equivalence between the non vanishing of the special bessel period and that of the corresponding central l value when pi is associated to a full modular holomorphic siegel cusp form of degree two which is a hecke eigenform and e is an imaginary quadratic extension of mathbb q

can one make any crash prediction in finance using the local hurst exponent idea abstract we apply the hurst exponent idea for investigation of djia index time series data the behavior of the local hurst exponent prior to drastic changes in financial series signal is analyzed the optimal length of the time window over which this exponent can be calculated in order to make some meaningful predictions is discussed our prediction hypothesis is verified with examples of 1929 and 1987 crashes as well as with more recent phenomena in stock market from the period 1995 to 2003 some interesting agreements are found

output of a neuronal population code in the population coding framework we consider how the response distributions affect output distribution a general theory for the output of neuronal population code is presented when the spike train is a renewal process under a given condition on the response distribution the most probable value of the output distribution is the center of input preferred values whereas in the other cases the most improbable value of the output distribution is the center of input preferred values or there are no most probable states depending on the exact form of the response distributions the variance of the output distributions can either enlarge or reduce the tuning width of the tuning curves

on the langlands functoriality for automorphic forms this is the extended notes of my lcctures on the langlands functoriality of automorphic forms which are in particular on the topics closely related to my recent work

depth zero supercuspidal l packets for inner forms of gsp4 abstract we show that for any tame regular discrete series parameter of g s p 4 or its inner form g u 2 d the l packet attached by the local langlands conjecture gan and takeda 2011 14 gan and tantono submitted for publication 15 agrees with the l packet of depth zero supercuspidal representations constructed by debacker and reeder 2009 12

on the genericity of cuspidal automorphic forms of so2n 1 this is a sequel of our work js06 we extend moeglin s results m97a and m97b from the even orthogonal groups to old orthogonal groups and complete our proof of the cap conjecture for irreducible cuspidal automoprhic representations of so2n 1 a with special bessel models we also give characterization of the vanishing of the central value of the standard l function of so2n 1 a in terms of theta correspondence as result we obtain the weak langlands functorial transfer from so2n 1 a to gl2n a for irreducible cuspidal automoprhic representations of so2n 1 a with special bessel models

markov properties in presence of measurement noise recently several powerful tools for the reconstruction of stochastic differential equations from measured data sets have been proposed e g siegert et al phys lett a 243 275 1998 hurn et al j time series anal 24 45 2003 efficient application of the methods however generally requires markov properties to be fulfilled this constraint typically seems to be violated on small scales which frequently is attributed to physical effects on the other hand measurement noise such as uncorrelated measurement and discretization errors has large impacts on the statistics of measurements on small scales we demonstrate that the presence of measurement noise likewise spoils markov properties of an underlying markov process this fact is promising for the further development of techniques for the reconstruction of stochastic processes from measured data since limitations at small scales might stem from artificial noise sources rather than from intrinsic properties of the dynamics of the underlying process measurement noise however can be controlled much better than the intrinsic dynamics of the underlying process

geometric and projection effects in kramers moyal analysis kramers moyal coefficients provide a simple and easily visualized method with which to analyze nonlinear stochastic time series one mechanism that can affect the estimation of the coefficients is geometric projection effects for some biologically inspired examples these effects are predicted and explored with a nonstochastic projection operator method and compared with direct numerical simulation of the systems langevin equations general features and characteristics are identified and the utility of the kramers moyal method is discussed projections of a system are in general non markovian but here the kramers moyal method remains useful and in any case the primary examples considered are found to be close to markovian

characterizing time series via complexity entropy curves the search for patterns in time series is a very common task when dealing with complex systems this is usually accomplished by employing a complexity measure such as entropies and fractal dimensions however such measures usually only capture a single aspect of the system dynamics here we propose a family of complexity measures for time series based on a generalization of the complexity entropy causality plane by replacing the shannon entropy by a monoparametric entropy tsallis q entropy and after considering the proper generalization of the statistical complexity q complexity we build up a parametric curve the q complexity entropy curve that is used for characterizing and classifying time series based on simple exact results and numerical simulations of stochastic processes we show that these curves can distinguish among different long range short range and oscillating correlated behaviors also we verify that simulated chaotic and stochastic time series can be distinguished based on whether these curves are open or closed we further test this technique in experimental scenarios related to chaotic laser intensity stock price sunspot and geomagnetic dynamics confirming its usefulness finally we prove that these curves enhance the automatic classification of time series with long range correlations and interbeat intervals of healthy subjects and patients with heart disease

