Hypercyclic tuples of operators on $C^n$ and $R^n$

A tuple $(T_1,\dots,T_n)$ of continuous linear operators on a topological vector space $X$ is called hypercyclic if there is $x\in X$ such that the the orbit of $x$ under the action of the semigroup generated by $T_1,\dots,T_n$ is dense in $X$. This concept was introduced by N.~Feldman, who have raised 7 questions on hypercyclic tuples. We answer those 4 of them, which can be dealt with on the level of operators on finite dimensional spaces. In
particular, we prove that the minimal cardinality of a hypercyclic tuple of operators on $\C^n$ (respectively, on $\R^n$) is $n+1$ (respectively, $\frac n2+\frac{5+(-1)^n}{4}$), that there are non-diagonalizable tuples of operators on $\R^2$ which possess an orbit being neither dense nor nowhere dense and construct a hypercyclic 6-tuple of operators on $\C^3$ such that every operator commuting with each member of the tuple is non-cyclic.

Turning the tide: A critique of Natural Semantic Metalanguage from a translation studies perspective

Starting from the premise that human communication is predicated on translational phenomena, this paper applies theoretical insights and practical findings from Translation Studies to a critique of Natural Semantic Metalanguage (NSM), a theory of semantic analysis developed by Anna Wierzbicka. Key tenets of NSM, i.e. (1) culture-specificity of complex concepts; (2) the existence of a small set of universal semantic primes; and (3) definition by reductive paraphrase, are discussed critically with reference to the notions of untranslatability, equivalence, and intra-lingual translation, respectively. It is argued that a broad spectrum of research and theoretical reflection in Translation Studies may successfully feed into the study of cognition, meaning, language, and communication. The interdisciplinary exchange between Translation Studies and linguistics may be properly balanced, with the former not only being informed by but also informing and interrogating the latter.

Hypercyclic operators on countably dimensional spaces

According to Grivaux, the group GL(X) of invertible linear operators on a separable infinite dimensional Banach space X acts transitively on the set s (X) of countable dense linearly independent subsets of X. As a consequence, each A? s (X) is an orbit of a hypercyclic operator on X. Furthermore, every countably dimensional normed space supports a hypercyclic operator. Recently Albanese extended this result to Fréchet spaces supporting a continuous norm. We show that for a separable infinite dimensional Fréchet space X, GL(X) acts transitively on s (X) if and only if X possesses a continuous norm. We also prove that every countably dimensional metrizable locally convex space supports a hypercyclic operator.

Translation suppression promotes stress granule formation and cell survival in response to cold shock

Cells respond to different types of stress by inhibition of protein synthesis and subsequent assembly of stress granules (SGs), cytoplasmic aggregates that contain stalled translation preinitiation complexes. Global translation is regulated through the translation initiation factor eukaryotic initiation factor 2a (eIF2a) and the mTOR pathway. Here we identify cold shock as a novel trigger of SG assembly in yeast and mammals. Whereas cold shock-induced SGs take hours to form, they dissolve within minutes when cells are returned to optimal growth temperatures. Cold shock causes eIF2a phosphorylation through the kinase PERK in mammalian cells, yet this pathway is not alone responsible for translation arrest and SG formation. In addition, cold shock leads to reduced mitochondrial function, energy depletion, concomitant activation of AMP-activated protein kinase (AMPK), and inhibition of mTOR signaling. Compound C, a pharmacological inhibitor of AMPK, prevents the formation of SGs and strongly reduces cellular survival in a translation-dependent manner. Our results demonstrate that cells actively suppress protein synthesis by parallel pathways, which induce SG formation and ensure cellular survival during hypothermia.

Dynamic oscillation of translation and stress granule formation mark the cellular response to virus infection

Virus infection-induced global protein synthesis suppression is linked to assembly of stress granules (SGs), cytosolic aggregates of stalled translation preinitiation complexes. To study long-term stress responses, we developed an imaging approach for extended observation and analysis of SG dynamics during persistent hepatitis C virus (HCV) infection. In combination with type 1 interferon, HCV infection induces highly dynamic assembly/disassembly of cytoplasmic SGs, concomitant with phases of active and stalled translation, delayed cell division, and prolonged cell survival. Double-stranded RNA (dsRNA), independent of viral replication, is sufficient to trigger these oscillations. Translation initiation factor eIF2a phosphorylation by protein kinase R mediates SG formation and translation arrest. This is antagonized by the upregulation of GADD34, the regulatory subunit of protein phosphatase 1 dephosphorylating eIF2a. Stress response oscillation is a general mechanism to prevent long-lasting translation repression and a conserved host cell reaction to multiple RNA viruses, which HCV may exploit to establish persistence.

Completely bounded disjointness preserving operators between Fourier algebras

In this paper, we characterize surjective completely bounded disjointness preserving linear operators on Fourier algebras of locally compact amenable groups. We show that such operators are given by weighted homomorphisms induced by piecewise affine proper maps. © 2011 Elsevier Inc.

The structure of compact disjointness preserving operators on continuous functions

Let T be a compact disjointness preserving linear operator from C0(X) into C0(Y), where X and Y are locally compact Hausdorff spaces. We show that T can be represented as a norm convergent countable sum of disjoint rank one operators. More precisely, T = Snd ?hn for a (possibly finite) sequence {xn }n of distinct points in X and a norm null sequence {hn }n of mutually disjoint functions in C0(Y). Moreover, we develop a graph theoretic method to describe the spectrum of such an operator

Lost in translation: Public policies, evidence-based practice, and Autism Spectrum Disorder

Prevalence rates of autism spectrum disorder have risen dramatically over the past few decades (now estimated at 1:50 children). The estimated total annual cost to the public purse in the United States is US$137 billion, with an individual lifetime cost in the United Kingdom estimated at between £0.8 million and £1.23 million depending on the level of functioning. The United Nations Convention for the Rights of Persons with Disabilities has enshrined full and equal human rights—for example, for inclusion, education and employment—and there is ample evidence that much can be achieved through adequate support and early intensive behavioural interventions. Not surprisingly, most governments worldwide have devised laws, policies, and strategies to improve services related to autism spectrum disorder, yet intriguingly the approaches differ considerably across the globe. Using Northern Ireland as a case in point, we look at relevant governmental documents and offer international comparisons that illustrate inconsistencies akin to a “postcode lottery” of services.

The Map Defines the Territory: Remodelling NGO Partnerships for Knowledge Translation in Transition Contexts

The initial impetus for a theoretical exploration of organisational relationships is based on case study research on a Bulgarian NGO's implementation of values and goals into practices under a guiding relationship from a very experienced UK organisation in the same field. Findings diverged from conventional accounts of developing NGOs' dependence on more developed counterparts and that case study findings characterised the inter- dependency between the two organisations as more alike to a collaborative knowledge ...

Successful translation of Academic Research into wider Economic Impact: University of Southampton, Distinguished Lecture

No abstract available