Rank-Based Analysis of Linear Models Using R

It is well-known that Wilcoxon procedures out perform least squares procedures when the data deviate from normality and/or contain outliers. These procedures can be generalized by introducing weights; yielding so-called weighted Wilcoxon (WW) techniques. In this paper we demonstrate how WW-estimates can be calculated using an L1 regression routine. More importantly, we present a collection of functions that can be used to implement a robust analysis of a linear model based on WW-estimates. For instance, estimation, tests of linear hypotheses, residual analyses, and diagnostics to detect differences in fits for various weighting schemes are discussed. We analyze a regression model, designed experiment, and autoregressive time series model for the sake of illustration. We have chosen to implement the suite of functions using the R statistical software package. Because R is freely available and runs on multiple platforms, WW-estimation and associated inference is now universally accessible.

Rank-Based Analysis of Linear Models Using R

It is well-known that Wilcoxon procedures out perform least squares procedures when the data deviate from normality and/or contain outliers. These procedures can be generalized by introducing weights; yielding so-called weighted Wilcoxon (WW) techniques. In this paper we demonstrate how WW-estimates can be calculated using an L1 regression routine. More importantly, we present a collection of functions that can be used to implement a robust analysis of a linear model based on WW-estimates. For instance, estimation, tests of linear hypotheses, residual analyses, and diagnostics to detect differences in fits for various weighting schemes are discussed. We analyze a regression model, designed experiment, and autoregressive time series model for the sake of illustration. We have chosen to implement the suite of functions using the R statistical software package. Because R is freely available and runs on multiple platforms, WW-estimation and associated inference is now universally accessible

Low Odor, High Yield Kraft Pulping

In laboratory cooks pure oxygen was profiled into the circulation line of a batch digester during two periods of the cooking cycle: The first injection occurred during the heating steps for the purpose of in-situ generation of polysulfide. This chip treatment was studied to explore stabilization against alkaline induced carbohydrate peeling and to increase pulp yield. Under optimum conditions small amounts of polysulfide were produced with yield increase of about 0.5% These increases fell below earlier reports suggesting that unknown differences in liquor composition may influence the relative amounts of polysulfide and thiosulfate generated during the oxidation. Consequently, further studies are required to understand the factors that influence the ratios of those two sulfur species

Partial survival and inelastic collapse for a randomly accelerated particle

We present an exact derivation of the survival probability of a randomly accelerated particle subject to partial absorption at the origin. We determine the persistence exponent and the amplitude associated to the decay of the survival probability at large times. For the problem of inelastic reflection at the origin, with coefficient of restitution $r$, we give a new derivation of the condition for inelastic collapse, $r<r_c=e^{-\pi/\sqrt{3}}$, and determine the persistence exponent exactly.Comment: 6 page

Simulation of a semiflexible polymer in a narrow cylindrical pore

The probability that a randomly accelerated particle in two dimensions has not yet left a simply connected domain ${\cal A}$ after a time $t$ decays as $e^{-E_0t}$ for long times. The same quantity $E_0$ also determines the confinement free energy per unit length $\Delta f=k_BT\thinspace E_0$ of a semiflexible polymer in a narrow cylindrical pore with cross section ${\cal A}$. From simulations of a randomly accelerated particle we estimate the universal amplitude of $\Delta f$ for both circular and rectangular cross sections.Comment: 10 pages, 2 eps figure

Simple Systems with Anomalous Dissipation and Energy Cascade

We analyze a class of linear shell models subject to stochastic forcing in finitely many degrees of freedom. The unforced systems considered formally conserve energy. Despite being formally conservative, we show that these dynamical systems support dissipative solutions (suitably defined) and, as a result, may admit unique (statistical) steady states when the forcing term is nonzero. This claim is demonstrated via the complete characterization of the solutions of the system above for specific choices of the coupling coefficients. The mechanism of anomalous dissipations is shown to arise via a cascade of the energy towards the modes ($a_n$) with higher $n$; this is responsible for solutions with interesting energy spectra, namely \EE |a_n|^2 scales as $n^{-\alpha}$ as $n\to\infty$. Here the exponents $\alpha$ depend on the coupling coefficients $c_n$ and \EE denotes expectation with respect to the equilibrium measure. This is reminiscent of the conjectured properties of the solutions of the Navier-Stokes equations in the inviscid limit and their accepted relationship with fully developed turbulence. Hence, these simple models illustrate some of the heuristic ideas that have been advanced to characterize turbulence, similar in that respect to the random passive scalar or random Burgers equation, but even simpler and fully solvable.Comment: 32 Page

