Generalized iterated wreath products of symmetric groups and generalized rooted trees correspondence

Consider the generalized iterated wreath product $S_{r_1}\wr \ldots \wr S_{r_k}$ of symmetric groups. We give a complete description of the traversal for the generalized iterated wreath product. We also prove an existence of a bijection between the equivalence classes of ordinary irreducible representations of the generalized iterated wreath product and orbits of labels on certain rooted trees. We find a recursion for the number of these labels and the degrees of irreducible representations of the generalized iterated wreath product. Finally, we give rough upper bound estimates for fast Fourier transforms.Comment: 18 pages, to appear in Advances in the Mathematical Sciences. arXiv admin note: text overlap with arXiv:1409.060

Generalized iterated wreath products of cyclic groups and rooted trees correspondence

Consider the generalized iterated wreath product $\mathbb{Z}_{r_1}\wr \mathbb{Z}_{r_2}\wr \ldots \wr \mathbb{Z}_{r_k}$ where $r_i \in \mathbb{N}$. We prove that the irreducible representations for this class of groups are indexed by a certain type of rooted trees. This provides a Bratteli diagram for the generalized iterated wreath product, a simple recursion formula for the number of irreducible representations, and a strategy to calculate the dimension of each irreducible representation. We calculate explicitly fast Fourier transforms (FFT) for this class of groups, giving literature's fastest FFT upper bound estimate.Comment: 15 pages, to appear in Advances in the Mathematical Science

Development and validation of the Arizona Cognitive Test Battery for Down syndrome

Neurocognitive assessment in individuals with intellectual disabilities requires a well-validated test battery. To meet this need, the Arizona Cognitive Test Battery (ACTB) has been developed specifically to assess the cognitive phenotype in Down syndrome (DS). The ACTB includes neuropsychological assessments chosen to 1) assess a range of skills, 2) be non-verbal so as to not confound the neuropsychological assessment with language demands, 3) have distributional properties appropriate for research studies to identify genetic modifiers of variation, 4) show sensitivity to within and between sample differences, 5) have specific correlates with brain function, and 6) be applicable to a wide age range and across contexts. The ACTB includes tests of general cognitive ability and prefrontal, hippocampal and cerebellar function. These tasks were drawn from the Cambridge Neuropsychological Testing Automated Battery (CANTAB) and other established paradigms. Alongside the cognitive testing battery we administered benchmark and parent-report assessments of cognition and behavior. Individuals with DS (n = 74, ages 7–38 years) and mental age (MA) matched controls (n = 50, ages 3–8 years) were tested across 3 sites. A subsample of these groups were used for between-group comparisons, including 55 individuals with DS and 36 mental age matched controls. The ACTB allows for low floor performance levels and participant loss. Floor effects were greater in younger children. Individuals with DS were impaired on a number ACTB tests in comparison to a MA-matched sample, with some areas of spared ability, particularly on tests requiring extensive motor coordination. Battery measures correlated with parent report of behavior and development. The ACTB provided consistent results across contexts, including home vs. lab visits, cross-site, and among individuals with a wide range of socio-economic backgrounds and differences in ethnicity. The ACTB will be useful in a range of outcome studies, including clinical trials and the identification of important genetic components of cognitive disability

Steroid receptor coactivator-1 modulates the function of Pomc neurons and energy homeostasis

Hypothalamic neurons expressing the anorectic peptide Pro-opiomelanocortin (Pomc) regulate food intake and body weight. Here, we show that Steroid Receptor Coactivator-1 (SRC-1) interacts with a target of leptin receptor activation, phosphorylated STAT3, to potentiate Pomc transcription. Deletion of SRC-1 in Pomc neurons in mice attenuates their depolarization by leptin, decreases Pomc expression and increases food intake leading to high-fat diet-induced obesity. In humans, fifteen rare heterozygous variants in SRC-1 found in severely obese individuals impair leptin-mediated Pomc reporter activity in cells, whilst four variants found in non-obese controls do not. In a knock-in mouse model of a loss of function human variant (SRC-1L1376P), leptin-induced depolarization of Pomc neurons and Pomc expression are significantly reduced, and food intake and body weight are increased. In summary, we demonstrate that SRC-1 modulates the function of hypothalamic Pomc neurons, and suggest that targeting SRC-1 may represent a useful therapeutic strategy for weight loss.Peer reviewe

The impact of viral mutations on recognition by SARS-CoV-2 specific T cells.

