Nonparametric spatial models for extremes: application to extreme temperature data

Estimating the probability of extreme temperature events is difficult because of limited records across time and the need to extrapolate the distributions of these events, as opposed to just the mean, to locations where observations are not available. Another related issue is the need to characterize the uncertainty in the estimated probability of extreme events at different locations. Although the tools for statistical modeling of univariate extremes are well-developed, extending these tools to model spatial extreme data is an active area of research. In this paper, in order to make inference about spatial extreme events, we introduce a new nonparametric model for extremes. We present a Dirichlet-based copula model that is a flexible alternative to parametric copula models such as the normal and t-copula. The proposed modelling approach is fitted using a Bayesian framework that allow us to take into account different sources of uncertainty in the data and models. We apply our methods to annual maximum temperature values in the east-south-central United States.     

A linear programming approach for linear programs with probabilistic constraints

We study a class of mixed-integer programs for solving linear programs with joint probabilistic constraints from random right-hand side vectors with finite distributions. We present greedy and dual heuristic algorithms that construct and solve a sequence of linear programs. We provide optimality gaps for our heuristic solutions via the linear programming relaxation of the extended mixed-integer formulation of Luedtke et al. (2010) [13] as well as via lower bounds produced by their cutting plane method. While we demonstrate through an extensive computational study the effectiveness and scalability of our heuristics, we also prove that the theoretical worst-case solution quality for these algorithms is arbitrarily far from optimal. Our computational study compares our heuristics against both the extended mixed-integer programming formulation and the cutting plane method of Luedtke et al. (2010) [13]. Our heuristics efficiently and consistently produce solutions with small optimality gaps, while for larger instances the extended formulation becomes intractable and the optimality gaps from the cutting plane method increase to over 5%.     

Two Strong Convergence Theorems for a Proximal Method in Reflexive Banach Spaces

Two strong convergence theorems for a proximal method for finding common zeroes of maximal monotone operators in reflexive Banach spaces are established. Both theorems take into account possible computational errors.     

High‐Temperature Spray‐Dried Polymer/Bacteria Microparticles for Electrospinning of Composite Nonwovens

Living Micrococcus luteus (M. luteus) and Escherichia coli (E. coli) are encapsulated in poly(vinyl alcohol), poly(vinylpyrrolidone), hydroxypropyl cellulose, and gelatin by high‐temperature spray drying. The challenge is the survival of the bacteria during the standard spray‐drying process at temperatures of 150 °C (M. luteus) and 120 °C (E. coli). Raman imaging and transmission electron microscopy indicate encapsulated bacteria in hollow composite microparticles. The versatility of the spray‐dried polymer bacteria microparticles is successfully proved by standard polymer solution–processing techniques such as electrospinning, even with harmful solvents, to water‐insoluble polyacrylonitrile, polystyrene, poly(methyl methacrylate), and poly(vinyl butyrate) nanofiber nonwovens, which opens numerous new opportunities for novel applications.     

Two Projection Algorithms for Solving the Split Common Fixed Point Problem

Journal of Optimization Theory and Applications - We study the split common fixed point problem for Bregman relatively nonexpansive operators in real reflexive Banach spaces. Using Bregman...     

Temperature variation of bubble domains in Dy0.3Tm0.7FeO3 mixed orthoferrite

Bubble domain structure in Dy_0.3Tm_0.7FeO₃ mixed orthoferrite was studied between room temperature and 480 K using the Faraday effect. Temperature dependence of the magnetization and domain wall energy density has been determined. Starting from the molecular field theory and one-ion theory of magnetocrystalline anisotropy, expressions describing a temperature dependence of the domain wall energy density in orthoferrites have been derived. In the expression for magnetocrystalline energy, uniaxial as well as cubic anisotropy have been accounted for.     

Indium

Analytical and Bioanalytical Chemistry -