Asymptotic analysis of mode-coupling theory of active nonlinear microrheology

We discuss a schematic model of mode-coupling theory for force-driven active nonlinear microrheology, where a single probe particle is pulled by a constant external force through a dense host medium. The model exhibits both a glass transition for the host, and a force-induced delocalization transition, where an initially localized probe inside the glassy host attains a nonvanishing steady-state velocity by locally melting the glass. Asymptotic expressions for the transient density correlation functions of the schematic model are derived, valid close to the transition points. There appear several nontrivial time scales relevant for the decay laws of the correlators. For the nonlinear friction coeffcient of the probe, the asymptotic expressions cause various regimes of power-law variation with the external force, and two-parameter scaling laws.Comment: 17 pages, 12 figure

The Behavior of the Renewal Sequence in Case the Tail of the Waiting-Time Distribution Is Regularly Varying with Index -1

A second-order asymptotic result for the probability of occurrence of a persistent and aperiodic recurrent event is given if the tail of the distribution of the waiting time for this event is regularly varying with index -1

Correlation Between Photosensitivity and Downwelling Irradiance in Mesopelagic Crustaceans

The current study determined behavioral and electrophysiological photosensitivities for three species of mesopelagic crustaceans: Pasiphaea multidentata Esmark, 1866 (Decapoda: Pasiphaeidae), Sergestes arcticus Kröyer, 1855 (Decapoda: Sergestidae), and Meganyctiphanes norvegica M. Sars, 1857 (Euphausiacea: Euphausiidae). In addition, in situ quantifications of the species’ vertical distributions in relation to downwelling irradiances were also determined in two locations in the northwest Atlantic Ocean, Wilkinson Basin (WB) and Oceanographer Canyon (OC). Data are from six 2-week cruises between June and September from 1995 to 2001. P. multidentata and M. norvegica were the most abundant large crustaceans in WB, and S. arcticus and M. norvegica were the most abundant large crustaceans in OC. The behavioral light sensitivity thresholds of P. multidentata and M. norvegica from WB were both 107 photons cm−2 s−1 and those of S. arcticus and M. norvegica from OC were both 108 photons cm−2 s−1. Electrophysiologically, P. multidentata was significantly more sensitive than M. norvegica from either location, S. arcticus was significantly more sensitive than M. norvegica from OC, and M. norvegica from WB was significantly more sensitive than M. norvegica from OC. A correlation was found between electrophysiologically measured photosensitivity and downwelling irradiance, with the most sensitive species, P. multidentata and S. arcticus, associated with the lowest irradiance at daytime depths. The photosensitivities of M. norvegicacollected from the clearer waters of OC were significantly lower than those of individuals collected from the more turbid WB waters. These results indicate that downwelling irradiance has a significant impact on interspecies and intraspecies vertical distribution patterns in the mesopelagic realm

Stochastic Transition States: Reaction Geometry amidst Noise

Classical transition state theory (TST) is the cornerstone of reaction rate theory. It postulates a partition of phase space into reactant and product regions, which are separated by a dividing surface that reactive trajectories must cross. In order not to overestimate the reaction rate, the dynamics must be free of recrossings of the dividing surface. This no-recrossing rule is difficult (and sometimes impossible) to enforce, however, when a chemical reaction takes place in a fluctuating environment such as a liquid. High-accuracy approximations to the rate are well known when the solvent forces are treated using stochastic representations, though again, exact no-recrossing surfaces have not been available. To generalize the exact limit of TST to reactive systems driven by noise, we introduce a time-dependent dividing surface that is stochastically moving in phase space such that it is crossed once and only once by each transition path

Decay of the Sinai Well in D dimensions

We study the decay law of the Sinai Well in $D$ dimensions and relate the behavior of the decay law to internal distributions that characterize the dynamics of the system. We show that the long time tail of the decay is algebraic ($1/t$), irrespective of the dimension $D$.Comment: 14 pages, Figures available under request. Revtex. Submitted to Phys. Rev. E.,e-mail: [email protected]

Patterns of recurrence and survival after surgery or stereotactic radiotherapy for early stage NSCLC

