Torsion points of order 2g+12g+1 on odd degree hyperelliptic curves of genus gg

Let $K$ be an algebraically closed field of characteristic different from $2$, $g$ a positive integer, $f(x)\in K[x]$ a degree $2g+1$ monic polynomial without repeated roots, $C_f: y^2=f(x)$ the corresponding genus g hyperelliptic curve over $K$, and $J$ the jacobian of $C_f$. We identify $C_f$ with the image of its canonical embedding into $J$ (the infinite point of $C_f$ goes to the zero of group law on $J$). It is known (arXiv:1809.03061 [math.AG]) that if $g>1$ then $C_f(K)$ does not contain torsion points, whose order lies between $3$ and $2g$. In this paper we study torsion points of order $2g+1$ on $C_f(K)$. Despite the striking difference between the cases of $g=1$ and $g> 1$, some of our results may be viewed as a generalization of well-known results about points of order $3$ on elliptic curves. E.g., if $p=2g+1$ is a prime that coincides with $char(K)$, then every odd degree genus $g$ hyperelliptic curve contains, at most, two points of order $p$. If $g$ is odd and $f(x)$ has real coefficients, then there are, at most, two real points of order $2g+1$ on $C_f$. If $f(x)$ has rational coefficients and $g<52$, then there are, at most, two rational points of order $2g+1$ on $C_f$. (However, there are exist genus $52$ hyperelliptic curves over the field of rational numbers that have, at least, four rational points of order 105.

Digging into Lipid Membrane Permeation for Cardiac Ion Channel Blocker d-Sotalol with All-Atom Simulations.

Interactions of drug molecules with lipid membranes play crucial role in their accessibility of cellular targets and can be an important predictor of their therapeutic and safety profiles. Very little is known about spatial localization of various drugs in the lipid bilayers, their active form (ionization state) or translocation rates and therefore potency to bind to different sites in membrane proteins. All-atom molecular simulations may help to map drug partitioning kinetics and thermodynamics, thus providing in-depth assessment of drug lipophilicity. As a proof of principle, we evaluated extensively lipid membrane partitioning of d-sotalol, well-known blocker of a cardiac potassium channel Kv11.1 encoded by the hERG gene, with reported substantial proclivity for arrhythmogenesis. We developed the positively charged (cationic) and neutral d-sotalol models, compatible with the biomolecular CHARMM force field, and subjected them to all-atom molecular dynamics (MD) simulations of drug partitioning through hydrated lipid membranes, aiming to elucidate thermodynamics and kinetics of their translocation and thus putative propensities for hydrophobic and aqueous hERG access. We found that only a neutral form of d-sotalol accumulates in the membrane interior and can move across the bilayer within millisecond time scale, and can be relevant to a lipophilic channel access. The computed water-membrane partitioning coefficient for this form is in good agreement with experiment. There is a large energetic barrier for a cationic form of the drug, dominant in water, to cross the membrane, resulting in slow membrane translocation kinetics. However, this form of the drug can be important for an aqueous access pathway through the intracellular gate of hERG. This route will likely occur after a neutral form of a drug crosses the membrane and subsequently re-protonates. Our study serves to demonstrate a first step toward a framework for multi-scale in silico safety pharmacology, and identifies some of the challenges that lie therein

Identifying factors for personalized strategies to motivate seniors to adopt a more active lifestyle

Purpose Sedentary lifestyles threaten the independence and wellbeing of the rapidly growing senior population1. This lack of physical activity contributes to symptoms of frailty2. Maintaining or increasing physical activity has many benefits3 and can increase senior independence3. The value of personal profiling (context of work, personal traits ...e tc.) according to personal drivers toward behavioral intention i s accepted. User profiling relates to the goal that the user aims to reach, while psychological factors relate to motivation towards behavior changes6. It is therefore necessary to investigate which profiling factors are important to create personalized motivational strategies for promotion of physical activities. Method In this observational study, community dwelling senior members of a local Dutch senior community center were asked to wear the Xiaomi Band step counters and record their daily activities in diary-like cultural probe with both open and closed questions. Personal trait information, including age, gender, their perceived age, perceived health, participant stage of change7 and their Regulatory Focus8, was collected at the beginning and end of the 3-month test period. Results & Discussion Of the 52 seniors initially recruited, 44 submitted diaries and 15 yielded complete step data. To explore the relationship between participant's personal traits and activities, a word search on the qualitative data from the diaries was done to find how often participants mentioned high, moderate and low intensity physical activity. The number of references which male and female participants made about these levels of physical activity was compared using a non-parametric test correlation analysis using Spearman's rho correlation efficient. With 95% confidence, this analysis implied that female participants undertook a higher diversity of physical activity in terms of intensity compared to male participants (Spearman's rho=0.878). This result suggests that gender is one important profiling factor concerning the promotion of physical activity. A similar analysis was conducted to examine the level of physical activity reported compared to participant's level of perceived health. This analysis indicated, with 99% confidence (Spearman's rho=0.698), that participants with higher perceived health undertook activities with more diverse levels of physical intensity. Further research is needed to see if health or self-efficacy could cause this correlation. In a linear regression analysis, no significant difference was found between the number of steps participants with a different regulatory focus8 (promotion or prevention) made. The number of steps participants completed was correlated with the months that the steps were taken in (February, March, or April). This could be possibly due to the improved weather and could suggest that personalized strategies addressing participant's environment or context can also increase motivation to physical activity

Influence of Sex/Gender and Race on Responses to Raltegravir Combined With Tenofovir-Emtricitabine in Treatment-Naive Human Immunodeficiency Virus-1 Infected Patients: Pooled Analyses of the STARTMRK and QDMRK Studies.

