Calculating and visualizing the density of states for simple quantum mechanical systems

We present a graphical approach to understanding the degeneracy, density of states, and cumulative state number for some simple quantum systems. By taking advantage of basic computing operations, we define a straightforward procedure for determining the relationship between discrete quantum energy levels and the corresponding density of states and cumulative level number. The density of states for a particle in a rigid box of various shapes and dimensions is examined and graphed. It is seen that the dimension of the box, rather than its shape, is the most important feature. In addition, we look at the density of states for a multi-particle system of identical bosons built on the single-particle spectra of those boxes. A simple model is used to explain how the N-particle density of states arises from the single particle system it is based on

Формирование эмоциональной культуры как компонента инновационной культуры студентов

Homozygosity has long been associated with rare, often devastating, Mendelian disorders1 and Darwin was one of the first to recognise that inbreeding reduces evolutionary fitness2. However, the effect of the more distant parental relatedness common in modern human populations is less well understood. Genomic data now allow us to investigate the effects of homozygosity on traits of public health importance by observing contiguous homozygous segments (runs of homozygosity, ROH), which are inferred to be homozygous along their complete length. Given the low levels of genome-wide homozygosity prevalent in most human populations, information is required on very large numbers of people to provide sufficient power3,4. Here we use ROH to study 16 health-related quantitative traits in 354,224 individuals from 102 cohorts and find statistically significant associations between summed runs of homozygosity (SROH) and four complex traits: height, forced expiratory lung volume in 1 second (FEV1), general cognitive ability (g) and educational attainment (nominal p<1 × 10−300, 2.1 × 10−6, 2.5 × 10−10, 1.8 × 10−10). In each case increased homozygosity was associated with decreased trait value, equivalent to the offspring of first cousins being 1.2 cm shorter and having 10 months less education. Similar effect sizes were found across four continental groups and populations with different degrees of genome-wide homozygosity, providing convincing evidence for the first time that homozygosity, rather than confounding, directly contributes to phenotypic variance. Contrary to earlier reports in substantially smaller samples5,6, no evidence was seen of an influence of genome-wide homozygosity on blood pressure and low density lipoprotein (LDL) cholesterol, or ten other cardio-metabolic traits. Since directional dominance is predicted for traits under directional evolutionary selection7, this study provides evidence that increased stature and cognitive function have been positively selected in human evolution, whereas many important risk factors for late-onset complex diseases may not have been

Effect of angiotensin-converting enzyme inhibitor and angiotensin receptor blocker initiation on organ support-free days in patients hospitalized with COVID-19

IMPORTANCE Overactivation of the renin-angiotensin system (RAS) may contribute to poor clinical outcomes in patients with COVID-19. Objective To determine whether angiotensin-converting enzyme (ACE) inhibitor or angiotensin receptor blocker (ARB) initiation improves outcomes in patients hospitalized for COVID-19. DESIGN, SETTING, AND PARTICIPANTS In an ongoing, adaptive platform randomized clinical trial, 721 critically ill and 58 non–critically ill hospitalized adults were randomized to receive an RAS inhibitor or control between March 16, 2021, and February 25, 2022, at 69 sites in 7 countries (final follow-up on June 1, 2022). INTERVENTIONS Patients were randomized to receive open-label initiation of an ACE inhibitor (n = 257), ARB (n = 248), ARB in combination with DMX-200 (a chemokine receptor-2 inhibitor; n = 10), or no RAS inhibitor (control; n = 264) for up to 10 days. MAIN OUTCOMES AND MEASURES The primary outcome was organ support–free days, a composite of hospital survival and days alive without cardiovascular or respiratory organ support through 21 days. The primary analysis was a bayesian cumulative logistic model. Odds ratios (ORs) greater than 1 represent improved outcomes. RESULTS On February 25, 2022, enrollment was discontinued due to safety concerns. Among 679 critically ill patients with available primary outcome data, the median age was 56 years and 239 participants (35.2%) were women. Median (IQR) organ support–free days among critically ill patients was 10 (–1 to 16) in the ACE inhibitor group (n = 231), 8 (–1 to 17) in the ARB group (n = 217), and 12 (0 to 17) in the control group (n = 231) (median adjusted odds ratios of 0.77 [95% bayesian credible interval, 0.58-1.06] for improvement for ACE inhibitor and 0.76 [95% credible interval, 0.56-1.05] for ARB compared with control). The posterior probabilities that ACE inhibitors and ARBs worsened organ support–free days compared with control were 94.9% and 95.4%, respectively. Hospital survival occurred in 166 of 231 critically ill participants (71.9%) in the ACE inhibitor group, 152 of 217 (70.0%) in the ARB group, and 182 of 231 (78.8%) in the control group (posterior probabilities that ACE inhibitor and ARB worsened hospital survival compared with control were 95.3% and 98.1%, respectively). CONCLUSIONS AND RELEVANCE In this trial, among critically ill adults with COVID-19, initiation of an ACE inhibitor or ARB did not improve, and likely worsened, clinical outcomes. TRIAL REGISTRATION ClinicalTrials.gov Identifier: NCT0273570

Millimeter wave spectrum and search for vinyl isocyanate toward Sgr B2(N) with ALMA

International audienceContext. The interstellar detections of isocyanic acid (HNCO), methyl isocyanate (CH3NCO), and very recently also ethyl isocyanate (C2H5NCO) invite the question of whether or not vinyl isocyanate (C2H3NCO) can be detected in the interstellar medium. There are only low-frequency spectroscopic data (&lt;40 GHz) available for this species in the literature, which makes predictions at higher frequencies rather uncertain, which in turn hampers searches for this molecule in space using millimeter (mm) wave astronomy. Aims. The aim of the present study is on one hand to extend the laboratory rotational spectrum of vinyl isocyanate to the mm wave region and on the other to search, for the first time, for its presence in the high-mass star-forming region Sgr B2, where other isocyanates and a plethora of complex organic molecules are observed. Methods. We recorded the pure rotational spectrum of vinyl isocyanate in the frequency regions 127.5-218 and 285-330 GHz using the Prague mm wave spectrometer. The spectral analysis was supported by high-level quantum-chemical calculations. On the astronomy side, we assumed local thermodynamic equilibrium to compute synthetic spectra of vinyl isocyanate and to search for it in the ReMoCA survey performed with the Atacama Large Millimeter/submillimeter Array (ALMA) toward the high-mass star-forming protocluster Sgr B2(N). Additionally, we searched for the related molecule ethyl isocyanate in the same source. Results. Accurate values for the rotational and centrifugal distortion constants are reported for the ground vibrational states of trans and cis vinyl isocyanate from the analysis of more than 1000 transitions. We report nondetections of vinyl and ethyl isocyanate toward the main hot core of Sgr B2(N). We find that vinyl and ethyl isocyanate are at least 11 and 3 times less abundant than methyl isocyanate in this source, respectively. Conclusions. Although the precise formation mechanism of interstellar methyl isocyanate itself remains uncertain, we infer from existing astrochemical models that our observational upper limit for the CH3NCO:C2H5NCO ratio in Sgr B2(N) is consistent with ethyl isocyanate being formed on dust grains via the abstraction or photodissociation of an H atom from methyl isocyanate, followed by the addition of a methyl radical. The dominance of such a process for ethyl isocyanate production, combined with the absence of an analogous mechanism for vinyl isocyanate, would indicate that the ratio C2H3NCO:C2H5NCO should be less than unity. Even though vinyl isocyanate was not detected toward Sgr B2(N), the results of this work represent a significant improvement on previous low-frequency studies and will help the astronomical community to continue searching for this species in the Universe