self dual instantons and holomorphic curves a gradient flow of a morse function on a compact riemannian manifold is said to be of morse smale type if the stable and unstable manifolds of any two critical points intersect transversally for such a morse smale gradient flow there is a chain complex generated by the critical points and graded by the morse index the boundary operator has as its x y entry the number of gradient flow lines running from x to y counted with appropriate signs whenever the difference of the morse indices is 1 the homology of this chain complex agrees with the homology of the underlying manifold m and this can be used to prove the morse inequalities cf 33 26 around 1986 floer generalized this idea to infinite dimensional variational problems in which every critical point has infinite morse index but the moduli spaces of connecting orbits form finite dimensional manifolds for every pair of critical points the dimensions of these spaces give rise to a relative morse index and the boundary operator is defined by counting connecting

minimal resolutions of algebras abstract a method is described for constructing the minimal projective resolution of an algebra considered as a bimodule over itself the method applies to an algebra presented as the quotient of a tensor algebra over a separable algebra by an ideal of relations that is either homogeneous or admissible with some additional finiteness restrictions in the latter case in particular it applies to any finite dimensional algebra over an algebraically closed field the method is illustrated by a number of examples viz truncated algebras monomial algebras and koszul algebras with the aim of unifying existing treatments of these in the literature

knots sutures and excision we develop monopole and instanton floer homology groups for balanced sutured manifolds in the spirit of 12 applications include a new proof of property p for knots

the density of solutions to multifractional stochastic volterra integro differential equations abstract the aim of this paper is to study the density of solutions to stochastic volterra integro differential equations with multifractional noises we prove the existence of the density of solutions and show that the density is bounded by lower and upper gaussian bounds

multi fractional generalized cauchy process and its application to teletraffic abstract the contributions given in this paper are in two aspects the first is to introduce a novel random function which we call the multi fractional generalized cauchy mgc process the second is to dissertate its application to network traffic for studying the multi fractal behavior of traffic on a point by point basis the introduced mgc process is with the time varying fractal dimension d t and the time varying hurst parameter h t the representations of the autocorrelation function acf and the power spectrum density psd of the mgc process are proposed besides the asymptotic expressions of the acf and psd of the mgc process are presented the computation formula of d t is given the mgc model may be a new tool to describe the multi fractal behavior of traffic precisely it may be used to reveal the local irregularity or local self similarity lss which is a small time scale behavior of traffic and global long term persistence or long range dependence lrd which is a large time scale behavior of traffic on a point by point basis the cast study with real traffic traces exhibits that the variance of d t is much greater than that of h t thus the present mgc model may provide a novel way to explain the fact that traffic has highly local irregularity while its lrd is robust

on quantum gauge theories in two dimensions two dimensional quantum yang mills theory is studied from three points of view i by standard physical methods ii by relating it to the largek limit of three dimensional chern simons theory and two dimensional conformal field theory iii by relating its weak coupling limit to the theory of reidemeister ray singer torsion the results obtained from the three points of view agree and give formulas for the volumes of the moduli spaces of representations of fundamental groups of two dimensional surfaces

fractional brownian motion and multifractional brownian motion of riemann liouville type the relationship between standard fractional brownian motion fbm and fbm based on the riemann liouville fractional integral or rl fbm is clarified the absence of stationary property in the increment process of rl fbm is compensated by a weaker property of local stationarity and the stationary property for the increments of the large time asymptotic rl fbm generalization of rl fbm to the rl multifractional brownian motion rl mbm can be carried out by replacing the constant holder exponent by a time dependent function rl mbm is shown to satisfy a weaker scaling property known as the local asymptotic self similarity this local scaling property can be translated into the small scale behaviour of the associated scalogram by using the wavelet transform

the localization sequence for the algebraic k theory of topological k theory we verify a conjecture of rognes by establishing a localization cofiber sequence of spectra k mathbb z to k ku to k ku to sigma k mathbb z for the algebraic k theory of topological k theory we deduce the existence of this sequence as a consequence of a devissage theorem identifying the k theory of the waldhausen category of finitely generated finite stage postnikov towers of modules over a connective a infty ring spectrum r with the quillen k theory of the abelian category of finitely generated pi 0 r modules

lagrangian floer theory on compact toric manifolds i we introduced the notion of weakly unobstructed lagrangian submanifolds and constructed their potential function po purely in terms of a model data in fooo3 in this article we carry out explicit calculations involving po on toric manifolds and study the relationship between this class of lagrangian submanifolds with the earlier work of givental g1 which advocates that the quantum cohomology ring is isomorphic to the jacobian ring of a certain function called the landau ginzburg superpotential combining this study with the results from fooo3 we also apply the study to various examples to illustrate its implications to symplectic topology of lagrangian fibers of toric manifolds in particular we relate it to the hamiltonian displacement property of lagrangian fibers and to entov polterovich s symplectic quasi states

towards a semiclassical theory of the quantum baker s map abstract we develop semiclassical 0 treatments of the quantum baker s map paying special attention to a the discrete and finite nature of its hilbert space and b the asymptotic analysis of the true quantum objects themselves new techniques are described at the theoretical level exact symbolic decomposition of the propagator and at the numerical level color graphics display of operators in the kirkwood representation both of which are of general interest for other quantized chaotic maps periodic orbit theory is tested numerically and we find that log corrections need to be included before an accurate calculation of the spectrum from periodic orbits can be achieved however the asymptotic analysis of the traces of the propagator reveals unexpected departures from standard semiclassical theory those anomalies which we compute explicitly in a few cases are traced ultimately to the discontinuity of the map and to the compactness of the phase space the analysis is far from complete but the results point towards the necessity of careful assessment of semiclassical folklore when applied to chaotic maps

