A statistical dynamics approach to the study of human health data: Resolving population scale diurnal variation in laboratory data

Statistical physics and information theory is applied to the clinical chemistry measurements present in a patient database containing 2.5 million patients' data over a 20-year period. Despite the seemingly naive approach of aggregating all patients over all times (with respect to particular clinical chemistry measurements), both a diurnal signal in the decay of the time-delayed mutual information and the presence of two sub-populations with differing health are detected. This provides a proof in principle that the highly fragmented data in electronic health records has potential for being useful in defining disease and human phenotypes.     

Full fitting analysis of the relative intermediate form factor measured by neutron spin echo

This paper describes the dynamics of a water-in-oil microemulsion from the dilute to the dense droplet region. Using the relative intermediate form factor method for neutron spin echo data analyses [M. Nagao, H. Seto, Phys. Rev. E 78 (2008) 011507], the shape and structure fluctuations of a droplet microemulsion are successfully decoupled. In the previous paper, we used the first cumulant analysis of the shape fluctuation model, while the full fitting form of the same model is applied in this paper. The final results of the fittings using the first cumulant approximation and the full form of the model are almost identical, and therefore, the validity of the method is strengthened. The estimated bending modulus of the surfactant membrane, κ, is basically the same, within the experimental errors, in the previous and present results. The κ is not affected much by an increase of the droplet concentration. A clear dynamic slowing down of the water droplets is highlighted at the length scale corresponding to the inter-droplet distance from the structure fluctuation analysis.     

Effects of composition grading at heterointefaces and layer thickness variations on Bragg mirror quality

GaAs/AlAs Bragg mirrors on GaAs with varied number of layer pairs were grown, by molecular beam epitaxy (MBE), to be applied for semiconductor saturable absorber mirrors (SESAMs) and intensity modulators. Due to the random variation of the growth rate, substrate surface roughness, and interdiffusion at the interfaces, precise control of the growth conditions of deposited layers poses a serious problem. Usually, thickness variations and composition grading at the heterointefaces result in variations of the mirror reflectivity. In this paper, the high resolution X-ray diffraction (HRXRD), optical reflectance, Rutherford backscattering/channelling (RBS), supported by numerical evaluation methods were employed to determine both the exact thickness of each layer and the composition grading at the interface between succeeding layers of GaAs/AlAs-based mirrors. To reduce ambiguity and to speed up the analysis, the rocking curves and RBS spectra were simulated concurrently, using results of one simulation to verify the others. This process was carried out until the best fit between experimental and calculated curves was achieved. The complementary use of both methods results in improved sensitivity and makes the whole process of evaluation of the thickness variation of each layer and the size of the composition grading at the interfaces less time consuming.     

Seasonal variability of cloud optical depth over northwestern China derived from CERES/MODIS satellite measurements

The seasonal variability of cloud optical depth over northwestern China derived from Clouds and the Earth＇s Radiant Energy System （CERES） Single Scanner Footprint （SSF） Aqua Moderate Resolution Imaging Spectroradiometer （MODIS） Edition IB data from July 2002 to June 2004 is presented. The regions of interest are those with Asia monsoon influence, the Tianshan and Qilian Mountains, and the Taklimakan Desert. The results show that the instantaneous measurements presented here are much higher than the previous results derived from International Satellite Cloud Climatology Project （ISCCP） D2 monthly mean data. Generally the measurements of cloud optical depth are the highest in summer and the lowest in winter, however, Taklimakan Desert has the lowest measurements in autumn. The regional variation is quite significant over northwestern China.     

The effect of a surface energy term on the distribution of phases in an elastic medium with a two‐well elastic potential

We consider the problem of minimizing among functions u:?^d?Ω→?^d, u_∣?Ω=0, and measurable subsets E of Ω. Here f_h⁺, f^? denote quadratic potentials defined on Ω¯×{symmetric d×d matrices}, h is the minimum energy of f_h⁺ and ε(u) is the symmetric gradient of the displacement field u. An equilibrium state û, Ê of J(u,E) is called one‐phase if E=?? or E=Ω, two‐phase otherwise. For two‐phase states, σ∣?E∩Ω∣ measures the effect of the separating surface, and we investigate the way in which the distribution of phases is affected by the choice of the parameters h??, σ>0. Additional results concern the smoothness of two‐phase equilibrium states and the behaviour of inf J(u,E) in the limit σ↓0. Moreover, we discuss the case of additional volume force potentials, and extend the previous results to non‐zero boundary values. Copyright © 2002 John Wiley & Sons, Ltd.     

The Integrated Density of States for Some Random Operators with Nonsign Definite Potentials

We study the integrated density of states of random Anderson-type additive and multiplicative perturbations of deterministic background operators for which the single-site potential does not have a fixed sign. Our main result states that, under a suitable assumption on the regularity of the random variables, the integrated density of states of such random operators is locally Hölder continuous at energies below the bottom of the essential spectrum of the background operator for any nonzero disorder, and at energies in the unperturbed spectral gaps, provided the randomness is sufficiently small. The result is based on a proof of a Wegner estimate with the correct volume dependence. The proof relies upon the L^p-theory of the spectral shift function for p?1 (Comm. Math. Phys.218 (2001), 113-130), and the vector field methods of Klopp (Comm. Math. Phys.167 (1995), 553-569). We discuss the application of this result to Schrödinger operators with random magnetic fields and to band-edge localization.     

On a Property of Subexponential Distributions

Let F be a distribution function (d.f.) on [0, ) with finite first moment m >0. We define the integrated tail distribution function F ₁ of F by F ₁(t)=m^-1 ₀ ^t (1- F(u))du, t0. In this paper, we obtain sufficient conditions under which implications FSF ₁S and F ₁S FS hold, where S is the class of subexponential distributions.     

Generalized One-Sided Laws for the Larger Observations of a Triangular Array

Consider independent and identically distributed random variables {X,X _nj , 1jn,n1} with density f(x)=px ^–p–1 I(x1), where p>0. We show that there exist unusual generalized Laws of the Iterated Logarithm involving the larger order statistics from our array.     

Calculation of electron wave functions and refractive index of Ne

The radial wave functions of inner electron shell and outer electron shell of a Ne atom were obtained by the approximate analytical method and tested by calculating the ground state energy of the Ne atom. The equivalent volume of electron cloud and the refractive index of Ne were calculated. The calculated refractive index agrees well with the experimental result. Relationship between the refractive index and the wave function of Ne was discovered. Supported by the New Star Program of Beijing Science and Technology, China (Grant No. 952870400), the Beijing Municipal Commission of Education, and the Excellent Young Teachers Program of Ministry of Education, China     

On pointwise convergence of Fourier series of radial functions in several variables

We prove the pointwise convergence of the Fourier series for radial functions in several variables, which in the case is the Dirichlet-Jordan theorem itself. In our proof the method for the case of the indicator function of the ball is very useful.