Cyclic homology for bornological coarse spaces

Funding Information: Open Access funding provided by Projekt DEAL. This work formed part of the author’s PhD thesis at Regensburg University. It is a pleasure to again acknowledge Ulrich Bunke, this work would not exist without him. The author also thanks Clara Löh, Denis-Charles Cisinski and Alexander Engel for helpful discussions, and the anonymous referees for constructive comments and recommendations. The author has been supported by the DFG Research Training Group GRK 1692 “Curvature, Cycles, and Cohomology” and by the DFG SFB 1085 “Higher Invariants”. Publisher Copyright: © 2020, The Author(s). Copyright: Copyright 2020 Elsevier B.V., All rights reserved.Peer reviewedPublisher PD

Controlled objects as a symmetric monoidal functor

The goal of this paper is to associate functorially to every symmetric monoidal additive category $\mathbf{A}$ with a strict $G$-action a lax symmetric monoidal functor $\mathbf{V}_{\mathbf{A}}^{G}:G\mathbf{BornCoarse}\to \mathbf{Add}_{\infty}$ from the symmetric monoidal category of $G$-bornological coarse spaces $G\mathbf{BornCoarse}$ to the symmetric monoidal $\infty$-category of additive categories $\mathbf{Add}_{\infty}$. This allows to refine equivariant coarse algebraic $K$-homology to a lax symmetric monoidal functor.Comment: 30 page

Hochschild homology, and a persistent approach via connectivity digraphs

We introduce a persistent Hochschild homology framework for directed graphs. Hochschild homology groups of (path algebras of) directed graphs vanish in degree $i\geq 2$. To extend them to higher degrees, we introduce the notion of connectivity digraphs and analyse two main examples; the first, arising from Atkin's $q$-connectivity, and the second, here called $n$-path digraphs, generalising the classical notion of line graphs. Based on a categorical setting for persistent homology, we propose a stable pipeline for computing persistent Hochschild homology groups. This pipeline is also amenable to other homology theories; for this reason, we complement our work with a survey on homology theories of digraphs.Comment: Comments are welcome

Promises and pitfalls of topological data analysis for brain connectivity analysis

Acknowledgment The authors thank Jakub Kopal for sharing the preprocessed fMRI time series and Barbora Bučková for sharing scripts for classification pipelinePeer reviewedPublisher PD

From the Mayer-Vietoris spectral sequence to \"uberhomology

We prove that the second page of the Mayer-Vietoris spectral sequence, with respect to anti-star covers, can be identified with another homological invariant of simplicial complexes: the $0$-degree \"uberhomology. Consequently, we obtain a combinatorial interpretation of the second page of the Mayer-Vietoris sequence in this context. This interpretation is then used to extend the computations of bold homology, which categorifies the connected domination polynomial at $-1$.Comment: 18 pages, comments are welcome! V2 published versio

Homological stability for general linear groups

Scopo della tesi è dare una dimostrazione completa e dettagliata di un teorema di stabilità omologica per gruppi generali lineari. Per la dimostrazione ci si basa su un articolo di N. Wahl, "Homological stability for general linear groups", in cui si dimostra un teorema generale di stabilità omologica in categorie opportune, dette categorie omogenee. Dopo aver presentato e studiato il caso generale, il problema di stabilità per gruppi generali lineari risulta essere un corollario del caso generale, in quanto tali gruppi possono esser visti come gruppi di automorfismi nella categoria dei moduli liberi finitamente generati. Infine, per poter applicare il teorema, si studiano dei particolari poset su cui i gruppi generali lineari agiscono, e si prova la loro aciclicità

Hochschild and cyclic homology for bornological coarse spaces

The main goal of the thesis is to construct equivariant coarse versions of the classical Hochschild and cyclic homologies of algebras. These are lax symmetric monoidal functors from the category of equivariant bornological coarse spaces to the cocomplete stable ∞-category of chain complexes and are called equivariant coarse Hochschild and cyclic homology. If k is a field, the evaluation at the one point bornological coarse space induces equivalences with the classical Hochschild and cyclic homologies of k. In the equivariant setting, the G-equivariant coarse Hochschild (cyclic) homology of (a canonical bornological coarse space associated to) the group G agrees with the classical Hochschild (cyclic) homology of the associated group algebra k[G]. The second aim of the thesis is the construction of natural transformations from equivariant coarse algebraic K-homology to equivariant coarse Hochschild and cyclic homology, and of natural transformations from equivariant coarse Hochschild and cyclic homology to equivariant coarse ordinary homology. This is achieved by using trace-like maps and gives a natural transformation from equivariant coarse algebraic K-homology to equivariant coarse ordinary homology. We conclude the dissertation with two additional investigations: we give a comparison result between the forget-control map for equivariant coarse Hochschild homology and the associated generalized assembly map, and we show a Segal-type localization theorem for equivariant Hochschild and cyclic homology

Environmental exposure to arsenic and chromium in an industrial area

Arsenic and chromium are widespread environmental contaminants that affect global health due to their toxicity and carcinogenicity. To date, few studies have investigated exposure to arsenic and chromium in a population residing in a high-risk environmental area. The aim of this study is to evaluate the exposure to arsenic and chromium in the general population with no occupational exposure to these metals, resident in the industrial area of Taranto, Southern Italy, through biological monitoring techniques. We measured the levels of chromium, inorganic arsenic, and methylated metabolites, in the urine samples of 279 subjects residing in Taranto and neighboring areas. Qualified health staff administered a standardized structured questionnaire investigating lifestyle habits and controlling for confounding factors. The biological monitoring data showed high urinary concentrations of both the heavy metals investigated, particularly Cr. On this basis, it will be necessary to carry out an organized environmental monitoring program, taking into consideration all exposure routes so as to correlate the environmental concentrations of these metals with the biomonitoring results

AURA: Atlas of UTR Regulatory Activity.

Abstract Summary: The Atlas of UTR Regulatory Activity (AURA) is a manually curated and comprehensive catalog of human mRNA untranslated regions (UTRs) and UTR regulatory annotations. Through its intuitive web interface, it provides full access to a wealth of information on UTRs that integrates phylogenetic conservation, RNA sequence and structure data, single nucleotide variation, gene expression and gene functional descriptions from literature and specialized databases. Availability: http://aura.science.unitn.it Contact: [email protected]; [email protected] Supplementary information: Supplementary data are available at Bioinformatics online