semiclassical dynamics in the strongly chaotic regime breaking the log time barrier we investigate the behavior of the quantum baker s transformation a system whose classical analogue is completely chaotic for time scales where the classical mechanics generates phase space structures on a scale smaller than planck s constant i e past the log time t ln 1 surprisingly we find that a semiclassical theory can accurately reproduce many features of the quantum evolution of a wave packet in this strongly mixing time regime

on the spectra of riemann liouville fractional brownian motion we study the spectrum of the fractional brownian motion of riemann liouville type using two approaches namely the double frequency spectral density and the wigner ville spectrum the bifrequency representation gives a complex valued function which contains two distinctive terms these terms can be identified as the diagonal and off diagonal distribution of the spectrum in a frequency frequency plane the physical interpretation of these two terms is briefly discussed a calculation of wigner ville spectrum gives an alternative way of representing the spectrum of this nonstationary process in the time frequency plane asymptotic approximation of the wigner ville spectrum is obtained we show that the large time average spectrum of riemann liouville fractional brownian motion exhibits a power law in the high frequency range

geometric composition in quilted floer theory abstract we prove that floer cohomology of cyclic lagrangian correspondences is invariant under transverse and embedded composition under a general set of assumptions

admissible subcategories in derived categories of moduli of vector bundles on curves abstract we show that the poincare bundle gives a fully faithful functor from the derived category of a curve of sufficiently high genus into the derived category of its moduli space of bundles of rank r with fixed determinant of degree 1 this generalises results of narasimhan and fonarev kuznetsov for the case of rank 2 and also gives an alternative proof of known results on deformations of universal bundles moreover we show that a twist of the embedding together with 2 exceptional line bundles gives the beginning of a semiorthogonal decomposition for the derived category of the moduli space

statistical properties of the yuan exchange rate index abstract we choice the yuan exchange rate index based on a basket of currencies as the effective exchange rate of the yuan and investigate the statistical properties of the yuan exchange rate index after china s exchange rate system reform on the 21st july 2005 after dividing the time series into two parts according to the change in the yuan exchange rate regime in july 2008 we compare the statistical properties of the yuan exchange rate index during these two periods we find that the distribution of the two return series has the exponential form we also perform the detrending moving average analysis dma and the multifractal detrending moving average analysis mfdma the two periods possess different degrees of long range correlations and the multifractal nature is also unveiled in these two time series significant difference is found in the scaling exponents q and singularity spectra f of the two periods obtained from the mfdma analysis besides in order to detect the sources of multifractality shuffling and phase randomization procedures are applied to destroy the long range temporal correlation and fat tailed distribution of the yuan exchange rate index respectively we find that the fat tailedness plays a critical role in the sources of multifractality in the first period while the long memory is the major cause in the second period the results suggest that the change in china s exchange rate regime in july 2008 gives rise to the different multifractal properties of the yuan exchange rate index in these two periods and thus has an effect on the effective exchange rate of the yuan after the exchange rate reform on the 21st july 2005

the mis specification of the expected rescaled adjusted range abstract rescaled range analysis has regained popularity in the recent econophysics literature as a means of identifying long term dependence in time series data conclusions derived from the rescaled adjusted range statistic are conditional however upon the choice of an appropriate benchmark against which calculated results can be compared one recent paper in physica a by couillard and davison physica a 348 2005 404 concludes that the anis and lloyd biometrika 63 1976 111 model of the expected rescaled adjusted range is more accurate than that proposed by peters fractal market analysis wiley new york 1994 this finding is contrary to the evidence presented by peters this paper reveals significant inconsistencies in the empirical results reported by peters which when considered support the conclusions of couillard and davison and explain the apparent contradiction in their results versus those of peters

financial multifractality and its subtleties an example of dax abstract detailed study of multifractal characteristics of the financial time series of asset values and of its returns is performed using a collection of the high frequency deutsche aktienindex data the tail index the renyi exponents based on the box counting algorithm for the graph d q and the generalized hurst exponents h q are computed in parallel for short and daily return times the results indicate a more complicated nature of the stock market dynamics than just consistent multifractal

research on the fractal structure in the chinese stock market abstract applying fractal theory this paper probes and discusses self similarity and scale invariance of the chinese stock market it analyses three kinds of scale indexes i e autocorrelation index hurst index and the scale index on the basis of detrended fluctuation analysis dfa algorithm and promotes dfa into a recursive algorithm using the three kinds of scale indexes we conduct empirical research on the chinese shanghai and shenzhen stock markets the results indicate that the rate of returns of the two stock markets does not obey the normal distribution a correlation exists between the stock price indexes over time scales the stock price indexes exhibit fractal time series it indicates that the policy guide hidden at the back influences the characteristic of the chinese stock market

record length requirement of long range dependent teletraffic abstract this article contributes the highlights mainly in two folds on the one hand it presents a formula to compute the upper bound of the variance of the correlation periodogram measurement of teletraffic traffic for short with long range dependence lrd for a given record length t and a given value of the hurst parameter h theorems 1 and 2 on the other hand it proposes two formulas for the computation of the variance upper bound of the correlation periodogram measurement of traffic of fractional gaussian noise fgn type and the generalized cauchy gc type respectively corollaries 1 and 2 they may constitute a reference guideline of record length requirement of traffic with lrd in addition record length requirement for the correlation periodogram measurement of traffic with either the schuster type or the bartlett one is studied and the present results about it show that both types of periodograms may be used for the correlation measurement of traffic with a pre desired variance bound of correlation estimation moreover real traffic in the internet archive by the special interest group on data communication under the association for computing machinery of us acm sigcomm is analyzed in the case study in this topic

