Computing Topological Persistence for Simplicial Maps

Algorithms for persistent homology and zigzag persistent homology are well-studied for persistence modules where homomorphisms are induced by inclusion maps. In this paper, we propose a practical algorithm for computing persistence under $\mathbb{Z}_2$ coefficients for a sequence of general simplicial maps and show how these maps arise naturally in some applications of topological data analysis. First, we observe that it is not hard to simulate simplicial maps by inclusion maps but not necessarily in a monotone direction. This, combined with the known algorithms for zigzag persistence, provides an algorithm for computing the persistence induced by simplicial maps. Our main result is that the above simple minded approach can be improved for a sequence of simplicial maps given in a monotone direction. A simplicial map can be decomposed into a set of elementary inclusions and vertex collapses--two atomic operations that can be supported efficiently with the notion of simplex annotations for computing persistent homology. A consistent annotation through these atomic operations implies the maintenance of a consistent cohomology basis, hence a homology basis by duality. While the idea of maintaining a cohomology basis through an inclusion is not new, maintaining them through a vertex collapse is new, which constitutes an important atomic operation for simulating simplicial maps. Annotations support the vertex collapse in addition to the usual inclusion quite naturally. Finally, we exhibit an application of this new tool in which we approximate the persistence diagram of a filtration of Rips complexes where vertex collapses are used to tame the blow-up in size.Comment: This is the revised and full version of the paper that is going to appear in the Proceedings of 30th Annual Symposium on Computational Geometr

Dimension Detection with Local Homology

Detecting the dimension of a hidden manifold from a point sample has become an important problem in the current data-driven era. Indeed, estimating the shape dimension is often the first step in studying the processes or phenomena associated to the data. Among the many dimension detection algorithms proposed in various fields, a few can provide theoretical guarantee on the correctness of the estimated dimension. However, the correctness usually requires certain regularity of the input: the input points are either uniformly randomly sampled in a statistical setting, or they form the so-called $(\varepsilon,\delta)$-sample which can be neither too dense nor too sparse. Here, we propose a purely topological technique to detect dimensions. Our algorithm is provably correct and works under a more relaxed sampling condition: we do not require uniformity, and we also allow Hausdorff noise. Our approach detects dimension by determining local homology. The computation of this topological structure is much less sensitive to the local distribution of points, which leads to the relaxation of the sampling conditions. Furthermore, by leveraging various developments in computational topology, we show that this local homology at a point $z$ can be computed \emph{exactly} for manifolds using Vietoris-Rips complexes whose vertices are confined within a local neighborhood of $z$. We implement our algorithm and demonstrate the accuracy and robustness of our method using both synthetic and real data sets

Topological analysis of scalar fields with outliers

Given a real-valued function $f$ defined over a manifold $M$ embedded in $\mathbb{R}^d$, we are interested in recovering structural information about $f$ from the sole information of its values on a finite sample $P$. Existing methods provide approximation to the persistence diagram of $f$ when geometric noise and functional noise are bounded. However, they fail in the presence of aberrant values, also called outliers, both in theory and practice. We propose a new algorithm that deals with outliers. We handle aberrant functional values with a method inspired from the k-nearest neighbors regression and the local median filtering, while the geometric outliers are handled using the distance to a measure. Combined with topological results on nested filtrations, our algorithm performs robust topological analysis of scalar fields in a wider range of noise models than handled by current methods. We provide theoretical guarantees and experimental results on the quality of our approximation of the sampled scalar field

Дисульфідні зв’язки у структурно-функціональній організації протеїнів

Обговорюються сучасні уявлення про роль дисульфідного зв’язку в забезпеченні структурно-функціональних властивостей протеїнів плазми крові. Узагальнюються нові підходи до можливостей рефолдингу рекомбінантних і секреторних протеїнів. Розглянуто проблему окисного фолдингу та значення дисульфідного зв’язку для посттрансляційного «дозрівання» секреторних протеїнів у порожнині ендоплазматичного ретикулума з участю редуктазної системи ензимів.Обсуждаются современные представления о роли дисульфидной связи в обеспечении структурно-функциональних свойств протеинов плазмы крови. Обобщаются новые подходы к возможностям рефолдинга рекомбинантных и секреторных протеинов. Рассмотрены проблема окислительного фолдинга и значение дисульфидной связи для посттрансляционного «созревания» секреторных протеинов в эндоплазматическом ретикулуме с участием редуктазной системы энзимов.Modern vision about disulfide bonds role in light of providing the structural and functional properties of blood plasma proteins is proposed. New approaches concerning recombinant and secretory proteins refolding are generalized. A problem concerning oxidative folding and disulfide bonds significance for secretory protein posttranslation ripening inside of endoplasmic reticulum with reductase enzyme system participation is discussed

Visible-light-driven coproduction of diesel precursors and hydrogen from lignocellulose-derived methylfurans

Photocatalytic hydrogen production from biomass is a promising alternative to water splitting thanks to the oxidation half-reaction being more facile and its ability to simultaneously produce solar fuels and value-added chemicals. Here, we demonstrate the coproduction of H2 and diesel fuel precursors from lignocellulose-derived methylfurans via acceptorless dehydrogenative C 12C coupling, using a Ru-doped ZnIn2S4 catalyst and driven by visible light. With this chemistry, up to 1.04\u2009g\u2009gcatalyst 121\u2009h 121 of diesel fuel precursors (~41% of which are precursors of branched-chain alkanes) are produced with selectivity higher than 96%, together with 6.0\u2009mmol\u2009gcatalyst 121\u2009h 121 of H2. Subsequent hydrodeoxygenation reactions yield the desired diesel fuels comprising straight- and branched-chain alkanes. We suggest that Ru dopants, substituted in the position of indium ions in the ZnIn2S4 matrix, improve charge separation efficiency, thereby accelerating C 12H activation for the coproduction of H2 and diesel fuel precursors

Genome editing reveals dmrt1 as an essential male sex-determining gene in Chinese tongue sole (Cynoglossus semilaevis)

Chinese tongue sole is a marine fish with ZW sex determination. Genome sequencing suggested that the Z-linked dmrt1 is a putative male determination gene, but direct genetic evidence is still lacking. Here we show that TALEN of dmrt1 efficiently induced mutations of this gene. The ZZ dmrt1 mutant fish developed ovary-like testis, and the spermatogenesis was disrupted. The female-related genes foxl2 and cyp19a1a were significantly increased in the gonad of the ZZ dmrt1 mutant. Conversely, the male-related genes Sox9a and Amh were significantly decreased. The dmrt1 deficient ZZ fish grew much faster than ZZ male control. Notably, we obtained an intersex ZW fish with a testis on one side and an ovary on the other side. This fish was chimeric for a dmrt1 mutation in the ovary, and wild-type dmrt1 in the testis. Our data provide the first functional evidence that dmrt1 is a male determining gene in tongue sole