Symplectic and orthogonal geometry

Thesis (M.A.)--Boston UniversityThis thesis treats metric structures and transformations of finite dimensional spaces over commutative fields. The definition of metric structures of spaces is given in the first section of the chapter I. How such metric structures can be described in terms of bases and how the expressions depend upon the choices of bases are then studied. The geometries where XY = 0 implies YX = 0 for any elements X,Y of the space are sought in section 2. The orthogonal and symplectic geometries are introduced as the only two types of geometries which satisfy this condition. In connection with metric structures of spaces, bilinear and quadratic forms are discussed in section 3. Metric structures of orthogonal geometries are shown to be determined by symmetric bilinear forms and those of symplectic geometries are determined by skew symmetric bilinear forms. A study of orthogonal geometries is shown·to be equivalent to a study of quadratic forms. Irreducible subspaces of orthogonal and symplectic geometries are discussed in section 4, by considering the properties of kernels, radicals and singularities of spaces and defining isotropic spaces and vectors. As a result one can see that an orthogonal geometry is an orthogonal sum of lines and that a nonsingular symplectic space is an orthogonal sum of hyperbolic planes. For example, a Euclidean space is an orthogonal sum of lines generated by the characteristic vectors of the matrix describing its metric structure. Reducing bilinear forms to its canonical forms, one can see that there exists only one non-singular symplectic space, if a dimension and a field are given. The subject of chapter II is mappings of spaces on which metric structures are defined. The definition of homomorphisms and isometries are first given in section_l and 2, together with their matrix representations relative to bases of spaces. Rotations and reflexions are then introduced as two types of isometries. In section 3, the definition of involutions is given. It then follows that every involution has a form -1u perpendicular lw, where U and W are mutually orthogonal subspaces. Some important properties of isometries on orthogonal geometries are stated in section 4. As examples, isometries on two- and three-dimensional Euclidean spaces and Lorentz transformations on two dimensional space are discussed in section 5 and 6. Finally orthogonal geometries of n-dimensional spaces over finite fields are discussed, together with an example of geometric structures and isometries of a two-dimensional orthogonal space over a field J3

Deep Learning-Based Average Consensus

In this study, we analyzed the problem of accelerating the linear average consensus algorithm for complex networks. We propose a data-driven approach to tuning the weights of temporal (i.e., time-varying) networks using deep learning techniques. Given a finite-time window, the proposed approach first unfolds the linear average consensus protocol to obtain a feedforward signal-flow graph, which is regarded as a neural network. The edge weights of the obtained neural network are then trained using standard deep learning techniques to minimize consensus error over a given finite-time window. Through this training process, we obtain a set of optimized time-varying weights, which yield faster consensus for a complex network. We also demonstrate that the proposed approach can be extended for infinite-time window problems. Numerical experiments revealed that our approach can achieve a significantly smaller consensus error compared to baseline strategies

Heme Orientation of Cavity Mutant Hemoglobins (His F8 → Gly) in Either α or β Subunits: Circular Dichroism, 1H NMR, and Resonance Raman Studies

Native human adult hemoglobin (Hb A) has mostly normal orientation of heme, whereas recombinant Hb A (rHb A) expressed in E. coli contains both normal and reversed orientations of heme. Hb A with the normal heme exhibits positive circular dichroism (CD) bands at both the Soret and 260-nm regions, while rHb A with the reversed heme shows a negative Soret and decreased 260-nm CD bands. In order to examine involvement of the proximal histidine (His F8) of either α or β subunits in determining the heme orientation, we prepared two cavity mutant Hbs, rHb(αH87G) and rHb(βH92G), with substitution of glycine for His F8 in the presence of imidazole. CD spectra of both cavity mutant Hbs did not show a negative Soret band, but instead exhibited positive bands with strong intensity at the both Soret and 260-nm regions, suggesting that the reversed heme scarcely exists in the cavity mutant Hbs. We confirmed by 1H NMR and resonance Raman (RR) spectroscopies that the cavity mutant Hbs have mainly the normal heme orientation in both the mutated and native subunits. These results indicate that the heme Fe-His F8 linkage in both α and β subunits influences the heme orientation, and that the heme orientation of one type of subunit is related to the heme orientation of the complementary subunits to be the same. The present study showed that CD and RR spectroscopies also provided powerful tools for the examination of the heme rotational disorder of Hb A, in addition to the usual 1H NMR technique. Chirality 28:585–592, 2016. © 2016 Wiley Periodicals, Inc. © 2016 Wiley Periodicals, Inc.Embargo Period 24 month