scale invariant distribution and multifractality of volatility multipliers in stock markets abstract the statistical properties of the multipliers of the absolute returns are investigated using 1 min high frequency data of financial time series the multiplier distribution is found to be independent of the box size s when s is larger than some crossover scale providing direct evidence of the existence of scale invariance in financial data the multipliers with base a 2 are well approximated by a normal distribution and the most probable multiplier scales as a power law with respect to the base a we unravel that the volatility multipliers possess multifractal nature which is independent of construction of the multipliers that is the values of s and a

morse theory for lagrangian intersections soit p une variete symplectique compacte et soit l p une sous variete lagrangienne avec 2 p l 0 pour un diffeomorphisme exact de p avec la propriete que l coupe l transversalement on demontre une inegalite de morse reliant l ensemble l l a la cohomologie de l

a comment on measuring the hurst exponent of financial time series abstract a fundamental hypothesis of quantitative finance is that stock price variations are independent and can be modeled using brownian motion in recent years it was proposed to use rescaled range analysis and its characteristic value the hurst exponent to test for independence in financial time series theoretically independent time series should be characterized by a hurst exponent of 1 2 however finite brownian motion data sets will always give a value of the hurst exponent larger than 1 2 and without an appropriate statistical test such a value can mistakenly be interpreted as evidence of long term memory we obtain a more precise statistical significance test for the hurst exponent and apply it to real financial data sets our empirical analysis shows no long term memory in some financial returns suggesting that brownian motion cannot be rejected as a model for price dynamics

path integrals in the symbol space of chaotic mappings we introduce a path integral like partition function for chaotic mappings this path integral is based on arbitrary non markovian stochastic processes generated by the symbolic dynamics of the map rather than the wiener process our approach can be regarded as an extension of the thermodynamic formalism to infinitely many inverse temperatures the concept of renyi entropies is generalized to entropy functionals a generalized transfer operator is introduced which allows us to calculate the entropy functionals with high numerical precision several examples are worked out in detail

weyl and riemann liouville multifractional ornstein uhlenbeck processes this paper considers two new multifractional stochastic processes namely the weyl multifractional ornstein uhlenbeck process and the riemann liouville multifractional ornstein uhlenbeck process basic properties of these processes such as locally self similar property and hausdorff dimension are studied the relationship between the multifractional ornstein uhlenbeck processes and the corresponding multifractional brownian motions is established

martingales detrending data and the efficient market hypothesis we discuss martingales detrending data and the efficient market hypothesis for stochastic processes x t with arbitrary diffusion coefficients d x t beginning with x independent drift coefficients r t we show that martingale stochastic processes generate uncorrelated generally nonstationary increments generally a test for a martingale is therefore a test for uncorrelated increments a detrended process with an x dependent drift coefficient is generally not a martingale and so we extend our analysis to include the class of x t dependent drift coefficients of interest in finance we explain why martingales look markovian at the level of both simple averages and 2 point correlations and while a markovian market has no memory to exploit and presumably cannot be beaten systematically it has never been shown that martingale memory cannot be exploited in 3 point or higher correlations to beat the market we generalize our markov scaling solutions presented earlier and also generalize the martingale formulation of the efficient market hypothesis emh to include x t dependent drift in log returns we also use the analysis of this paper to correct a misstatement of the fair game condition in terms of serial correlations in fama s paper on the emh we end with a discussion of levy scharacterization of brownian motion and prove that an arbitrary martingale is topologically inequivalent to a wiener process

the symplectic sum formula for gromov witten invariants in the symplectic category there is a connect sum operation that glues symplectic manifolds by identifying neighborhoods of embedded codimension two submanifolds this paper establishes a formula for the gromov witten invariants of a symplectic sum z x y in terms of the relative gw invariants of x and y several applications to enumerative geometry are given gromov witten invariants are counts of holomorphic maps into symplectic manifolds to define them on a symplectic manifold x w one introduces an almost complex structure j compatible with the symplectic form w and

hurst exponent estimation of locally self similar gaussian processes using sample quantiles this paper is devoted to the introduction of a new class of consistent estimators of the fractal dimension of locally self similar gaussian processes these estimators are based on convex combinations of sample quantiles of discrete variations of a sample path over a discrete grid of the interval 0 1 we derive the almost sure convergence and the asymptotic normality for these estimators the key ingredient is a bahadur representation for sample quantiles of non linear functions of gaussians sequences with correlation function decreasing as k alpha l k for some alpha 0 and some slowly varying function l cdot

inhomogeneous scaling behaviors in malaysian foreign currency exchange rates in this paper we investigate the fractal scaling behaviors of foreign currency exchange rates with respect to malaysian currency ringgit malaysia these time series are examined piecewise before and after the currency control imposed in 1st september 1998 using the monofractal model based on fractional brownian motion the global hurst exponents are determined using the r s analysis the detrended fluctuation analysis and the method of second moment using the correlation coefficients the limitation of these monofractal analyses is discussed the usual multifractal analysis reveals that there exists a wide range of hurst exponents in each of the time series a new method of modelling the multifractal time series based on multifractional brownian motion with time varying hurst exponents is studied

