On zeros of irreducible characters lying in a normal subgroup

[EN] Let N be a normal subgroup of a finite group G. In this paper, we consider the elements g of N such that x(g)¿0 for all irreducible characters x of G. Such an element is said to be non-vanishing in G. Let p be a prime. If all p-elements of N satisfy the previous property, then we prove that N has a normal Sylow p-subgroup. As a consequence, we also study certain arithmetical properties of the G-conjugacy class sizes of the elements of N which are zeros of some irreducible character of G. In particular, if N=G, then new contributions are obtained.The first author is supported by Proyecto Prometeo II/2015/011, Generalitat Valenciana (Spain). The research of the second author is partially funded by the Istituto Nazionale di Alta Matematica - INdAM. The third author acknowledges the predoctoral grant ACIF/2016/170, Generalitat Valenciana (Spain). The first and third authors are also supported by Proyecto PGC2018-096872-B-I00, Ministerio de Ciencia, Innovacion y Universidades (Spain).Felipe Román, MJ.; Grittini, N.; Ortiz-Sotomayor, VM. (2020). On zeros of irreducible characters lying in a normal subgroup. Annali di Matematica Pura ed Applicata (1923 -). 199:1777-1789. https://doi.org/10.1007/s10231-020-00942-1S17771789199Beltrán, A., Felipe, M.J.: Prime powers as conjugacy class lengths of $$\pi$$-elements. Bull. Aust. Math. Soc. 69, 317–325 (2004)Beltrán, A., Felipe, M.J., Malle, G., Moretó, A., Navarro, G., Sanus, L., Solomon, R., Tiep, P.H.: Nilpotent and abelian Hall subgroups in finite groups. Trans. Am. Math. Soc. 368, 2497–2513 (2016)Berkovich, Y., Kazarin, L.S.: Indices of elements and normal structure of finite groups. J. Algebra 283, 564–583 (2005)Bianchi, M., Chillag, D., Lewis, M.L., Pacifici, E.: Character degree graphs that are complete graphs. Proc. Am. Math. Soc. 135, 671–676 (2007)Brough, J., Kong, Q.: On vanishing criteria that control finite group structure II. Bull. Aust. Math. Soc. 98, 251–257 (2018)Brough, J.: Non-vanishing elements in finite groups. J. Algebra 460, 387–391 (2016)Dolfi, S., Pacifici, E., Sanus, L., Spiga, P.: On the orders of zeros of irreducible characters. J. Algebra 321, 345–352 (2009)Grüninger, M.: Two remarks about non-vanishing elements in finite groups. J. Algebra 460, 366–369 (2016)Isaacs, I.M.: Character Theory of Finite Groups. Academic Press Inc., London (1976)Isaacs, I.M., Navarro, G., Wolf, T.R.: Finite group elements where no irreducible character vanishes. J. Algebra 222, 413–423 (1999)Malle, G., Navarro, G.: Characterizing normal Sylow $$p$$-subgroups by character degrees. J. Algebra 370, 402–406 (2012)Malle, G., Navarro, G., Olsson, J.B.: Zeros of characters of finite groups. J. Group Theory 3, 353–368 (2000)The GAP Group: GAP—Groups, Algorithms, and Programming. Version 4.10.0 (2018). http://www.gap-system.or

Remarks on singular Cayley graphs and vanishing elements of simple groups

Let Γ be a finite graph and let A(Γ) be its adjacency matrix. Then Γ is singular if A(Γ) is singular. The singularity of graphs is of certain interest in graph theory and algebraic combinatorics. Here we investigate this problem for Cayley graphs Cay(G,H) when G is a finite group and when the connecting set H is a union of conjugacy classes of G. In this situation, the singularity problem reduces to finding an irreducible character χ of G for which ∑h∈Hχ(h)=0. At this stage, we focus on the case when H is a single conjugacy class hG of G; in this case, the above equality is equivalent to χ(h)=0 . Much is known in this situation, with essential information coming from the block theory of representations of finite groups. An element h∈G is called vanishing if χ(h)=0 for some irreducible character χ of G. We study vanishing elements mainly in finite simple groups and in alternating groups in particular. We suggest some approaches for constructing singular Cayley graphs