how random is your heart beat we measure the content of random uncorrelated noise in heart rate variability using a general method of noise level estimation using a coarse grained entropy we show that usually except for atrial fibrillation the level of such noise is within 5 15 of the variance of the data and that the variability due to the linearly correlated processes is dominant in all cases analyzed but atrial fibrillation the nonlinear deterministic content of heart rate variability remains significant and may not be ignored

the local converse theorem for so 2n 1 and applications in this paper we characterize irreducible generic representations of so 2n 1 k where k is a p adic field by means of twisted local gamma factors the local converse theorem as applications we prove that two irreducible generic cuspidal automorphic representations of so 2n 1 a where a is the ring of adeles of a number field are equivalent if their local components are equivalent at almost all local places the rigidity theorem and prove the local langlands reciprocity conjecture for generic supercuspidal representations of so 2n 1 k

relating invariant linear form and local epsilon factors via global methods we use the recent proof of jacquet s conjecture due to harris and kudla hk and the burger sarnak principle see bs to give a proof of the relationship between the existence of trilinear forms on representations of gl 2 k u for a non archimedean local field k u and local epsilon factors which was earlier proved only in the odd residue characteristic by this author in p1 theorem 1 4 the method used is very flexible and gives a global proof of a theorem of saito and tunnell about characters of gl 2 using a theorem of waldspurger w theorem 2 about period integrals for gl 2 and also an extension of the theorem of saito and tunnell by this author in p3 theorem 1 2 which was earlier proved only in odd residue characteristic in the appendix to this article h saito gives a local proof of lemma 4 which plays an important role in the article

on the local converse theorem and the descent theorem in families in this paper we prove an analogue of jacquet s conjecture on the local converse theorem for ell adic families of co whittaker representations of mathrm gl n f where f is a finite extension of mathbb q p and ell ne p we also prove an analogue of jacquet s conjecture for a descent theorem which asks for the smallest collection of gamma factors determining the subring of definition of an ell adic family these two theorems are closely related to the local langlands correspondence in ell adic families

stochastic heart rate model can reveal pathologic cardiac dynamics a simple one dimensional langevin type stochastic difference equation can simulate the heart rate fluctuations in a time scale from minutes to hours the model consists of a deterministic nonlinear part and a stochastic part typical of gaussian noise and both parts can be directly determined from measured heart rate data data from healthy subjects typically exhibit the deterministic part with two or more stable fixed points studies of 15 congestive heart failure subjects reveal that the deterministic part of pathologic heart dynamics has no clear stable fixed points direct simulations of the stochastic model for normal and pathologic cases can produce statistical parameters similar to those of real subjects results directly indicate that pathologic situations simplify the heart rate control system

permutation entropy and detrend fluctuation analysis for the natural complexity of cardiac heart interbeat signals abstract we compute fractal dimension and permutation entropy for healthy and people who have experienced heart failure our result shows that permutation entropy is a suitable approach as well as detrend fluctuation analysis dfa the result of dfa shows that the fractal dimensions for healthy and heart failure are different as well as the permutation entropy result the fluctuation value for permutation entropy for an individual who has experienced heart failure is bigger than for a healthy person there is some specific change in the interbeat signal of a person who has experienced heart failure but there is not previous trend for a healthy person

financial time series modeling using the hurst exponent abstract this study aims to enhance the understanding of logarithmic asset returns in particular more emphasis is given to the long memory property of financial returns a well documented stylized fact however in the presence of structural breaks other studies suggest that statistical tools such as the autocorrelation function acf can wrongly indicate long memory we propose an insensitive to structural breaks method to test for dependence between distant observations furthermore a model which combines memory in returns and memory in absolute returns is developed in two stages first return series are segmented with respect to changes in the volatility and then the two parameters of the model are estimated to assess the capabilities of the model historical prices of the standard and poor 500 index s p500 financial time stocks exchange 100 index ftse100 deutsche boerse ag german stock index dax and crude oil are used 1 given the estimated parameters and the volatility within each regime 10000 vectors are generated and compared to the original data in terms of the kolmogorov smirnov k s statistical test the obtained results suggest that long memory is present and provide evidence that the additional memory information captured by the model improves financial returns modeling

