Randomized Observation Periods for the Compound Poisson Risk Model: Dividends

In the framework of the classical compound Poisson process in collective risk theory, we study a modification of the horizontal dividend barrier strategy by introducing random observation times at which dividends can be paid and ruin can be observed. This model contains both the continuous-time and the discrete-time risk model as a limit and represents a certain type of bridge between them which still enables the explicit calculation of moments of total discounted dividend payments until ruin. Numerical illustrations for several sets of parameters are given and the effect of random observation times on the performance of the dividend strategy is studie

Opposing effects of TIGAR- and RAC1-derived ROS on Wnt-driven proliferation in the mouse intestine

Reactive oxygen species (ROS) participate in numerous cell responses, including proliferation, DNA damage, and cell death. Based on these disparate activities, both promotion and inhibition of ROS have been proposed for cancer therapy. However, how the ROS response is determined is not clear. We examined the activities of ROS in a model of Apc deletion, where loss of the Wnt target gene Myc both rescues APC loss and prevents ROS accumulation. Following APC loss, Myc has been shown to up-regulate RAC1 to promote proliferative ROS through NADPH oxidase (NOX). However, APC loss also increased the expression of TIGAR, which functions to limit ROS. To explore this paradox, we used three-dimensional (3D) cultures and in vivo models to show that deletion of TIGAR increased ROS damage and inhibited proliferation. These responses were suppressed by limiting damaging ROS but enhanced by lowering proproliferative NOX-derived ROS. Despite having opposing effects on ROS levels, loss of TIGAR and RAC1 cooperated to suppress intestinal proliferation following APC loss. Our results indicate that the pro- and anti-proliferative effects of ROS can be independently modulated in the same cell, with two key targets in the Wnt pathway functioning to integrate the different ROS signals for optimal cell proliferation

Optical Polarization and Spectral Variability in the M87 Jet

During the last decade, M87's jet has been the site of an extraordinary variability event, with one knot (HST-1) increasing by over a factor 100 in brightness. Variability was also seen on timescales of months in the nuclear flux. Here we discuss the optical-UV polarization and spectral variability of these components, which show vastly different behavior. HST-1 shows a highly significant correlation between flux and polarization, with P increasing from $\sim 20$ at minimum to >40% at maximum, while the orientation of its electric vector stayed constant. HST-1's optical-UV spectrum is very hard ($\alpha_{UV-O}\sim0.5$, $F_\nu\propto\nu^{-\alpha}$), and displays "hard lags" during epochs 2004.9-2005.5, including the peak of the flare, with soft lags at later epochs. We interpret the behavior of HST-1 as enhanced particle acceleration in a shock, with cooling from both particle aging and the relaxation of the compression. We set 2$\sigma$ upper limits of $0.5 \delta$ parsecs and 1.02$c$ on the size and advance speed of the flaring region. The slight deviation of the electric vector orientation from the jet PA, makes it likely that on smaller scales the flaring region has either a double or twisted structure. By contrast, the nucleus displays much more rapid variability, with a highly variable electric vector orientation and 'looping' in the $(I,P)$ plane. The nucleus has a much steeper spectrum ($\alpha_{UV-O} \sim 1.5$) but does not show UV-optical spectral variability. Its behavior can be interpreted as either a helical distortion to a steady jet or a shock propagating through a helical jet.Comment: 14 pages, 7 figures, ApJ, in pres

Perturbative QCD Fragmentation Functions for BcB_c and Bc∗B_c^* Production

The dominant production mechanism for ${\bar b} c$ bound states in high energy processes is the production of a high energy ${\bar b}$ or $c$ quark, followed by its fragmentation into the ${\bar b} c$ state. We calculate the fragmentation functions for the production of the S-wave states $B_c$ and $B_c^*$ to leading order in the QCD coupling constant. The fragmentation probabilities for ${\bar b} \rightarrow B_c$ and ${\bar b} \rightarrow B_c^*$ are approximately $2.2 \times 10^{-4}$ and $3.1 \times 10^{-4}$, while those for $c \rightarrow B_c$ and $c \rightarrow B_c^*$ are smaller by almost two orders of magnitude.Comment: Latex, 12 pages, 3 figures available upon request, NUHEP-TH-93-