Stages of steady diffusion growth of a gas bubble in strongly supersaturated gas-liquid solution

Gas bubble growth as a result of diffusion flux of dissolved gas molecules from the surrounding supersaturated solution to the bubble surface is studied. The condition of the flux steadiness is revealed. A limitation from below on the bubble radius is considered. Its fulfillment guarantees the smallness of fluctuation influence on bubble growth and irreversibility of this process. Under the conditions of steadiness of diffusion flux three stages of bubble growth are marked out. With account for Laplace forces in the bubble intervals of bubble size change and time intervals of these stages are found. The trend of the third stage towards the self-similar regime of the bubble growth, when Laplace forces in the bubble are completely neglected, is described analytically.Comment: 22 page

Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group

We study Sobolev-type metrics of fractional order $s\geq0$ on the group \Diff_c(M) of compactly supported diffeomorphisms of a manifold $M$. We show that for the important special case $M=S^1$ the geodesic distance on \Diff_c(S^1) vanishes if and only if $s\leq\frac12$. For other manifolds we obtain a partial characterization: the geodesic distance on \Diff_c(M) vanishes for $M=\R\times N, s<\frac12$ and for $M=S^1\times N, s\leq\frac12$, with $N$ being a compact Riemannian manifold. On the other hand the geodesic distance on \Diff_c(M) is positive for $\dim(M)=1, s>\frac12$ and $\dim(M)\geq2, s\geq1$. For $M=\R^n$ we discuss the geodesic equations for these metrics. For $n=1$ we obtain some well known PDEs of hydrodynamics: Burgers' equation for $s=0$, the modified Constantin-Lax-Majda equation for $s=\frac 12$ and the Camassa-Holm equation for $s=1$.Comment: 16 pages. Final versio

Quantum Inequalities for the Electromagnetic Field

A quantum inequality for the quantized electromagnetic field is developed for observers in static curved spacetimes. The quantum inequality derived is a generalized expression given by a mode function expansion of the four-vector potential, and the sampling function used to weight the energy integrals is left arbitrary up to the constraints that it be a positive, continuous function of unit area and that it decays at infinity. Examples of the quantum inequality are developed for Minkowski spacetime, Rindler spacetime and the Einstein closed universe.Comment: 19 pages, 1 table and 1 figure. RevTex styl

Full-length transcriptome reconstruction reveals a large diversity of RNA and protein isoforms in rat hippocampus

Gene annotation is a critical resource in genomics research. Many computational approaches have been developed to assemble transcriptomes based on high-throughput short-read sequencing, however, only with limited accuracy. Here, we combine next-generation and third-generation sequencing to reconstruct a full-length transcriptome in the rat hippocampus, which is further validated using independent 5´ and 3´-end profiling approaches. In total, we detect 28,268 full-length transcripts (FLTs), covering 6,380 RefSeq genes and 849 unannotated loci. Based on these FLTs, we discover co-occurring alternative RNA processing events. Integrating with polysome profiling and ribosome footprinting data, we predict isoform-specific translational status and reconstruct an open reading frame (ORF)-eome. Notably, a high proportion of the predicted ORFs are validated by mass spectrometry-based proteomics. Moreover, we identify isoforms with subcellular localization pattern in neurons. Collectively, our data advance our knowledge of RNA and protein isoform diversity in the rat brain and provide a rich resource for functional studies

On the verge of Umdeutung in Minnesota: Van Vleck and the correspondence principle (Part One)

In October 1924, the Physical Review, a relatively minor journal at the time, published a remarkable two-part paper by John H. Van Vleck, working in virtual isolation at the University of Minnesota. Van Vleck combined advanced techniques of classical mechanics with Bohr's correspondence principle and Einstein's quantum theory of radiation to find quantum analogues of classical expressions for the emission, absorption, and dispersion of radiation. For modern readers Van Vleck's paper is much easier to follow than the famous paper by Kramers and Heisenberg on dispersion theory, which covers similar terrain and is widely credited to have led directly to Heisenberg's "Umdeutung" paper. This makes Van Vleck's paper extremely valuable for the reconstruction of the genesis of matrix mechanics. It also makes it tempting to ask why Van Vleck did not take the next step and develop matrix mechanics himself.Comment: 82 page

Sex Disparities in Arrest Outcomes for Domestic Violence

Domestic violence arrests have been historically focused on protecting women and children from abusive men. Arrest patterns continue to reflect this bias with more men arrested for domestic violence compared to women. Such potential gender variations in arrest patterns pave the way to the investigation of disparities by sex of the offender in domestic violence arrests. This study utilizes data from a quantitative dataset that includes responses by police officers who completed a specially mandated checklist after responding to a domestic dispute. The results showed that while females are arrested quite often in domestic disputes, there remains a significant difference in the arrest outcome whereby male suspects were more likely to be arrested than female suspects. Regression models further indicated differences based on sex and certain predictors of arrest, which supported sex-based rationales in arrests for domestic violence.Yeshttps://us.sagepub.com/en-us/nam/manuscript-submission-guideline

