Convergence results for projected line-search methods on varieties of low-rank matrices via \L{}ojasiewicz inequality

The aim of this paper is to derive convergence results for projected line-search methods on the real-algebraic variety $\mathcal{M}_{\le k}$ of real $m \times n$ matrices of rank at most $k$. Such methods extend Riemannian optimization methods, which are successfully used on the smooth manifold $\mathcal{M}_k$ of rank-$k$ matrices, to its closure by taking steps along gradient-related directions in the tangent cone, and afterwards projecting back to $\mathcal{M}_{\le k}$. Considering such a method circumvents the difficulties which arise from the nonclosedness and the unbounded curvature of $\mathcal{M}_k$. The pointwise convergence is obtained for real-analytic functions on the basis of a \L{}ojasiewicz inequality for the projection of the antigradient to the tangent cone. If the derived limit point lies on the smooth part of $\mathcal{M}_{\le k}$, i.e. in $\mathcal{M}_k$, this boils down to more or less known results, but with the benefit that asymptotic convergence rate estimates (for specific step-sizes) can be obtained without an a priori curvature bound, simply from the fact that the limit lies on a smooth manifold. At the same time, one can give a convincing justification for assuming critical points to lie in $\mathcal{M}_k$: if $X$ is a critical point of $f$ on $\mathcal{M}_{\le k}$, then either $X$ has rank $k$, or $\nabla f(X) = 0$

Eine Translokase für Makromoleküle in Mitochondrien von Trypanosomen

Mitochondrial protein import is mediated by complex machineries in the outer and inner membrane that have been studied in detail in yeast and mammals. Here we review our work of the corresponding machineries in the mitochondrion of Trypanosoma brucei. We conclude that the import machineries in the two systems are surprisingly different considering that they have the same functions. Moreover, we discuss the dual role the trypanosomal outer membrane translocase has in mitochondrial protein and tRNA import

Covariation of Mitochondrial Genome Size with Gene Lengths: Evidence for Gene Length Reduction During Mitochondrial Evolution

Reduction of genome size and gene shortening have been observed in a number of parasitic and mutualistic intracellular symbionts. Reduction of coding capacity is also a unifying principle in the evolutionary history of mitochondria, but little is known about the evolution of gene length in mitochondria. The genes for cytochrome c oxidase subunits I-III, cytochrome b, and the large and small subunit rRNAs are, with very few exceptions, always found on the mitochondrial genome. These resident mitochondrial genes can therefore be used to test whether the reduction in gene lengths observed in a number of intracellular symbionts is also seen in mitochondria. Here we show that resident mitochondrial gene products are shorter than their corresponding counterparts in α-proteobacteria and, furthermore, that the reduction of mitochondrial genome size is correlated with a reduction in the length of the corresponding resident gene products. We show that relative genomic AT content, which has been identified as a factor influencing gene lengths in other systems, cannot explain gene length/genome size covariance observed in mitochondria. Our data are therefore in agreement with the idea that gene length evolves as a consequence of selection for smaller genomes, either to avoid accumulation of deleterious mutations or triggered by selection for a replication advantag

Minimal peptide length required to span the mitochondrial protein translocases in Trypanosoma brucei

Mitochondrial protein import depends on heterooligomeric translocases in the outer and inner membranes. Using import substrates consisting of various lengths of the N-terminal part of mitochondrial dihydrolipoamide dehydrogenase (LDH) fused to dihydrofolate reductase we present an in vivo analysis showing that in Trypanosoma brucei at least 96 aa of mature LDH are required to efficiently produce an import intermediate that spans both translocases. This is different to yeast, where around 50 aa are sufficient to achieve the same task and likely reflects the different arrangement and architecture of the trypanosomal mitochondrial translocases. Furthermore, we show that formation of the stuck import intermediate leads to a strong growth inhibition suggesting that, depending on the length of the LDH, the import channels in the translocases are quantitatively blocked

DNA segregation in mitochondria and beyond: insights from the trypanosomal tripartite attachment complex.

The tripartite attachment complex (TAC) of the single mitochondrion of trypanosomes allows precise segregation of its single nucleoid mitochondrial genome during cytokinesis. It couples the segregation of the duplicated mitochondrial genome to the segregation of the basal bodies of the flagella. Here, we provide a model of the molecular architecture of the TAC that explains how its eight essential subunits connect the basal body, across the mitochondrial membranes, with the mitochondrial genome. We also discuss how the TAC subunits are imported into the mitochondrion and how they assemble to form a new TAC. Finally, we present a comparative analysis of the trypanosomal TAC with open and closed mitotic spindles, which reveals conserved concepts between these diverse DNA segregation systems

Проектирование технологического процесса изготовления цилиндра и оснастки

РЕФЕРАТ Выпускная квалификационная работа 98 с., 12 рис., 27 табл., 7 источников, 6 прил. Ключевые слова: цилиндр, оснастка, литье, сверление, приспособление, технологический процесс. Объектом исследования является проектирование технологического процесса изготовления цилиндра Цель работы: проектирование технологического процесса изготовления цилиндра и оснастки В процессе исследования проводились анализ технологического процесса, технико-экономическая анализ, конструирование приспособления для сверления В результате выполнения работы был разработан технологический процесс изготовления детали цилиндр и сконструировано приспособление для сверления Основные конструктивные, технологические и технико-эксплуатационные характеристики: сконструированное приспособление для сверлABSTRACT Final qualifying work 98 p., 12 Fig., 27 tab., 7 springs, 6 ADJ. Key words: cylinder, tooling, casting, drilling, fitting, process. The object of study is (are) the Design of technological process of manufacturing of cylinder Goal – to Design the technological process of manufacturing of cylinder and snap In the process of investigation the analysis of the technological feasibility analysis, designing fixtures for drilling The result of the work was developed technological process of manufacturing parts and the cylinder fixture is designed for drilling The basic constructive, technological, technical-operational and features: the fixture is Designed for drilling consists of a casing, rod rack, cover, cylinder, prisms and the plate conductor. Level of implementation: the te

A multi-scale, multi-wavelength source extraction method: getsources

We present a multi-scale, multi-wavelength source extraction algorithm called getsources. Although it has been designed primarily for use in the far-infrared surveys of Galactic star-forming regions with Herschel, the method can be applied to many other astronomical images. Instead of the traditional approach of extracting sources in the observed images, the new method analyzes fine spatial decompositions of original images across a wide range of scales and across all wavebands. It cleans those single-scale images of noise and background, and constructs wavelength-independent single-scale detection images that preserve information in both spatial and wavelength dimensions. Sources are detected in the combined detection images by following the evolution of their segmentation masks across all spatial scales. Measurements of the source properties are done in the original background-subtracted images at each wavelength; the background is estimated by interpolation under the source footprints and overlapping sources are deblended in an iterative procedure. In addition to the main catalog of sources, various catalogs and images are produced that aid scientific exploitation of the extraction results. We illustrate the performance of getsources on Herschel images by extracting sources in sub-fields of the Aquila and Rosette star-forming regions. The source extraction code and validation images with a reference extraction catalog are freely available.Comment: 31 pages, 27 figures, to be published in Astronomy & Astrophysic