absence of absolutely continuous spectrum of floquet operators the spectrum of the floquet operator associated with time periodic perturbations of discrete hamiltonians is considered if the gap between successive eigenvalues j of the unperturbed hamiltonian grows as j j 1 j and the multiplicity of j grows asj with 0 asj tends to infinity then the corresponding floquet operator possesses no absolutely continuous spectrum provided the perturbation is smooth enough

eigenvalues for infinite matrices this paper is concerned with the problem of determining the location of eigenvalues for diagonally dominant infinite matrices upper and lower bounds for eigenvalues are established for tridiagonal matrices a numerical procedure for improving the bounds is given and the approximation of the eigenvectors is also discussed the techniques are illustrated for the solution of the well known mathieu s equation

perturbation of an eigenvalue from a dense point spectrum an example we study an example of a perturbed floquet hamiltonian depending on a coupling constant the spectrum is pure point and dense we pick up an eigenvalue namely and show the existence of a function defined on such that for all 0 is a point of density for the set i and the rayleigh schrodinger perturbation series represents an asymptotic series for the function all ideas are developed and demonstrated when treating the explicit example but some of them are expected to have an essentially wider range of application

phase correlation of foreign exchange time series abstract correlation of foreign exchange rates in currency markets is investigated based on the empirical data of usd dem and usd jpy exchange rates for a period from february 1 1986 to december 31 1996 the return of exchange time series is first decomposed into a number of intrinsic mode functions imfs by the empirical mode decomposition method the instantaneous phases of the resultant imfs calculated by the hilbert transform are then used to characterize the behaviors of pricing transmissions and the correlation is probed by measuring the phase differences between two imfs in the same order from the distribution of phase differences our results show explicitly that the correlations are stronger in daily time scale than in longer time scales the demonstration for the correlations in periods of 1986 1989 and 1990 1993 indicates two exchange rates in the former period were more correlated than in the latter period the result is consistent with the observations from the cross correlation calculation

dynamics of competition between collectivity and noise in the stock market abstract detailed study of the financial empirical correlation matrix of the 30 companies which deutsche aktienindex dax comprised during the period of the last 11 years using the time window of 30 trading days is presented this allows clear identification of a nontrivial time dependence of the resulting correlations in addition as a rule the drawdowns are always accompanied by a sizable separation of one strong collective eigenstate of the correlation matrix which at the same time reduces the variance of the noise states the opposite applies to drawups in this case the dynamics spreads more uniformly over the eigenstates which results in an increase of the total information entropy analogous study of the market corresponding to daw jones industrial average djia leads to similar conclusions in the latter case however the correlations are weaker on average one possible reason for this effect is that the market represented by djia is less susceptible to various external factors than the one represented by dax

test of equal gamma distribution means with unknown and unequal shape parameters an approximate f test is provided for testing the equality of means for two gamma distributions when the shape parameters may be unknown and unequal the corresponding confidence intervals associated with this test provide confidence intervals for the ratio of means when the shape parameters are unknown and unequal the approximation is studied by monte carlo simulation and asymptotic results are also derived an approximate f test for equal shape parameters is also studied

scaling and memory in volatility return intervals in financial markets abstract for both stock and currency markets we study the return intervals between the daily volatilities of the price changes that are above a certain threshold q we find that the distribution function pq scales with the mean return interval as the scaling function f x is similar in form for all seven stocks and for all seven currency databases analyzed and f x is consistent with a power law form f x x with 2 we also quantify how the conditional distribution pq 0 depends on the previous return interval 0 and find that small or large return intervals are more likely to be followed by small or large return intervals this clustering of the volatility return intervals is a previously unrecognized phenomenon that we relate to the long term correlations known to be present in the volatility econophysics fluctuations extreme values long term correlations long term memory

noise dressing of financial correlation matrices we show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of multivariate time series the central result of the present study which focuses on the case of financial price fluctuations is the remarkable agreement between the theoretical prediction based on the assumption that the correlation matrix is random and empirical data concerning the density of eigenvalues associated to the time series of the different stocks of the s 500 or other major markets in particular the present study raises serious doubts on the blind use of empirical correlation matrices for risk management

distributions of singular values for some random matrices the singular value decomposition is a matrix decomposition technique widely used in the analysis of multivariate data such as complex space time images obtained in both physical and biological systems in this paper we examine the distribution of singular values of low rank matrices corrupted by additive noise past studies have been limited to uniform uncorrelated noise using diagrammatic and saddle point integration techniques we extend these results to heterogeneous and correlated noise sources we also provide perturbative estimates of error bars on the reconstructed low rank matrix obtained by truncating a singular value decomposition 1999 the american physical society