time dependent hurst exponent in financial time series abstract we calculate the hurst exponent h t of several time series by dynamical implementation of a recently proposed scaling technique the detrending moving average dma in order to assess the accuracy of the technique we calculate the exponent h t for artificial series simulating monofractal brownian paths with assigned hurst exponents h we next calculate the exponent h t for the return of high frequency tick by tick sampled every minute series of the german market we find a much more pronounced time variability in the local scaling exponent of financial series compared to the artificial ones the dma algorithm allows the calculation of the exponent h t without any a priori assumption on the stochastic process and on the probability distribution function of the random variables as happens for example in the case of the kitagawa grid and the extended kalmann filtering methods the present technique examines the local scaling exponent h t around a given instant of time this is a significant advance with respect to the standard wavelet transform or to the higher order power spectrum technique which instead operate on the global properties of the series by legendre or fourier transform of qth order moments

spike output jitter mean firing time and coefficient of variation to understand how a single neurone processes information it is critical to examine the relationship between input and output marsalek koch and maunsell s study focused on output jitter standard deviation of output interpike interval found that for the integrate and fire if whereas an input distribution with a more slowly decreasing tail induces divergence of output jitter exact formulae for mean firing time are also obtained which enable us to estimate the coefficient of variation the i f model with leakage is also briefly considered

moment analysis of the hodgkin huxley system with additive noise abstract we consider a classical space clamped hodgkin huxley hh model neuron stimulated by a current which has a mean together with additive gaussian white noise of amplitude a system of 14 deterministic first order nonlinear differential equations is derived for the first and second order moments means variances and covariances of the voltage v and the subsidiary variables n m and h the system of equations is integrated numerically with a fourth order runge kutta method as long as the variances as determined by these deterministic equations remain small the latter accurately approximate the first and second order moments of the stochastic hodgkin huxley system describing spiking neurons on the other hand for certain values of when rhythmic spiking is inhibited by larger amplitude noise the solutions of the moment equation strongly overestimate the moments of the voltage a more refined analysis of the nature of such irregularities leads to precise insights about the effects of noise on the hodgkin huxley system for suitable values of which enable rhythmic spiking we analyze by numerical examples from both simulation and solutions of the moment equations the three factors which tend to promote its cessation namely the increasing variance the nature and shape of the basins of attraction of the limit cycle and stable equilibrium point and the speed of the process

compatible systems of symplectic galois representations and the inverse galois problem iii automorphic construction of compatible systems with suitable local properties this article is the third and last part of a series of three articles about compatible systems of symplectic galois representations and applications to the inverse galois problem this part proves the following new result for the inverse galois problem for symplectic groups for any even positive integer n and any positive integer d mathrm psp n mathbb f ell d or mathrm pgsp n mathbb f ell d occurs as a galois group over the rational numbers for a positive density set of primes ell the result depends on some work of arthur s which is conditional but expected to become unconditional soon the result is obtained by showing the existence of a regular algebraic self dual cuspidal automorphic representation of hbox gl n mathbb a mathbb q with local types chosen so as to obtain a compatible system of galois representations to which the results from part ii of this series apply

statistical properties of the volatility of price fluctuations we study the statistical properties of volatility measured by locally averaging over a time window t the absolute value of price changes over a short time interval ensuremath delta t we analyze the s 500 stock index for the 13 year period jan 1984 to dec 1996 we find that the cumulative distribution of the volatility is consistent with a power law asymptotic behavior characterized by an exponent ensuremath mu ensuremath approx 3 similar to what is found for the distribution of price changes the volatility distribution retains the same functional form for a range of values of t further we study the volatility correlations by using the power spectrum analysis both methods support a power law decay of the correlation function and give consistent estimates of the relevant scaling exponents also both methods show the presence of a crossover at approximately 1 5 days in addition we extend these results to the volatility of individual companies by analyzing a data base comprising all trades for the largest 500 u s companies over the two year period jan 1994 to dec 1995