exponentially damped levy flights multiscaling and exchange rates abstract we employ our previously suggested exponentially damped levy flight physica a 326 2003 544 to study the multiscaling properties of 30 daily exchange rates against the us dollar together with a fictitious euro dollar rate physica a 286 2000 353 though multiscaling is not theoretically seen in either stable levy processes or abruptly truncated levy flights it is even characteristic of smoothly truncated levy flights phys lett a 266 2000 282 eur phys j b 4 1998 143 we have already defined a class of quasi stable processes in connection with the finding that single scaling is pervasive among the dollar price of foreign currencies physica a 323 2003 601 here we show that the same goes as far as multiscaling is concerned our novel findings incidentally reinforce the case for real world relevance of the levy flights for modeling financial prices

long term memory in stock market prices a test for long term memory that is robust to short range dependence is developed it is a modification of the r s statistic and the relevant asymptotic sampling theory is derived via functional central limit theory contrary to previous findings when applied to daily and monthly stock returns indexes over several time periods this test yields no evidence of long range dependence once short range dependence is accounted for monte carlo experiments show that the modified r s test has power against at least two specific models of long term memory suggesting that models with short range dependence may adequately capture the behavior of historical stock returns copyright 1991 by the econometric society

quivers floer cohomology and braid group actions we consider the derived categories of modules over a certain family a m of graded rings and floer cohomology of lagrangian intersections in the symplectic manifolds which are the milnor fibres of simple singularities of type a m we show that each of these two rather different objects encodes the topology of curves on an m 1 punctured disc we prove that the braid group b m 1 acts faithfully on the derived category of a m modules and that it injects into the symplectic mapping class group of milnor fibers the philosophy behind our results is as follows using floer cohomology one should be able to associate to the milnor fibre a triangulated category its construction has not been carried out in detail this triangulated category should contain a full subcategory which is equivalent up to a slight difference in the grading to the derived category of a m modules the full embedding would connect the two occurrences of the braid group thus explaining the similarity between them

fractional langevin equations of distributed order distributed order fractional langevin like equations are introduced and applied to describe anomalous diffusion without unique diffusion or scaling exponent it is shown that these fractional langevin equations of distributed order can be used to model the kinetics of retarding subdiffusion whose scaling exponent decreases with time and the strongly anomalous ultraslow diffusion with mean square displacement which varies asymptotically as a power of logarithm of time

scale invariance and universality of economic fluctuations in recent years physicists have begun to apply concepts and methods of statistical physics to study economic problems and the neologism econophysics is increasingly used to refer to this work much recent work is focused on understanding the statistical properties of time series one reason for this interest is that economic systems are examples of complex interacting systems for which a huge amount of data exist and it is possible that economic time series viewed from a dierent perspective might yield new results this manuscript is a brief summary of a talk that was designed to address the question of whether two of the pillars of the eld of phase transitions and critical phenomena scale invariance and universality can be useful in guiding research on economics we shall see that while scale invariance has been tested for many years universality is relatively less frequently discussed this article reviews the results of two recent studies i the probability distribution of stock price uctuations stock price uctuations occur in all magnitudes in analogy to earthquakes from tiny uctuations to drastic events such as market crashes the distribution of price uctuations decays with a power law tail well outside the levy stable regime and describes uctuations that dier in size by as much as eight orders of magnitude ii quantifying business rm uctuations we analyze the computstat database comprising all publicly traded united states manufacturing companies within the years 1974 1993 we nd that the distributions of growth rates is dierent for dierent bins of rm size with a width that varies inversely with a power of rm size similar variation is found for other complex organizations including country size university research budget size and size of species of bird populations c 2000 elsevier science b v all rights reserved

generalized ornstein uhlenbeck processes and associated self similar processes we consider three types of generalized ornstein uhlenbeck processes the stationary process obtained from the lamperti transformation of fractional brownian motion the process with stretched exponential covariance and the process obtained from the solution of the fractional langevin equation these stationary gaussian processes have many common properties such as the fact that their local covariances share a similar structure and they exhibit identical spectral densities at large frequency limit in addition the generalized ornstein uhlenbeck processes can be shown to be local stationary representations of fractional brownian motion two new self similar gaussian processes in addition to fractional brownian motion are obtained by applying the inverse lamperti transformation to the generalized ornstein uhlenbeck processes we study some of the properties of these self similar processes such as the long range dependence we give a simulation of their sample paths based on numerical karhunan loeve expansion

power law of quiet time distribution in the korean stock market abstract we report the quiet time probability distribution of the absolute return in the korean stock market index we define the quiet time as a time interval during the absolute return of the stock index that are above a threshold r c through an exponential bin plot we observe that the quiet time distribution qtd shows power law behavior p f t t for a range of threshold values the quiet time distribution has two scaling regimes separated by the crossover time t c 200 min the power law exponents of the quiet time distribution decrease when the return time t increases in the late time regime t t c the power law exponents are independent of the threshold within the error bars for the fixed return time the scaled qtd is characterized by a scaling function such as p f t 1 t f t t where the scaling function f x x 2 and t is the average quiet time the scaling exponents 2 depend on the return time t and are independent of the threshold r c the average quiet time follows the power law such as t r c where the exponents depend on the return time t

sw gr from the seiberg witten equations to pseudo holomorphic curves the purpose of this article is to explain how pseudo holomorphic curves in a symplectic 4 manifold can be constructed from solutions to the seiberg witten equations as such the main theorem proved here theorem 1 3 is an existence theorem for pseudo holomorphic curves this article thus provides a proof of roughly half of the main theorem in the announcement t1 that theorem theorem 4 1 asserts an equivalence between the seiberg witten invariants for a symplectic manifold and a certain gromov invariant which counts with signs the number of pseudoholomorphic curves in a given homology class the seiberg witten invariants were introduced to mathematicians by witten w based on his joint work with nat seiberg sw1 sw2 a description of these invariants is given in section 1 see also km1 t1 suffice it to say here that when x is a compact oriented 4 dimensional manifold with

