Fractional Generalizations of Filtering Problems and Their Associated Fractional Zakai Equation

In this paper we discuss fractional generalizations of the filtering problem. The ”fractional” nature comes from time-changed state or observation processes, basic ingredients of the filtering problem. The mathematical feature of the fractional filtering problem emerges as the Riemann-Liouville or Caputo-Djrbashian fractional derivative in the associated Zakai equation. We discuss fractional generalizations of the nonlinear filtering problem whose state and observation processes are driven by time-changed Brownian motion or/and Lévy process

Fractional Generalizations of Zakai Equation and Some Solution Methods

The paper discusses fractional generalizations of Zakai equations arising in filtering problems. The derivation of the fractional Zakai equation, existence and uniqueness of its solution, as well as some methods of solution to the fractional filtering problem, including fractional version of the particle flow method, are presented

Flight Investigation at High Speeds of Profile Drag of Wing of a P-47D Airplane Having Production Surfaces Covered with Camouflage Paint

Wing section outboard of flap was tested by wake surveys in Mach range of 0.25 - 0.78 and lift coefficient range 0.06 - 0.69. Results indicated that minimum profile-drag coefficient of 0.0097 was attained for lift coefficients from 0.16 to 0.25 at Mach less than 0.67. Below Mach number at which compressibility shock occurred, variations in Mach of 0.2 had negligible effect on profile drag coefficient. Shock was not evident until critical Mach was exceeded by 0.025

Stochastic Particle Flow for Nonlinear High-Dimensional Filtering Problems

A series of novel filters for probabilistic inference that propose an alternative way of performing Bayesian updates, called particle flow filters, have been attracting recent interest. These filters provide approximate solutions to nonlinear filtering problems. They do so by defining a continuum of densities between the prior probability density and the posterior, i.e. the filtering density. Building on these methods' successes, we propose a novel filter. The new filter aims to address the shortcomings of sequential Monte Carlo methods when applied to important nonlinear high-dimensional filtering problems. The novel filter uses equally weighted samples, each of which is associated with a local solution of the Fokker-Planck equation. This hybrid of Monte Carlo and local parametric approximation gives rise to a global approximation of the filtering density of interest. We show that, when compared with state-of-the-art methods, the Gaussian-mixture implementation of the new filtering technique, which we call Stochastic Particle Flow, has utility in the context of benchmark nonlinear high-dimensional filtering problems. In addition, we extend the original particle flow filters for tackling multi-target multi-sensor tracking problems to enable a comparison with the new filter

Staphylococcus aureus with reduced susceptibility to vancomycin isolated from a patient with fatal bacteremia.

A Staphylococcus aureus isolate with reduced susceptibility to vancomycin was obtained from a dialysis patient with a fatal case of bacteremia. Comparison of the isolate with two methicillin-resistant S. aureus (MRSA) isolated obtained from the same patient 4 months earlier suggests that the S. aureus with reduced susceptibility to vancomycin emerged from the MRSA strain with which the patient was infected. Atypical phenotypic characteristics, including weak or negative latex-agglutination test results, weak or negative-slide coagulase test results, heterogeneous morphologic features, slow rate of growth, and vancomycin susceptibility (by disk diffusion test) were observed

Finishing the euchromatic sequence of the human genome

The sequence of the human genome encodes the genetic instructions for human physiology, as well as rich information about human evolution. In 2001, the International Human Genome Sequencing Consortium reported a draft sequence of the euchromatic portion of the human genome. Since then, the international collaboration has worked to convert this draft into a genome sequence with high accuracy and nearly complete coverage. Here, we report the result of this finishing process. The current genome sequence (Build 35) contains 2.85 billion nucleotides interrupted by only 341 gaps. It covers ∼99% of the euchromatic genome and is accurate to an error rate of ∼1 event per 100,000 bases. Many of the remaining euchromatic gaps are associated with segmental duplications and will require focused work with new methods. The near-complete sequence, the first for a vertebrate, greatly improves the precision of biological analyses of the human genome including studies of gene number, birth and death. Notably, the human enome seems to encode only 20,000-25,000 protein-coding genes. The genome sequence reported here should serve as a firm foundation for biomedical research in the decades ahead