Survival of a Diffusing Particle in a Transverse Shear Flow: A First-Passage Problem with Continuously Varying Persistence Exponent

We consider a particle diffusing in the y-direction, dy/dt=\eta(t), subject to a transverse shear flow in the x-direction, dx/dt=f(y), where x \ge 0 and x=0 is an absorbing boundary. We treat the class of models defined by f(y) = \pm v_{\pm}(\pm y)^\alpha where the upper (lower) sign refers to y>0 (y<0). We show that the particle survives with probability Q(t) \sim t^{-\theta} with \theta = 1/4, independent of \alpha, if v_{+}=v_{-}. If v_{+} \ne v_{-}, however, we show that \theta depends on both \alpha and the ratio v_{+}/v_{-}, and we determine this dependence.Comment: 4 page

Peracute Infection of Swine With Salmonella

It has recently been experimentally demonstrated that pigs exposed naturally to Salmonella on the floor of abattoir holding pens can become infected between two and six hours after being placed in the pens. In addition we have demonstrated that tonsillar tissue are almost immediately culture positive following such exposure under experimental conditions. The objective of this study was to determine the shortest amount of time necessary for infection of selected tissues and to determine if the tonsil served as a route for Salmonella entry into lymphoid tissues draining the tonsil. Forty-four Salmonella-negative, market age pigs (90 to 110 kg) were fasted overnight and exposed to approximately 2 X 106 Salmonella enterica serotype Typhimurium strain X4232 (nalidixic acid resistant). The bacteria were mixed with a fecal slurry and the slurry spread on the floor of the pens. Pigs were euthanized at 15, 30, 45, 60 and 120 minutes following initial exposure. Tonsil of the soft palate, medial retropharyngeal lymph node, ileocecal lymph node, a five centimeter section of the terminal ileum, cecal contents and 100 ml of blood were cultured for Salmonella. Strain X4232 was isolated from 98 % (43/44) of tonsils. Strain X4232 was isolated from the ileocecal lymph node within 45 minutes (2/9 pigs), terminal ileum within 15 minutes (1/9 pigs), cecal contents within 15 minutes (1/9 pigs), and blood within 45 minutes (1/9 pigs). Strain X4232 was not recovered from the medial retropharyngeal lymph node, indicating that the organism did not move rapidly into this node from the tonsil of the soft palate. Results of this study indicate that Salmonella can be recovered from selected tissues in market age swine in less than the normal two hour abattoir holding time

Effects of Transport Memory and Nonlinear Damping in a Generalized Fisher's Equation

Memory effects in transport require, for their incorporation into reaction diffusion investigations, a generalization of traditional equations. The well-known Fisher's equation, which combines diffusion with a logistic nonlinearity, is generalized to include memory effects and traveling wave solutions of the equation are found. Comparison is made with alternate generalization procedures.Comment: 6 pages, 4 figures, RevTeX

CLASS B2108+213: A new wide separation gravitational lens system

We present observations of CLASS B2108+213, the widest separation gravitational lens system discovered by the Cosmic Lens All-Sky Survey. Radio imaging using the VLA at 8.46 GHz and MERLIN at 5 GHz shows two compact components separated by 4.56 arcsec with a faint third component in between which we believe is emission from a lensing galaxy. 5-GHz VLBA observations reveal milliarcsecond-scale structure in the two lensed images that is consistent with gravitational lensing. Optical emission from the two lensed images and two lensing galaxies within the Einstein radius is detected in Hubble Space Telescope imaging. Furthermore, an optical gravitational arc, associated with the strongest lensed component, has been detected. Surrounding the system are a number of faint galaxies which may help explain the wide image separation. A plausible mass distribution model for CLASS B2108+213 is also presented.Comment: 9 pages, 8 figures, accepted for publication in MNRA