A large-deviations principle for all the cluster sizes of a sparse Erdős–Rényi graph

Let (Formula presented.) be the Erdős–Rényi graph with connection probability (Formula presented.) as N → ∞ for a fixed t ∈ (0, ∞). We derive a large-deviations principle for the empirical measure of the sizes of all the connected components of (Formula presented.), registered according to microscopic sizes (i.e., of finite order), macroscopic ones (i.e., of order N), and mesoscopic ones (everything in between). The rate function explicitly describes the microscopic and macroscopic components and the fraction of vertices in components of mesoscopic sizes. Moreover, it clearly captures the well known phase transition at t = 1 as part of a comprehensive picture. The proofs rely on elementary combinatorics and on known estimates and asymptotics for the probability that subgraphs are connected. We also draw conclusions for the strongly related model of the multiplicative coalescent, the Marcus–Lushnikov coagulation model with monodisperse initial condition, and its gelation phase transition

A large-deviations approach to gelation

A large-deviations principle (LDP) is derived for the state at fixed time, of the multiplicative coalescent in the large particle number limit. The rate function is explicit and describes each of the three parts of the state: microscopic, mesoscopic and macroscopic. In particular, it clearly captures the well known gelation phase transition given by the formation of a particle containing a positive fraction of the system mass. Via a standard map of the multiplicative coalescent onto a time-dependent version of the Erdős-Rényi random graph, our results can also be rephrased as an LDP for the component sizes in that graph. The proofs rely on estimates and asymptotics for the probability that smaller Erdős-Rényi graphs are connected

Multiple time scales in cataclysmic binaries. The low-field magnetic dwarf nova DO Draconis

We study the variability of the cataclysmic variable DO Dra, on time-scales of between minutes and decades. The characteristic decay time dt/dm=0.902(3) days/mag was estimated from our 3 nights of CCD R observations. The quiescent data show a photometric wave with a cycle about 303(15)d. We analyzed the profile of the composite (or mean) outburst. We discovered however, that a variety of different outburst heights and durations had occurred, contrary to theoretical predictions. With increasing maximum brightness, we find that the decay time also increases; this is in contrast to the model predictions, which indicate that outbursts should have a constant shape. This is interpreted as representing the presence of outburst-to-outburst variability of the magnetospheric radius. A presence of a number of missed weak narrow outbursts is predicted from this statistical relationship. A new type of variability is detected, during 3 subsequent nights in 2007: periodic (during one nightly run) oscillations with rapidly-decreasing frequency from 86 to 47 cycles/day and a semi-amplitude increasing from 0.06 to 0. 10, during a monotonic brightness increase from 14. 27 to 14. 13. This phenomenon was observed only during an unusually prolonged event of about 1 mag brightening in 2007 (lasting till autumn), during which no (expected) outburst was detected. We refer to this behaviour as to the transient periodic oscillations (TPO). To study this new and interesting phenomenon, new regular photometric and spectral (in a target of opportunity mode) observations are required.Comment: 12pages, 8figures, accepted in Astronomy and Astrophysic

β Cell function and plasma insulin clearance in people with obesity and different glycemic status

