Karhunen-Lo\`eve expansion for a generalization of Wiener bridge

We derive a Karhunen-Lo\`eve expansion of the Gauss process $B_t - g(t)\int_0^1 g'(u)\,d B_u$, $t\in[0,1]$, where $(B_t)_{t\in[0,1]}$ is a standard Wiener process and $g:[0,1]\to R$ is a twice continuously differentiable function with $g(0) = 0$ and $\int_0^1 (g'(u))^2\,d u =1$. This process is an important limit process in the theory of goodness-of-fit tests. We formulate two special cases with the function $g(t)=\frac{\sqrt{2}}{\pi}\sin(\pi t)$, $t\in[0,1]$, and $g(t)=t$, $t\in[0,1]$, respectively. The latter one corresponds to the Wiener bridge over $[0,1]$ from $0$ to $0$.Comment: 25 pages, 1 figure. The appendix is extende

Helicity Observation of Weak and Strong Fields

We report in this letter our analysis of a large sample of photospheric vector magnetic field measurements. Our sample consists of 17200 vector magnetograms obtained from January 1997 to August 2004 by Huairou Solar Observing Station of the Chinese National Astronomical Observatory. Two physical quantities, $\alpha$ and current helicity, are calculated and their signs and amplitudes are studied in a search for solar cycle variations. Different from other studies of the same type, we calculate these quantities for weak ($100G1000G$) fields separately. For weak fields, we find that the signs of both $\alpha$ and current helicity are consistent with the established hemispheric rule during most years of the solar cycle and their magnitudes show a rough tendency of decreasing with the development of solar cycle. Analysis of strong fields gives an interesting result: Both $\alpha$ and current helicity present a sign opposite to that of weak fields. Implications of these observations on dynamo theory and helicity production are also briefly discussed.Comment: accepted for publication in ApJ Lette

Disability in Kazakhstan : an evaluation of official data

In order to answer the questions of (a) what is the true pattern of disability in Kazakhstan; (b) whether the incidence of disability is decreasing; and (c) what is the life expectancy of Kazakhstan's disabled, this paper attempts first to create an historical picture of disability in Kazakhstan by analyzing government population statistics and studying the evolution of disability determination procedure in the former Soviet Union and independent Kazakhstan. Doing so is not a trivial task, as there has been almost no systematic research, either in Russian or English. The paper concludes that the optimistic official picture of disability patterns in Kazakhstan is almost certainly inaccurate. The paper details that the quality of official disability data is high, and much can be learned from the patterns. However, changing definitions and strictness of enforcement make time series comparisons problematic, and the improvements in adult disability recorded are inconsistent both with trends for children, and with mortality trends. Rather, the authors note that barriers for applying disability benefits have increased and incentives to report disabilities have decreased markedly in the past 15 years, so that it is virtually certain that there is substantial hidden disability.Population Policies,Disease Control&Prevention,Disability,,Social Protections&Assistance

Kazakhstan's Pension System: Pressures for Change and Dramatic Reforms

Five years ago, Kazakhstan embarked on a dramatic reform of its pension and social security system in order to move from an unsustainable public defined benefit ("solidarity") system to one of defined mandatory contributions (accumulative system). While assessment of long-run success is premature, early results have exceeded expectations. This paper considers the reform's rationale and initial impact: Why did the Government of Kazakhstan decide to introduce a new pension system? What advantages did the state perceive? Was the Government's decision appropriate, and what alternatives existed? The paper also analyzes pension reform issues that have yet to be fully resolved.

Fertility and Marriage in Kazakhstan's Transition Period: Implications for Social Security Policy

Seven years ago, Kazakhstan embarked on a dramatic reform of its pension and social security system in order to move from an unsustainable public defined benefit ("solidarity") system to one of defined mandatory contributions (accumulative system). While much has been written on the financial implications for individual contributors, and on macro budgetary impacts, there has been no examination of how changing demographic structure is likely to affect the size of vulnerable pools. This paper explores the impact of these changes, and links demographic structure to economic performance. Focusing on changes in nuptiality (marriage) and fertility, we conclude that demographic structural shifts will increase overall system risk, but that current trends are favorable.

Constructing solutions to the Bj\"orling problem for isothermic surfaces by structure preserving discretization

In this article, we study an analog of the Bj\"orling problem for isothermic surfaces (that are more general than minimal surfaces): given a real analytic curve $\gamma$ in ${\mathbb R}^3$, and two analytic non-vanishing orthogonal vector fields $v$ and $w$ along $\gamma$, find an isothermic surface that is tangent to $\gamma$ and that has $v$ and $w$ as principal directions of curvature. We prove that solutions to that problem can be obtained by constructing a family of discrete isothermic surfaces (in the sense of Bobenko and Pinkall) from data that is sampled along $\gamma$, and passing to the limit of vanishing mesh size. The proof relies on a rephrasing of the Gauss-Codazzi-system as analytic Cauchy problem and an in-depth-analysis of its discretization which is induced from the geometry of discrete isothermic surfaces. The discrete-to-continuous limit is carried out for the Christoffel and the Darboux transformations as well.Comment: 29 pages, some figure

Pension Reform in Central Asia: An Overview

Seven years ago, Kazakhstan embarked on a dramatic reform of its pension and social security system in order to move from a public defined benefit ("solidarity") system to one of defined mandatory contributions (accumulative system). At the same time, Kyrgyzstan embarked on a move to a notional defined contribution (NDC) system that has made little progress. Today, major reforms are being planned in both Uzbekistan and Tajikistan as well. This paper surveys the reforms that have taken place, discusses the planned reforms, and places them in the underlying fiscal and demographic contexts of the various countries in the region.

On a new conformal functional for simplicial surfaces

We introduce a smooth quadratic conformal functional and its weighted version $$W_2=\sum_e \beta^2(e)\quad W_{2,w}=\sum_e (n_i+n_j)\beta^2(e),$$ where $\beta(e)$ is the extrinsic intersection angle of the circumcircles of the triangles of the mesh sharing the edge $e=(ij)$ and $n_i$ is the valence of vertex $i$. Besides minimizing the squared local conformal discrete Willmore energy $W$ this functional also minimizes local differences of the angles $\beta$. We investigate the minimizers of this functionals for simplicial spheres and simplicial surfaces of nontrivial topology. Several remarkable facts are observed. In particular for most of randomly generated simplicial polyhedra the minimizers of $W_2$ and $W_{2,w}$ are inscribed polyhedra. We demonstrate also some applications in geometry processing, for example, a conformal deformation of surfaces to the round sphere. A partial theoretical explanation through quadratic optimization theory of some observed phenomena is presented.Comment: 14 pages, 8 figures, to appear in the proceedings of "Curves and Surfaces, 8th International Conference", June 201