On the trace of the antipode and higher indicators

We introduce two kinds of gauge invariants for any finite-dimensional Hopf algebra H. When H is semisimple over C, these invariants are respectively, the trace of the map induced by the antipode on the endomorphism ring of a self-dual simple module, and the higher Frobenius-Schur indicators of the regular representation. We further study the values of these higher indicators in the context of complex semisimple quasi-Hopf algebras H. We prove that these indicators are non-negative provided the module category over H is modular, and that for a prime p, the p-th indicator is equal to 1 if, and only if, p is a factor of dim H. As an application, we show the existence of a non-trivial self-dual simple H-module with bounded dimension which is determined by the value of the second indicator.Comment: additional references, fixed some typos, minor additions including a questions and some remark

The managerial mechanism of future competitive technical specialists vocational training: The Russian experience

© 2016, Econjournals. All rights reserved.The relevance of the paper is reasoned by the search for adequate mechanisms to manage vocational training of future competitive technical specialists. Modern economies demand the training of technical specialists’ new generation ready to project and engineering, production and technological, organizational and management, science and research, service and operational professional activities, as well as the fulfillment of skilled work using modern equipment for the developed technological process. One of the variants of the organization of vocational training of future competitive technical specialists is based on the integration of educational curricula of different levels (primary, secondary and high). The purpose of the paper is to develop a managerial mechanism for future competitive technical specialists’ training based on the integration of educational curricula at different levels (primary, secondary and high). The leading method is the method of action research, allowing obtain new knowledge on the managerial mechanism for vocational training of specialists, capable of a certain type of practical activities, self-organization and competitiveness on the labor market through the integration of primary, secondary and high levels of educational curricula. The article defines the essence of integrated educational curricula of primary, secondary and high levels of vocational training; it justifies the organization of control and assessment procedures of students’ vocational training through the integration of educational curricula at different levels; proposes an algorithm of students’ selection to study on integrated educational curricula. Paper Submissions can be useful for research and teaching staff of technical specialists’ vocational training system, experts of training and retraining centers in the training content’s selection and structuring of research universities’ scientific and pedagogical staff development

Кинетика бифилярно-контролируемых движений свободных тел

A free solid body S regular movement in accordance with some wanted time-space rule is considered. This movement is effected by a system of forces, including the appropriate distributed mass forces of inertia of the body, its constant force of gravity and the two variables in magnitude and in the direction of the tensile force of the pair associated with the body flexible control leashes. Leashes tension forces, adequate to these conditions and the rule of the wanted movement of the body S are defined. A mathematical model of such movement is presented.Рассмотрено регулярное движение свободного твердого тела S, совершаемое по некоторому искомому пространственно-временному закону. Движение осуществляется под действием системы сил, включающей соответствующие распределенные массовые силы инерции этого тела, его постоянную силу тяжести и две переменные по модулю и по направлению силы натяжения пары связанных с телом S его гибких управляющих поводков. Определены силы натяжения поводков, адекватные данным условиям и закону искомого движения тела S. Представлена его математическая модель

Conditional Tek Promoter-Driven Deletion of Arginyltransferase in the Germ Line Causes Defects in Gametogenesis and Early Embryonic Lethality in Mice

Posttranslational protein arginylation mediated by Ate1 is essential for cardiovascular development, actin cytoskeleton functioning, and cell migration. Ate1 plays a role in the regulation of cytoskeleton and is essential for cardiovascular development and angiogenesis—capillary remodeling driven by in-tissue migration of endothelial cells. To address the role of Ate1 in cytoskeleton-dependent processes and endothelial cell function during development, we produced a conditional mouse knockout with Ate1 deletion driven by Tek endothelial receptor tyrosine kinase promoter expressed in the endothelium and in the germ line. Contrary to expectations, Tek-Ate1 mice were viable and had no visible angiogenesis-related phenotypes; however, these mice showed reproductive defects, with high rates of embryonic lethality in the second generation, at stages much earlier than the complete Ate1 knockout strain. While some of the early lethality originated from the subpopulation of embryos with homozygous Tek-Cre transgene—a problem that has not previously been reported for this commercial mouse strain—a distinct subpopulation of embryos had lethality at early post-implantation stages that could be explained only by a previously unknown defect in gametogenesis originating from Tek-driven Ate1 deletion in premeiotic germs cells. These results demonstrate a novel role of Ate1 in germ cell development

Hopf algebras and Markov chains: Two examples and a theory

The operation of squaring (coproduct followed by product) in a combinatorial Hopf algebra is shown to induce a Markov chain in natural bases. Chains constructed in this way include widely studied methods of card shuffling, a natural "rock-breaking" process, and Markov chains on simplicial complexes. Many of these chains can be explictly diagonalized using the primitive elements of the algebra and the combinatorics of the free Lie algebra. For card shuffling, this gives an explicit description of the eigenvectors. For rock-breaking, an explicit description of the quasi-stationary distribution and sharp rates to absorption follow.Comment: 51 pages, 17 figures. (Typographical errors corrected. Further fixes will only appear on the version on Amy Pang's website, the arXiv version will not be updated.

