Random matrix theory and fund of funds portfolio optimisation

The proprietary nature of Hedge Fund investing means that it is common practise for managers to release minimal information about their returns. The construction of a fund of hedge funds portfolio requires a correlation matrix which often has to be estimated using a relatively small sample of monthly returns data which induces noise. In this paper, random matrix theory (RMT) is applied to a cross-correlation matrix C, constructed using hedge fund returns data. The analysis reveals a number of eigenvalues that deviate from the spectrum suggested by RMT. The components of the deviating eigenvectors are found to correspond to distinct groups of strategies that are applied by hedge fund managers. The inverse participation ratio is used to quantify the number of components that participate in each eigenvector. Finally, the correlation matrix is cleaned by separating the noisy part from the non-noisy part of C. This technique is found to greatly reduce the difference between the predicted and realised risk of a portfolio, leading to an improved risk profile for a fund of hedge funds.     

有源光纤环等效时间脉冲复制研究

对利用半导体光放大器有源光纤环为光等效时间采样提供低失真脉冲序列的方法进行了研究。分析了提高复制精度的辅助直流光非线性增益抑制方法,并给出基于递推方式,可进一步提高采样精度的后处理算法。通过实验验证了辅助直流光注入对复制器非线性增益的抑制作用;以及在不充分辅助直流光注入条件下,利用后处理算法抑制非线性误差的效果。结果显示利用半导体光放大器有源光纤环结合后处理算法可以有效地为光等效时间采样提供特性一致、误差可处理的时序脉冲序列。     

Distance distribution functions of replication origins in HeLa and glioma human cells according to the data of confocal microscopy

The distribution of replication origins in the nuclei of different cells is studied by confocal microscopy. Based on the obtained images, three-dimensional maps of the positions of the origin centers is constructed and the distribution functions of the pair distances between them are calculated. It is established that the distance distribution function for HeLa and glioma human cells is linear at sizes up to 2 μm, which indicates that the size of the origin system is close to 2. The amplitude of the distance distribution function at small sizes has a power dependence on the nucleus size and is inversely proportional to the nucleus volume to the power of 0.9. Thus, the replication-origin distribution in a nucleus cannot be described by a model with a single Hausdorff dimension in the whole range of sizes.     

On nonlinear irreversible processes I

A functional integral expression of the two gate probability distribution function is obtained and the integral is performed in a “semiclassical” approximation. Based on this approximation, it is shown that the expression of the many gate probability distribution function in terms of two dissipation functions, which Onsager and Machlup presented before as the extension of Boltzmann's principle, is valid also for nonlinear processes with a slight modification of definition of the dissipation functions. Only the case that all the variables are even functions of time is treated for simplicity.     

Calculation of the Gluon Distribution Function Using Alternative Method for the Proton Structure Function

A calculation of the proton structure function F2(x,Q2) is reported with an approximation method that relates the reduced cross section derivative and the F2(x, Q2) scaling violation at low x by using quadratic form for the structure function. This quadratic form approximation method can be used to determine the structure function F2 (x, Q2)from the HERA reduced cross section data taken at low x. This new approach can determine the structure functions F2(x,Q2) with reasonable precision even for low x values which have not been investigated. We observe that the Q2 dependence is quadratic over the full kinematic covered range. To test the validity of our new determined structure functions, wefind the gluon distribution function in the leading order approximation with our new calculation for the structure functions and compare them with the QCD parton distribution functions.     

Calculation of the Gluon Distribution Function Using Alternative Method for the Proton Structure Function

A calculation of the proton structure function F2(x,Q^2) is reported with an approximation method that relates the reduced cross section derivative and the F2(x, Q^2) scaling violation at low x by using quadratic form for the structure function. This quadratic form approximation method can be used to determine the structure function F2 (x, Q^2) from the HERA reduced cross section data taken at low x. This new approach can determine the structure functions F2(x,Q^2) with reasonable precision even for low x values which have not been investigated. We observe that the Q^2 dependence is quadratic over the full kinematic covered range. To test the validity of our new determined structure functions, we find the gluon distribution function in the leading order approximation with our new calculation for the structure functions and compare them with the QCD parton distribution functions.     

How Xenopus laevis replicates DNA reliably even though its origins of replication are located and initiated stochastically

DNA replication in Xenopus laevis is extremely reliable, failing to complete before cell division no more than once in 10 000 times; yet replication origin sites are located and initiated stochastically. Using a model based on 1D theories of nucleation and growth and using concepts from extreme-value statistics, we derive the distribution of replication times given a particular initiation function. We show that the experimentally observed initiation strategy for Xenopus laevis meets the reliability constraint and is close to the one that requires the fewest resources of a cell.     