We identify amino acid variants within dominant SARS-CoV-2 T cell epitopes by interrogating global sequence data. Several variants within nucleocapsid and ORF3a epitopes have arisen independently in multiple lineages and result in loss of recognition by epitope-specific T cells assessed by IFN-γ and cytotoxic killing assays. Complete loss of T cell responsiveness was seen due to Q213K in the A∗01:01-restricted CD8+ ORF3a epitope FTSDYYQLY207-215; due to P13L, P13S, and P13T in the B∗27:05-restricted CD8+ nucleocapsid epitope QRNAPRITF9-17; and due to T362I and P365S in the A∗03:01/A∗11:01-restricted CD8+ nucleocapsid epitope KTFPPTEPK361-369. CD8+ T cell lines unable to recognize variant epitopes have diverse T cell receptor repertoires. These data demonstrate the potential for T cell evasion and highlight the need for ongoing surveillance for variants capable of escaping T cell as well as humoral immunity.This work is supported by the UK Medical Research Council (MRC); Chinese Academy of Medical Sciences(CAMS) Innovation Fund for Medical Sciences (CIFMS), China; National Institute for Health Research (NIHR)Oxford Biomedical Research Centre, and UK Researchand Innovation (UKRI)/NIHR through the UK Coro-navirus Immunology Consortium (UK-CIC). Sequencing of SARS-CoV-2 samples and collation of data wasundertaken by the COG-UK CONSORTIUM. COG-UK is supported by funding from the Medical ResearchCouncil (MRC) part of UK Research & Innovation (UKRI),the National Institute of Health Research (NIHR),and Genome Research Limited, operating as the Wellcome Sanger Institute. T.I.d.S. is supported by a Well-come Trust Intermediate Clinical Fellowship (110058/Z/15/Z). L.T. is supported by the Wellcome Trust(grant number 205228/Z/16/Z) and by theUniversity of Liverpool Centre for Excellence in Infectious DiseaseResearch (CEIDR). S.D. is funded by an NIHR GlobalResearch Professorship (NIHR300791). L.T. and S.C.M.are also supported by the U.S. Food and Drug Administration Medical Countermeasures Initiative contract75F40120C00085 and the National Institute for Health Research Health Protection Research Unit (HPRU) inEmerging and Zoonotic Infections (NIHR200907) at University of Liverpool inpartnership with Public HealthEngland (PHE), in collaboration with Liverpool School of Tropical Medicine and the University of Oxford.L.T. is based at the University of Liverpool. M.D.P. is funded by the NIHR Sheffield Biomedical ResearchCentre (BRC – IS-BRC-1215-20017). ISARIC4C is supported by the MRC (grant no MC_PC_19059). J.C.K.is a Wellcome Investigator (WT204969/Z/16/Z) and supported by NIHR Oxford Biomedical Research Centreand CIFMS. The views expressed are those of the authors and not necessarily those of the NIHR or MRC

Low-frequency variation in TP53 has large effects on head circumference and intracranial volume.

Cranial growth and development is a complex process which affects the closely related traits of head circumference (HC) and intracranial volume (ICV). The underlying genetic influences shaping these traits during the transition from childhood to adulthood are little understood, but might include both age-specific genetic factors and low-frequency genetic variation. Here, we model the developmental genetic architecture of HC, showing this is genetically stable and correlated with genetic determinants of ICV. Investigating up to 46,000 children and adults of European descent, we identify association with final HC and/or final ICV + HC at 9 novel common and low-frequency loci, illustrating that genetic variation from a wide allele frequency spectrum contributes to cranial growth. The largest effects are reported for low-frequency variants within TP53, with 0.5 cm wider heads in increaser-allele carriers versus non-carriers during mid-childhood, suggesting a previously unrecognized role of TP53 transcripts in human cranial development

The UK10K project identifies rare variants in health and disease

M. Kivimäki työryhmäjäsen.The contribution of rare and low-frequency variants to human traits is largely unexplored. Here we describe insights from sequencing whole genomes (low read depth, 7x) or exomes (high read depth, 80x) of nearly 10,000 individuals from population-based and disease collections. In extensively phenotyped cohorts we characterize over 24 million novel sequence variants, generate a highly accurate imputation reference panel and identify novel alleles associated with levels of triglycerides (APOB), adiponectin (ADIPOQ) and low-density lipoprotein cholesterol (LDLR and RGAG1) from single-marker and rare variant aggregation tests. We describe population structure and functional annotation of rare and low-frequency variants, use the data to estimate the benefits of sequencing for association studies, and summarize lessons from disease-specific collections. Finally, we make available an extensive resource, including individual-level genetic and phenotypic data and web-based tools to facilitate the exploration of association results.Peer reviewe