Search results for "Theorem"

Evolutionary implications of intron-exon distribution and the properties and sequences of the RPL10A gene in eukaryotes.

2013

The RPL10A gene encodes the RPL10 protein, required for joining 40S and 60S subunits into a functional 80S ribosome. This highly conserved gene, ubiquitous across all eukaryotic super-groups, is characterized by a variable number of spliceosomal introns, present in most organisms. These properties facilitate the recognition of orthologs among distant taxa and thus comparative studies of sequences as well as the distribution and properties of introns in taxonomically distant groups of eukaryotes. The present study examined the multiple ways in which RPL10A conservation vs. sequence changes in the gene over the course of evolution, including in exons, introns, and the encoded proteins, can be…

Homeomorphisms of finite distortion : from the unit ball to cusp domains in R^{3}

2016

Bayesian joint modeling of bivariate longitudinal and competing risks data: An application to study patient-ventilator asynchronies in critical care …

2017

Mechanical ventilation is a common procedure of life support in intensive care. Patient-ventilator asynchronies (PVAs) occur when the timing of the ventilator cycle is not simultaneous with the timing of the patient respiratory cycle. The association between severity markers and the events death or alive discharge has been acknowledged before, however, little is known about the addition of PVAs data to the analyses. We used an index of asynchronies (AI) to measure PVAs and the SOFA (sequential organ failure assessment) score to assess overall severity. To investigate the added value of including the AI, we propose a Bayesian joint model of bivariate longitudinal and competing risks data. Th…

Rolle's Theorem Fails in l2

1996

S. Typhimurium virulence changes caused by exposure to different non-thermal preservation treatments using C. elegans

2017

The aims of this research study were: (i) to postulate Caenorhabditis elegans (C. elegans) as a useful organism to describe infection by Salmonella enterica serovar Typhimurium (S. Typhimurium), and (ii) to evaluate changes in virulence of S. Typhimurium when subjected repetitively to different antimicrobial treatments. Specifically, cauliflower by-product infusion, High Hydrostatic Pressure (HHP), and Pulsed Electric Fields (PEF). This study was carried out by feeding C. elegans with different microbial populations: E. coli OP50 (optimal conditions), untreated S. Typhimurium, S. Typhimurium treated once and three times with cauliflower by-product infusion, S. Typhimurium treated once and f…

Optional Sampling Theorems

2020

In Chapter 9 we saw that martingales are transformed into martingales if we apply certain admissible gambling strategies. In this chapter, we establish a similar stability property for martingales that are stopped at a random time (optional sampling and optional stopping). In order also to obtain these results for submartingales and supermartingales, in the first section, we start with a decomposition theorem for adapted processes. We show the optional sampling and optional stopping theorems in the second section. The chapter finishes with the investigation of random stopping times with an infinite time horizon.

The Sehgal’s Fixed Point Result in the Framework of ρ-Space

2022

In this paper, we prove a fixed point theorem of Sehgal type (see Sehgal, V.M., Proc Amer Math Soc 23: 631–634, 1969) in a more general setting of ρ-space (see Secelean, N.A. and Wardowski, D., Results Math, 72: 919–935, 2017). In this way, we can find, as particular cases, some results of Sehgal type in metric, b-metric and rectangular b-metric spaces.

Module categories of finite Hopf algebroids, and self-duality

2017

International audience; We characterize the module categories of suitably finite Hopf algebroids (more precisely, $X_R$-bialgebras in the sense of Takeuchi (1977) that are Hopf and finite in the sense of a work by the author (2000)) as those $k$-linear abelian monoidal categories that are module categories of some algebra, and admit dual objects for "sufficiently many" of their objects. Then we proceed to show that in many situations the Hopf algebroid can be chosen to be self-dual, in a sense to be made precise. This generalizes a result of Pfeiffer for pivotal fusion categories and the weak Hopf algebras associated to them.

Sesquilinear forms associated to sequences on Hilbert spaces

2019

The possibility of defining sesquilinear forms starting from one or two sequences of elements of a Hilbert space is investigated. One can associate operators to these forms and in particular look for conditions to apply representation theorems of sesquilinear forms, such as Kato's theorems. The associated operators correspond to classical frame operators or weakly-defined multipliers in the bounded context. In general some properties of them, such as the invertibility and the resolvent set, are related to properties of the sesquilinear forms. As an upshot of this approach new features of sequences (or pairs of sequences) which are semi-frames (or reproducing pairs) are obtained.

Analysis of the Overdispersed Clock in the Short-Term Evolution of Hepatitis C Virus: Using the E1/E2 Gene Sequences to Infer Infection Dates in a Si…

2006

Abstract The assumption of a molecular clock for dating events from sequence information is often frustrated by the presence of heterogeneity among evolutionary rates due, among other factors, to positively selected sites. In this work, our goal is to explore methods to estimate infection dates from sequence analysis. One such method, based on site stripping for clock detection, was proposed to unravel the clocklike molecular evolution in sequences showing high variability of evolutionary rates and in the presence of positive selection. Other alternatives imply accommodating heterogeneity in evolutionary rates at various levels, without eliminating any information from the data. Here we pre…