Search results for "homology"

The complex of words and Nakaoka stability

2005

We give a new simple proof of the exactness of the complex of injective words and use it to prove Nakaoka's homology stability for symmetric groups. The methods are generalized to show acyclicity in low degrees for the complex of words in "general position". Hm(§ni1;Z) = Hm(§n;Z) for n=2 > m where §n denotes the permutation group of n elements. An elementary proof of this fact has not been available in the literature. In the first section the complex C⁄(m) of abelian groups is studied which in de- gree n is freely generated by injective words of length n. The alphabet consists of m letters. The complex C⁄(m) has the only non vanishing homology in degree m (Theorem 1). This is a result of F.…

Towards Vorst's conjecture in positive characteristic

2018

Vorst's conjecture relates the regularity of a ring with the $\mathbb{A}^1$-homotopy invariance of its $K$-theory. We show a variant of this conjecture in positive characteristic.

Automorphisms of simplicial complexes and their Stanley-Reisner rings

1997

Optimal rates of convergence for persistence diagrams in Topological Data Analysis

2013

Computational topology has recently known an important development toward data analysis, giving birth to the field of topological data analysis. Topological persistence, or persistent homology, appears as a fundamental tool in this field. In this paper, we study topological persistence in general metric spaces, with a statistical approach. We show that the use of persistent homology can be naturally considered in general statistical frameworks and persistence diagrams can be used as statistics with interesting convergence properties. Some numerical experiments are performed in various contexts to illustrate our results.

Computation of the topological type of a real Riemann surface

2012

We present an algorithm for the computation of the topological type of a real compact Riemann surface associated to an algebraic curve, i.e., its genus and the properties of the set of fixed points of the anti-holomorphic involution $\tau$, namely, the number of its connected components, and whether this set divides the surface into one or two connected components. This is achieved by transforming an arbitrary canonical homology basis to a homology basis where the $\mathcal{A}$-cycles are invariant under the anti-holomorphic involution $\tau$.

Homology of pseudodifferential operators on manifolds with fibered cusps

2003

The Hochschild homology of the algebra of pseudodifferential operators on a manifold with fibered cusps, introduced by Mazzeo and Melrose, is studied and computed using the approach of Brylinski and Getzler. One of the main technical tools is a new convergence criterion for tri-filtered half-plane spectral sequences. Using trace-like functionals that generate the 0 0 -dimensional Hochschild cohomology groups, the index of a fully elliptic fibered cusp operator is expressed as the sum of a local contribution of Atiyah-Singer type and a global term on the boundary. We announce a result relating this boundary term to the adiabatic limit of the eta invariant in a particular case.

CRISPR sequences are sometimes erroneously translated and can contaminate public databases with spurious proteins containing spaced repeats

2020

© The Author(s) 2020.

Separation properties of continuous maps in codimension 1 and geometrical applications

1992

Abstract Nuno Ballesteros, J.J. and M.C. Romero Fuster, Separation properties of continuous maps in codimension 1 and geometrical applications, Topology and its Applications 46 (1992) 107-111. We show that the image of a proper closed continuous map, f , from an n -manifold X to an ( n + 1)-manifold Y , such that H 1 (Y; Z 2 ) =0 , separates Y into at least two connected components provided the self-intersections set of f is not dense in any connected component of Y . We also obtain some geometrical applications.

Sorting signals in the cytosolic tail of membrane proteins involved in the interaction with plant ARF1 and coatomer.

2004

Summary In mammals and yeast, a cytosolic dilysine motif is critical for endoplasmic reticulum (ER) localization of type I membrane proteins. Retrograde transport of type I membrane proteins containing dilysine motifs at their cytoplasmic carboxy (C)-terminal tail involves the interaction of these motifs with the COPI coat. The C-terminal dilysine motif has also been shown to confer ER localization to type I membrane proteins in plant cells. Using in vitro binding assays, we have analyzed sorting motifs in the cytosolic tail of membrane proteins, which may be involved in the interaction with components of the COPI coat in plant cells. We show that a dilysine motif in the −3,−4 position (rel…

New enveloped dsRNA phage from freshwater habitat.

2015

Cystoviridae is a family of bacteriophages with a tri-segmented dsRNA genome enclosed in a tri-layered virion structure. Here, we present a new putative member of the Cystoviridae family, bacteriophage ϕNN. ϕNN was isolated from a Finnish lake in contrast to the previously identified cystoviruses, which originate from various legume samples collected in the USA. The nucleotide sequence of the virus reveals a strong genetic similarity (~80 % for the L-segments, ~55 % for the M-segments and ~84 % for the S-segments) to Pseudomonas phage ϕ6, the type member of the virus family. However, the relationship between ϕNN and other cystoviruses is more distant. In general, proteins located in the int…