On vanishing class sizes in finite groups

© 2017 Elsevier Inc. Let G be a finite group. An element g of G is called a vanishing element if there exists an irreducible character χ of G such that χ(g)=0; in this case, we say that the conjugacy class of g is a vanishing conjugacy class. In this paper, we discuss some arithmetical properties concerning the sizes of the vanishing conjugacy classes in a finite group

Conjugacy classes of finite groups and graph regularity

Given a finite group $G$, denote by $\Gamma(G)$ the simple undirected graph whose vertices are the distinct sizes of noncentral conjugacy classes of $G$, and set two vertices of $\Gamma(G)$ to be adjacent if and only if they are not coprime numbers. In this note we prove that, if $\Gamma(G)$ is a $k$-regular graph with $k\geq 1$, then $\Gamma(G)$ is a complete graph with $k+1$ vertices

On solvable groups with one vanishing class size

Copyright © The Author(s), 2020. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh. Let G be a finite group, and let cs(G) be the set of conjugacy class sizes of G. Recalling that an element g of G is called a vanishing element if there exists an irreducible character of G taking the value 0 on g, we consider one particular subset of cs(G), namely, the set vcs(G) whose elements are the conjugacy class sizes of the vanishing elements of G. Motivated by the results inBianchi et al. (2020, J. Group Theory, 23, 79-83), we describe the class of the finite groups G such that vcs(G) consists of a single element under the assumption that G is supersolvable or G has a normal Sylow 2-subgroup (in particular, groups of odd order are covered). As a particular case, we also get a characterization of finite groups having a single vanishing conjugacy class size which is either a prime power or square-free

Gene Function Classification Using Bayesian Models with Hierarchy-Based Priors

We investigate the application of hierarchical classification schemes to the annotation of gene function based on several characteristics of protein sequences including phylogenic descriptors, sequence based attributes, and predicted secondary structure. We discuss three Bayesian models and compare their performance in terms of predictive accuracy. These models are the ordinary multinomial logit (MNL) model, a hierarchical model based on a set of nested MNL models, and a MNL model with a prior that introduces correlations between the parameters for classes that are nearby in the hierarchy. We also provide a new scheme for combining different sources of information. We use these models to predict the functional class of Open Reading Frames (ORFs) from the E. coli genome. The results from all three models show substantial improvement over previous methods, which were based on the C5 algorithm. The MNL model using a prior based on the hierarchy outperforms both the non-hierarchical MNL model and the nested MNL model. In contrast to previous attempts at combining these sources of information, our approach results in a higher accuracy rate when compared to models that use each data source alone. Together, these results show that gene function can be predicted with higher accuracy than previously achieved, using Bayesian models that incorporate suitable prior information

Negative Effects of Paternal Age on Children's Neurocognitive Outcomes Can Be Explained by Maternal Education and Number of Siblings

Background: Recent findings suggest advanced paternal age may be associated with impaired child outcomes, in particular, neurocognitive skills. Such patterns are worrisome given relatively universal trends in advanced countries toward delayed nuptiality and fertility. But nature and nurture are both important for child outcomes, and it is important to control for both when drawing inferences about either pathway. Methods and Findings: We examined cross-sectional patterns in six developmental outcome measures among children in the U.S. Collaborative Perinatal Project (n = 31,346). Many of these outcomes at 8 mo, 4 y, and 7 y of age (Bayley scales, Stanford Binet Intelligence Scale, Graham-Ernhart Block Sort Test, Wechsler Intelligence Scale for Children, Wide Range Achievement Test) are negatively correlated with paternal age when important family characteristics such as maternal education and number of siblings are not included as covariates. But controlling for family characteristics in general and mother’s education in particular renders the effect of paternal age statistically insignificant for most developmental measures. Conclusions: Assortative mating produces interesting relationships between maternal and paternal characteristics that can inject spurious correlation into observational studies via omitted variable bias. Controlling for both nature and nurture reveals little residual evidence of a link between child neurocognitive outcomes and paternal age in these data. Result

