Functoriality and duality in Morse-Conley-Floer homology

In~\cite{rotvandervorst} a homology theory --Morse-Conley-Floer homology-- for isolated invariant sets of arbitrary flows on finite dimensional manifolds is developed. In this paper we investigate functoriality and duality of this homology theory. As a preliminary we investigate functoriality in Morse homology. Functoriality for Morse homology of closed manifolds is known~\cite{abbondandoloschwarz, aizenbudzapolski,audindamian, kronheimermrowka, schwarz}, but the proofs use isomorphisms to other homology theories. We give direct proofs by analyzing appropriate moduli spaces. The notions of isolating map and flow map allows the results to generalize to local Morse homology and Morse-Conley-Floer homology. We prove Poincar\'e type duality statements for local Morse homology and Morse-Conley-Floer homology.Comment: To appear in the Journal of Fixed Point theory and its Application

Morse-Conley-Floer Homology

For Morse-Smale pairs on a smooth, closed manifold the Morse-Smale-Witten chain complex can be defined. The associated Morse homology is isomorphic to the singular homology of the manifold and yields the classical Morse relations for Morse functions. A similar approach can be used to define homological invariants for isolated invariant sets of flows on a smooth manifold, which gives an analogue of the Conley index and the Morse-Conley relations. The approach will be referred to as Morse-Conley-Floer homology

Continuation Sheaves in Dynamics: Sheaf Cohomology and Bifurcation

Continuation of algebraic structures in families of dynamical systems is described using category theory, sheaves, and lattice algebras. Well-known concepts in dynamics, such as attractors or invariant sets, are formulated as functors on appropriate categories of dynamical systems mapping to categories of lattices, posets, rings or abelian groups. Sheaves are constructed from such functors, which encode data about the continuation of structure as system parameters vary. Similarly, morphisms for the sheaves in question arise from natural transformations. This framework is applied to a variety of lattice algebras and ring structures associated to dynamical systems, whose algebraic properties carry over to their respective sheaves. Furthermore, the cohomology of these sheaves are algebraic invariants which contain information about bifurcations of the parametrized systems

The Drosophila homologue of Rootletin is required for mechanosensory function and ciliary rootlet formation in chordotonal sensory neurons

BACKGROUND: In vertebrates, rootletin is the major structural component of the ciliary rootlet and is also part of the tether linking the centrioles of the centrosome. Various functions have been ascribed to the rootlet, including maintenance of ciliary integrity through anchoring and facilitation of transport to the cilium or at the base of the cilium. In Drosophila, Rootletin function has not been explored. RESULTS: In the Drosophila embryo, Rootletin is expressed exclusively in cell lineages of type I sensory neurons, the only somatic cells bearing a cilium. Expression is strongest in mechanosensory chordotonal neurons. Knock-down of Rootletin results in loss of ciliary rootlet in these neurons and severe disruption of their sensory function. However, the sensory cilium appears largely normal in structure and in localisation of proteins suggesting no strong defect in ciliogenesis. No evidence was found for a defect in cell division. CONCLUSIONS: The role of Rootletin as a component of the ciliary rootlet is conserved in Drosophila. In contrast, lack of a general role in cell division is consistent with lack of centriole tethering during the centrosome cycle in Drosophila. Although our evidence is consistent with an anchoring role for the rootlet, severe loss of mechanosensory function of chordotonal (Ch) neurons upon Rootletin knock-down may suggest a direct role for the rootlet in the mechanotransduction mechanism itself

Global Impact of the COVID-19 Pandemic on Cerebral Venous Thrombosis and Mortality

Background and purpose: Recent studies suggested an increased incidence of cerebral venous thrombosis (CVT) during the coronavirus disease 2019 (COVID-19) pandemic. We evaluated the volume of CVT hospitalization and in-hospital mortality during the 1st year of the COVID-19 pandemic compared to the preceding year. Methods: We conducted a cross-sectional retrospective study of 171 stroke centers from 49 countries. We recorded COVID-19 admission volumes, CVT hospitalization, and CVT in-hospital mortality from January 1, 2019, to May 31, 2021. CVT diagnoses were identified by International Classification of Disease-10 (ICD-10) codes or stroke databases. We additionally sought to compare the same metrics in the first 5 months of 2021 compared to the corresponding months in 2019 and 2020 (ClinicalTrials.gov Identifier: NCT04934020). Results: There were 2,313 CVT admissions across the 1-year pre-pandemic (2019) and pandemic year (2020); no differences in CVT volume or CVT mortality were observed. During the first 5 months of 2021, there was an increase in CVT volumes compared to 2019 (27.5%; 95% confidence interval [CI], 24.2 to 32.0; P<0.0001) and 2020 (41.4%; 95% CI, 37.0 to 46.0; P<0.0001). A COVID-19 diagnosis was present in 7.6% (132/1,738) of CVT hospitalizations. CVT was present in 0.04% (103/292,080) of COVID-19 hospitalizations. During the first pandemic year, CVT mortality was higher in patients who were COVID positive compared to COVID negative patients (8/53 [15.0%] vs. 41/910 [4.5%], P=0.004). There was an increase in CVT mortality during the first 5 months of pandemic years 2020 and 2021 compared to the first 5 months of the pre-pandemic year 2019 (2019 vs. 2020: 2.26% vs. 4.74%, P=0.05; 2019 vs. 2021: 2.26% vs. 4.99%, P=0.03). In the first 5 months of 2021, there were 26 cases of vaccine-induced immune thrombotic thrombocytopenia (VITT), resulting in six deaths. Conclusions: During the 1st year of the COVID-19 pandemic, CVT hospitalization volume and CVT in-hospital mortality did not change compared to the prior year. COVID-19 diagnosis was associated with higher CVT in-hospital mortality. During the first 5 months of 2021, there was an increase in CVT hospitalization volume and increase in CVT-related mortality, partially attributable to VITT