The Classical Binary and Triplet Distribution Functions for Two Component Plasma

The equilibrium properties of a multi‐component plasma of charged particles that interact through the coulomb and short‐range potentials are investigated. In particular, this article presents density expansions of the reduced distribution functions for more particles, our calculations are based on the Bogoliubov‐Born‐Green‐Kirkwood‐Yvon (BBGKY) hierarchy, we used the results to calculate the binary and triplet distribution functions. We obtained the analytical form of the classical triplet distribution functions for two component plasma; one of them is based on the Kirkwood superposition approximation (KSA) which is consisting of the assumption that the potential in a set of three particles is the sum of the three pair potentials, this is equivalent to assuming that the triplet distribution function is the product of the three radial distribution functions, and the other form is calculated by integration the triplet distribution function (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Unconventional application of the two-flux approximation for the calculation of the Ambartsumyan-Chandrasekhar function and the angular spectrum of the backward-scattered radiation for a semi-infinite isotropically scattering medium

It is commonly accepted that the Schwarzschild-Schuster two-flux approximation (1905, 1914) can be employed only for the calculation of the energy characteristics of the radiation field (energy density and energy flux density) and cannot be used to characterize the angular distribution of radiation field. However, such an inference is not valid. In several cases, one can calculate the radiation intensity inside matter and the reflected radiation with the aid of this simplest approximation in the transport theory. In this work, we use the results of the simplest one-parameter variant of the two-flux approximation to calculate the angular distribution (reflection function) of the radiation reflected by a semi-infinite isotropically scattering dissipative medium when a relatively broad beam is incident on the medium at an arbitrary angle relative to the surface. We do not employ the invariance principle and demonstrate that the reflection function exhibits the multiplicative property. It can be represented as a product of three functions: the reflection function corresponding to the single scattering and two identical h functions, which have the same physical meaning as the Ambartsumyan-Chandrasekhar function (H) has. This circumstance allows a relatively easy derivation of simple analytical expressions for the H function, total reflectance, and reflection function. We can easily determine the relative contribution of the true single scattering in the photon backscattering at an arbitrary probability of photon survival Λ. We compare all of the parameters of the backscattered radiation with the data resulting from the calculations using the exact theory of Ambartsumyan, Chandrasekhar, et al., which was developed decades after the two-flux approximation. Thus, we avoid the application of fine mathematical methods (the Wiener-Hopf method, the Case method of singular functions, etc.) and obtain simple analytical expressions for the parameters of the scattered radiation. Note that the simplicity of the expressions is supplemented with unexpectedly high accuracy. The results demonstrate the unknown possibilities offered by the two-flux approximation, which is the simplest approximate method to solve the equations of transport theory. We assume that the method can be employed in the calculations of the angular characteristics of the reflected radiation for media whose single scattering is described using complicated (in comparison with isotropic) laws.     

中心快度区的双轻子不变质量分布

推广先前作者采用的夸克和π的相空间分布函数的Boltzmann近似到一个完全的表示,利用快度区的温度计算出粒子密度后,在Bjorken的(1+1)维的纵向膨胀系统中研究了双轻子的产生.发现推广的近似分布函数很大地改变了预言的夸克物质形成的特征双轻子分布.     

Extraction of Structure Function and Gluon Distribution Function at Low-x from Cross Section Derivative by Regge Behavior

An approximation method based on Regge behavior is presented. This new method relates the reduced cross section derivative and the structure function Regge behavior at low x. With the use of this approximation method, the C and λ parameters are calculated from the HERA reduced cross section data taken at low-x. Also, we calculate the structure functions F₂(x,Q²) even for low-x values, which have not been investigated. To test the validity of calculated structure functions, we find the gluon distribution function in the Leading order approximation based on Regge behaviour of structure function and compare to the NLO QCD fit to H1 data and NLO parton distribution function.     

Evolution behavior of catalytically activated replication-decline in a coagulation process

We propose a catalytically activated replication-decline model of three species, in which two aggregates of the same species can coagulate themselves, an A aggregate of any size can replicate itself with the help of B aggregates, and the decline of A aggregate occurs under the catalysis of C aggregates. By means of mean-field rate equations, we derive the asymptotic solutions of the aggregate size distribution ak（t） of species A, which is found to depend strongly on the competition among three mechanisms： the self-coagulation of species A, the replication of species A catalyzed by species B, and the decline of species A catalyzed by species C. When the self-coagulation of species A dominates the system, the aggregate size distribution a~（t） satisfies the conventional scaling form. When the catalyzed replication process dominates the system, ak（t） takes the generalized scaling form. When the catalyzed decline process dominates the system, ak（t） approaches the modified scaling form.     

