On the Kolmogorov Inequality for M Φ -Norm

In this paper, we prove the Kolmogorov inequality for M | -norms generated by concave functions (with the same constants as in the Kolmogorov inequality).     

Nonlinear continuous-discrete filtering using kernel density estimatesand functional integrals

We develop filter algorithms for nonlinear stochastic differential equations with discrete time measurements (continuous-discrete state space model). The apriori density (time update) is computed by Monte Carlo simulations of the Fokker-Planck equation using kernel density estimators and measurement updates are obtained by using the extended Kalman filter (EKF) updates. For small sampling intervals, a discretized continuous sampling approach (DCS) is used. A third algorithm utilizes a functional (path) integral representation of the transition density (functional integral filter FIF). The kernel density filter (KDF), DCS, and FIF are compared with the EKF and the Gaussian sum filter by using a Ginzburg-Landau-equation and a stochastic volatility model.     

A GENERATIVE MODEL OF INCOME DISTRIBUTION: FORMALIZATION WITH ITERATED INVESTMENT GAME

The purpose of this paper is to formalize a simple model that theoretically connects individuals' rational choice at the micro level to income distribution, which is subject to the Gibrat's law empirically, as social structure at macro level. We use an iterated investment game as a baseline model in which a player has a binary choice between investing and not investing. Given parameters which prescribe the payoff structure of the game are the prize density γ and the rate of return R. Method of analysis is a simulation with computation. We investigate changes in the Gini coefficient and skewness of the total profit distribution, as the parameters varied as follows: 0 ≤ γ ≤ 1, R = 0.5, 1, 2, 3, and n (the number of times that the game is repeated) = 5, 10. As a result of analysis, we derive the implication that the Gini coefficient increases up to critical point, where 0 ≤ γ ≤ 1/(R + 1), then decreases as prize density increases, where 1/(R + 1) < γ ≤ 1. Furthermore, we show that our model, with cumulative effect, generates a lognormal distribution under the condition that 1/(R + 1) < γ ≤ 1.     

The Inequality Process Versus the Saved Wealth Model: Which Is the More Likely to Imply an Analogue of Thermodynamics in Social Science?

The Inequality Process (IP) and the Saved Wealth Model (SW) are theories of income distribution. The IP's social science metatheory requires its stationary distribution to fit the distribution of labor income conditioned on education. The SW is a modification of the particle system model of the kinetic theory of gases (KTG), the basis of gas thermodynamics. The IP is a particle system similar to the SW and KTG. This article shows that the IP passes the empirical test required of it by social science theory better than the SW. The IP's advantage increases as the U.S. labor force becomes more educated. The IP may the better bet to imply an analogue of thermodynamics in social science.     

Extreme rays for the large cone of hermitian generalized matrix functions

Given a <artwork name="GLMA31007ei1">-valued function f with domain <artwork name="GLMA31007ei2">, the symmetric group on {1,2,…, m}, we define the generalized matrix function [ f ](?), or d_f (?), in the usual way on the set of all m× m complex matrices. Letting <artwork name="GLMA31007ei3"> denote the set of all m× m positive semi-definite Hermitian matrices we consider the cone K _m whose elements are the Hermitian functions <artwork name="GLMA31007ei4"> such that [ f ]( A)≥0 for all <artwork name="GLMA31007ei5">. The extreme rays in K _m are fundamental to an understanding of the linear inequalities that result by restricting the generalized matrix functions [ f ](?) to the sets <artwork name="GLMA31007ei6">. In particular, the resolution of Lieb's permanent dominance conjecture, and certain similar conjectures such as the conjecture of Soules, will likely require identification and careful analysis of these rays. Grone, Merris, and Watkins have shown that the determinant function det(?), which is [ f ](?) if f is the signum function, is extreme in K _m for each m. We identify additional rays that are extreme for all m. In particular, we associate with each 2-term partition <artwork name="GLMA31007ei7"> of {1,2,…, m} an element <artwork name="GLMA31007ei8"> that is shown to be extreme in K _m for each m. If <artwork name="GLMA31007ei9"> is trivial, then <artwork name="GLMA31007ei10"> reduces to the determinant function; hence, our results are a natural extension of the result of Grone, Merris, and Watkins. Moreover <artwork name="GLMA31007ei11">, like det ( A), is expressible as a function of the eigenvalues of certain matrices related to A. Additional classes of extreme rays are also presented.     

Bayesian Inference and Prediction of Gaussian Random Fields Based on Censored Data

This work develops a Bayesian approach to perform inference and prediction in Gaussian random fields based on spatial censored data. These type of data occur often in the earth sciences due either to limitations of the measuring device or particular features of the sampling process used to collect the data. Inference and prediction on the underlying Gaussian random field is performed, through data augmentation, by using Markov chain Monte Carlo methods. Previous approaches to deal with spatial censored data are reviewed, and their limitations pointed out. The proposed Bayesian approach is applied to a spatial dataset of depths of a geologic horizon that contains both left- and right-censored data, and comparisons are made between inferences based on the censored data and inferences based on “complete data” obtained by two imputation methods. It is seen that the differences in inference between the two approaches can be substantial.     

刘徽不等式与祖冲之不等式的注记

利用微分学方法给出刘徽不等式与祖冲之不等式的证明;得到两个关于双曲函数的不等式;还得到两个关于单位圆内接正n边形周长与π之间关系的不等式.     

An improved feasible QP-free algorithm for inequality constrained optimization

In this paper, an improved feasible QP-free method is proposed to solve nonlinear inequality constrained optimization problems. Here, a new modified method is presented to obtain the revised feasible descent direction. In view of the computational cost, the most attractive feature of the new algorithm is that only one system of linear equations is required to obtain the revised feasible descent direction. Thereby, per single iteration, it is only necessary to solve three systems of linear equations with the same coefficient matrix. In particular, without the positive definiteness assumption on the Hessian estimate, the proposed algorithm is still global convergence. Under some suitable conditions, the superlinear convergence rate is obtained.     

On the approximate inverse method in SPECT image reconstruction

ABSTRACT

In this paper, we first study the smoothing properties of the attenuated Radon transform with complex-valued coefficients. Then on the basis of the framework of Sobolev spaces and the method of the approximate inverse, we derive a reconstruction algorithm. Finally, we extend the results of Rigaud and Lakhal to the attenuated Radon transform with complex-valued coefficients.