impact of correlated inputs on the output of the integrate and fire model for the integrate and fire model with or without reversal potentials we consider how correlated inputs affect the variability of cellular output for both models the variability of efferent spike trains measured by coefficient of variation cv of the interspike interval is a nondecreasing function of input correlation when the correlation coefficient is greater than 0 09 the cv of the integrate and fire model without reversal potentials is always above 0 5 no matter how strong the inhibitory inputs when the correlation coefficient is greater than 0 05 cv for the integrateand fire model with reversal potentials is always above 0 5 independent of the strength of the inhibitory inputs under a given condition on correlation coefficients we find that correlated poisson processes can be decomposed into independent poisson processes we also develop a novel method to estimate the distribution density of the first passage time of the integrate and fire model

stochastic order parameter equation of isometric force production revealed by drift diffusion estimates we address two questions that are central to understanding human motor control variability what kind of dynamical components contribute to motor control variability i e deterministic and or random ones and how are those components structured to this end we derive a stochastic order parameter equation for isometric force production from experimental data using drift diffusion estimates we show that the force variability increases with the required force output because of a decrease of deterministic stability and an accompanying increase of noise intensity a structural analysis reveals that the deterministic component consists of a linear control loop while the random component involves a noise source that scales with force output in addition we present evidence for the existence of a subject independent overall noise level of human isometric force production

lifting of generic depth zero representations of classical groups abstract we describe how generic depth zero supercuspidal representations of classical groups lift to a general linear group the main tool is a computation of reducibility points of certain parabolically induced representations

mutual information identifies spurious hurst phenomena in resting state eeg and fmri data long range memory in time series is often quantified by the hurst exponent h a measure of the signal s variance across several time scales we analyze neurophysiological time series from electroencephalography eeg and functional magnetic resonance imaging fmri resting state experiments with two standard hurst exponent estimators and with the time lagged mutual information function applied to discretized versions of the signals a confidence interval for the mutual information function is obtained from surrogate markov processes with equilibrium distribution and transition matrix identical to the underlying signal for eeg signals we construct an additional mutual information confidence interval from a short range correlated tenth order autoregressive model we reproduce the previously described hurst phenomenon h 0 5 in the analytical amplitude of alpha frequency band oscillations in eeg microstate sequences and in fmri signals but we show that the hurst phenomenon occurs without long range memory in the information theoretical sense we find that the mutual information function of neurophysiological data behaves differently from fractional gaussian noise fgn for which the hurst phenomenon is a sufficient condition to prove long range memory two other well characterized short range correlated stochastic processes ornstein uhlenbeck cox ingersoll ross also yield h 0 5 whereas their mutual information functions lie within the markovian confidence intervals similar to neural signals in these processes which do not have long range memory by construction a spurious hurst phenomenon occurs due to slow relaxation times and heteroscedasticity time varying conditional variance in summary we find that mutual information correctly distinguishes long range from short range dependence in the theoretical and experimental cases discussed our results also suggest that the stationary fgn process is not sufficient to describe neural data which seem to belong to a more general class of stochastic processes in which multiscale variance effects produce hurst phenomena without long range dependence in our experimental data the hurst phenomenon and long range memory appear as different system properties that should be estimated and interpreted independently

varieties of long memory models long memory is defined as a series having a slowly declining correlogram or equivalently an infinite spectrum at zero frequency fractional integrated processes have such properties but here it is pointed out that a number of other processes can also be long memory including generalized fractionally integrated models arising from aggregation time changing coefficient models and possibly nonlinear models it seems that there are many classes of processes that deserve further study the relevance of long memory is illustrated using absolute returns from a daily stock market index