Obstructive Sleep Apnea Alters Sleep Stage Transition Dynamics

Enhanced characterization of sleep architecture, compared with routine polysomnographic metrics such as stage percentages and sleep efficiency, may improve the predictive phenotyping of fragmented sleep. One approach involves using stage transition analysis to characterize sleep continuity.We analyzed hypnograms from Sleep Heart Health Study (SHHS) participants using the following stage designations: wake after sleep onset (WASO), non-rapid eye movement (NREM) sleep, and REM sleep. We show that individual patient hypnograms contain insufficient number of bouts to adequately describe the transition kinetics, necessitating pooling of data. We compared a control group of individuals free of medications, obstructive sleep apnea (OSA), medical co-morbidities, or sleepiness (n = 374) with mild (n = 496) or severe OSA (n = 338). WASO, REM sleep, and NREM sleep bout durations exhibited multi-exponential temporal dynamics. The presence of OSA accelerated the "decay" rate of NREM and REM sleep bouts, resulting in instability manifesting as shorter bouts and increased number of stage transitions. For WASO bouts, previously attributed to a power law process, a multi-exponential decay described the data well. Simulations demonstrated that a multi-exponential process can mimic a power law distribution.OSA alters sleep architecture dynamics by decreasing the temporal stability of NREM and REM sleep bouts. Multi-exponential fitting is superior to routine mono-exponential fitting, and may thus provide improved predictive metrics of sleep continuity. However, because a single night of sleep contains insufficient transitions to characterize these dynamics, extended monitoring of sleep, probably at home, would be necessary for individualized clinical application

Hand-held cell phone use while driving legislation and observed driver behavior among population sub-groups in the United States

Abstract Background Cell phone use behaviors are known to vary across demographic sub-groups and geographic locations. This study examined whether universal hand-held calling while driving bans were associated with lower road-side observed hand-held cell phone conversations across drivers of different ages (16–24, 25–59, ≥60 years), sexes, races (White, African American, or other), ruralities (suburban, rural, or urban), and regions (Northeast, Midwest, South, and West). Methods Data from the 2008–2013 National Occupant Protection Use Survey were merged with states’ cell phone use while driving legislation. The exposure was presence of a universal hand-held cell phone ban at time of observation. Logistic regression was used to assess the odds of drivers having a hand-held cell phone conversation. Sub-groups differences were assessed using models with interaction terms. Results When universal hand-held cell phone bans were effective, hand-held cell phone conversations were lower across all driver demographic sub-groups and regions. Sub-group differences existed among the sexes (p-value, <0.0001) and regions (p-value, 0.0003). Compared to states without universal hand-held cell phone bans, the adjusted odds ratio (aOR) of a driver hand-held phone conversation was 0.34 [95% confidence interval (CI): 0.28, 0.41] for females versus 0.47 (CI 0.40, 0.55) for males and 0.31 (CI 0.25, 0.38) for drivers in Western states compared to 0.47 (CI 0.30, 0.72) in the Northeast and 0.50 (CI 0.38, 0.66) in the South. Conclusions The presence of universal hand-held cell phone bans were associated lower hand-held cell phone conversations across all driver sub-groups and regions. Hand-held phone conversations were particularly lower among female drivers and those from Western states when these bans were in effect. Public health interventions concerning hand-held cell phone use while driving could reasonably target all drivers

Exclusive Leptoproduction of rho^0 Mesons from Hydrogen at Intermediate Virtual Photon Energies

Measurements of the cross section for exclusive virtual-photoproduction of rho^0 mesons from hydrogen are reported. The data were collected by the HERMES experiment using 27.5 GeV positrons incident on a hydrogen gas target in the HERA storage ring. The invariant mass W of the photon-nucleon system ranges from 4.0 to 6.0 GeV, while the negative squared four-momentum Q^2 of the virtual photon varies from 0.7 to 5.0 GeV^2. The present data together with most of the previous data at W > 4 GeV are well described by a model that infers the W-dependence of the cross section from the dependence on the Bjorken scaling variable x of the unpolarized structure function for deep-inelastic scattering. In addition, a model calculation based on Off-Forward Parton Distributions gives a fairly good account of the longitudinal component of the rho^0 production cross section for Q^2 > 2 GeV^2.Comment: 10 pages, 6 embedded figures, LaTeX for SVJour(epj) document class. Revisions: curves added to Fig. 1, several clarifications added to tex