A functional variant in the Stearoyl-CoA desaturase gene promoter enhances fatty acid desaturation in pork

There is growing public concern about reducing saturated fat intake. Stearoyl-CoA desaturase (SCD) is the lipogenic enzyme responsible for the biosynthesis of oleic acid (18:1) by desaturating stearic acid (18:0). Here we describe a total of 18 mutations in the promoter and 3′ non-coding region of the pig SCD gene and provide evidence that allele T at AY487830:g.2228T>C in the promoter region enhances fat desaturation (the ratio 18:1/18:0 in muscle increases from 3.78 to 4.43 in opposite homozygotes) without affecting fat content (18:0+18:1, intramuscular fat content, and backfat thickness). No mutations that could affect the functionality of the protein were found in the coding region. First, we proved in a purebred Duroc line that the C-T-A haplotype of the 3 single nucleotide polymorphisms (SNPs) (g.2108C>T; g.2228T>C; g.2281A>G) of the promoter region was additively associated to enhanced 18:1/18:0 both in muscle and subcutaneous fat, but not in liver. We show that this association was consistent over a 10-year period of overlapping generations and, in line with these results, that the C-T-A haplotype displayed greater SCD mRNA expression in muscle. The effect of this haplotype was validated both internally, by comparing opposite homozygote siblings, and externally, by using experimental Duroc-based crossbreds. Second, the g.2281A>G and the g.2108C>T SNPs were excluded as causative mutations using new and previously published data, restricting the causality to g.2228T>C SNP, the last source of genetic variation within the haplotype. This mutation is positioned in the core sequence of several putative transcription factor binding sites, so that there are several plausible mechanisms by which allele T enhances 18:1/18:0 and, consequently, the proportion of monounsaturated to saturated fat.This research was supported by grants from the Spanish Ministry of Science and Innovation (AGL2009-09779 and AGL2012-33529). RRF is recipient of a PhD scholarship from the Spanish Ministry of Science and Innovation (BES-2010-034607). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of manuscript

Global Impact of the COVID-19 Pandemic on Cerebral Venous Thrombosis and Mortality.

BACKGROUND AND PURPOSE: Recent studies suggested an increased incidence of cerebral venous thrombosis (CVT) during the coronavirus disease 2019 (COVID-19) pandemic. We evaluated the volume of CVT hospitalization and in-hospital mortality during the 1st year of the COVID-19 pandemic compared to the preceding year. METHODS: We conducted a cross-sectional retrospective study of 171 stroke centers from 49 countries. We recorded COVID-19 admission volumes, CVT hospitalization, and CVT in-hospital mortality from January 1, 2019, to May 31, 2021. CVT diagnoses were identified by International Classification of Disease-10 (ICD-10) codes or stroke databases. We additionally sought to compare the same metrics in the first 5 months of 2021 compared to the corresponding months in 2019 and 2020 (ClinicalTrials.gov Identifier: NCT04934020). RESULTS: There were 2,313 CVT admissions across the 1-year pre-pandemic (2019) and pandemic year (2020); no differences in CVT volume or CVT mortality were observed. During the first 5 months of 2021, there was an increase in CVT volumes compared to 2019 (27.5%; 95% confidence interval [CI], 24.2 to 32.0; P<0.0001) and 2020 (41.4%; 95% CI, 37.0 to 46.0; P<0.0001). A COVID-19 diagnosis was present in 7.6% (132/1,738) of CVT hospitalizations. CVT was present in 0.04% (103/292,080) of COVID-19 hospitalizations. During the first pandemic year, CVT mortality was higher in patients who were COVID positive compared to COVID negative patients (8/53 [15.0%] vs. 41/910 [4.5%], P=0.004). There was an increase in CVT mortality during the first 5 months of pandemic years 2020 and 2021 compared to the first 5 months of the pre-pandemic year 2019 (2019 vs. 2020: 2.26% vs. 4.74%, P=0.05; 2019 vs. 2021: 2.26% vs. 4.99%, P=0.03). In the first 5 months of 2021, there were 26 cases of vaccine-induced immune thrombotic thrombocytopenia (VITT), resulting in six deaths. CONCLUSIONS: During the 1st year of the COVID-19 pandemic, CVT hospitalization volume and CVT in-hospital mortality did not change compared to the prior year. COVID-19 diagnosis was associated with higher CVT in-hospital mortality. During the first 5 months of 2021, there was an increase in CVT hospitalization volume and increase in CVT-related mortality, partially attributable to VITT

Functoriality and duality in Morse-Conley-Floer homology

In [J. Topol. Anal. 6 (2014), 305-338], we have developed a homology theory (Morse-Conley-Floer homology) for isolated invariant sets of arbitrary flows on finite-dimensional manifolds. In this paper, we investigate functoriality and duality of this homology theory. As a preliminary, we investigate functoriality in Morse homology. Functoriality for Morse homology of closed manifolds is known, but the proofs use isomorphisms to other homology theories. We give direct proofs by analyzing appropriate moduli spaces. The notions of isolated map and flow map allow the results to generalize to local Morse homology and Morse-Conley-Floer homology. We prove Poincar,-type duality statements for local Morse homology and Morse-Conley-Floer homology

Closed Characteristics of Second-Order Lagrangians

We study the existence of closed characteristics on three-dimensional energy manifolds of second-order Lagrangian systems. These manifolds are always noncompact, connected, and not necessarily of contact type. Using the specific geometry of these manifolds, we prove that the number of closed characteristics on a prescribed energy manifold is bounded below by its second Betti number, which is easily computable from the Lagrangian