kramers moyal coefficients in the analysis and modeling of heart rate variability modeling of recorded time series may be used as a method of analysis for heart rate variability studies in particular the extraction of the first two kramers moyal coefficients has been used in this context recently the method was applied to a wide range of signal analysis from financial data to physiological and biological time series modeling of the signal is important for the prediction and interpretation of the dynamics underlying the process the method requires the determination of the markov time obtaining the drift and diffusion term of the kramers moyal expansion is crucial for the modeling of the original time series with the langevin equation both tabar comput sci eng 8 54 2006 and t kuusela phys rev e 69 031916 2004 suggested that these terms may be used to distinguish healthy subjects from those with heart failure the research groups applied a somewhat different methodology and obtained substantially different ranges of the markov time we show that the two studies may be considered consistent with each other as kuusela analyzed 24 h recordings while tabar analyzed daytime and nighttime recordings separately however both groups suggested using the langevin equation for modeling of time series which requires the fluctuation force to be a gaussian we analyzed heart rate variability recordings for ten young male age 26 4 3 y healthy subjects 24 h recordings were analyzed and 6 h long daytime and nighttime fragments were selected similar properties of the data were observed in all recordings but all the nighttime data and seven of the ten 24 h series exhibited higher order non negligible kramers moyal coefficients in such a case the reconstruction of the time series using the langevin equation is impossible the non negligible higher order coefficients are due to autocorrelation in the data this effect may be interpreted as a result of a physiological phenomenon especially occurring for nighttime data respiratory sinus arrhythmia rsa we detrended the nighttime recordings for the healthy subjects and obtained an asymmetry in the dependence of the diffusion term on the rescaled heart rate this asymmetry seems to be an effect of different time scales during the inspiration and the expiration phase of breathing the asymmetry was significantly decreased in the diffusion term found for detrended nighttime recordings obtained from five hypertrophic cardiomyopathy hcm patients we conclude that the effect of rsa is decreased in the heart rate variability of hcm patients a result which may contribute to a better medical diagnosis by supplying a new quantitative measure of rsa

dynamics of moment neuronal networks a theoretical framework is developed for moment neuronal networks mnns within this framework the behavior of the system of spiking neurons is specified in terms of the first and second order statistics of their interspike intervals i e the mean the variance and the cross correlations of spike activity since neurons emit and receive spike trains which can be described by renewal but generally non poisson processes we first derive a suitable diffusion type approximation of such processes two approximation schemes are introduced the usual approximation scheme uas and the ornstein uhlenbeck scheme it is found that both schemes approximate well the input output characteristics of spiking models such as the if and the hodgkin huxley models the mnn framework is then developed according to the uas scheme and its predictions are tested on a few examples

scaling and universality in animate and inanimate systems we illustrate the general principle that in biophysics econophysics and possibly even city growth the conceptual framework provided by scaling and universality may be of use in making sense of complex statistical data specifically we discuss recent work on dna sequences heartbeat intervals avalanche like lung inflation urban growth and company growth although our main focus is on data we also discuss statistical mechanical models

behaviors of spike output jitter in the integrate and fire model we consider behaviors of output jitter in the simplest spiking model the integrate and fire model the full spectrum of behaviors is found the output jitter is sensitive to the input distribution and can be a constant diverge to infinity or converge to zero exact formulas for the convergence or the divergence of output jitter are given our results suggest that the exponential distribution is the critical case a faster rate of decrease in the distribution tail as compared to the exponential distribution tail ensures the convergence of output jitter whereas slower decay in the distribution tail causes the divergence of output jitter

a proof of the finite field analogue of jacquet s conjecture in this paper the proof of the finite field analogue of jacquet s conjecture on local converse theorem for cuspidal representations of general linear groups is given more precisely the set of twisted gamma factors of pi big gamma pi times tau psi mid tau in scr g t 1 le t le big n over 2 big big together with a central character omega pi determine uniquely up to isomorphism the irreducible cuspidal representation pi of rm gl n bbb f q where cal g t denotes the set of irreducible generic representations of rm gl t bbb f q and bbb f q denotes a finite field of q elements

improved estimation of fokker planck equations through optimization an improved method for the description of hierarchical complex systems by means of a fokker planck equation is presented in particular the limited memory broyden fletcher goldfarb shanno algorithm for constraint problems is used to minimize the distance between the numerical solutions of the fokker planck equation and the empirical probability density functions and thus to estimate properly the drift and diffusion term of the fokker planck equation the optimization routine is applied to a time series of velocity measurements obtained from a turbulent helium gas jet in order to demonstrate the benefits and to quantify the improvements of this optimization routine