the sampling properties of hurst exponent estimates abstract the classical rescaled adjusted range r s statistic is a popular and robust tool for identifying fractal structures and long term dependence in time series data subsequent to mandelbrot and wallis water resour res 4 1968 909 who proposed the statistic be measured over several subseries contained within the whole series length the use overlapping vs contiguous subseries has been a source of some debate amongst r s theorists this study examines the distributional characteristics of rescaled adjusted range and hurst exponent estimates derived using overlapping vs contiguous subseries henceforth closing debate on the issue of relative bias due to either technique confidence intervals for the statistical significance of the hurst exponent are also determined

multifractality in stock indexes fact or fiction abstract multifractal analysis and extensive statistical tests are performed upon intraday minutely data within individual trading days for four stock market indexes including hsi szsc s p 500 and nasdaq to check whether the indexes instead of the returns possess multifractality we find that the mass exponent q is linear and the singularity q is close to 1 for all trading days and all indexes furthermore we find strong evidence showing that the scaling behaviors of the original data sets cannot be distinguished from those of shuffled time series hence the so called multifractality in the intraday stock market indexes is merely an illusion

scaling stability and distribution of the high frequency returns of the ibex35 index abstract in this paper we perform a statistical analysis of the high frequency returns of the ibex35 madrid stock exchange index we find that its probability distribution seems to be stable over different time scales a stylized fact observed in many different financial time series however an in depth analysis of the data using maximum likelihood estimation and different goodness of fit tests rejects the levy stable law as a plausible underlying probabilistic model the analysis shows that the normal inverse gaussian distribution provides an overall fit for the data better than any of the other subclasses of the family of generalized hyperbolic distributions and certainly much better than the levy stable laws furthermore the right resp left tail of the distribution seems to follow a power law with exponent 4 60 resp 4 28 finally we present evidence that the observed stability is due to temporal correlations or non stationarities of the data

the symplectic nature of fundamental groups of surfaces soit 7b g la categorie des groupes de lie g avec une forme bilineaire symetrique non singuliere b sur l algebre de lie soit le groupe fondamental d une surface orientee close de genre 1 et soit 7b s la categorie des out espaces symplectiques alors la correspondance g b hom g g b definit un foncteur 7b g 7b s ou b est la structure symplectique sur hom g g definie par b

econophysics financial time series from a statistical physics point of view in recent years physicists have started applying concepts and methods of statistical physics to study economic problems the word econophysics is sometimes used to refer to this work much recent work is focused on understanding the statistical properties of nancial time series one reason for this interest is that nancial markets are examples of complex interacting systems for which a huge amount of data exist and it is possible that nancial time series viewed from a dierent perspective might yield new results this article reviews the results of three recent phenomenological studies i the probability distribution of stock price uctuations stock price uctuations occur in all magnitudes in analogy to earthquakes from tiny uctuations to drastic events such as market crashes the distribution of price uctuations decays with a power law tail well outside the levy stable regime and describes uctuations that dier by as much as eight orders of magnitude in addition this distribution preserves its functional form for uctuations on time scales that dier by three orders of magnitude from 1 min up to approximately 10 d ii correlations in nancial time series while price uctuations themselves have rapidly decaying correlations the magnitude of uctuations measured by either the absolute value or the square of the price uctuations has correlations that decay as a power law and persist for several months iii correlations among dierent companies the third result bears on the application of random matrix theory to understand the correlations among price uctuations of any two dierent stocks from a study of the eigenvalue statistics of the cross correlation matrix constructed from price uctuations of the leading 1000 stocks we nd that the largest 1 of the eigenvalues and the corresponding eigenvectors show systematic deviations from the predictions for a random matrix whereas the rest of the eigenvalues conform to random matrix behavior suggesting that these 1 of the eigenvalues contain system specic information about correlated time evolution of dierent companies c 2000 published by elsevier science b v all rights reserved

products of floer cohomology of torus fibers in toric fano manifolds we compute the ring structure of floer cohomology groups of lagrangian torus fibers in some toric fano manifolds continuing the study of co related a formulas hold for a transversal choice of chains two different computations are provided a direct calculation using the classification of holomorphic discs by oh and the author in co and another method by using an analogue of divisor equation in gromov witten invariants to the case of discs floer cohomology rings are shown to be isomorphic to clifford algebras whose quadratic forms are given by the hessians of functions w which turn out to be the superpotentials of landau ginzburg mirrors in the case of open image in new window this proves the prediction made by hori kapustin and li by b model calculations via physical arguments the latter method also provides correspondence between higher derivatives of the superpotential of lg mirror with the higher products of the a or l algebra of the lagrangian submanifold

similarities and differences between physics and economics in this opening talk we discuss some of the similarities between work being done by economists and by physicists seeking to contribute to economics we also mention some of the dierences in the approaches taken and justify these dierent approaches by developing the argument that by approaching the same problem from dierent points of view new results might emerge in particular we review some recent results for example the 1nding that there are two new universal scaling models in economics i the 3uctuation of price changes of any stock market is characterized by a pdf which is a simple power law with exponent 4 that extends over 10 2 standard deviations a factor of 10 8 on the y axis ii for a wide range of economic organizations the histogram that shows how size of organization is inversely correlated to 3uc tuations in size with an exponent 1 6 neither of these two new laws has a 1rm theoretical foundation we also discuss results that are reminiscent of phase transitions in spin systems where the divergent behavior of the response function at the critical point zero magnetic 1eld leads to large 3uctuations c 2001 published by elsevier science b v

