Inverse statistics in the foreign exchange market

We investigate intra-day foreign exchange (FX) time series using the inverse statistic analysis developed by Simonsen et al. (Eur. Phys. J. 27 (2002) 583) and Jensen et al. (Physica A 324 (2003) 338). Specifically, we study the time-averaged distributions of waiting times needed to obtain a certain increase (decrease) ρ in the price of an investment. The analysis is performed for the Deutsch Mark (DM) against the US$ for the full year of 1998, but similar results are obtained for the Japanese Yen against the US$. With high statistical significance, the presence of “resonance peaks” in the waiting time distributions is established. Such peaks are a consequence of the trading habits of the market participants as they are not present in the corresponding tick (business) waiting time distributions. Furthermore, a new stylized fact, is observed for the (normalized) waiting time distribution in the form of a power law Pdf. This result is achieved by rescaling of the physical waiting time by the corresponding tick time thereby partially removing scale-dependent features of the market activity.     

Gain–loss asymmetry for emerging stock markets

Stock indexes for some European emerging markets are analyzed using an investment-horizon approach. Austrian ATX index and Dow Jones have been studied and compared with several emerging European markets. The optimal investment horizons are plotted as a function of an absolute return value. Gain–loss asymmetry, originally found for American DJIA index, is observed for all analyzed data. It is shown, that this asymmetry has different character for emerging and for established markets. For established markets, gain curve lies typically above loss curve, whereas in the case of emerging markets the situation is just the opposite. We propose a measure quantifying the gain–loss asymmetry that clearly exhibits a difference between emerging and established markets.     

Nonextensive statistics and incomplete information

We comment on some open questions and theoretical peculiarities in Tsallis nonextensive statistical mechanics. It is shown that the theoretical basis of the successful Tsallis' generalized exponential distribution shows some worrying properties with the conventional normalization and the escort probability. These theoretical difficulties may be avoided by introducing an so called incomplete normalization allowing to deduce Tsallis' generalized distribution in a more convincing and consistent way. Received 29 October 2001 and Received in final form 30 January 2002     

The relation between properties of Gentile statistics and fractional statistics of anyon

In this paper, we discuss the relationship of two kinds of intermediate-statistics, the Gentile statistics and the fractional statistics of anyons. The anyon winding number representation is introduced. We construct the transformation between anyon winding number representation and the occupation number representation of particles of Gentile statistics. We study intermediate-statistics quantum bracket and coherent states for anyons in the winding number representation. We demonstrate that anyons can be simulated by Gentile statistics with a geometric phase.     

Inverse filtering

Inverse filtering is a noninvasive method of producing a glottogram thought to reflect the vibratory motions of the vocal fold. The flow glottogram provides information related to the type of phonation, the sound pressure level, the regularity of vocal fold vibrations, and to the presence or absence of vocal fold closure. Limited data, speech samples, filter tuning, and lack of unanimity on waveform display and interpretation have contributed to slow application of the techniques to the clinical population. The author argues the technique has utility in both diagnosis and treatment     

偏度最大化多通道逆滤波语音去混响研究*

房间混响会降低语音质量和语音可懂度。高阶统计量是衡量非高斯性的重要参量,基于语音非高斯特性可实现语音去混响。本文提出一种基于高阶统计量的多通道语音去混响方法,该方法首次用多通道语音信号线性预测残差的三阶统计量偏度（Skewness）构造代价函数,以去混响重建信号线性预测残差的偏度最大化为目标自适应地更新逆滤波器;同时结合语音信号的产生模型,提出基于偏度准则的线性预测与房间脉冲响应逆滤波联合估计方法,进一步提高去混响算法性能。实验结果表明,该方法相较于已有的基于线性预测残差四阶统计量峰度（Kurtosis）的方法具有更好的去混响效果,且对噪声具有更强的鲁棒性。     

Inverse solutions to radiative-transfer problems with partially transparent boundaries and diffuse reflection

Analytical techniques are used to solve a class of inverse radiative-transfer problems relevant to finite and semi-infinite plane-parallel media. While the assumption of isotropic scattering is made, diffuse reflection is allowed at the surface, for the semi-infinite case, and at both surfaces for the case of a finite layer. For the general case based on a semi-infinite medium, a cubic algebraic equation is used to define the basic result, but for the specific case of a semi-infinite medium illuminated by a constant incident distribution of radiation, very simple exact expressions are developed for the albedo for single scattering ? and the coefficient for diffuse reflection ρ. Analytical results are also developed (again in terms of a cubic algebraic equation) for the case of a finite layer with equal reflection coefficients relevant to the two surfaces. For the general case of a finite layer with unequal reflection coefficients, two specific formulations are given. The first algorithm is based on a system of three quadratic algebraic equations for the two reflection coefficients ρ₁ and ρ₂ and the single-scattering albedo ?. Secondly, an elimination between these three algebraic equations is carried out to yield two coupled algebraic equations for ρ₁ and ρ₂ plus an explicit expression for ? in terms of ρ₁ and ρ₂. In addition, an exact expression for τ₀, the optical thickness of the finite layer, is developed in terms of ?, ρ₁ and ρ₂. As is typical with the considered class of inverse problems in radiative transfer, all surface quantities are either specified or considered available from experimental measurements. All basic results are tested numerically.     

Inverse spectral theory for random Jacobi matrices

We give necessary and sufficient conditions for a Herglotz function to be thew-function of a random stationary Jacobi matrix.This paper is dedicated to the memory of Mark Kac.     

