Rate of Convergence of Space Time Approximations for stochastic evolution equations

Stochastic evolution equations in Banach spaces with unbounded nonlinear drift and diffusion operators driven by a finite dimensional Brownian motion are considered. Under some regularity condition assumed for the solution, the rate of convergence of various numerical approximations are estimated under strong monotonicity and Lipschitz conditions. The abstract setting involves general consistency conditions and is then applied to a class of quasilinear stochastic PDEs of parabolic type.Comment: 33 page

A Smirnov-Bickel-Rosenblatt theorem for compactly-supported wavelets

In nonparametric statistical problems, we wish to find an estimator of an unknown function f. We can split its error into bias and variance terms; Smirnov, Bickel and Rosenblatt have shown that, for a histogram or kernel estimate, the supremum norm of the variance term is asymptotically distributed as a Gumbel random variable. In the following, we prove a version of this result for estimators using compactly-supported wavelets, a popular tool in nonparametric statistics. Our result relies on an assumption on the nature of the wavelet, which must be verified by provably-good numerical approximations. We verify our assumption for Daubechies wavelets and symlets, with N = 6, ..., 20 vanishing moments; larger values of N, and other wavelet bases, are easily checked, and we conjecture that our assumption holds also in those cases

The Electroweak Phase Transition on Orbifolds with Gauge-Higgs Unification

The dynamics of five dimensional Wilson line phases at finite temperature is studied in the one-loop approximation. We show that at temperatures of order T \sim 1/L, where L is the length of the compact space, the gauge symmetry is always restored and the electroweak phase transition appears to be of first order. Particular attention is devoted to the study of a recently proposed five dimensional orbifold model (on S1/Z2) where the Wilson line phase is identified with the Higgs field (gauge-Higgs unification). Interestingly enough, an estimate of the leading higher-loop ``daisy'' (or ``ring'') diagram contributions to the effective potential in a simple five dimensional model, seems to suggest that the electroweak phase transition can be studied in perturbation theory even for Higgs masses above the current experimental limit of 114 GeV. The transition is still of first order for such values of the Higgs mass. If large localized gauge kinetic terms are present, the transition might be strong enough to give baryogenesis at the electroweak transition.Comment: 35 pages, 34 figures; v2: discussion on higher loop contributions improved, two figures added, minor correction

Gravitomagnetism and the Clock Effect

The main theoretical aspects of gravitomagnetism are reviewed. It is shown that the gravitomagnetic precession of a gyroscope is intimately connected with the special temporal structure around a rotating mass that is revealed by the gravitomagnetic clock effect. This remarkable effect, which involves the difference in the proper periods of a standard clock in prograde and retrograde circular geodesic orbits around a rotating mass, is discussed in detail. The implications of this effect for the notion of ``inertial dragging'' in the general theory of relativity are presented. The theory of the clock effect is developed within the PPN framework and the possibility of measuring it via spaceborne clocks is examined.Comment: 27 pages, LaTeX, submitted to Proc. Bad Honnef Meeting on: GYROS, CLOCKS, AND INTERFEROMETERS: TESTING GENERAL RELATIVITY IN SPACE (22 - 27 August 1999; Bad Honnef, Germany

Search for the decay K+ to pi+ gamma gamma in the pi+ momentum region P>213 MeV/c

We have searched for the K+ to pi+ gamma gamma decay in the kinematic region with pi+ momentum close to the end point. No events were observed, and the 90% confidence-level upper limit on the partial branching ratio was obtained, B(K+ to pi+ gamma gamma, P>213 MeV/c) < 8.3 x 10-9 under the assumption of chiral perturbation theory including next-to-leading order ``unitarity'' corrections. The same data were used to determine an upper limit on the K+ to pi+ gamma branching ratio of 2.3 x 10-9 at the 90% confidence level.Comment: 15 pages, 3 figures; no change in the results, accepted for publication in Physics Letters

Strangeness nuclear physics: a critical review on selected topics

Selected topics in strangeness nuclear physics are critically reviewed. This includes production, structure and weak decay of $\Lambda$--Hypernuclei, the $\bar K$ nuclear interaction and the possible existence of $\bar K$ bound states in nuclei. Perspectives for future studies on these issues are also outlined.Comment: 63 pages, 51 figures, accepted for publication on European Physical Journal

An HDAC6-dependent surveillance mechanism suppresses tau-mediated neurodegeneration and cognitive decline