gevrey formal power series of wannier stark ladders we consider time independent schr odinger equations in one dimension with both periodic and stark potentials by means of an iterative procedure we obtain a formal power series for the wannier stark ladders in the case of strongly singular periodic potentials we prove that such a formal power series is of gevrey type

floquet spectrum for two level systems in quasiperiodic time dependent fields we study the time evolution ofn level quantum systems under quasiperiodic time dependent perturbations the problem is formulated in terms of the spectral properties of a quasienergy operator defined in an enlarged hilbert space or equivalently of a generalized floquet operator we discuss criteria for the appearance of pure point as well as continuous spectrum corresponding respectively to stable quasiperiodic dynamics and to unstable chaotic behavior we discuss two types of mechanisms that lead to instability the first one is due to near resonances while the second one is of topological nature and can be present for arbitrary ratios between the frequencies of the perturbation we treat explicitly an example of this type the stability of the pure point spectrum under small perturbations is proven using kam techniques

asymmetrical singularities in real world signals we generalize the wavelet transform modulus maxima approach in order to analyze positive and negative changes separately and show different singularity spectra depending on the direction of changes in i human heartbeat interval data during sympathetic blockade ii time series of daytime human physical activity of healthy individuals but not of patients with debilitating fatigue and iii daily stock price records of the nikkei 225 in the period 1990 2002 but not of the s p 500 we conclude that the analysis of asymmetrical singularities provides deeper insights into the underlying complexity of real world signals that can greatly enhance our understanding of the mechanisms determining the systems dynamics

limit points of eigenvalues of truncated tridiagonal operators let t be the tridiagonal operator ten a n e n 1 a n 1 e n 1 b n e n te 1 a 1 e 2 b 1 e 1 acting on a fixed orthonormal basis e n n 1 2 of a hilbert space h let p n be the orthogonal projection on the finite dimensional space h n spanned by the elements e 1 e 2 e n and let t n be the truncated operator t n p n tp n if t has a unique self adjoint extension then the set t there exists a sequence of eigenvalues n of t n with the property n contains the spectrum t of t and examples show that in general t t for many reasons the knowledge of the equality t a t is important in this paper sufficient conditions are presented such that t t

phase distribution and phase correlation of financial time series the scaling phase distribution and phase correlation of financial time series are investigated based on the dow jones industry average and nasdaq 10 min intraday data for a period from 1 aug 1997 to 31 dec 2003 the returns of the two indices are shown to have nice scaling behaviors and belong to stable distributions according to the criterion of l evy s ensuremath alpha stable distribution condition an approach catching characteristic features of financial time series based on the concept of instantaneous phase is further proposed to study the phase distribution and correlation analysis of the phase distribution concludes that return time series fall into a class which is different from other nonstationary time series the correlation between returns of the two indices probed by the distribution of phase difference indicates that there was a remarkable change of trading activities after the event of the 9 11 attack and this change persisted in later trading activities

the characteristic function for jacobi matrices with applications abstract we introduce a class of jacobi operators with discrete spectra which is characterized by a simple convergence condition with any operator j from this class we associate a characteristic function as an analytic function on a suitable domain and show that its zero set actually coincides with the set of eigenvalues of j in that domain as an application we construct several examples of jacobi matrices for which the characteristic function can be expressed in terms of special functions in more detail we study the example where the diagonal sequence of j is linear while the neighboring parallels to the diagonal are constant

empirical mode decomposition and synchrogram approach to cardiorespiratory synchronization we use the empirical mode decomposition method to decompose experimental respiratory signals into a set of intrinsic mode functions imfs and consider one of these imfs as a respiratory rhythm we then use the hilbert spectral analysis to calculate the instantaneous phase of the imf heartbeat data are finally incorporated to construct the cardiorespiratory synchrogram which is a visual tool for inspecting synchronization we perform analysis on 20 data sets collected by the harvard medical school from ten young 21 34 years old and ten elderly 68 81 years old rigorously screened healthy subjects our results support the existence of cardiorespiratory synchronization we also investigate the origin of the cardiorespiratory synchronization by addressing the problem of correlations between regularities of respiratory and cardiac signals our analysis shows that regularity of respiratory signals plays a dominant role in the cardiorespiratory synchronization