a characteristic time scale in dollar yen exchange rates abstract here we analyze tick data of yen dollar exchange using random walk methods we find that there exists a characteristic time scale approximately at 10 min according to the results at time scales shorter than 10 min the market exhibits anti persistence meaning that it self organizes so as to restore a given tendency for time scales longer than 10 min the market approaches a behavior appropriate to pure brownian motion

does the singular value decomposition entropy have predictive power for stock market evidence from the shenzhen stock market abstract this paper analyzes the predictive ability of the singular value decomposition entropy for the shenzhen component index based on different scales it is found that the predictive ability of the entropy for the index is affected by the width of moving time windows and the structural break in stock market by moving time windows with one year the predictive power of singular value decomposition entropy of shenzhen stock market for its component index is found after the reform of non tradable shares

floer cohomology and pencils of quadrics there is a classical relationship in algebraic geometry between a hyperelliptic curve and an associated pencil of quadric hypersurfaces we investigate symplectic aspects of this relationship with a view to applications in low dimensional topology

asymptotic green functions a generalized semiclassical approach for scattering by multiple barrier potentials we show how quantum mechanical barrier reflection and transmission coefficients and can be obtained from asymptotic green functions we exemplify our results by calculating such coefficients for the rosen morse rm potential for multiple barrier potentials v x jv j x where each v j goes to zero for x we derive the asymptotic green functions by a generalized semiclassical approximation which is based on the usual sum over classical paths considered only in the classically allowed regions and includes local quantum effects through the individual j and j the approach is applied to double rm potentials and to woods saxon barriers we obtain analytical expressions for the transmission and reflection probabilities of these potentials which are very accurate when compared with exact numerical calculations being much better than the usual wkb approximation finally we briefly discuss how to extend the present method to other kinds of potential

path integral representation of fractional harmonic oscillator abstract fractional oscillator process can be obtained as the solution to the fractional langevin equation there exist two types of fractional oscillator processes based on the choice of fractional integro differential operators namely weyl and riemann liouville an operator identity for the fractional differential operators associated with the fractional oscillators is derived it allows the solution of fractional langevin equations to be obtained by simple inversion the relationship between these two fractional oscillator processes is studied the operator identity also plays an important role in the derivation of the path integral representation of the fractional oscillator processes relevant quantities such as two point and n point functions can be calculated from the generating functions

fokker planck equation and path integral representation of the fractional ornstein uhlenbeck process with two indices this paper considers the fokker planck equation and path integral formulation of the fractional ornstein uhlenbeck process parametrized by two indices the effective fokker planck equation of this process is derived from the associated fractional langevin equation the path integral representation of the process is constructed and the basic quantities are evaluated

braid group actions on derived categories of coherent sheaves this paper gives a construction of braid group actions on the derived category of coherent sheaves on a variety x the motivation for this is m kontsevich s homological mirror conjecture together with the occurrence of certain braid group actions in symplectic geometry one of the main results is that when dim x geq 2 our braid group actions are always faithful we describe conjectural mirror symmetries between smoothings and resolutions of singularities which lead us to find examples of braid group actions arising from crepant resolutions of various singularities relations with the mckay correspondence and with exceptional sheaves on fano manifolds are given moreover the case of an elliptic curve is worked out in some detail

scaling in the norwegian stock market the main objective of this paper is to investigate the validity of the much used assumptions that stock market returns follow a random walk and are normally distributed for this purpose the concepts of chaos theory and fractals are applied two independent models are used to examine price variations in the norwegian and us stock markets the first model used is the range over standard deviation or r s statistic which tests for persistence or antipersistence in the time series both the norwegian and us stock markets show significant persistence caused by long run memory components in the series in addition an average non periodic cycle of four years is found for the us stock market these results are not consistent with the random walk assumption the second model investigates the distributional scaling behaviour of the high frequency price variations in the norwegian stock market the results show a remarkable constant scaling behaviour between different time intervals this means that there is no intrinsic time scale for the dynamics of stock price variations the relationship can be expressed through a scaling exponent describing the development of the distributions as the time scale changes this description may be important when constructing or improving pricing models such that they coincide more closely with the observed market behaviour the empirical distributions of high frequency price variations for the norwegian stock market is then compared to the levy stable distribution with the relevant scaling exponent found by using the r s and distributional scaling analysis good agreement is found between the levy profile and the empirical distribution for price variations less than 6 standard deviations covering almost three orders of magnitude in the data for probabilities larger than 6 standard deviations there seem to be an exponential fall off from the levy profile in the tails which indicates that the second moment may be finite

toric structures on the moduli space of flat connections on a riemann surface volumes and the moment map abstract in earlier papers we constructed a hamiltonian torus action on an open dense set in the moduli space of flat su 2 connections on a compact riemann surface where the dimension of the torus is half the dimension of the moduli space this torus action shows that this set can be viewed symplectically as a noncompact toric variety the number of integral points of the moment map for the torus action turns out to be identical to the verlinde dimension d g k as an application we furnish a new proof of the relation between the large k limit of d g k and the volume of the moduli space from our point of view this relation follows from the equality between the symplectic volume of a toric variety and the euclidean volume of the image of the moment map similar considerations are shown to give rise to the volumes of moduli spaces of parabolic bundles on a riemann surface knowledge of these volumes has been shown to allow a proof of the verlinde formula for the dimension of the space of holomorphic sections of line bundles on this space

