Nurturing Talent HE STEM Project Report

This is the final report outlining the findings of our evaluation of a Widening Participation initiative involving young members of the Somali community in Brent, London

Order theory and interpolation in operator algebras

We continue our study of operator algebras with and contractive approximate identities (cais). In earlier papers we have introduced and studied a new notion of positivity in operator algebras, with an eye to extending certain C*-algebraic results and theories to more general algebras. Here we continue to develop this positivity and its associated ordering, proving many foundational facts. We also give many applications, for example to noncommutative topology, noncommutative peak sets, lifting problems, peak interpolation, approximate identities, and to order relations between an operator algebra and the C*-algebra it generates. In much of this it is not necessary that the algebra have an approximate identity. Many of our results apply immediately to function algebras, but we will not take the time to point these out, although most of these applications seem new.Comment: 27 pages. arXiv admin note: substantial text overlap with arXiv:1308.272

Operator algebras with contractive approximate identities: Weak compactness and the spectrum

We continue our study of operator algebras with contractive approximate identities (cais) by presenting a couple of interesting examples of operator algebras with cais, which in particular answer questions raised in previous papers in this series, for example about whether, roughly speaking, `weak compactness' of an operator algebra, or the lack of it, can be seen in the spectra of its elements.Comment: 11 pages. To appear Journal of Functional Analysis. arXiv admin note: substantial text overlap with arXiv:1308.272

Ideals and hereditary subalgebras in operator algebras

This paper may be viewed as having two aims. First, we continue our study of algebras of operators on a Hilbert space which have a contractive approximate identity, this time from a more Banach algebraic point of view. Namely, we mainly investigate topics concerned with the ideal structure, and hereditary subalgebras (HSA's), which are in some sense generalization of ideals. Second, we study properties of operator algebras which are hereditary subalgebras in their bidual, or equivalently which are `weakly compact'. We also give several examples answering natural questions that arise in such an investigation.Comment: 24 page

An Assessment of Mental Health Services for Veterans in the State of Texas

This report describes the complex challenges faced by veterans and their families in seeking, navigating, and attaining adequate mental health care in Texas. There are 1.7 million veterans in Texas, comprising 8.6 percent of the adult population. According to the U.S. Department of Veteran Affairs (VA), the number of veterans requiring mental health services has grown dramatically and will continue to increase, making veterans’ mental health care an urgent issue in Texas. The federal agencies responsible for military and veterans mental health care, the U.S. Department of Defense (DoD) and the VA, have created new programs and invested significant financial and staff resources. Despite barriers to addressing veterans mental health needs. Texas state agencies have increased funding and instituted new mental health programs supporting returning veterans. Nonprofit agencies focused on veteran’s mental health have multiplied across Texas and the U.S. over the past decade to fill gaps in care. While these organizations provide a growing and increasingly diverse set of resources for veterans to extend the scope of support, volunteer efforts can suffer from fragmentation and overlap. The report identifies current practices, challenges, and opportunities within and across each group of service providers. The report draws on government reports, scholarly literature, and agency websites, as well as interviews with counselors, Veteran Service Officers, nonprofit providers, state officials, and veterans themselves. This report offers five recommendations toward the goal that veterans’ mental health care in Texas become comprehensive, inclusive, effective, and efficient. First, there is a need for greater inter-agency communication across organizations, improved outreach efforts, and increased services for hard-to-reach populations, such as homeless veterans. Second, federal agencies ought to address staff shortages, improve the transition from DoD to VA care, and increase feedback. Third, at the state level, specialized services are needed to address unique veterans’ needs concentrated in cities across Texas as well as those dispersed in rural areas. Fourth, providers can improve mental health care by integrating social services and law enforcement. Fifth, both veterans and providers can benefit if they recognize opportunities for cooperation and coordination and work towards long-term goals that emphasize outcomes that improve the lives of returning veterans. This research was funded in part by the Jack S. Blanton Research Fellowship and the George A. Roberts Research Fellowship of the IC² Institute.IC2 Institut

Improved Adaptive Rejection Metropolis Sampling Algorithms

Markov Chain Monte Carlo (MCMC) methods, such as the Metropolis-Hastings (MH) algorithm, are widely used for Bayesian inference. One of the most important issues for any MCMC method is the convergence of the Markov chain, which depends crucially on a suitable choice of the proposal density. Adaptive Rejection Metropolis Sampling (ARMS) is a well-known MH scheme that generates samples from one-dimensional target densities making use of adaptive piecewise proposals constructed using support points taken from rejected samples. In this work we pinpoint a crucial drawback in the adaptive procedure in ARMS: support points might never be added inside regions where the proposal is below the target. When this happens in many regions it leads to a poor performance of ARMS, with the proposal never converging to the target. In order to overcome this limitation we propose two improved adaptive schemes for constructing the proposal. The first one is a direct modification of the ARMS procedure that incorporates support points inside regions where the proposal is below the target, while satisfying the diminishing adaptation property, one of the required conditions to assure the convergence of the Markov chain. The second one is an adaptive independent MH algorithm with the ability to learn from all previous samples except for the current state of the chain, thus also guaranteeing the convergence to the invariant density. These two new schemes improve the adaptive strategy of ARMS, thus simplifying the complexity in the construction of the proposals. Numerical results show that the new techniques provide better performance w.r.t. the standard ARMS.Comment: Matlab code provided in http://a2rms.sourceforge.net