Renorming spaces with greedy bases

We study the problem of improving the greedy constant or the democracy constant of a basis of a Banach space by renorming. We prove that every Banach space with a greedy basis can be renormed, for a given \vare>0, so that the basis becomes (1+\vare)-democratic, and hence (2+\vare)-greedy, with respect to the new norm. If in addition the basis is bidemocratic, then there is a renorming so that in the new norm the basis is (1+\vare)-greedy. We also prove that in the latter result the additional assumption of the basis being bidemocratic can be removed for a large class of bases. Applications include the Haar systems in $L_p[0,1]$, $1<p<\infty$, and in dyadic Hardy space $H_1$, as well as the unit vector basis of Tsirelson space

Sexual HIV Risk Among Male Parolees and Their Female Partners: The Relate Project

Background: The massively disproportionate impact of America’s prison boom on communities of color has raised questions about how incarceration may affect health disparities, including disparities in HIV. Primary partners are an important source of influence on sexual health. In this paper, we investigate sexual HIV risk among male-female couples following a man’s release from prison. Methods: We draw upon data from the Relate Project, a novel cross-sectional survey of recently released men and their female partners in Oakland and San Francisco, California (N=344). Inferential analyses use the actor-partner model to explore actor and partner effects on sexual HIV risk outcomes. Results: Dyadic analyses of sexual HIV risk among male parolees and their female partners paint a complex portrait of couples affected by incarceration and of partners’ influences on each other. Findings indicate that demographic factors such as education level and employment status, individual psycho-social factors such as perception of risk, and relationship factors such as commitment and power affect sexual HIV risk outcomes. Conclusion: The Relate Project provides a novel dataset for the dyadic analysis of sexual risk among male parolees and their female partners, and results highlight the importance of focusing on the couple as a unit when assessing HIV risk and protective behaviors. Results also indicate potentially fruitful avenues for population-specific interventions that may help to reduce sexual health disparities among couples affected by incarceration

Involutions on Banach Spaces and Reflexivity

spaces. E is said to be finitely representable in F if, given e&gt; 0 and a finite dimensional subspace E0 of E, there exists a subspace F0 of F such that d(E0, F0) _&lt; 1 + e, where d(E0, F0) = inf { T T-1 ß T is an isomorphism from E0 onto F0} denotes the Banach-Mazur distance coefficient. E is said to be super-reflexive if every Banach space which is finitely representable in E is re-flexive. Super-reflexivity has been characterized in terms of the notion of J-convexity: suppose that n&gt; _ 1 and that e&gt; 0; E is said to be J(n, e)-convex if, for all Xl,..., x, • in the unit ball of E, we have inf Xl q-&apos;&apos; &apos; q- Xk-- Xk+l..... Xn I-- • 7 /-- e. l&lt;k&lt;n--1 The &quot;if &quot; part of the following theorem was proved in [12] and [5], and the &quot;only if &quot; part was proved in [10]. TnEOaEM A. E is super-ret•exive //&apos;and only iœE is J(n, e)-convex for some n&gt; 1 ande&gt; 0

Coefficient Quantization for Frames in Banach Spaces

Let $(e_i)$ be a fundamental system of a Banach space. We consider the problem of approximating linear combinations of elements of this system by linear combinations using quantized coefficients. We will concentrate on systems which are possibly redundant. Our model for this situation will be frames in Banach spaces.Comment: 33 page

Identification of functional apple scab resistance gene promoters

Apple scab (Venturia inaequalis) is one of the most damaging diseases affecting commercial apple production. Some wild Malus species possess resistance against apple scab. One gene, HcrVf2, from a cluster of three genes derived from the wild apple Malus floribunda clone 821, has recently been shown to confer resistance to apple scab when transferred into a scab-susceptible apple variety. For this proof-of-function experiment, the use of the 35S promoter from Cauliflower mosaic virus was reliable and appropriate. However, in order to reduce the amount of non-plant DNA in genetically modified apple to a minimum, with the aim of increasing genetically modified organism acceptability, these genes would ideally be regulated by their own promoters. In this study, sequences from the promoter region of the three members of the HcrVf gene family were compared. Promoter constructs containing progressive 5′ deletions were prepared and used for functional analyses. Qualitative assessment confirmed promoter activity in apple. Quantitative promoter comparison was carried out in tobacco (Nicotiana glutinosa) and led to the identification of several promoter regions with different strengths from a basal level to half the strength of the 35S promoter from Cauliflower mosaic viru