generating the fukaya categories of hamiltonian g manifolds abstract let g be a compact lie group and let k be a field of characteristic p geq 0 such that h g has no p torsion if p 0 we show that a free lagrangian orbit of a hamiltonian g action on a compact monotone symplectic manifold x split generates an idempotent summand of the monotone fukaya category mathcal f x k if and only if it represents a nonzero object of that summand slightly more general results are also provided our result is based on an explicit understanding of the wrapped fukaya category mathcal w t g k through koszul twisted complexes involving the zero section and a cotangent fibre and on a functor d b mathcal w t g k to d b mathcal f x times x k canonically associated to the hamiltonian g action on x we explore several examples which can be studied in a uniform manner including toric fano varieties and certain grassmannians

path integrals and edge corrections for torus maps abstract we derive general path integrals for quantum maps in the torus and discuss the physical interpretation of the poisson sums that arise comparing the case of the cat map with the baker s map we relate the exactness of the semiclassical approximation for the former to the possibility of combining the poisson sum into a single smooth integral the processes of taking the trace and the semiclassical approximation for the baker s map do not commute we derive an approximation that includes edge corrections for the integrals in the map and we obtain some improvement over the usual semiclassical approximation even if only poisson terms with stationary points are kept

finite groups acting linearly hochschild cohomology and the cup product abstract when a finite group acts linearly on a complex vector space the natural semi direct product of the group and the polynomial ring over the space forms a skew group algebra this algebra plays the role of the coordinate ring of the resulting orbifold and serves as a substitute for the ring of invariant polynomials from the viewpoint of geometry and physics its hochschild cohomology predicts various hecke algebras and deformations of the orbifold in this article we investigate the ring structure of the hochschild cohomology of the skew group algebra we show that the cup product coincides with a natural smash product transferring the cohomology of a group action into a group action on cohomology we express the algebraic structure of hochschild cohomology in terms of a partial order on the group modulo the kernel of the action this partial order arises after assigning to each group element the codimension of its fixed point space we describe the algebraic structure for coxeter groups where this partial order is given by the reflection length function a similar combinatorial description holds for an infinite family of complex reflection groups

efficiency of thai stock markets detrended fluctuation analysis the evolution of hurst exponent of set index over time as a measure of market efficiency is examined by dfa method it is found that during the study period hurst exponent tends to decrease to the ideal value 0 5 i e the market becomes more efficient this finding readily conforms to the assertion that emerging markets are becoming more efficient additionally the development of hurst exponent during november 2006 to march 2015 of set index compared to mai index is investigated the result shows that the deviation of the hurst exponent from 0 5 for the mai index is larger than that of the set index this implies that set is more efficient than mai and thus supports the assumption that market capitalization has significant influence on market efficiency

characterizing abrupt changes in the stock prices using a wavelet decomposition method abstract abrupt changes in the stock prices either upwards or downwards are usually preceded by an oscillatory behavior with frequencies that tend to increase as the moment of transition becomes closer the wavelet decomposition methods may be useful for analysis of this oscillations with varying frequencies because they provide simultaneous information on the frequency scale and localization in time translation however in order to use the wavelet decomposition certain requirements have to be satisfied so that the linear and cyclic trends are eliminated by standard least squares techniques the coefficients obtained by the wavelet decomposition can be represented in a graphical form a threshold can then be established to characterize the likelihood of a short time abrupt change in the stock prices actual data from the sao paulo stock exchange bolsa de valores de sao paulo were used in this work to illustrate the proposed method

quantitatively investigating the locally weak stationarity of modified multifractional gaussian noise a b s t r a c t we suggest that there exists a critical point h 0 70 of the local holder exponent h t for describing the weak stationary stationary for short property of the modified multifractional gaussian noise mmgn from the point of view of engineering more precisely when h t 0 70 for t 0 the stationarity of mmgn is conditional relying on the variation ranges of h t when h t 0 70 on the other side mmgn is unconditionally stationary yielding a consequence that short memory mmgn is stationary in addition for h t 0 70 we introduce the concept of stationary range denoted by hmin hmax it means that corr r h t1 r h t2 0 70 if h t1 h t2 hmin hmax where r h t1 and r h t2 are the autocorrelation functions of mmgn with h t1 and h t2 for t1 t2 respectively and corr r h t1 r h t2 is the correlation coefficient between r h t1 and r h t2 we present a set of stationary ranges which may be used for a quantitative description of the local stationarity of mmgn a case study is demonstrated for applying the present method to testing the stationarity of a real traffic trace

a new combined approach on hurst exponent estimate and its applications in realized volatility abstract the purpose of this paper is to propose a new estimator of hurst exponent based on the combined information of the conventional rescaled range methods we demonstrate the superiority of the proposed estimator by monte carlo simulations and the applications in estimating the hurst exponent of daily volatility series in chinese stock market moreover we indicate the impact of the type of estimator and structural break on the estimating results of hurst exponent

exact lagrangians in a_n surface singularities in this paper we classify lagrangian spheres in a n surface singularities up to hamiltonian isotopy combining with a result of ritter geom funct anal 20 3 779 816 2010 this yields a complete classification of exact lagrangians in a n surface singularities our main new tool is the application of a technique which we call ball swappings and its relative version

holomorphic disks and topological invariants for closed three manifolds the aim of this article is to introduce certain topological invariants for closed oriented three manifolds y equipped with a spiny structure given a heegaard splitting of y u 0o u u 1 these theories are variants of the lagrangian floer homology for the g fold symmetric product of relative to certain totally real subspaces associated to u 0 and u 1