estimation of drift and diffusion functions from time series data a maximum likelihood framework complex systems are characterized by a huge number of degrees of freedom often interacting in a nonlinear manner in many cases macroscopic states however can be characterized by a small number of order parameters that obey stochastic dynamics in time recently techniques for the estimation of the corresponding stochastic differential equations from measured data have been introduced this paper develops a framework for the estimation of the functions and their respective bayesian posterior confidence regions based on likelihood estimators in succession approximations are introduced that significantly improve the efficiency of the estimation procedure while being consistent with standard approaches to the problem this paper solves important problems concerning the applicability and the accuracy of estimated parameters

stochastic time series with strong correlated measurement noise markov analysis in n dimensions an extension and generalization of a recently presented approach for the analysis of langevin type stochastic processes in the presence of strong measurement noise is presented for a stochastic process in n dimensions which is superimposed with strong exponentially correlated gaussian distributed measurement noise it is possible to extract the strength and the correlation functions of the noise as well as polynomial approximations of the drift and diffusion functions of the underlying process

model transition under local theta correspondence abstract we study model transition for representations occurring in the local theta correspondence between split even special orthogonal groups and symplectic groups over a non archimedean local field of characteristic zero

on the nonvanishing of the central value of the rankin selberg l functions first published in journal of the american mathematical society in volume 17 issue 3 published by the american mathematical society

behavior of integrate and fire and hodgkin huxley models with correlated inputs we assess both numerically and theoretically how positively correlated poisson inputs affect the output of the integrate and fire and hodgkin huxley models for the integrate and fire model the variability of efferent spike trains is an increasing function of input correlation and of the ratio between inhibitory and excitatory inputs interestingly for the hodgkin huxley model the variability of efferent spike trains is a decreasing function of input correlation and for fixed input correlation it is almost independent of the ratio between inhibitory and excitatory inputs in terms of the signal to noise ratio of efferent spike trains the integrate and fire model works better in an environment of asynchronous inputs but the hodgkin huxley model has an advantage for more synchronous correlated inputs in conclusion the integrate and fire and hodgkin huxley models respond to correlated inputs in totally opposite ways

multi affine model for the velocity distribution in fully turbulent flows a simple multi affine model for the velocity distribution in fully developed turbulent flows is introduced to capture the essential features of the underlying geometry of the velocity field the authors show that in this model the various relevant quantities characterizing different aspects of turbulence can be readily calculated a simultaneous good agreement is found with the available experimental data for the velocity structure functions the dq spectra obtained from studies of the velocity derivatives and the exponent describing the scaling of the spectrum of the kinetic energy fluctuations their results are obtained analytically assuming a single free parameter the fractal dimension of the region where the dominating contribution to dissipation comes from is estimated to be d approximately 2 88

nonstationary langevin equation statistical properties and application to explain effects observed in cardiological time series using the langevin equation we develop the model of a stochastic process subject to a given time dependent regulatory mechanism the effects of this nonstationarity on the statistical properties of the time series i e on global and conditional probability densities and on the moments of the distribution are derived application of these results on simple model trends allows one to approximate cardiological data and thus to explain effects recently observed in the reconstruction of the deterministic part of the langevin equation for time series of heart rate

a langevin equation for the rates of currency exchange based on the markov analysis we propose a method for analyzing the data for the rates of exchange of various currencies versus the u s dollar the method analyzes the return time series of the data as a markov process and develops an effective equation which reconstructs it we find that the markov time scale i e the time scale over which the data are markov correlated is one day for the majority of the daily exchange rates that we analyze we derive an effective langevin equation to describe the fluctuations in the rates the equation contains two quantities d 1 and d 2 representing the drift and diffusion coefficients respectively we demonstrate how the two coefficients are estimated directly from the data without using any assumptions or models for the underlying stochastic time series that represent the daily rates of exchange of various currencies versus the u s dollar r 2007 elsevier b v all rights reserved

coherent and random sequences in financial fluctuations abstract the detrended fluctuation analysis dfa is used to sort out temporal correlations in financial data its usefulness for the investigations of long range power law correlations in economic sequences is shown our findings of persistent and antipersistent sequences are suprisingly similar to those for dna sequences which appeared as a mosaic of coding and non coding patches