Higher serum vitamin D3 levels are associated with better cognitive test performance in patients with Alzheimer's disease

Background/Aims: Recent studies suggest that vitamin D metabolites may be important for preserving cognitive function via specific neuroprotective effects. No large studies have examined the association between vitamin D status and cognition. Methods: In this cross-sectional study, we analyzed the serum 25-hydroxyvitamin D3levels and Mini-Mental State Examination (MMSE) test scores of 225 older outpatients who were diagnosed as having probable Alzheimer's disease (AD). In addition to the 25-hydroxyvitamin D3levels, we analyzed the serum vitamin B1, B6and B12levels. Results: An association was found between MMSE test scores and serum 25-hydroxyvitamin D3levels, with a β-coefficient of 0.05 (p = 0.01). Vitamin-D-sufficient patients had significantly higher MMSE scores as compared to vitamin-D-insufficient ones. No association was found with the other serum vitamin levels. Conclusions: These data support the idea that a relationship exists between vitamin D status and cognition in patients with probable AD. However, given the cross-sectional design of this study, no causality can be concluded. Further prospective studies are needed to specify the contribution of vitamin D status to the onset and course of cognitive decline and AD. Copyrigh

Glucose modifies the effect of endovascular thrombectomy in patients with acute stroke: a pooled-data meta-analysis

Background and Purpose: Hyperglycemia is a negative prognostic factor following acute ischemic stroke but is not known whether glucose is associated with the effects of endovascular thrombectomy in patients with large vessel stroke. In a pooled-data meta-analysis, we analyzed whether serum glucose is a treatment modifier of the efficacy of endovascular thrombectomy in acute stroke. Methods: Seven randomized trials compared endovascular thrombectomy with standard care between 2010 and 2017 (HERMES Collaboration). 1764 patients with large vessel stroke were allocated to endovascular thrombectomy (n=871) or standard care (n=893). Measurements included blood glucose on admission and functional outcome [modified Rankin Scale (mRS) range: 0-6; lower scores indicating less disability] at 3 months. The primary analysis evaluated whether glucose modified the effect of EVT over standard care on functional outcome, using ordinal logistic regression to test the interaction between treatment and glucose level. Results: Median (IQR) serum glucose on admission was 120 (104-140) mg/dl [6.6mmol/l (5.7-7.7) mmol/l]. Endovascular thrombectomy (EVT) was better than standard care in the overall pooled-data analysis [common odds ratio (acOR), 2.00 (95% CI 1.69–2.38); however, lower glucose levels were associated with greater effects of EVT over standard care. The interaction was nonlinear such that significant interactions were found in subgroups of patients split at glucose &lt; or &gt; 90mg/dl (5.0mmol/l) [(p=0.019 for interaction, acOR 3.81 (95% CI 1.73–8.41) for patients &lt; 90 mg/dl vs 1.83 (95% CI 1.53–2.19) for patients &gt; 90 mg/dl], and glucose &lt; or &gt; 100mg/dl (5.5mmol/l) [(p=0.004 for interaction, acOR 3.17 (95% CI 2.04–4.93) vs acOR 1.72 (95% CI 1.42–2.08)], but not between subgroups above these levels of glucose. Conclusions: Endovascular thrombectomy improved stroke outcomes compared to standard treatment regardless of glucose levels but the treatment effects were larger at lower glucose levels, with significant interaction effects persisting up to 90 to 100mg/dl (5.0-5.5mmol/l). Whether tight control of glucose improves the efficacy of endovascular thrombectomy following large vessel stroke warrants appropriate testing

Approximate Bisimulations for Sodium Channel Dynamics

Abstract. This paper shows that, in the context of the Iyer et al. 67-variable cardiac myocycte model (IMW), it is possible to replace the detailed 13-state continuous-time MDP model of the sodium-channel dy-namics, with a much simpler Hodgkin-Huxley (HH)-like two-state sodium-channel model, while only incurring a bounded approximation error. The technical basis for this result is the construction of an approximate bisim-ulation between the HH and IMW channel models, both of which are input-controlled (voltage in this case) continuous-time Markov chains. The construction of the appropriate approximate bisimulation, as well as the overall result regarding the behavior of this modified IMW model, in-volves: (1) The identification of the voltage-dependent parameters of the m and h gates in the HH-type channel, based on the observations of the IMW channel. (2) Proving that the distance between observations of the two channels never exceeds a given error. (3) Exploring the sensitivity of the overall IMW model to the HH-type sodium-channel approximation. Our extensive simulation results experimentally validate our findings, for varying IMW-type input stimuli