IntroductionSurgery is the standard treatment for early stage non–small-cell lung cancer (NSCLC). For medically inoperable patients, stereotactic ablative radiotherapy (SABR) has emerged as widely used standard treatment. The aim of this study was to analyze survival and patterns of tumor recurrence in patients with clinical stage I NSCLC treated with surgery or SABR.MethodsClinical data from all subsequent fluoro-deoxyglucose positron emission tomography/computed tomography-based stage I NSCLC patients (cT1-T2aN0M0) treated with surgery or SABR at our center between 2007 and 2010 were collected. Primary endpoints were overall survival and tumor recurrences/new primary lung tumors. Treatment groups were compared using multivariable Cox regression and competing risk analyses.ResultsThree hundred-forty patients treated with surgery (n = 143) or SABR (n = 197) were included. Surgical patients were younger, had a better WHO performance status and less comorbidities. After adjustment for prognostic covariables, treatment did not influence overall survival (adjusted hazard ratio [HR], SABR versus surgery 1.07; 95% confidence interval [CI]: 0.74–1.54; p = 0.73). Local control and distant recurrence were equal, whereas locoregional recurrences were significantly more frequent after SABR compared with surgery (adjusted sub-HR 2.51; 95% CI: 1.10–5.70; p = 0.028). Nodal failure (HR: 2.16; 95% CI: 1.34–3.48) and distant metastases (HR: 2.12; 95% CI: 1.52–2.97), but not local failure (HR: 1.00; 95% CI: 0.53–1.89) predicted overall survival.ConclusionsIn patients with fluoro-deoxyglucose positron emission tomography/computed tomography-based stage I NSCLC, SABR confers worse locoregional tumor control because of more nodal failures compared with surgery, stressing the need to improve mediastinal and hilar staging

The Tychonoff uniqueness theorem for the G-heat equation

In this paper, we obtain the Tychonoff uniqueness theorem for the G-heat equation

The Measure of the Orthogonal Polynomials Related to Fibonacci Chains: The Periodic Case

The spectral measure for the two families of orthogonal polynomial systems related to periodic chains with N-particle elementary unit and nearest neighbour harmonic interaction is computed using two different methods. The interest is in the orthogonal polynomials related to Fibonacci chains in the periodic approximation. The relation of the measure to appropriately defined Green's functions is established.Comment: 19 pages, TeX, 3 scanned figures, uuencoded file, original figures on request, some misprints corrected, tbp: J. Phys.

Content Uniformity of Over-the-Counter Melatonin

Dietary supplements are loosely regulated in comparison to over-the-counter and prescription drugs. Numerous tests for safety and efficacy are required before drugs can be marketed. However, the Food and Drug Administration does not require thorough examination of supplements before they are sold. Dietary supplements generally adhere to the phrase, “safe, until proven unsafe,” with safety determined solely through post-market adverse event reports. Substandard regulation of supplement manufacturing leads to warranted doubt about the safety and efficacy of dietary supplements. Within the dietary supplement market there are regulatory bodies, such as the United States Pharmacopeia (USP), that provide optional verification services to manufacturers. If utilized, these regulatory bodies ensure that manufacturers meet specific standards in regard to Current Good Manufacturing Practices (cGMP), purity of ingredients, and overall integrity of their product. Numerous studies have revealed a history of inaccuracies in supplement product labeling. Researchers conducting these studies consistently conclude that there is a need for stricter regulation and finer application of cGMP within supplement manufacturing companies. One of the most popular dietary supplements on the market, melatonin, has been the focus in a number of studies evaluating supplement product content integrity. Melatonin is commonly used to treat insomnia and to cure symptoms of jet lag. According to past research, these melatonin products often contain an amount of active ingredient that significantly differs from respective product labeling. Most research regarding melatonin product integrity has occurred outside of the past ten years, leaving the need for newer research. Melatonin 3 mg will be purchased from six different manufacturers with three manufacturers possessing USP verification. Within each manufacturer, melatonin 3 mg from five separate lot numbers will be purchased. Ten tablets from each bottle (totaling 300 tablets) will be analyzed using a high-pressure liquid chromatography machine in order to determine actual melatonin content in each tablet. Data will be recorded and compared to determine accuracy of product labeling and batch-to-batch content uniformity. Data from USP-verified melatonin will be compared with non-verified products in order to determine if regulatory body verification is effective at improving content uniformity

Challenges in microbial ecology: building predictive understanding of community function and dynamics

he importance of microbial communities (MCs) cannot be overstated. MCs underpin the biogeochemical cycles of the earth’s soil, oceans and the atmosphere, and perform ecosystem functions that impact plants, animals and humans. Yet our ability to predict and manage the function of these highly complex, dynamically changing communities is limited. Building predictive models that link MC composition to function is a key emerging challenge in microbial ecology. Here, we argue that addressing this challenge requires close coordination of experimental data collection and method development with mathematical model building. We discuss specific examples where model–experiment integration has already resulted in important insights into MC function and structure. We also highlight key research questions that still demand better integration of experiments and models. We argue that such integration is needed to achieve significant progress in our understanding of MC dynamics and function, and we make specific practical suggestions as to how this could be achieved