BackgroundIt is unclear how excess adiposity and insulin resistance affect β cell function, insulin secretion, and insulin clearance in people with obesity.MethodsWe used a hyperinsulinemic-euglycemic clamp procedure and a modified oral glucose tolerance test to evaluate the interrelationships among obesity, insulin sensitivity, insulin kinetics, and glycemic status in 5 groups of individuals: normoglycemic lean and obese individuals with (a) normal fasting glucose and normal glucose tolerance (Ob-NFG-NGT), (b) NFG and impaired glucose tolerance (Ob-NFG-IGT), (c) impaired fasting glucose and IGT (Ob-IFG-IGT), or (d) type 2 diabetes (Ob-T2D).ResultsGlucose-stimulated insulin secretion (GSIS), an assessment of β cell function, was greater in the Ob-NFG-NGT and Ob-NFG-IGT groups than in the lean group, even when insulin sensitivity was matched in the obese and lean groups. Insulin sensitivity, not GSIS, was decreased in the Ob-NFG-IGT group compared with the Ob-NFG-NGT group, whereas GSIS, not insulin sensitivity, was decreased in the Ob-IFG-IGT and Ob-T2D groups compared with the Ob-NFG-NGT and Ob-NFG-IGT groups. Insulin clearance was directly related to insulin sensitivity and inversely related to the postprandial increase in insulin secretion and plasma insulin concentration.ConclusionIncreased adiposity per se, not insulin resistance, enhanced insulin secretion in people with obesity. The obesity-induced increase in insulin secretion, in conjunction with a decrease in insulin clearance, sufficiently raised the plasma insulin concentrations needed to maintain normoglycemia in individuals with moderate, but not severe, insulin resistance. A deterioration in β cell function, not a decrease in insulin sensitivity, was a determinant of IFG and ultimately leads to T2D.CLINICAL TRIALS REGISTRATIONClinicalTrials.gov NCT02706262, NCT04131166, and NCT01977560.FUNDINGNIH (P30 DK056341, P30 DK020579, and UL1 TR000448); American Diabetes Association (1-18-ICTS-119); Longer Life Foundation; Pershing Square Foundation; and Washington University-Centene ARCH Personalized Medicine Initiative (P19-00559)

Search for the electric dipole moment of the electron with thorium monoxide

The electric dipole moment of the electron (eEDM) is a signature of CP-violating physics beyond the Standard Model. We describe an ongoing experiment to measure or set improved limits to the eEDM, using a cold beam of thorium monoxide (ThO) molecules. The metastable $H {}^3\Delta_1$ state in ThO has important advantages for such an experiment. We argue that the statistical uncertainty of an eEDM measurement could be improved by as much as 3 orders of magnitude compared to the current experimental limit, in a first-generation apparatus using a cold ThO beam. We describe our measurements of the $H$ state lifetime and the production of ThO molecules in a beam, which provide crucial data for the eEDM sensitivity estimate. ThO also has ideal properties for the rejection of a number of known systematic errors; these properties and their implications are described.Comment: v2: Equation (11) correcte

The Effect of Early vs. Normal Calf Weaning on Feedlot Performance and Herd Management: A Cross-Discipline Case Study

A study of early vs. normal weaning of calves concludes that early weaning improves feedlot production efficiency, reducing per day and per pound feedlot production costs. Early weaned steers finished higher thus feedlot profitability was not affected. Early weaning has a positive affect on cow health and pasture utilization rates.Livestock Production/Industries,

Effects of Large-Scale Convection on p-mode Frequencies

We describe an approach for finding the eigenfrequencies of solar acoustic modes (p modes) in a convective envelope in the WKB limit. This approximation restricts us to examining the effects of fluid motions which are large compared to the mode wavelength, but allows us to treat the three-dimensional mode as a localized ray. The method of adiabatic switching is then used to investigate the frequency shifts resulting from simple perturbations to a polytropic model of the convection zone as well as from two basic models of a convective cell. We find that although solely depth-dependent perturbations can give frequency shifts which are first order in the strength of the perturbation, models of convective cells generate downward frequency shifts which are second order in the perturbation strength. These results may have implications for resolving the differences between eigenfrequencies derived from solar models and those found from helioseismic observations.Comment: 27 pages + 6 figures; accepted for publication in Ap

Effect of various dopant elements on primary graphite growth

Five spheroidal graphite cast irons were investigated, a usual ferritic grade and four pearlitic alloys containing Cu and doped with Sb, Sn and Ti. These alloys were remelted in a graphite crucible, leading to volatilization of the magnesium added for spheroidization and to carbon saturation of the liquid. The alloys were then cooled down and maintained at a temperature above the eutectic temperature. During this step, primary graphite could develop showing various features depending on the doping elements added. The largest effects were that of Ti which greatly reduces graphite nucleation and growth, and that of Sb which leads to rounded agglomerates instead of lamellar graphite. The samples have been investigated with secondary ion mass spectrometry to enlighten distribution of elements in primary graphite. SIMS analysis showed almost even distribution of elements, including Mg and Al (from the inoculant) in the ferritic grade, while uneven distribution was evident in all doped alloys. Investigations are going on to clarify if the uneven distribution is associated with structural defects in the graphite precipitates