Tauopathies including Alzheimer’s disease (AD) are marked by the accumulation of aberrantly modified tau proteins. Acetylated tau, in particular, has recently been implicated in neurodegeneration and cognitive decline. HDAC6 reversibly regulates tau acetylation, but its role in tauopathy progression remains unclear. Here, we identified an HDAC6-chaperone complex that targets aberrantly modified tau. HDAC6 not only deacetylates tau but also suppresses tau hyperphosphorylation within the microtubule-binding region. In neurons and human AD brain, HDAC6 becomes co-aggregated within focal tau swellings and human AD neuritic plaques. Using mass spectrometry, we identify a novel HDAC6-regulated tau acetylation site as a disease specific marker for 3R/4R and 3R tauopathies, supporting uniquely modified tau species in different neurodegenerative disorders. Tau transgenic mice lacking HDAC6 show reduced survival characterized by accelerated tau pathology and cognitive decline. We propose that a HDAC6-dependent surveillance mechanism suppresses toxic tau accumulation, which may protect against the progression of AD and related tauopathies

Heavy quarkonium: progress, puzzles, and opportunities

A golden age for heavy quarkonium physics dawned a decade ago, initiated by the confluence of exciting advances in quantum chromodynamics (QCD) and an explosion of related experimental activity. The early years of this period were chronicled in the Quarkonium Working Group (QWG) CERN Yellow Report (YR) in 2004, which presented a comprehensive review of the status of the field at that time and provided specific recommendations for further progress. However, the broad spectrum of subsequent breakthroughs, surprises, and continuing puzzles could only be partially anticipated. Since the release of the YR, the BESII program concluded only to give birth to BESIII; the $B$-factories and CLEO-c flourished; quarkonium production and polarization measurements at HERA and the Tevatron matured; and heavy-ion collisions at RHIC have opened a window on the deconfinement regime. All these experiments leave legacies of quality, precision, and unsolved mysteries for quarkonium physics, and therefore beg for continuing investigations. The plethora of newly-found quarkonium-like states unleashed a flood of theoretical investigations into new forms of matter such as quark-gluon hybrids, mesonic molecules, and tetraquarks. Measurements of the spectroscopy, decays, production, and in-medium behavior of c\bar{c}, b\bar{b}, and b\bar{c} bound states have been shown to validate some theoretical approaches to QCD and highlight lack of quantitative success for others. The intriguing details of quarkonium suppression in heavy-ion collisions that have emerged from RHIC have elevated the importance of separating hot- and cold-nuclear-matter effects in quark-gluon plasma studies. This review systematically addresses all these matters and concludes by prioritizing directions for ongoing and future efforts.Comment: 182 pages, 112 figures. Editors: N. Brambilla, S. Eidelman, B. K. Heltsley, R. Vogt. Section Coordinators: G. T. Bodwin, E. Eichten, A. D. Frawley, A. B. Meyer, R. E. Mitchell, V. Papadimitriou, P. Petreczky, A. A. Petrov, P. Robbe, A. Vair

Structure–activity Relationships of Amyloid Beta-aggregation Inhibitors Based on Curcumin: Influence of Linker Length and Flexibility

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66293/1/j.1747-0285.2007.00557.x.pd

Randomized Trial of Metformin, Ivermectin, and Fluvoxamine for Covid-19

BACKGROUND Early treatment to prevent severe coronavirus disease 2019 (Covid-19) is an important component of the comprehensive response to the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic. METHODS In this phase 3, double-blind, randomized, placebo-controlled trial, we used a 2-by-3 factorial design to test the effectiveness of three repurposed drugs - metformin, ivermectin, and fluvoxamine - in preventing serious SARS-CoV-2 infection in nonhospitalized adults who had been enrolled within 3 days after a confirmed diagnosis of infection and less than 7 days after the onset of symptoms. The patients were between the ages of 30 and 85 years, and all had either overweight or obesity. The primary composite end point was hypoxemia (≤93% oxygen saturation on home oximetry), emergency department visit, hospitalization, or death. All analyses used controls who had undergone concurrent randomization and were adjusted for SARSCoV-2 vaccination and receipt of other trial medications. RESULTS A total of 1431 patients underwent randomization; of these patients, 1323 were included in the primary analysis. The median age of the patients was 46 years; 56% were female (6% of whom were pregnant), and 52% had been vaccinated. The adjusted odds ratio for a primary event was 0.84 (95% confidence interval [CI], 0.66 to 1.09; P=0.19) with metformin, 1.05 (95% CI, 0.76 to 1.45; P=0.78) with ivermectin, and 0.94 (95% CI, 0.66 to 1.36; P=0.75) with fluvoxamine. In prespecified secondary analyses, the adjusted odds ratio for emergency department visit, hospitalization, or death was 0.58 (95% CI, 0.35 to 0.94) with metformin, 1.39 (95% CI, 0.72 to 2.69) with ivermectin, and 1.17 (95% CI, 0.57 to 2.40) with fluvoxamine. The adjusted odds ratio for hospitalization or death was 0.47 (95% CI, 0.20 to 1.11) with metformin, 0.73 (95% CI, 0.19 to 2.77) with ivermectin, and 1.11 (95% CI, 0.33 to 3.76) with fluvoxamine. CONCLUSIONS None of the three medications that were evaluated prevented the occurrence of hypoxemia, an emergency department visit, hospitalization, or death associated with Covid-19