Chaotic Diffusion on Periodic Orbits: The Perturbed Arnol'd Cat Map

Chaotic diffusion on periodic orbits (POs) is studied for the perturbed Arnol'd cat map on a cylinder, in a range of perturbation parameters corresponding to an extended structural-stability regime of the system on the torus. The diffusion coefficient is calculated using the following PO formulas: (a) The curvature expansion of the Ruelle zeta function. (b) The average of the PO winding-number squared, $w^{2}$, weighted by a stability factor. (c) The uniform (nonweighted) average of $w^{2}$. The results from formulas (a) and (b) agree very well with those obtained by standard methods, for all the perturbation parameters considered. Formula (c) gives reasonably accurate results for sufficiently small parameters corresponding also to cases of a considerably nonuniform hyperbolicity. This is due to {\em uniformity sum rules} satisfied by the PO Lyapunov eigenvalues at {\em fixed} $w$. These sum rules follow from general arguments and are supported by much numerical evidence.Comment: 6 Tables, 2 Figures (postscript); To appear in Physical Review

Contracting on litigation

Two risk‐averse litigants with different subjective beliefs negotiate in the shadow of a pending trial. Through contingent contracts, the litigants can mitigate risk and/or speculate on the trial outcome. Contingent contracting decreases the settlement rate and increases the volume and costs of litigation. These contingent contracts mimic the services provided by third‐party investors, including litigation funders and insurance companies. The litigants (weakly) prefer to contract with risk‐neutral third parties when the capital market is transaction‐cost free. However, contracting with third parties further decreases the settlement rate, increases the costs of litigation, and may increase the aggregate cost of risk bearing.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/149242/1/rand12274.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/149242/2/rand12274_am.pd

A historical perspective on the discovery of statins

Cholesterol is essential for the functioning of all human organs, but it is nevertheless the cause of coronary heart disease. Over the course of nearly a century of investigation, scientists have developed several lines of evidence that establish the causal connection between blood cholesterol, atherosclerosis, and coronary heart disease. Building on that knowledge, scientists and the pharmaceutical industry have successfully developed a remarkably effective class of drugs—the statins—that lower cholesterol levels in blood and reduce the frequency of heart attacks

Leucine-rich repeat kinase-2 (LRRK2) modulates paraquat-induced inflammatory sickness and stress phenotype

Background: Leucine-rich repeat kinase 2 (LRRK2) is a common gene implicated in Parkinson's disease (PD) and is also thought to be fundamentally involved in numerous immune functions. Thus, we assessed the role of LRRK2 in the context of the effects of the environmental toxicant, paraquat, that has been implicated in PD and is known to affect inflammatory processes. Methods: Male LRRK2 knockout (KO) and transgenic mice bearing the G2019S LRRK2 mutation (aged 6-8 months) or their littermate controls were exposed to paraquat (two times per week for 3 weeks), and sickness measures, motivational scores, and total home-cage activity levels were assessed. Following sacrifice, western blot and ELISA assays were performed to

Search for Gravitational Waves Associated with Gamma-Ray Bursts Detected by Fermi and Swift during the LIGO-Virgo Run O3b

We search for gravitational-wave signals associated with gamma-ray bursts (GRBs) detected by the Fermi and Swift satellites during the second half of the third observing run of Advanced LIGO and Advanced Virgo (2019 November 1 15:00 UTC-2020 March 27 17:00 UTC). We conduct two independent searches: A generic gravitational-wave transients search to analyze 86 GRBs and an analysis to target binary mergers with at least one neutron star as short GRB progenitors for 17 events. We find no significant evidence for gravitational-wave signals associated with any of these GRBs. A weighted binomial test of the combined results finds no evidence for subthreshold gravitational-wave signals associated with this GRB ensemble either. We use several source types and signal morphologies during the searches, resulting in lower bounds on the estimated distance to each GRB. Finally, we constrain the population of low-luminosity short GRBs using results from the first to the third observing runs of Advanced LIGO and Advanced Virgo. The resulting population is in accordance with the local binary neutron star merger rate. © 2022. The Author(s). Published by the American Astronomical Society

Narrowband Searches for Continuous and Long-duration Transient Gravitational Waves from Known Pulsars in the LIGO-Virgo Third Observing Run

Isolated neutron stars that are asymmetric with respect to their spin axis are possible sources of detectable continuous gravitational waves. This paper presents a fully coherent search for such signals from eighteen pulsars in data from LIGO and Virgo's third observing run (O3). For known pulsars, efficient and sensitive matched-filter searches can be carried out if one assumes the gravitational radiation is phase-locked to the electromagnetic emission. In the search presented here, we relax this assumption and allow both the frequency and the time derivative of the frequency of the gravitational waves to vary in a small range around those inferred from electromagnetic observations. We find no evidence for continuous gravitational waves, and set upper limits on the strain amplitude for each target. These limits are more constraining for seven of the targets than the spin-down limit defined by ascribing all rotational energy loss to gravitational radiation. In an additional search, we look in O3 data for long-duration (hours-months) transient gravitational waves in the aftermath of pulsar glitches for six targets with a total of nine glitches. We report two marginal outliers from this search, but find no clear evidence for such emission either. The resulting duration-dependent strain upper limits do not surpass indirect energy constraints for any of these targets. © 2022. The Author(s). Published by the American Astronomical Society