On polynomially integrable domains in Euclidean spaces

Let $D$ be a bounded domain in $\mathbb R^n,$ with smooth boundary. Denote $V_D(\omega,t), \ \omega \in S^{n-1}, t \in \mathbb R,$ the Radon transform of the characteristic function $\chi_{D}$ of the domain $D,$ i.e., the $(n-1)-$ dimensional volume of the intersection $D$ with the hyperplane $\{x \in \mathbb R^n: =t \}.$ If the domain $D$ is an ellipsoid, then the function $V_D$ is algebraic and if, in addition, the dimension $n$ is odd, then $V(\omega,t)$ is a polynomial with respect to $t.$ Whether odd-dimensional ellipsoids are the only bounded smooth domains with such a property? The article is devoted to partial verification and discussion of this question

Exact properties of Frobenius numbers and fraction of the symmetric semigroups in the weak limit for n=3

We generalize and prove a hypothesis by V. Arnold on the parity of Frobenius number. For the case of symmetric semigroups with three generators of Frobenius numbers we found an exact formula, which in a sense is the sum of two Sylvester's formulaes. We prove that the fraction of the symmetric semigroups is vanishing in the weak limit

Health Care Resource Utilization and Related Costs of Patients With CKD From the United States: A Report From the DISCOVER CKD Retrospective Cohort

Introduction: It is well established that chronic kidney disease (CKD) results in a significant burden on patients’ health and health care providers. However, detailed estimates of the health care resource utilization (HCRU) of CKD are limited, particularly those which consider severity, comorbidities, and payer type. This study aimed to bridge this evidence gap by reporting contemporary HCRU and costs in patients with CKD across the US health care providers. Methods: Cost and HCRU estimates of CKD and reduced kidney function without CKD (estimated glomerular filtration rate [eGFR]: 60−75 and urine albumin-to-creatinine ratio [UACR]: <30) were derived for US patients included in the DISCOVER CKD cohort study, using linked inpatient and outpatient data from the limited claims-EMR data set (LCED) and TriNetX database. Patients with a history of transplant or undergoing dialysis were not included. HCRU and costs were stratified by CKD severity using UACR and eGFR. Results: Overall health care costs ranged from $26,889 (A1) to$42,139 (A3), and from $28,627 (G2) to$42,902 (G5) per patient per year (PPPY), demonstrating a considerable early disease burden which continued to increase with declining kidney function. The PPPY costs of later stage CKD were particularly notable for patients with concomitant heart failure ($50,191 [A3]) and those covered by commercial payers ($55,735 [A3]). Conclusions: Health care costs and resource use associated with CKD and reduced kidney function pose a substantial burden across health care systems and payers, increasing in line with CKD progression. Early CKD screening, particularly of UACR, paired with proactive disease management may provide both an improvement to patient outcomes and a significant HCRU and cost saving to health care providers

Fidelity Variants of RNA Dependent RNA Polymerases Uncover an Indirect, Mutagenic Activity of Amiloride Compounds

In a screen for RNA mutagen resistance, we isolated a high fidelity RNA dependent RNA polymerase (RdRp) variant of Coxsackie virus B3 (CVB3). Curiously, this variant A372V is also resistant to amiloride. We hypothesize that amiloride has a previously undescribed mutagenic activity. Indeed, amiloride compounds increase the mutation frequencies of CVB3 and poliovirus and high fidelity variants of both viruses are more resistant to this effect. We hypothesize that this mutagenic activity is mediated through alterations in intracellular ions such as Mg2+ and Mn2+, which in turn increase virus mutation frequency by affecting RdRp fidelity. Furthermore, we show that another amiloride-resistant RdRp variant, S299T, is completely resistant to this mutagenic activity and unaffected by changes in ion concentrations. We show that RdRp variants resist the mutagenic activity of amiloride via two different mechanisms: 1) increased fidelity that generates virus populations presenting lower basal mutation frequencies or 2) resisting changes in divalent cation concentrations that affect polymerase fidelity. Our results uncover a new antiviral approach based on mutagenesis

Direct Detection of Electroweak-Interacting Dark Matter

Assuming that the lightest neutral component in an SU(2)L gauge multiplet is the main ingredient of dark matter in the universe, we calculate the elastic scattering cross section of the dark matter with nucleon, which is an important quantity for the direct detection experiments. When the dark matter is a real scalar or a Majorana fermion which has only electroweak gauge interactions, the scattering with quarks and gluon are induced through one- and two-loop quantum processes, respectively, and both of them give rise to comparable contributions to the elastic scattering cross section. We evaluate all of the contributions at the leading order and find that there is an accidental cancellation among them. As a result, the spin-independent cross section is found to be O(10^-(46-48)) cm^2, which is far below the current experimental bounds.Comment: 19 pages, 7 figures, published versio

Thermodynamics of an ideal generalized gas:II Means of order α\alpha

The property that power means are monotonically increasing functions of their order is shown to be the basis of the second laws not only for processes involving heat conduction but also for processes involving deformations. In an $L$-potentail equilibration the final state will be one of maximum entropy, while in an entropy equilibrium the final state will be one of minimum $L$. A metric space is connected with the power means, and the distance between means of different order is related to the Carnot efficiency. In the ideal classical gas limit, the average change in the entropy is shown to be proportional to the difference between the Shannon and R\'enyi entropies for nonextensive systems that are multifractal in nature. The $L$-potential, like the internal energy, is a Schur convex function of the empirical temperature, which satisfies Jensen's inequality, and serves as a measure of the tendency to uniformity in processes involving pure thermal conduction.Comment: 8 page

Anarchy in the UK: Detailed genetic analysis of worker reproduction in a naturally occurring British anarchistic honeybee, Apis mellifera, colony using DNA microsatellites

Anarchistic behaviour is a very rare phenotype of honeybee colonies. In an anarchistic colony, many workers’ sons are reared in the presence of the queen. Anarchy has previously been described in only two Australian colonies. Here we report on a first detailed genetic analysis of a British anarchistic colony. Male pupae were present in great abundance above the queen excluder, which was clearly indicative of extensive worker reproduction and is the hallmark of anarchy. Seventeen microsatellite loci were used to analyse these male pupae, allowing us to address whether all the males were indeed workers’ sons, and how many worker patrilines and individual workers produced them. In the sample, 95 of 96 of the males were definitely workers’ sons. Given that ≈ 1% of workers’ sons were genetically indistinguishable from queen’s sons, this suggests that workers do not move any queen-laid eggs between the part of the colony where the queen is present to the area above the queen excluder which the queen cannot enter. The colony had 16 patrilines, with an effective number of patrilines of 9.85. The 75 males that could be assigned with certainty to a patriline came from 7 patrilines, with an effective number of 4.21. They were the offspring of at least 19 workers. This is in contrast to the two previously studied Australian naturally occurring anarchist colonies, in which most of the workers’ sons were offspring of one patriline. The high number of patrilines producing males leads to a low mean relatedness between laying workers and males of the colony. We discuss the importance of studying such colonies in the understanding of worker policing and its evolution

Survival and associated factors in 268 adults with Pompe disease prior to treatment with enzyme replacement therapy

Background: Pompe disease is a rare lysosomal storage disorder characterized by muscle weakness and wasting. The majority of adult patients have slowly progressive disease, which gradually impairs mobility and respiratory function and may lead to wheelchair and ventilator dependency. It is as yet unknown to what extent the disease reduces the life span of these patients. Our objective was to determine the survival of adults with P