Upper Hausdorff dimension estimates for invariant sets of evolutionary systems on Hilbert manifolds

summary:We prove a generalization of the Douady-Oesterlé theorem on the upper bound of the Hausdorff dimension of an invariant set of a smooth map on an infinite dimensional manifold. It is assumed that the linearization of this map is a noncompact linear operator. A similar estimate is given for the Hausdorff dimension of an invariant set of a dynamical system generated by a differential equation on a Hilbert manifold

Más allá del PIB : estimación del "Indicador de Progreso Genuino" para Uruguay entre los años 2006-2013

Ante la necesidad que tienen los países de medir simultáneamente el bienestar económico, social y ambiental, en lugar de medir únicamente la actividad económica, resulta necesario contar con un indicador que consolide estos elementos en un marco común para mostrar el progreso neto de las tres dimensiones. El PIB sigue siendo uno de los indicadores más utilizados para medir el desempeño económico, aunque presenta limitaciones ampliamente reconocidas. El Indicador de Progreso Genuino (GPI) es un enfoque más integral para evaluar el bienestar que las medidas convencionales como el PIB, recogiendo en su medición las tres dimensiones del crecimiento sostenible. A pesar de que las tendencias en el crecimiento del PIB pueden correlacionarse con el bienestar durante un período, existe evidencia empírica que sugiere que puede haber un punto más allá del cual el crecimiento continuo en el PIB deja de contribuir a las mejoras en la calidad de vida dentro de una sociedad (Max-Neef, 1995). En el presente trabajo se estimó el GPI para Uruguay en el período 2006- 2013, con el objetivo de poner a prueba esta afirmación en el período de mayor crecimiento económico del país. Los resultados generales indican que el aumento de la actividad económica vino acompañado de un aumento en el bienestar, a pesar de que existen algunas dimensiones, como la contaminación del agua, los costos del crimen, de los desplazamientos y de los accidentes de vehículos, que evolucionan desfavorablemente

The random case of Conley's theorem

The well-known Conley's theorem states that the complement of chain recurrent set equals the union of all connecting orbits of the flow $\phi$ on the compact metric space $X$, i.e. $X-\mathcal{CR}(\phi)=\bigcup [B(A)-A]$, where $\mathcal{CR}(\phi)$ denotes the chain recurrent set of $\phi$, $A$ stands for an attractor and $B(A)$ is the basin determined by $A$. In this paper we show that by appropriately selecting the definition of random attractor, in fact we define a random local attractor to be the $\omega$-limit set of some random pre-attractor surrounding it, and by considering appropriate measurability, in fact we also consider the universal $\sigma$-algebra $\mathcal F^u$-measurability besides $\mathcal F$-measurability, we are able to obtain the random case of Conley's theorem.Comment: 15 page

Putative pathogenicity genes of Phytophthora cinnamomi identified via RNA-Seq analysis of pre-infection structures

Phytophthora cinnamomi is an economically important oomycete that infects more than 3,000 plant species. We aimed to identify the repertoire of genes expressed during preinfection stages by analysing an RNA-Seq library of cysts and germinating cysts of a P. cinnamomi isolate, originating from Persea americana. Over 70,000 transcripts were identified from 225,049 contigs, assembled from 13 million Illumina paired-end reads. Contaminant sequences were eliminated, resulting in 37,534 transcripts used in further analysis. A total of 1,394 transcripts had a putative role in pathogenesis. Genes aiding in detoxification and metabolite transport (cytochrome P450 and ABC transporters) and protection against oxidative stress were most abundant, followed by the genes coding cell wall degrading enzymes. The transcript set included 44 putative RXLR effector genes and genes encoding elicitin and necrosis-inducing proteins. Expression patterns of seven putative pathogenicity genes (encoding RXLR-, necrosis-inducing Phytophthora protein 1 (NPP1), elicitin, polygalacturonase, cellulose binding and elicitor lectin (CBEL), mucin, and adhesion proteins) were assessed across four in vitro developmental stages of P. cinnamomi. High expression of these genes in zoospores suggests their functional importance in the subsequent developmental stage, germination of cysts, implying a role in pre-infection. This work is the first step towards understanding the molecular basis of infection strategies employed by P. cinnamomi.Supplement 1: Online Resource 1, 2, 3, 4, 5, 9.Supplement 2: Online Resource 6 .Supplement 3: Online Resource 7.Supplement 4: Online Resource 8.The National Research Foundation (NRF) and The Hans Merensky Foundation.http://link.springer.com/journal/106582018-01-31hb2017GeneticsMicrobiology and Plant PathologyPlant Scienc

The random case of Conley's theorem: III. Random semiflow case and Morse decomposition

In the first part of this paper, we generalize the results of the author \cite{Liu,Liu2} from the random flow case to the random semiflow case, i.e. we obtain Conley decomposition theorem for infinite dimensional random dynamical systems. In the second part, by introducing the backward orbit for random semiflow, we are able to decompose invariant random compact set (e.g. global random attractor) into random Morse sets and connecting orbits between them, which generalizes the Morse decomposition of invariant sets originated from Conley \cite{Con} to the random semiflow setting and gives the positive answer to an open problem put forward by Caraballo and Langa \cite{CL}.Comment: 21 pages, no figur

Identification of pathogenicity genes in Phytophthora cinnamomi

No abstractDissertation (MSc)--University of Pretoria, 2013.GeneticsMScUnrestricte