基于P3近似的空间分辨漫反射研究

光源附近组织的空间分辨漫反射是近年来生物医学光子学领域的一个研究热点,其目的是发展一种能够测定活体生物组织光学参量的新技术。漫射近似理论研究光源附近组织的空间分辨漫反射具有很大局限性。P3近似理论考虑了相函数的三阶矩,能较准确地描述光源附近组织的光辐射分布。研究了基于P3近似的空间分辨漫反射,从输运理论的PN方程组出发,导出了P3近似方程组和P3近似的格林函数解;阐述了漫射近似与P1近似的关系,给出了外推边界条件下,准直光束近似后的P3近似漫反射率的完整表示,讨论了相函数二阶参量对P3近似漫反射的影响,并与漫射近似和蒙特卡罗模拟结果进行了比较,指出了P3近似的应用范围。     

Plasma response functions,fluctuation-dissipation relations and the velocity-average-approximation

We derive and list relationships for quadratic and cubic static response functions and connect them with three- and four-point functions through generalized fluctuation-dissipation relations. We also introduce the useful concept of “response function of the second kind.” to describe the reponse of a system through the perturbation of its two-point functions. Next, we point out that the VAA (velocity-average-approximation) introduced earlier as a part of a dynamical approximation scheme for strongly coupled one-component plasmas is exact in the static limit. This observation, combined with the fluctuation-dissipation relations, allows one to derive a hierarchy of equations for response functions of increasing nonlinearity, which is equivalent to the BGY hierarchy for particle distribution functions.     

The structure of the water dimer

A previously reported self consistent approximation for the pair distribution function is applied to inverse power potentials. Results are reported for the first six virial coefficients over the full range of such potentials. The thermodynamic properties and pair distributions functions are presented for the inverse sixth and twelfth power potentials and are shown to be in close agreement with the results of molecular dynamics and Monte Carlo calculations.     

Using relative entropy to find optimal approximations: An application to simple fluids

We develop a maximum relative entropy formalism to generate optimal approximations to probability distributions. The central results consist of (a) justifying the use of relative entropy as the uniquely natural criterion to select a preferred approximation from within a family of trial parameterized distributions, and (b) to obtain the optimal approximation by marginalizing over parameters using the method of maximum entropy and information geometry. As an illustration we apply our method to simple fluids. The “exact” canonical distribution is approximated by that of a fluid of hard spheres. The proposed method first determines the preferred value of the hard-sphere diameter, and then obtains an optimal hard-sphere approximation by a suitably weighed average over different hard-sphere diameters. This leads to a considerable improvement in accounting for the soft-core nature of the interatomic potential. As a numerical demonstration, the radial distribution function and the equation of state for a Lennard-Jones fluid (argon) are compared with results from molecular dynamics simulations.     

The effect of anisotropy of a rough sea surface on the generation of acoustic radiation

A model that relates the frequency-angular characteristics of wind waves on the sea surface to the frequency spectrum of acoustic radiation generated by them is constructed. Based on empirical wave energy distribution functions, it is shown that, in the vicinity of the peak of the wind wave spectrum, the intensity of acoustic radiation strongly depends on the model chosen for the angular distribution function ?(α) and on its parameters. At high frequencies, four to five times higher than the dominant wave frequency, it is possible to assume that, to a first approximation, ?(α) = const. In the intermediate frequency range, between the dominant frequency and the high frequencies, the predominant contribution to the sound radiation is made by the waves that travel in the direction close to orthogonal with respect to the wind.     

Violation of the Porod law in a freely cooling granular gas in one dimension

We study a model of freely cooling inelastic granular gas in one dimension, with a restitution coefficient which approaches the elastic limit below a relative velocity scale delta. While at early times (tdelta;{-1}) it exhibits a new fluctuation-dominated phase ordering state. We find distinct scaling behavior for the (i) density distribution function, (ii) occupied and empty gap distribution functions, (iii) the density structure function, and (iv) the velocity structure function, as compared to the completely inelastic sticky gas. The spatial structure functions (iii) and (iv) violate the Porod law. Within a mean-field approximation, the exponents describing the structure functions are related to those describing the spatial gap distribution functions.     

显示反射全息图单光束相干复制技术

描述用单光束激光复活制银盐白光显示反射全息图的技术，本技术的关键：１）母全息图的颜色必须恢复到满足其布拉格条件；２）复制所用的光波与记录母全息图时的参考的相同；（３）复制所用的激光采用平行偏振，以减少界面反射；９４）采用白糖溶液作为折射率匹配液，取得极佳效果。