An analysis of national target groups for monovalent 2009 pandemic influenza vaccine and trivalent seasonal influenza vaccines in 2009-10 and 2010-11

<p>Abstract</p> <p>Background</p> <p>Vaccination is generally considered to be the best primary prevention measure against influenza virus infection. Many countries encourage specific target groups of people to undertake vaccination, often with financial subsidies or a priority list. To understand differential patterns of national target groups for influenza vaccination before, during and after the 2009 influenza pandemic, we reviewed and analyzed the country-specific policies in the corresponding time periods.</p> <p>Methods</p> <p>Information on prioritized groups targeted to receive seasonal and pandemic influenza vaccines was derived from a multi-step internet search of official health department websites, press releases, media sources and academic journal articles. We assessed the frequency and consistency of targeting 20 different groups within populations which are associated with age, underlying medical conditions, role or occupations among different countries and vaccines. Information on subsidies provided to specific target groups was also extracted.</p> <p>Results</p> <p>We analyzed target groups for 33 (seasonal 2009 and 2009-10 vaccines), 72 (monovalent pandemic 2009-10 vaccine) and 34 (seasonal 2010 and 2010-11 vaccines) countries. In 2009-10, the elderly, those with chronic illness and health care workers were common targets for the seasonal vaccine. Comparatively, the elderly, care home residents and workers, animal contacts and close contacts were less frequently targeted to receive the pandemic vaccine. Pregnant women, obese persons, essential community workers and health care workers, however, were more commonly targeted. After the pandemic, pregnant women, obese persons, health care and care home workers, and close contacts were more commonly targeted to receive the seasonal vaccine compared to 2009-10, showing continued influence from the pandemic. Many of the countries provided free vaccines, partial subsidies, reimbursements or national health insurance coverage to specific target groups and over one-third of the countries offered universal subsidy regarding the pandemic vaccine. There was also some inconsistency between countries in target groups.</p> <p>Conclusions</p> <p>Differences in target groups between countries may reflect variable objectives as well as uncertainties regarding the transmission dynamics, severity and age-specific immunity against influenza viruses before and after vaccination. Clarification on these points is essential to elucidate optimal and object-oriented vaccination strategies.</p

Game Theory of Social Distancing in Response to an Epidemic

Social distancing practices are changes in behavior that prevent disease transmission by reducing contact rates between susceptible individuals and infected individuals who may transmit the disease. Social distancing practices can reduce the severity of an epidemic, but the benefits of social distancing depend on the extent to which it is used by individuals. Individuals are sometimes reluctant to pay the costs inherent in social distancing, and this can limit its effectiveness as a control measure. This paper formulates a differential-game to identify how individuals would best use social distancing and related self-protective behaviors during an epidemic. The epidemic is described by a simple, well-mixed ordinary differential equation model. We use the differential game to study potential value of social distancing as a mitigation measure by calculating the equilibrium behaviors under a variety of cost-functions. Numerical methods are used to calculate the total costs of an epidemic under equilibrium behaviors as a function of the time to mass vaccination, following epidemic identification. The key parameters in the analysis are the basic reproduction number and the baseline efficiency of social distancing. The results show that social distancing is most beneficial to individuals for basic reproduction numbers around 2. In the absence of vaccination or other intervention measures, optimal social distancing never recovers more than 30% of the cost of infection. We also show how the window of opportunity for vaccine development lengthens as the efficiency of social distancing and detection improve

Genetic association study of QT interval highlights role for calcium signaling pathways in myocardial repolarization.

