Completed cohomology of Shimura curves and a p-adic Jacquet-Langlands correspondence

We study indefinite quaternion algebras over totally real fields F, and give an example of a cohomological construction of p-adic Jacquet-Langlands functoriality using completed cohomology. We also study the (tame) levels of p-adic automorphic forms on these quaternion algebras and give an analogue of Mazur's `level lowering' principle.Comment: Updated version. Contains some minor corrections compared to the published versio

Global Considerations in Hierarchical Clustering Reveal Meaningful Patterns in Data

BACKGROUND: A hierarchy, characterized by tree-like relationships, is a natural method of organizing data in various domains. When considering an unsupervised machine learning routine, such as clustering, a bottom-up hierarchical (BU, agglomerative) algorithm is used as a default and is often the only method applied. METHODOLOGY/PRINCIPAL FINDINGS: We show that hierarchical clustering that involve global considerations, such as top-down (TD, divisive), or glocal (global-local) algorithms are better suited to reveal meaningful patterns in the data. This is demonstrated, by testing the correspondence between the results of several algorithms (TD, glocal and BU) and the correct annotations provided by experts. The correspondence was tested in multiple domains including gene expression experiments, stock trade records and functional protein families. The performance of each of the algorithms is evaluated by statistical criteria that are assigned to clusters (nodes of the hierarchy tree) based on expert-labeled data. Whereas TD algorithms perform better on global patterns, BU algorithms perform well and are advantageous when finer granularity of the data is sought. In addition, a novel TD algorithm that is based on genuine density of the data points is presented and is shown to outperform other divisive and agglomerative methods. Application of the algorithm to more than 500 protein sequences belonging to ion-channels illustrates the potential of the method for inferring overlooked functional annotations. ClustTree, a graphical Matlab toolbox for applying various hierarchical clustering algorithms and testing their quality is made available. CONCLUSIONS: Although currently rarely used, global approaches, in particular, TD or glocal algorithms, should be considered in the exploratory process of clustering. In general, applying unsupervised clustering methods can leverage the quality of manually-created mapping of proteins families. As demonstrated, it can also provide insights in erroneous and missed annotations

Generation and physiological roles of linear ubiquitin chains

Ubiquitination now ranks with phosphorylation as one of the best-studied post-translational modifications of proteins with broad regulatory roles across all of biology. Ubiquitination usually involves the addition of ubiquitin chains to target protein molecules, and these may be of eight different types, seven of which involve the linkage of one of the seven internal lysine (K) residues in one ubiquitin molecule to the carboxy-terminal diglycine of the next. In the eighth, the so-called linear ubiquitin chains, the linkage is between the amino-terminal amino group of methionine on a ubiquitin that is conjugated with a target protein and the carboxy-terminal carboxy group of the incoming ubiquitin. Physiological roles are well established for K48-linked chains, which are essential for signaling proteasomal degradation of proteins, and for K63-linked chains, which play a part in recruitment of DNA repair enzymes, cell signaling and endocytosis. We focus here on linear ubiquitin chains, how they are assembled, and how three different avenues of research have indicated physiological roles for linear ubiquitination in innate and adaptive immunity and suppression of inflammation

Index Cohesive Force Analysis Reveals That the US Market Became Prone to Systemic Collapses Since 2002

BACKGROUND: The 2007-2009 financial crisis, and its fallout, has strongly emphasized the need to define new ways and measures to study and assess the stock market dynamics. METHODOLOGY/PRINCIPAL FINDINGS: The S&P500 dynamics during 4/1999-4/2010 is investigated in terms of the index cohesive force (ICF--the balance between the stock correlations and the partial correlations after subtraction of the index contribution), and the Eigenvalue entropy of the stock correlation matrices. We found a rapid market transition at the end of 2001 from a flexible state of low ICF into a stiff (nonflexible) state of high ICF that is prone to market systemic collapses. The stiff state is also marked by strong effect of the market index on the stock-stock correlations as well as bursts of high stock correlations reminiscence of epileptic brain activity. CONCLUSIONS/SIGNIFICANCE: The market dynamical states, stability and transition between economic states was studies using new quantitative measures. Doing so shed new light on the origin and nature of the current crisis. The new approach is likely to be applicable to other classes of complex systems from gene networks to the human brain

Принципы организации обследования пациентов в пульмонологии

Organization principles of examination of patients with pulmonary diseases are considered. The structure of re-examination center in case of digital prophylactic X-ray chest units application is offered.Рассматриваются принципы организации дообследования пациентов в пульмонологии. Представлена структура центра дообследования для случая, когда профилактические исследования легких у населения проводятся с применением малодозовых цифровых флюорографических установок

Six operations and Lefschetz-Verdier formula for Deligne-Mumford stacks

Laszlo and Olsson constructed Grothendieck's six operations for constructible complexes on Artin stacks in \'etale cohomology under an assumption of finite cohomological dimension, with base change established on the level of sheaves. In this article we give a more direct construction of the six operations for complexes on Deligne-Mumford stacks without the finiteness assumption and establish base change theorems in derived categories. One key tool in our construction is the theory of gluing finitely many pseudofunctors developed in arXiv:1211.1877. As an application, we prove a Lefschetz-Verdier formula for Deligne-Mumford stacks. We include both torsion and $\ell$-adic coefficients.Comment: 62 pages. v5, v4: minor improvements; v3: added a Lefschetz-Verdier formula; v2: moved the appendix in v1 to arXiv:1211.187