BACKGROUND: Antiretroviral therapy in human immunodeficiency virus (HIV)-infected women and blacks merits particular scrutiny because these groups have been underrepresented in clinical trials. METHODS: To document the effects of raltegravir across sex and racial lines, we conducted a pooled subgroup analysis of the efficacy and safety of raltegravir 400 mg BID plus tenofovir-emtricitabine by sex (women vs men) and self-identified race (black vs non-black) using phase 3 studies in treatment-naive patients. RESULTS: Study participants included 42 black women, 102 non-black women, 48 black men, and 477 non-black men. Clade B infections were less common in women (43.8%) than men (84.6%) and in blacks (45.6%) than non-blacks (80.5%). Baseline CD4 counts were ≤200 cells/µL in 52.2% of blacks and 31.6% of non-blacks. Black men had the largest proportion of patients with baseline CD4 counts/µL and the highest nontreatment-related discontinuation rate among the 4 sex-by-race subgroups. Human immunodeficiency virus-ribonucleic acid levels/mL were achieved at week 48 in 92.7% (95% confidence interval [CI], 80.1-98.5) of black women, 93.6% (95% CI, 86.6-97.6) of non-black women, 82.9% (95% CI, 67.9-92.8) of black men, and 91.4% (95% CI, 88.4-93.8) of non-black men. Serious clinical adverse events were reported in 9.0% of women versus 8.8% of men and in 11.1% of blacks versus 8.5% of non-blacks. CONCLUSIONS: In this post hoc analysis of patients with previously untreated HIV-1 infection receiving raltegravir plus tenofovir-emtricitabine, generally comparable results were achieved across sex and racial subgroups. However, black men had a lower response rate than either black women or non-black men, partially attributable to lower baseline CD4 counts and higher discontinuation rates

Orthogonal Bases of Invariants in Tensor Models

Representation theory provides a suitable framework to count and classify invariants in tensor models. We show that there are two natural ways of counting invariants, one for arbitrary rank of the gauge group and a second, which is only valid for large N. We construct bases of invariant operators based on the counting, and compute correlators of their elements. The basis associated with finite N diagonalizes the two-point function of the theory and it is analogous to the restricted Schur basis used in matrix models. We comment on future lines of investigation.Comment: Two overlapping but independent results are merged to a joint work. 16 pages, 1 tabl

Non-holomorphic multi-matrix gauge invariant operators based on Brauer algebra

We present an orthogonal basis of gauge invariant operators constructed from some complex matrices for the free matrix field, where operators are expressed with the help of Brauer algebra. This is a generalisation of our previous work for a signle complex matrix. We also discuss the matrix quantum mechanics relevant to N=4 SYM on S^{3} times R. A commuting set of conserved operators whose eigenstates are given by the orthogonal basis is shown by using enhanced symmetries at zero coupling.Comment: 29 pages, typos corrected, references adde

A millennium-length reconstruction of Bear River stream flow, Utah

The Bear River contributes more water to the eastern Great Basin than any other river system. It is also the most significant source of water for the burgeoning Wasatch Front metropolitan area in northern Utah. Despite its importance for water resources for the region’s agricultural, urban, and wildlife needs, our understanding of the variability of Bear River’s stream flow derives entirely from the short instrumental record (1943–2010). Here we present a 1200-year calibrated and verified tree-ring reconstruction of stream flow for the Bear River that explains 67% of the variance of the instrumental record over the period from 1943 to 2010. Furthermore, we developed this reconstruction from a species that is not typically used for dendroclimatology, Utah juniper (Juniperus osteosperma). We identify highly significant periodicity in our reconstruction at quasi-decadal (7–8 year), multi-decadal (30 year), and centennial (>50 years) scales. The latter half of the 20th century was found to be the 2nd wettest (∼40-year) period of the past 1200 years, while the first half of the 20th century marked the 4th driest period. The most severe period of reduced stream flow occurred during the Medieval Warm Period (ca. mid-1200s CE) and persisted for ∼70 years. Upper-level circulation anomalies suggest that atmospheric teleconnections originating in the western tropical Pacific are responsible for the delivery of precipitation to the Bear River watershed during the October–December (OND) season of the previous year. The Bear River flow was compared to recent reconstructions of the other tributaries to the Great Salt Lake (GSL) and the GSL level. Implications for water management could be drawn from the observation that the latter half of the 20th century was the 2nd wettest in 1200 years, and that management for future water supply should take into account the stream flow variability over the past millennium