the empirical mode decomposition and the hilbert spectrum for nonlinear and non stationary time series analysis a new method for analysing nonlinear and non stationary data has been developed the key part of the method is the empirical mode decomposition method with which any complicated data set can be dec

on the eigenvalue problem for a particular class of finite jacobi matrices abstract a function f with simple and nice algebraic properties is defined on a subset of the space of complex sequences some special functions are expressible in terms of f first of all the bessel functions of first kind a compact formula in terms of the function f is given for the determinant of a jacobi matrix further we focus on the particular class of jacobi matrices of odd dimension whose parallels to the diagonal are constant and whose diagonal depends linearly on the index a formula is derived for the characteristic function yet another formula is presented in which the characteristic function is expressed in terms of the function f in a simple and compact manner a special basis is constructed in which the jacobi matrix becomes a sum of a diagonal matrix and a rank one matrix operator a vector valued function on the complex plain is constructed having the property that its values on spectral points of the jacobi matrix are equal to corresponding eigenvectors

on the common zeros of bessel functions using a functional analytic method we give some results concerning common zeros of the ordinary bessel functions j z of first kind with respect to and fixed z a lower bound for the common zero z of the bessel functions j z j z where are known is also given

universal and nonuniversal properties of cross correlations in financial time series we use methods of random matrix theory to analyze the cross correlation matrix c of stock price changes of the largest 1000 u s companies for the 2 year period 1994 1995 we find that the statistics of most of the eigenvalues in the spectrum of c agree with the predictions of random matrix theory but there are deviations for a few of the largest eigenvalues we find that c has the universal properties of the gaussian orthogonal ensemble of random matrices furthermore we analyze the eigenvectors of c through their inverse participation ratio and find eigenvectors with large ratios at both edges of the eigenvalue spectrum a situation reminiscent of localization theory results

exponential distribution of financial returns at mesoscopic time lags a new stylized fact we study the probability distribution of stock returns at mesoscopic time lags return horizons ranging from about an hour to about a month while at shorter microscopic time lags the distribution has power law tails for mesoscopic times the bulk of the distribution more than 99 of the probability follows an exponential law the slope of the exponential function is determined by the variance of returns which increases proportionally to the time lag at longer times the exponential law continuously evolves into gaussian distribution the exponential to gaussian crossover is well described by the analytical solution of the heston model with stochastic volatility r 2004 elsevier b v all rights reserved

model for correlations in stock markets we propose a group model for correlations in stock markets in the group model the markets are composed of several groups within which the stock price fluctuations are correlated the spectral properties of empirical correlation matrices reported recently are well understood from the model it provides the connection between the spectral properties of the empirical correlation matrix and the structure of correlations in stock markets

orthogonal polynomials associated with coulomb wave functions abstract a new class of orthogonal polynomials associated with coulomb wave functions is introduced these polynomials play a role analogous to that the lommel polynomials have in the theory of bessel functions the orthogonality measure for this new class is described in detail in addition the orthogonality measure problem is discussed on a more general level apart from this various identities derived for the new orthogonal polynomials may be viewed as generalizations of certain formulas known from the theory of bessel functions a key role in these derivations is played by a jacobi tridiagonal matrix j l whose eigenvalues coincide with the reciprocal values of the zeros of the regular coulomb wave function f l the spectral zeta function corresponding to the regular coulomb wave function or more precisely to the respective tridiagonal matrix is studied as well

statistical properties dynamic conditional correlation and scaling analysis evidence from dow jones and nasdaq high frequency data abstract this paper investigates statistical properties of high frequency intraday stock returns across various frequencies both time series and panel data are utilized to explore the properties of probability distribution dynamic conditional correlations and scaling analysis in dow jones industrial average djia and nasdaq intraday returns across 10 min 30 min 60 min 120 min and 390 min frequencies the evidence shows that both returns and volatility standard deviation increase with the increasing scaling from 10 min to 390 min intervals by fitting an ar 1 garch 1 1 model to intraday data we find that ar 1 coefficients are negative for djia returns and positive for nasdaq exhibiting a positive and negative feedback strategy in djia and nasdaq respectively the evidence also shows that these coefficients are statistically significant for either including or excluding opening returns for the 10 min and 30 min frequencies by examining the dynamic conditional correlation between the djia and the nasdaq across different frequencies a positive correlation ranging from 0 6 to 0 8 was found in addition the variance of the dynamic correlation coefficients is decreasing and appears to be stable for the 2001 2003 period finally both returns on djia and nasdaq satisfy the stable levy distributions implying that both markets can converge to equilibrium by self governing mechanism after shocks results of this work provide relevant implications for investors and policy makers