multifractal detrended cross correlation analysis of gold price and sensex abstract this paper studies the variation of autocorrelation and cross correlation coefficients of gold price and sensex fluctuations with time the paper uses mfdfa and mfdxa methodologies sensex plays a more dominant role in the variation of cross correlations it is observed that the cross correlation coefficients can be linked with the stability of the market the market is most stable when the two series are most correlated

modeling of financial data comparison of the truncated levy flight and the arch 1 and garch 1 1 processes we compare our results on empirical analysis of nancia l data with simulations of two stochastic models of the dynamics of stock market prices the two models are i the truncated l evy igh t recently introduced by us and ii the arch 1 and garch 1 1 processes we n d that the tlf well describes the scaling and its breakdown observed in empirical data while it is not able to properly describe the uctuation s of volatility empirically detected the arch 1 and garch 1 1 models are able to describe the probability density function of price changes at a given time horizon but both fail to describe the scaling properties of the pdfs for short time horizons c 1998 elsevier science b v all rights reserved

1 f noise decomposition in random telegraph signals using the wavelet transform abstract by using the continuous wavelet transform with haar basis the second order properties of the wavelet coefficients are derived for the random telegraph signal rts and for the 1 f noise which is obtained by summation of many rtss the correlation structure of the haar wavelet coefficients for these processes is found for the wavelet spectrum of the 1 f noise some characteristics related to the distribution of the relaxation times of the rts are derived a statistical test based on the characterization of the time evolution of the scalogram is developed which allows to detect non stationarity in the times s which compose the 1 f process and to identify the time scales of the relaxation times where the non stationarity is localized the proposed method allows to distinguish noise signals with 1 f power spectral density generated by rtss and thus gives informations on the origin of this type of 1 f noise which cannot be obtained using the fourier transform or other methods based on second order statistical analysis the reported treatment is applied to both simulated and experimental signals the present analysis is based on the mcwhorter 1 f noise and germanium surface properties in r h kingstone ed semiconductor surface physics university of pennsylvania press philadelphia pa 1957 pp 207 228 model of low frequency electric noise and the obtained results are expected to prove especially useful for semiconductor devices

multifractal properties of chinese stock market in shanghai abstract in this article we apply three methods of multifractal analysis partition function method singular spectrum method and multifractal detrended fluctuation analysis method to analyze the closing index fluctuations of shanghai stock market during the past seven years we have found that shanghai stock market has weak multifractal features and there are long range power law correlations between index series the shapes of singular spectrums do not change with time scales and their strengths weaken when the scales shorten but when the orders of partition function increase the strengths of multifractal increase the singular spectrums become rougher and the general hurst exponents decrease these results provide solid and important values for further study on the dynamic mechanism of stock market price fluctuation

long range correlations and nonstationarity in the brazilian stock market abstract we report an empirical study of the ibovespa index of the sao paulo stock exchange in which we detect the existence of long range correlations to analyze our data we introduce a rescaled variant of the usual detrended fluctuation analysis that allows us to obtain the hurst exponent through a one parameter fitting we also compute a time dependent hurst exponent h t using 3 year moving time windows in particular we find that before the launch of the collor plan in 1990 the curve h t remains in general well above 1 2 while afterwards it stays close to 1 2 we thus argue that the structural reforms set off by the collor plan has lead to a more efficient stock market in brazil we also suggest that the time dependence of the ibovespa hurst exponent could be described in terms of a multifractional brownian motion

the symplectic arc algebra is formal this is the author accepted manuscript the final version is available from duke university press via http dx doi org 10 1215 00127094 3449459

multifractal detrended cross correlation analysis of foreign exchange and sensex fluctuation in indian perspective abstract the manuscript studies autocorrelation and cross correlation of sensex fluctuations and forex exchange rate in respect to indian scenario multifractal detrended fluctuation analysis mfdfa and multifractal detrended cross correlation analysis mfdxa were employed to study the correlation between the two series it was observed that the two series are strongly cross correlated the change of degree of cross correlation with time was studied and the results are interpreted qualitatively

correlations in economic time series a financial index of the new york stock exchange the sp here f is called the crossover frequency iii we confirm these results using the dfa detrended fluctuation analysis method see fig 2b which allows accurate estimates of exponents independent of local trends

on bandlimitedness and lag limitedness of fractional gaussian noise abstract the contributions of this short paper are two fold we shall show two interesting properties of fractional gaussian noise fgn namely its bandlimitedness and lag limitedness the computation formulas for the maximum frequency of bandlimited fgn and the maximum lag of lag limited fgn are proposed in addition we will give a new explanation of the statistical dependences of fgn based on the present bandlimitedness and lag limitedness of fgn

floer theory for negative line bundles via gromov witten invariants abstract we prove that the gw theory of negative line bundles m tot l b determines the symplectic cohomology indeed s h m is the quotient of q h m by the kernel of a power of quantum cup product by c 1 l we prove this also for negative vector bundles and the top chern class we calculate s h and q h for o n c p m for example for o 1 m is the blow up of c m 1 at the origin and s h m has rank m we prove kodaira vanishing for very negative l s h 0 and serre vanishing if we twist a complex vector bundle by a large power of l s h 0 observe s h m 0 iff c 1 l is nilpotent in q h m this implies oancea s result b 2 b 0 s h m 0 we prove the weinstein conjecture for any contact hypersurface surrounding the zero section of a negative line bundle for symplectic manifolds x conical at infinity we build a homomorphism from 1 ham l x to invertibles in s h x this is similar to seidel s representation for closed x except now they are not invertibles in q h x