Search results for "Indel"

Gδ covers of compact spaces

2018

We solve a long standing question due to Arhangel'skii by constructing a compact space which has a Gδ cover with no continuum-sized (Gδ)-dense subcollection. We also prove that in a countably compact weakly Lindelöf normal space of countable tightness, every Gδ cover has a -sized subcollection with a Gδ-dense union and that in a Lindelöf space with a base of multiplicity continuum, every Gδ cover has a continuum sized subcover. We finally apply our results to obtain a bound on the cardinality of homogeneous spaces which refines De La Vega's celebrated theorem on the cardinality of homogeneous compacta of countable tightness.

Fully reliable a posteriori error control for evolutionary problems

2015

On closures of discrete sets

2018

The depth of a topological space $X$ ($g(X)$) is defined as the supremum of the cardinalities of closures of discrete subsets of $X$. Solving a problem of Mart\'inez-Ruiz, Ram\'irez-P\'aramo and Romero-Morales, we prove that the cardinal inequality $|X| \leq g(X)^{L(X) \cdot F(X)}$ holds for every Hausdorff space $X$, where $L(X)$ is the Lindel\"of number of $X$ and $F(X)$ is the supremum of the cardinalities of the free sequences in $X$.

Preservation of genetic and regulatory robustness in ancient gene duplicates of Saccharomyces cerevisiae

2014

[EN] Biological systems remain robust against certain genetic and environmental challenges. Robustness allows the exploration of ecological adaptations. It is unclear what factors contribute to increasing robustness. Gene duplication has been considered to increase genetic robustness through functional redundancy, accelerating the evolution of novel functions. However, recent findings have questioned the link between duplication and robustness. In particular, it remains elusive whether ancient duplicates still bear potential for innovation through preserved redundancy and robustness. Here we have investigated this question by evolving the yeast Saccharomyces cerevisiae for 2200 generations …

Sequence diversity in the pe_pgrs genes of Mycobacterium tuberculosis is independent of human T cell recognition.

2014

ABSTRACT The Mycobacterium tuberculosis genome includes the large family of pe_pgrs genes, whose functions are unknown. Because of precedents in other pathogens in which gene families showing high sequence variation are involved in antigenic variation, a similar role has been proposed for the pe_pgrs genes. However, the impact of immune selection on pe_pgrs genes has not been examined. Here, we sequenced 27 pe_pgrs genes in 94 clinical strains from five phylogenetic lineages of the M. tuberculosis complex (MTBC). We found that pe_pgrs genes were overall more diverse than the remainder of the MTBC genome, but individual members of the family varied widely in their nucleotide diversity and in…

The Rate and Molecular Spectrum of Spontaneous Mutations in Arabidopsis thaliana

2010

Evolution in Action Rates of evolution in gene and genome sequences have been estimated, but these estimates are subject to error because many of the steps of evolution over the ages are not directly measurable or are hidden under subsequent changes. Ossowski et al. (p. 92 ) now provide a more accurate measurement of how often spontaneous mutations arise in a nuclear genome. Mutations arising over 30 generations were compared by sequencing DNA from individual Arabidopsis thaliana plants. UV- and deamination-induced mutagenesis appeared to bias the type of mutations found.

Upper bounds for the tightness of the $$G_\delta $$-topology

2021

We prove that if X is a regular space with no uncountable free sequences, then the tightness of its $$G_\delta $$ topology is at most the continuum and if X is, in addition, assumed to be Lindelof then its $$G_\delta $$ topology contains no free sequences of length larger then the continuum. We also show that, surprisingly, the higher cardinal generalization of our theorem does not hold, by constructing a regular space with no free sequences of length larger than $$\omega _1$$ , but whose $$G_\delta $$ topology can have arbitrarily large tightness.

A note on rank 2 diagonals

2020

<p>We solve two questions regarding spaces with a (G<sub>δ</sub>)-diagonal of rank 2. One is a question of Basile, Bella and Ridderbos about weakly Lindelöf spaces with a G<sub>δ</sub>-diagonal of rank 2 and the other is a question of Arhangel’skii and Bella asking whether every space with a diagonal of rank 2 and cellularity continuum has cardinality at most continuum.</p>

On the cardinality of almost discretely Lindelof spaces

2016

A space is said to be almost discretely Lindelof if every discrete subset can be covered by a Lindelof subspace. Juhasz et al. (Weakly linearly Lindelof monotonically normal spaces are Lindelof, preprint, arXiv:1610.04506 ) asked whether every almost discretely Lindelof first-countable Hausdorff space has cardinality at most continuum. We prove that this is the case under $$2^{<{\mathfrak {c}}}={\mathfrak {c}}$$ (which is a consequence of Martin’s Axiom, for example) and for Urysohn spaces in ZFC, thus improving a result by Juhasz et al. (First-countable and almost discretely Lindelof $$T_3$$ spaces have cardinality at most continuum, preprint, arXiv:1612.06651 ). We conclude with a few rel…

Guaranteed error bounds for a class of Picard-Lindelöf iteration methods

2013

We present a new version of the Picard-Lindelof method for ordinary dif- ¨ ferential equations (ODEs) supplied with guaranteed and explicitly computable upper bounds of an approximation error. The upper bounds are based on the Ostrowski estimates and the Banach fixed point theorem for contractive operators. The estimates derived in the paper take into account interpolation and integration errors and, therefore, provide objective information on the accuracy of computed approximations. peerReviewed