Helicobacter pylori Evolution: Lineage- Specific Adaptations in Homologs of Eukaryotic Sel1-Like Genes

Geographic partitioning is postulated to foster divergence of Helicobacter pylori populations as an adaptive response to local differences in predominant host physiology. H. pylori's ability to establish persistent infection despite host inflammatory responses likely involves active management of host defenses using bacterial proteins that may themselves be targets for adaptive evolution. Sequenced H. pylori genomes encode a family of eight or nine secreted proteins containing repeat motifs that are characteristic of the eukaryotic Sel1 regulatory protein, whereas the related Campylobacter and Wolinella genomes each contain only one or two such “Sel1-like repeat” (SLR) genes (“slr genes”). Signatures of positive selection (ratio of nonsynonymous to synonymous mutations, dN/dS = ω > 1) were evident in the evolutionary history of H. pylori slr gene family expansion. Sequence analysis of six of these slr genes (hp0160, hp0211, hp0235, hp0519, hp0628, and hp1117) from representative East Asian, European, and African H. pylori strains revealed that all but hp0628 had undergone positive selection, with different amino acids often selected in different regions. Most striking was a divergence of Japanese and Korean alleles of hp0519, with Japanese alleles having undergone particularly strong positive selection (ωJ > 25), whereas alleles of other genes from these populations were intermingled. Homology-based structural modeling localized most residues under positive selection to SLR protein surfaces. Rapid evolution of certain slr genes in specific H. pylori lineages suggests a model of adaptive change driven by selection for fine-tuning of host responses, and facilitated by geographic isolation. Characterization of such local adaptations should help elucidate how H. pylori manages persistent infection, and potentially lead to interventions tailored to diverse human populations

The whole blood transcriptional regulation landscape in 465 COVID-19 infected samples from Japan COVID-19 Task Force

「コロナ制圧タスクフォース」COVID-19患者由来の血液細胞における遺伝子発現の網羅的解析 --重症度に応じた遺伝子発現の変化には、ヒトゲノム配列の個人差が影響する--. 京都大学プレスリリース. 2022-08-23.Coronavirus disease 2019 (COVID-19) is a recently-emerged infectious disease that has caused millions of deaths, where comprehensive understanding of disease mechanisms is still unestablished. In particular, studies of gene expression dynamics and regulation landscape in COVID-19 infected individuals are limited. Here, we report on a thorough analysis of whole blood RNA-seq data from 465 genotyped samples from the Japan COVID-19 Task Force, including 359 severe and 106 non-severe COVID-19 cases. We discover 1169 putative causal expression quantitative trait loci (eQTLs) including 34 possible colocalizations with biobank fine-mapping results of hematopoietic traits in a Japanese population, 1549 putative causal splice QTLs (sQTLs; e.g. two independent sQTLs at TOR1AIP1), as well as biologically interpretable trans-eQTL examples (e.g., REST and STING1), all fine-mapped at single variant resolution. We perform differential gene expression analysis to elucidate 198 genes with increased expression in severe COVID-19 cases and enriched for innate immune-related functions. Finally, we evaluate the limited but non-zero effect of COVID-19 phenotype on eQTL discovery, and highlight the presence of COVID-19 severity-interaction eQTLs (ieQTLs; e.g., CLEC4C and MYBL2). Our study provides a comprehensive catalog of whole blood regulatory variants in Japanese, as well as a reference for transcriptional landscapes in response to COVID-19 infection