self dual representations of division algebras and weil groups a contrast irreducible selfdual representations of any group fall into two classes those which carry a symmetric bilinear form and the others which carry an alternating bilinear form the langlands correspondence which matches the irreducible representations of the weil group of a local field k of dimension n with the irreducible representations of the invertible elements of a division algebra d over k of index n takes selfdual representations to selfdual representations in this paper we use global methods to study how the langlands correspondence behaves relative to this distinction among selfdual representations we prove in particular that for n even is symplectic if and only if is orthogonal more generally we treat the case of gl m b for b a division algebra over k of index r and n mr

integrate and fire and hodgkin huxley models with current inputs for the integrate and fire model and the hodgkin huxley model we consider how current inputs including wave and square wave affect their outputs firstly the usual approximation is employed to approximate the models with current inputs which quantitatively reveals the difference between instantaneous and noninstantaneous current inputs when the rising time of wave inputs is long or the ratio between the inhibitory and excitatory inputs is close to one the usual approximation fails to approximate the wave inputs in the integrate and fire model for the hodgkin huxley model the usual approximation in general gives an unsatisfying approximation a novel approach based upon a superposition of coloured and white noise is then proposed to replace the usual approximation numerical results show that the novel approach substantially improves the approximation within widely physiologically reasonable regions of the rising time of wave inputs

stochastic model for heart rate fluctuations a normal human heart rate shows complex fluctuations in time which is natural because the heart rate is controlled by a large number of different feedback control loops these unpredictable fluctuations have been shown to display fractal dynamics long term correlations and 1 f noise these characterizations are statistical and they have been widely studied and used but much less is known about the detailed time evolution dynamics of the heart rate control mechanism here we show that a simple one dimensional langevin type stochastic difference equation can accurately model the heart rate fluctuations in a time scale from minutes to hours the model consists of a deterministic nonlinear part and a stochastic part typical to gaussian noise and both parts can be directly determined from the measured heart rate data studies of 27 healthy subjects reveal that in most cases the deterministic part has a form typically seen in bistable systems there are two stable fixed points and one unstable one

analysis of time series from stochastic processes analysis of time series from stochastic processes governed by a langevin equation is discussed several applications for the analysis are proposed based on estimates of drift and diffusion coefficients of the fokker planck equation the coefficients are estimated directly from a time series the applications are illustrated by examples employing various synthetic time series and experimental time series from metal cutting

applications of statistical physics to economic and financial topics abstract problems in economy and finance have started to attract the interest of statistical physicists fundamental problems pertain to the existence or not of long medium short range power law correlations in economic systems as well as to the presence of financial cycles methods like the extended detrended fluctuation analysis and the multi affine analysis are recalled emphasizing their value in sorting out correlation ranges and predictability among spectacular results the possibility of crash predictions is indicated the well known financial analyst technique the so called moving average is shown to raise questions about fractional brownian motion properties finally the m k zipf method and the i variability diagram technique are presented for sorting out short range correlations analogies with other fields of modern applied statistical physics are also presented in view of some universal openess

theta distinguished representations inflation and the symmetric square l function a theta distinguished representation is a quotient of a tensor of exceptional representations where exceptional is in the sense of kazhdan and patterson we study relations between theta distinguished representations of mathrm gl n and mathrm gspin 2n 1 in the case of mathrm gspin 2n 1 or mathrm so 2n 1 exceptional or small representations were constructed by bump friedberg and ginzburg we prove a rodier type hereditary property a tempered representation tau is distinguished if and only if the representation mathrm i tau induced to mathrm gspin 2n 1 is distinguished and the multiplicity of both quotients is at most one if tau is supercuspidal and distinguished then so is the langlands quotient of mathrm i tau as a corollary we characterize supercuspidal distinguished representations in terms of the pole of the symmetric square l function at s 0

minimum memory for generating rare events we classify the rare events of structured memoryful stochastic processes and use this to analyze sequential and parallel generators for these events given a stochastic process we introduce a method to construct a process whose typical realizations are a given process rare events this leads to an expression for the minimum memory required to generate rare events we then show that the recently discovered classical quantum ambiguity of simplicity also occurs when comparing the structure of process fluctuations