Fast TV Regularization for 2D Maximum Penalized Likelihood Estimation

Total Variation-based regularization, well established for image processing applications such as denoising, was recently introduced for Maximum Penalized Likelihood Estimation (MPLE) as an effective way to estimate nonsmooth probability densities. While the estimates show promise for a variety of applications, the nonlinearity of the regularization leads to computational challenges, especially in multidimensions. In this article we present a numerical methodology, based upon the Split Bregman L1 minimization technique, that overcomes these challenges, allowing for the fast and accurate computation of 2D TV-based MPLE. We test the methodology with several examples, including V-fold cross-validation with large 2D datasets, and highlight the application of TV-based MPLE to point process crime modeling. The proposed algorithm is implemented as the Matlab function TVMPLE. The Matlab (mex) code and datasets for examples and simulations are available as online supplements.     

环戊噻嗪的合成工艺改进

以溴代环戊烷和丙二酸二乙酯为起始原料,经缩合、水解、脱羧、还原、氧化、环合六个步骤合成了目标化合物环戊噻嗪;所得产物结构经核磁共振氢谱和质谱确证,产物纯度经高效液相色谱(HPLC)归一化法测定.结果表明,目标产物总收率可达25.5%,纯度为99.4%;经过改进的工艺条件稳定,操作简便,收率明显提高,适合于工业化生产.     

Verification of model for adsorption and reduction of chromium(VI) by Escherichia coli 33456 using chitosan bead as a supporting medium

A non-steady-state mathematical model system for the kinetics of adsorption and reduction of Cr(VI) by Escherichia coli (E. coli) biofilm on chitosan bead (EBCB) process was derived. The mechanisms in the model system included Cr(VI) adsorption by chitosan beads, Cr(VI) bioreduction by E. coli cells and Cr(VI) mass transport diffusion. Batch kinetic tests were performed to determine surface diffusivity of Cr(VI), adsorption parameters for Cr(VI) and biokinetic parameters of E. coli 33456. Experiments were conducted using an EBCB reactor system with high recycled rate to approximate a completely-mixed flow reactor for model verification. The experimental results indicated that E. coli biofilm bioregenerated the chitosan beads after E. coli biofilm has grown significantly. Cr(VI) reducing efficiency by E. coli was about 84% when Cr(VI) concentration in the influent was 5 mg/L at a steady-state condition. The concentration of suspended E. coli cells reached up to 10 mg/L while the thickness of attached E. coli cells was estimated to be 150 μm at a steady-state condition by model prediction. The comparisons of experimental data and model simulation show that EBCB model system for Cr(VI) adsorption and reduction can predict the experimental results well.     

Remarks on maximal meanstandard devition ratio in undiscounted mdps

In the steady state of an undiscounted Markov decision process, we consider the problem to find an optimal stationary probability distribution that maximizes the mean standard deviation ratio among all the stationary probability distributions. The problem injects considerations in MDPs from the relative point of view     

Chemical synthesis and magnetic properties of HCP and FCC nickel nanoparticles

In this study, we successfully synthesized single-phase hexagonal closed packed (HCP) and face-centered cubic (FCC) nickel nanoparticles via reduction of nickel nitrate hexahydrate and nickel acetate tetrahydrate, respectively, in polyethylene glycol-200. Structural information of the as-synthesized nickel nanoparticles are studied by X-ray diffraction (XRD) as a function of the molar concentration of the nickel precursor. XRD results reveal that low concentrations of nickel precursor (0.005?M and below) favor the HCP, while high concentrations favor the mixture of HCP and FCC crystal structures. Particle size of HCP structure is found in the range of ～15?nm via transmission electron microscope analysis. Vibratory sample magnetometer is employed to study its magnetic behavior and the results reveal that FCC crystalline phase shows ferromagnetic nature with high saturation magnetization (M _s?～?39.6?emu?gm^?1) as compared to metastable HCP crystalline structure (M _s?～?2?emu?gm^?1). The surfactants bonding on the surface of nickel nanoparticles are studied.     

Computation of Spatial Covariance Matrices

In an earlier article, Ghosh derived the density for the distance between two points uniformly and independently distributed in a rectangle. This article extends that work to include the case where the two points lie in two different rectangles in a lattice. This density allows one to find the expected value of certain functions of this distance between rectangles analytically or by one-dimensional numerical integration.

In the case of isotropic spatial models or spatial models with geometric anisotropy terms for agricultural experiments one can use these theoretical results to compute the covariance between the yields in different rectangular plots. As the numerical integration is one-dimensional these results are computed quickly and accurately. The types of covariance functions used come from the Matérn and power families of processes. Analytic results are derived for the de Wijs process, a member of both families and for the power models also.

Software in R is available. Examples of the code are given for fitting spatial models to the Fairfield Smith data. Other methods for the estimation of the covariance matrices are discussed and their pros and cons are outlined.     

Existence of solutions in variational relation problems without convexity

Two main existence conditions for solutions of variational relation problems are established without convexity. The first one is based on a finite solvability property and the second one on generalized KKM mappings. These conditions unify and strengthen several existing results in the literature on the topic. A model of satisficing process by rejection is considered which gives an economic interpretation of the introduced concepts.     

An LDQBD process under degradation,inspection, and two types of repair

A warm standby n-system with operational and repair times following phase-type distributions is considered. The online unit goes through degradating levels, determined by inspections. Two types of repairs are performed, preventive and corrective, depending on the degradation level. The standby units undergo corrective repair. This systems is governed by a level-dependent-quasi-birth-and-death proces (LDQBD process), whose generator is constructed. The availability, rate of occurrence of failures, and other quantities of interest are calculated. A numerical example including an optimization problem and illustrating the calculations is presented. This system extend other previously studied in the literature.