random diffusion and leverage effect in financial markets we prove that brownian market models with random diffusion coefficients provide an exact measure of the leverage effect j p bouchaud et al phys rev lett 87 228701 2001 this empirical fact asserts that past returns are anticorrelated with future diffusion coefficient several models with random diffusion have been suggested but without a quantitative study of the leverage effect our analysis lets us to fully estimate all parameters involved and allows a deeper study of correlated random diffusion models that may have practical implications for many aspects of financial markets

the eigenvalue problem for infinite compact complex symmetric matrices with application to the numerical computation of complex zeros of j0 z ij1 z and of bessel functions jm z of any real order m abstract consider computing simple eigenvalues of a given compact infinite matrix re garded as operating in the complex hilbert space l 2 by computing the eigenvalues of the truncated finite matrices and taking an obvious limit in this paper we deal with a special case where the given matrix is compact complex and symmetric but not necessarily hermitian two examples of application are studied the first is con cerned with the equation j 0 z ij 1 z 0 appearing in the analysis of the solitary wave runup on a sloping beach and the second with the zeros of the bessel function j m z of any real order m in each case the problem is reformulated as an eigenvalue problem for a compact complex symmetric tridiagonal matrix operator in l 2 whose eigenvalues are all simple a complete error analysis for the numerical solution by truncation is given based on the general theorems proved in this paper where the usefulness of the seldom used generalized rayleigh quotient is demonstrated

semi analytical karhunen loeve representation of irregular waves based on the prolate spheroidal wave functions abstract a new semi analytical approach is presented to solving the matrix eigenvalue problem or the integral equation in karhunen loeve k l representation of random data such as irregular ocean waves instead of direct numerical approach to this matrix eigenvalue problem which may suffer from the computational inaccuracy for big data a pair of integral and differential equations are considered which are related to the so called prolate spheroidal wave functions pswf first the pswf is expressed as a summation of a small number of the analytical legendre functions after substituting them into the pswf differential equation a much smaller size matrix eigenvalue problem is obtained than the direct numerical k l matrix eigenvalue problem by solving this with a minimal numerical effort the pswf and the associated eigenvalue of the pswf differential equation are obtained then the eigenvalue of the pswf integral equation is analytically expressed by the functional values of the pswf and the eigenvalues obtained in the pswf differential equation finally the analytically expressed pswfs and the eigenvalues in the pwsf integral equation are used to form the kernel matrix in the k l integral equation for the representation of exemplary wave data such as ordinary irregular waves it is found that with the same accuracy the required memory size of the present method is smaller than that of the direct numerical k l representation and the computation time of the present method is shorter than that of the semi analytical method based on the sinusoidal functions

stochastic dynamical model for stock stock correlations we propose a model of coupled random walks for stock stock correlations the walks in the model are coupled via a mechanism that the displacement price change of each walk stock is activated by the price gradients over some underlying network we assume that the network has two underlying structures describing the correlations among the stocks of the whole market and among those within individual groups respectively each with a coupling parameter controlling the degree of correlation the model provides the interpretation of the features displayed in the distribution of the eigenvalues for the correlation matrix of real market on the level of time sequences we verify that such modeling indeed gives good fitting for the market data of us stocks

non poisson intermittent events in price formation in a ising spin model of market abstract the formation of price in a financial market is modelled as a chain of ising spin with three fundamental figures of trading we investigate the time behaviour of the model and we compare the results with the real euro usd change rate by using the test of local poisson hypothesis we show that this minimal model leads to clustering and declustering in the volatility signal typical of the real market data

a comparison between several correlated stochastic volatility models abstract we compare the most common stochastic volatility models such as the ornstein uhlenbeck ou the heston and the exponential ou models we try to decide which is the most appropriate one by studying their volatility autocorrelation and leverage effect and thus outline the limitations of each model we add empirical research on market indices confirming the universality of the leverage and volatility correlations