The QT interval, an electrocardiographic measure reflecting myocardial repolarization, is a heritable trait. QT prolongation is a risk factor for ventricular arrhythmias and sudden cardiac death (SCD) and could indicate the presence of the potentially lethal mendelian long-QT syndrome (LQTS). Using a genome-wide association and replication study in up to 100,000 individuals, we identified 35 common variant loci associated with QT interval that collectively explain ∼8-10% of QT-interval variation and highlight the importance of calcium regulation in myocardial repolarization. Rare variant analysis of 6 new QT interval-associated loci in 298 unrelated probands with LQTS identified coding variants not found in controls but of uncertain causality and therefore requiring validation. Several newly identified loci encode proteins that physically interact with other recognized repolarization proteins. Our integration of common variant association, expression and orthogonal protein-protein interaction screens provides new insights into cardiac electrophysiology and identifies new candidate genes for ventricular arrhythmias, LQTS and SCD

Potential therapeutic implications of new insights into respiratory syncytial virus disease

Viral bronchiolitis is the most common cause of hospitalization in infants under 6 months of age, and 70% of all cases of bronchiolitis are caused by respiratory syncytial virus (RSV). Early RSV infection is associated with respiratory problems such as asthma and wheezing later in life. RSV infection is usually spread by contaminated secretions and infects the upper then lower respiratory tracts. Infected cells release proinflammatory cytokines and chemokines, including IL-1, tumor necrosis factor-α, IL-6, and IL-8. These activate other cells and recruit inflammatory cells, including macrophages, neutrophils, eosinophils, and T lymphocytes, into the airway wall and surrounding tissues. The pattern of cytokine production by T lymphocytes can be biased toward 'T-helper-1' or 'T-helper-2' cytokines, depending on the local immunologic environment, infection history, and host genetics. T-helper-1 responses are generally efficient in antiviral defense, but young infants have an inherent bias toward T-helper-2 responses. The ideal intervention for RSV infection would be preventive, but the options are currently limited. Vaccines based on protein subunits, live attenuated strains of RSV, DNA vaccines, and synthetic peptides are being developed; passive antibody therapy is at present impractical in otherwise healthy children. Effective vaccines for use in neonates continue to be elusive but simply delaying infection beyond the first 6 months of life might reduce the delayed morbidity associated with infantile disease

LRP16 Integrates into NF-κB Transcriptional Complex and Is Required for Its Functional Activation

BACKGROUND: Nuclear factor κB (NF-κB)-mediated pathways have been widely implicated in cell survival, development and tumor progression. Although the molecular events of determining NF-κB translocation from cytoplasm to nucleus have been extensively documented, the regulatory mechanisms of NF-κB activity inside the nucleus are still poorly understood. Being a special member of macro domain proteins, LRP16 was previously identified as a coactivator of both estrogen receptor and androgen receptor, and as an interactor of NF-κB coactivator UXT. Here, we investigated the regulatory role of LRP16 on NF-κB activation. METHODOLOGY: GST pull-down and coimmunoprecipitation (CoIP) assays assessed protein-protein interactions. The functional activity of NF-κB was assessed by luciferase assays, changes in expression of its target genes, and its DNA binding ability. Annexin V staining and flow cytometry analysis were used to evaluate cell apoptosis. Immunohistochemical staining of LRP16 and enzyme-linked immunosorbent assay-based evaluation of active NF-κB were performed on primary human gastric carcinoma samples. RESULTS: We demonstrate that LRP16 integrates into NF-κB transcriptional complex through associating with its p65 component. RNA interference knockdown of the endogenous LRP16 in cells leads to impaired NF-κB activity and significantly attenuated NF-κB-dependent gene expression. Mechanistic analysis revealed that knockdown of LRP16 did not affect tumor necrosis factor α (TNF-α)-induced nuclear translocation of NF-κB, but blunted the formation or stabilization of functional NF-κB/p300/CREB-binding protein transcription complex in the nucleus. In addition, knockdown of LRP16 also sensitizes cells to apoptosis induced by TNF-α. Finally, a positive link between LRP16 expression intensity in nuclei of tumor cells and NF-κB activity was preliminarily established in human gastric carcinoma specimens. CONCLUSIONS: Our findings not only indicate that LRP16 is a crucial regulator for NF-κB activation inside the nucleus, but also suggest that LRP16 may be an important contributor to the aberrant activation of NF-κB in tumors