Prime movers : mechanochemistry of mitotic kinesins

Mitotic spindles are self-organizing protein machines that harness teams of multiple force generators to drive chromosome segregation. Kinesins are key members of these force-generating teams. Different kinesins walk directionally along dynamic microtubules, anchor, crosslink, align and sort microtubules into polarized bundles, and influence microtubule dynamics by interacting with microtubule tips. The mechanochemical mechanisms of these kinesins are specialized to enable each type to make a specific contribution to spindle self-organization and chromosome segregation

Phosphorylation controls autoinhibition of cytoplasmic linker protein-170

Author Posting. © American Society for Cell Biology, 2010. This article is posted here by permission of American Society for Cell Biology for personal use, not for redistribution. The definitive version was published in Molecular Biology of the Cell 21 (2010): 2661-2673, doi:10.1091/mbc.E09-12-1036.Cytoplasmic linker protein (CLIP)-170 is a microtubule (MT) plus-end-tracking protein that regulates MT dynamics and links MT plus ends to different intracellular structures. We have shown previously that intramolecular association between the N and C termini results in autoinhibition of CLIP-170, thus altering its binding to MTs and the dynactin subunit p150Glued (J. Cell Biol. 2004: 166, 1003–1014). In this study, we demonstrate that conformational changes in CLIP-170 are regulated by phosphorylation that enhances the affinity between the N- and C-terminal domains. By using site-directed mutagenesis and phosphoproteomic analysis, we mapped the phosphorylation sites in the third serine-rich region of CLIP-170. A phosphorylation-deficient mutant of CLIP-170 displays an "open" conformation and a higher binding affinity for growing MT ends and p150Glued as compared with nonmutated protein, whereas a phosphomimetic mutant confined to the "folded back" conformation shows decreased MT association and does not interact with p150Glued. We conclude that phosphorylation regulates CLIP-170 conformational changes resulting in its autoinhibition.This work was supported by National Institutes of Health grant GM-25062 (to G.G.B.); Netherlands Organization for Scientific Research grants (to A. A. and N. G.); a Cancer Genomics Centre grant (to J.v.H.); and Presidential Program of Russian Academy of Sciences and RFBP grant 05-04-4915 (to E.S.N.)

Arginyltransferase suppresses cell tumorigenic potential and inversely correlates with metastases in human cancers

Arginylation is an emerging post-translational modification mediated by arginyltransferase (ATE1) that is essential for mammalian embryogenesis and regulation of the cytoskeleton. Here, we discovered that Ate1-knockout (KO) embryonic fibroblasts exhibit tumorigenic properties, including abnormally rapid contact-independent growth, reduced ability to form cell-cell contacts and chromosomal aberrations. Ate1-KO fibroblasts can form large colonies in Matrigel and exhibit invasive behavior, unlike wild-type fibroblasts. Furthermore, Ate1-KO cells form tumors in subcutaneous xenograft assays in immunocompromised mice. Abnormal growth in these cells can be partially rescued by reintroduction of stably expressed specific Ate1 isoforms, which also reduce the ability of these cells to form tumors. Tumor array studies and bioinformatics analysis show that Ate1 is downregulated in several types of human cancer samples at the protein level, and that its transcription level inversely correlates with metastatic progression and patient survival. We conclude that Ate1-KO results in carcinogenic transformation of cultured fibroblasts, suggesting that in addition to its previously known activities Ate1 gene is essential for tumor suppression and also likely participates in suppression of metastatic growth. © 2016 Macmillan Publishers Limited, part of Springer Nature

The elegans of spindle assembly

The Caenorhabditis elegans one-cell embryo is a powerful system in which to study microtubule organization because this large cell assembles both meiotic and mitotic spindles within the same cytoplasm over the course of 1 h in a stereotypical manner. The fertilized oocyte assembles two consecutive acentrosomal meiotic spindles that function to reduce the replicated maternal diploid set of chromosomes to a single-copy haploid set. The resulting maternal DNA then unites with the paternal DNA to form a zygotic diploid complement, around which a centrosome-based mitotic spindle forms. The early C. elegans embryo is amenable to live-cell imaging and electron tomography, permitting a detailed structural comparison of the meiotic and mitotic modes of spindle assembly