special functions and spectrum of jacobi matrices abstract several examples of jacobi matrices with an explicitly solvable spectral problem are worked out in detail in all discussed cases the spectrum is discrete and coincides with the set of zeros of a special function moreover the components of corresponding eigenvectors are expressible in terms of special functions as well our approach is based on a recently developed formalism providing us with explicit expressions for the characteristic function and eigenvectors of jacobi matrices this is done under an assumption of a simple convergence condition on matrix entries among the treated special functions there are regular coulomb wave functions confluent hypergeometric functions q bessel functions and q confluent hypergeometric functions in addition in the case of q bessel functions we derive several useful identities

multiscale analysis of blood pressure signals we describe the multiresolution wavelet analysis of blood pressure waves in vasovagal syncope affected patients compared with those in healthy people using haar and gaussian bases a comparison between scale dependent and scale independent measures discriminating the two classes of subjects is made what emerges is a sort of equivalence between these two methodological approaches that is both methods reach the same statistical significance of separation between the two classes

quantum averaging for driven systems with resonances abstract we discuss the effects of resonances in driven quantum systems within the context of quantum averaging techniques in the floquet representation we consider in particular iterative methods of kam type and the extensions needed to take into account resonances the approach consists in separating the coupling terms into resonant and nonresonant components at a given scale of time and intensity the nonresonant part can be treated with perturbative techniques which we formulate in terms of kam type unitary transformations that are close to the identity these can be interpreted as averaging procedures with respect to the dynamics defined by effective uncoupled hamiltonians the resonant parts are treated with a different kind of unitary transfomations that are not close to the identity and are adapted to the structure of the resonances they can be interpreted as a renormalization of the uncoupled hamiltonian that yields an effective dressed hamiltonian around which a perturbation expansion can be developed the combination of these two ingredients provides a strongly improved approximation technique

waiting time distributions of the volatility in the italian mib30 index clustering or poisson functions abstract we investigate the time behaviour of the italian mib30 stock index collected every minute during two months in the period from may 17 2006 up to july 24 2006 we find short range correlations in the price returns and on the contrary a long persistent time lag and slow decay in the autocorrelation functions of volatility besides we find that the probability density functions pdfs of returns show fat tails which are well fit by the log normal model of castaing b castaing y gagne e j hopfinger physica d 46 1990 177 and a convergence toward a normal distribution for large time scales we also find that the pdfs of volatility for short time horizons fit better with a log normal distribution than with a gaussian most of these features characterize the indexes and stocks of the largest american european and asian markets we also investigate the distribution of stochastic separation between isolated strong events in the volatility signal this is interesting because this gives us a deeper understanding about the price formation process by using a test for the occurrence of local poisson hypothesis we show that the process we examined strongly departs from a poisson statistics the origin of this failure stemming from the presence of temporal clustering and of a certain amount of memory

phase transition phenomenon a compound measure analysis abstract this study investigates the well documented phenomenon of phase transition in financial markets using combined information from both return and volume changes within short time intervals we suggest a new measure for the phase transition behaviour of markets calculated as a return distribution conditional on local variance in volume imbalance and show that this measure successfully captures phase transition behaviour under various conditions we analyse the intraday trade and quote dataset from the kospi 200 index futures which includes detailed information on the original order size and the type of each initiating investor we find that among these two competing factors the submitted order size yields more explanatory power on the phenomenon of market phase transition than the investor type

c algebras and numerical linear algebra given a self adjoint operator a on a hilbert space suppose that one wishes to compute the spectrum of a numerically in practice these problems often arise in such a way that the matrix of a relative to a natural basis is sparse for example discretized second order differential operators can be represented by doubly infinite tridiagonal matrices in these cases it is easy and natural to compute the eigenvalues of large n n submatrices of the infinite operator matrix and to hope that if n is large enough then the resulting distribution of eigenvalues will give a good approximation to the spectrum of a numerical analysts call this the galerkin method while this hope is often realized in practice it often fails as well and it can fail in spectacular ways the sequence of eigenvalue distributions may not converge as n or they may converge to something that has little to do with the original operator a at another level even the meaning of convergence has not been made precise in general in this paper we determine the proper general setting in which one can expect convergence and we describe the asymptotic behavior of the n n eigenvalue distributions in all but the most pathological cases under appropriate hypotheses we establish a precise limit theorem which shows how the spectrum of a is recovered from the sequence of eigenvalues of the n n compressions in broader terms our results have led us to the conclusion that numerical problems involving infinite dimensional operators require a reformulation in terms ofc algebras indeed it is only when the single operator a is viewed as an element of an appropriate c algebra a that one can see the precise nature of the limit of the n n eigenvalue distributions the limit is associated with a tracial state on a normally a is highly noncommutative and in our main applications it is a simple c algebra having a unique tracial state we obtain precise asymptotic results for operators which represent discretized hamiltonians of one dimensional quantum systems with arbitrary continuous potentials