Reproductive medicine in northwest Argentina: traditional and institutional systems

<p>Abstract</p> <p>Background</p> <p>The state of conservation of the traditional cultures of Northwest Argentina is variable and somewhat problematic but to a lesser or a greater extent all the peoples are related to an hegemonic culture. We present a case study carried out in the rural communities of the Yungas biome (Salta) where the extent of isolation varies as does the type of access to public health services. The use of medicinal plants in the area is ordinary and widely spread.</p> <p>Methods</p> <p>The data can be organized in two categories, as medical systems public records (for the regional hospital at Los Toldos), and as ethnobotanical sets. A total of 59 surveys to 40 interviewees were undertaken using a semi structured questionnaire. We present an analysis of the relative importance of the medicinal herbs used in reproductive medicine considering the plants used in the traditional medical system and the factors that can affect the relationship between formal medicine and patients. We further analized how the degree of accessibility to the local hospital influences the diversity of use of plant species used to assist deliveries and to decrease infant mortality in children minor than one year of age.</p> <p>Results</p> <p>In reproductive medicine, 13 ailments and/or different physiological states are locally identified and treated. Local population uses 108 ethnospecies for this kind of illnesses. According to the local conception the hot/cold imbalance could be the principal cause for reproductive illnesses; pregnancy may have natural or supernatural origin, post partum and menstruation involve similar sanitary risks, and neonatal care has a strong magic connotation. In relation with the formal medicine, the more accessible is the health center the more women assist to it. We have not found a relation between accessibility and infant mortality.</p> <p>Conclusion</p> <p>In the local reproductive medicine, most of the practices are concerned with the hot/cold balance. According to their importance the factors involved are: the family medicine, the midwife, and the formal doctors. Plants have an important role; however there is a lack of total agreement among the families who use them. Reluctance to institutional deliveries may be due to the weak relationship between patients and doctors, and the lack of logistic assistance to delivering mothers coming from far away locations.</p

Erythropoietin overrides the triggering effect of DNA platination products in a mouse model of Cisplatin-induced neuropathy

<p>Abstract</p> <p>Background</p> <p>Cisplatin mediates its antineoplastic activity by formation of distinct DNA intrastrand cross links. The clinical efficacy and desirable dose escalations of cisplatin are restricted by the accumulation of DNA lesions in dorsal root ganglion (DRG) cells leading to sensory polyneuropathy (PNP). We investigated in a mouse model by which mechanism recombinant erythropoietin (rhEPO) protects the peripheral nervous system from structural and functional damage caused by cisplatin treatment with special emphasis on DNA damage burden.</p> <p>Results</p> <p>A cumulative dose of 16 mg cisplatin/kg resulted in clear electrophysiological signs of neuropathy, which were significantly attenuated by concomitant erythropoietin (cisplatin 32,48 m/s ± 1,68 m/s; cisplatin + rhEPO 49,66 m/s ± 1,26 m/s; control 55,01 m/s ± 1,88 m/s; p < 0,001). The co-application of rhEPO, however, did not alter the level of unrepaired cisplatin-DNA lesions accumulating in DRG target cells. Micro-morphological analyses of the sciatic nerve from cisplatin-exposed mice showed damaged myelin sheaths and mitochondria. Co-administered rhEPO inhibited myelin sheaths from structural injuries and resulted in an increased number of intact mitochondria.</p> <p>Conclusion</p> <p>The protective effect of recombinant erythropoietin is not mediated by reducing the burden of DNA platination in the target cells, but it is likely to be due to a higher resistance of the target cells to the adverse effect of DNA damage. The increased frequency of intact mitochondria might also contribute to this protective role.</p