Ensemble and trajectory statistics in a nonlinear partial differential equation

We have examined the influence of parametric noise on the solution behavioru(t, x) of a nonlinear initial value() problem arising in cell kinetics. In terms of ensemble statistics, the eventual limiting solution mean and variance are well-characterized functions of the noise statistics, and and depend on . When noise is continuously present along the trajectory, and are independent of the noise statistics and . However, in their evolution toward and , both _u (t, x) and _u ² (t, x) depend on the noise and.     

Inverse problem of ship propeller cavitationnoise radiation

I.IntroductionInthecourseofnavigation,shipsinevitablyproducevariouskindsofnoiseradiation,whichbringusimportantinformation.Ononehand,manyresearchersdevotethemselvestothestudyofthetime-frequency-amplitudedomaincharacteristicsoftheshipnoiseradiationfield,whichistheregularmethodforstudyingthenoiseradiation,i.e.,thedirectproblem.ontheotherhand,theyareworkinghardatmakinguseofthelloiseradiationtoinferthestateofshipnavigationandtheconditionofthemainaPparatusonboard,etc.,andthisistheinverseproblemofthe…     

Inverse problems of aggregation processes

The coagulation frequency is the key ingredient in the population balance (Smoluchowski) equation of coagulation kinetics. An inverse problem is formulated to extract the coagulation frequency from transient size distributions when these distributions are self-similar. Two numerical examples illustrate the procedure. The first demonstrates the inverse problem for the recovery of singular coagulation frequencies, while the second shows the procedure when self-similarity is approximate. Transient droplet coagulation experiments in a turbulent flow field have been performed. The resulting size distributions are observed to be self-similar. The inverse problem is used to determine the drop coagulation frequency. This frequency shows significant deviation from the coagulation frequencies derived from simple models of drop-drop interactions in a turbulent flow field.     

Generalized algebra within a nonextensive statistics

By considering generalized logarithm and exponential functions used in nonextensive statistics, the four usual algebraic operators: addition, subtraction, product and division, are generalized. The properties of the generalized operators are investigated. Some standard properties are preserved, e.g. associativity, commutativity and existence of neutral elements. On the contrary, the distributivity law and the opposite element are no more universal within the generalized algebra.     

Brillouin statistics vindicated

Brillouin statistics have been recently derived from a general theory of indistinguishable classical particles. We derive Brillouin's formulas by a random process ruling the growth of the physical system. This growth process is concerned with distinguishable and observable events, which have nothing to do with (in)distinguishability of particles.     

Gentile statistics and restricted partitions

In a recent paper (Tranet al, Ann. Phys.311, 204 (2004)), some asymptotic number theoretical results on the partitioning of an integer were derived exploiting its connection to the quantum density of states of a many-particle system. We generalise these results to obtain an asymptotic formula for therestricted or coloured partitionsp _k ^s (n), which is the number of partitions of an integern into the summand of sth powers of integers such that each power of a given integer may occur utmostk times. While the method is not rigorous, it reproduces the well-known asymptotic results fors = 1 apart from yielding more general results for arbitrary values ofs.     

Non-Gaussian statistics,Maxwellian derivation and stellar polytropes

In this letter we discuss two aspects of non-Gaussian statistics. In the first, we show that Maxwell’s first derivation of the stationary distribution function for a dilute gas can be extended in the context of Kaniadakis statistics. In the second, by investigating the stellar system, we study the Kaniadakis analytical relation between the entropic parameter κ$\kappa$ and the stellar polytrope index n$n$. We compare also the Kaniadakis relation n=n(κ)$n=n\left(\kappa \right)$ with n=n(q)$n=n\left(q\right)$ proposed in the Tsallis framework.     

Energy distribution and energy fluctuation in Tsallis statistics

The energy distribution and the energy fluctuation in the Tsallis canonical ensemble are studied with the OLM formalism but following a new way. The resulting formula for the energy fluctuation is not the same as that in previous work [L.Y. Liu, J.L. Du, Physica A 387 (2008) 5417]. In discussing the application of an ideal gas, we find that the energy fluctuation can not be negligible in the thermodynamic limit, showing the ensemble nonequivalence for this case in Tsallis statistics. We investigate the energy fluctuation with a Tsallis generalized canonical distribution studied by Plastino and Plastino [A.R. Plastino, A. Plastino, Phys. Lett. A 193 (1994) 140] for describing a system in contact with a finite heat bath. For this situation, the two formulae for the energy fluctuation are shown to be equivalent, while the nonextensive parameter q$q$ plays a very important role.     

Extrema statistics of Wiener-Einstein processes in one,two, and three dimensions

The maxima and first-passage-time statistics of Wiener-Einstein processes are evaluated analytically in one, two, and three dimensions. We show that the mean square maximum displacement has the same time dependence as the mean square displacement, i.e., it grows linearly with time. The ratio of the mean square maximum to the mean square displacement is shown to decrease with increasing dimensionality. We also calculate the mean first passage time for the process to attain a given absolute displacement and find that it grows as the square of the displacementand is independent of the dimensionality of the process. In addition, we evaluate the dispersion of maxima and of first passage times and discuss their dependence on dimensionality.Supported in part by the National Science Foundation under Grant CHE 75-20624.     

Spectral statistics and the Dzyaloshinsky–Moriya interaction of nanomagnet

The spectral statistics of nanomagnet V₁₅ is studied. We study the dependence of the Dzyaloshinsky–Moriya interaction in V₁₅ on the spectral statistics.