dynamic fluctuations of cross correlations in multi time scale abstract with the empirical mode decomposition we investigate the dynamic fluctuations of cross correlations in multi time scale in this approach the time series of price returns in financial markets is decomposed into a small number of intrinsic mode functions and the corresponding time series of phases can be obtained with the hilbert transform through the empirical mode decomposition we uncover that the cross correlations between stocks change significantly for different time scales and exhibit singular behaviors during a financial crisis with the phase correlation analysis we observe that the cross correlations between market indices vary also for different time scales dividing the total time interval into two sub intervals by the year 2007 we detect that the market indices are much more correlated after 2007

computation of multiple eigenvalues of infinite tridiagonal matrices in this paper it is first given as a necessary and sufficient condition that infinite matrices of a certain type have double eigenvalues the computation of such double eigenvalues is enabled by the newton method of two variables the three term recurrence relations obtained from its eigenvalue problem evp subsume the well known relations of a the zeros of j v z b the zeros of zj f v z hj v z c the evp of the mathieu differential equation and d the evp of the spheroidal wave equation the results of experiments are shown for the three cases a c for the computation of their double pairs

the eigenvalue problem for infinite complex symmetric tridiagonal matrices with application abstract we consider an infinite complex symmetric not necessarily hermitian tridiagonal matrix t whose diagonal elements diverge to in modulus and whose off diagonal elements are bounded we regard t as a linear operator mapping a maximal domain in the hilbert space l2 into l2 assuming the existence of t 1 we consider the problem of approximating a given simple eigenvalue of t by an eigenvalue n of tn and nth order principal submatrix of t let x x 1 x 2 t be an eigenvector corresponding to assuming xtx 0 and f n 1 x n 1 x n 0 as n we show that there exists a sequence n of tn such that n f n 1 x n 1 1 o 1 x t x 0 where fn 1 represents the n n 1 element of t application to the following problems is included a solve jv z 0 for v given z 0 and b compute the eigenvalues of the mathieu equation fortunately the existence of t 1 need not be verified for these examples since we may show that t i with taken appropriately has an inverse

a two sample test of equal gamma distribution scale parameters with unknown common shape parameter an approximate f test for the equality of two gamma distribution scale parameters given equal but unknown shape parameters is proposed and investigated the test is obtained by replacing the shape parameter by its maximum likelihood estimate monte carlo and asymptotic results show that in many cases this substitution does not seriously affect the nominal test size additionally these results can be used to modify the test to more closely achieve the desired size an example from a cloud seeding experiment is given

testing parameters of a gamma distribution for small samples the gamma distribution is relevant to numerous areas of application in the physical environmental and biological sciences the focus of this paper is on testing the shape scale and mean of the gamma distribution testing the shape parameter of the gamma distribution is relevant to failure time modeling where it can be used to determine if the failure rate is constant increasing or decreasing testing the scale parameter is also relevant to problems in survival analysis where when the shape parameter 1 the reciprocal of the scale parameter measures the hazard function finally testing the mean of the gamma distribution allows us to determine if the average concentration of an environmental contaminant is higher lower or equivalent to a health based standard in this paper we first derive new small sample based tests and then via simulation we study the type i error rate and statistical power of these tests results of these simulation studies reveal that in terms of maintaining type i error

an efficiency robust nonparametric test for scale change for data from a gamma distribution when testing whether two samples came from a common distribution against the alternative that they differ in scale the asymptotically most powerful rank test depends on the density function underlying the data in some applications it is only known that the data are from a gamma distribution with increasing hazard rate i e the value of the shape parameter k is known to be 1 if the optimum test savage 1956 for data from an exponential law k 1 is used when the true value of k is much larger a loss of power or asymptotic relative efliciency results indeed the are of the exponential scores test relative to the optimum rank test for large k is about 81 4 this article presents the maximin efficiency robust test for the gamma k 1 family that has an asymptotic efficiency of at least 95 relative to the optimum test for each member of the family the test can be calculated using standard statistical packages and is illustrated on real data

paths to globally generalized synchronization in scale free networks we apply the auxiliary system approach to study paths to globally generalized synchronization in scale free networks of identical chaotic oscillators including h enon maps logistic maps and lorentz oscillators as the coupling strength ensuremath epsilon between nodes of the network is increased transitions from partially to globally generalized synchronization and intermittent behaviors near the synchronization thresholds are found the generalized synchronization starts from the hubs of the network and then spreads throughout the whole network with the increase of ensuremath epsilon our result is useful for understanding the synchronization process in complex networks

multiresolution wavelet analysis of heartbeat intervals discriminates healthy patients from those with cardiac pathology we applied multiresolution wavelet analysis to the sequence of times between human heartbeats r ensuremath r intervals and have found a scale window between 16 and 32 heartbeat intervals over which the widths of the r ensuremath r wavelet coefficients fall into disjoint sets for normal and heart failure patients this has enabled us to correctly classify every patient in a standard data set as belonging either to the heart failure or normal group with 100 accuracy thereby providing a clinically significant measure of the presence of heart failure from the r ensuremath r intervals alone comparison is made with previous approaches which have provided only statistically significant measures

on the probable error of the ratio of two gamma means summary the two sample student s t interval can be derived by parametric bootstrap coverage calibration of the naive plug in interval that fails to account for the estimation of the common variance parameter the same technique results in an essentially exact confidence interval for the ratio of two means based on independent samples from gamma distributions the gamma problem is more difficult computationally because an exact pivot is not available however the computational burden of bootstrap calibration can be reduced to a routine level using the fact that the ratio of sample means is proportional to an exact f variate that is independent of the conditional maximum likelihood estimator of the shape parameter the density of the conditional estimator can be approximated with extreme accuracy using the p formula and a rejection sampler can be used to simulate from this approximate density this greatly simplifies bootstrap calibration in this context an alternative interval is obtained by inverting an exact test described by jensen 1986 simulation studies suggest that the two intervals have similar performance in terms of length and coverage in practice we recommend the bootstrap calibration method because it is much simpler to implement and is more versatile

an alternative proof of a theorem of stieltjes and related results abstract let p n x n 1 be the orthogonal polynomials defined by a n p n 1 x a n 1 p n 1 x b n p n x xp n x p 0 x 0 p 1 x 1 where both sequences a n and b n are bounded and a n 0 assume that x is the unique up to a constant distribution function which corresponds to the measure of orthogonality of p n x and denote by s the spectrum of x alternative proofs of a theorem due to stieltjes and of a conjecture due to maki concerning the limit points of s are given a typical example to the maki s conjecture together with a general result concerning the density of the zeros of the polynomials p n x covers as a particular case a theorem of chihara which generalizes the well known theorem of blumenthal

fluctuations in the zeros of differentiable gaussian processes the stochastic point processes formed by the zero crossings or extremal points of differentiable stationary gaussian processes are studied as a function of their autocorrelation function the properties of these point processes are mapped to the space formed by the parameters appearing in the autocorrelation function their adopted form being sensitive to the structure of the autocorrelation function principally in the vicinity of the origin the distribution for the number of zeros occurring in an asymptotically large interval are approximately negative binomial or binomial depending upon whether the relative variance or fano factor is greater or less than unity the correlation properties of the zeros are such that they are repelled from each other or are antibunched if the autocorrelation function of the gaussian process is characterized by a single scale size but occur in clusters if more than one characteristic scale size is present the intervals between zeros can be interpreted in terms of the autocorrelation function of the zeros themselves when bunching occurs the interval density becomes bimodal indicating the interval sizes within and between the clusters the interevent periods are statistically dependent on one another with densities whose asymptotic behavior is governed by that of the autocorrelation function of the gaussian process at large delay times poisson distributed fluctuations of the zeros occur only exceptionally but never form a poisson process

complex jacobi matrices complex jacobi matrices play an important role in the study of asymptotics and zero distribution of formal orthogonal polynomials fops the latter are essential tools in several fields of numerical analysis for instance in the context of iterative methods for solving large systems of linear equations or in the study of pade approximation and jacobi continued fractions in this paper we present some known and some new results on fops in terms of spectral properties of the underlying infinite jacobi matrix with a special emphasis to unbounded recurrence coefficients here we recover several classical results for real jacobi matrices the inverse problem of characterizing properties of the jacobi operator in terms of fops and other solutions of a given three term recurrence is also investigated this enables us to give results on the approximation of the resolvent by inverses of finite sections with applications to the convergence of pade approximants