Estimation in high dimensions: a geometric perspective

This tutorial provides an exposition of a flexible geometric framework for high dimensional estimation problems with constraints. The tutorial develops geometric intuition about high dimensional sets, justifies it with some results of asymptotic convex geometry, and demonstrates connections between geometric results and estimation problems. The theory is illustrated with applications to sparse recovery, matrix completion, quantization, linear and logistic regression and generalized linear models.Comment: 56 pages, 9 figures. Multiple minor change

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Interacting for the environment:Engaging Goffman in pro-environmental action

Whilst there are profound disagreements about how more sustainable forms of living might be achieved, most research on pro-environmental action recognises it as a fundamentally social challenge – demanding shifts not merely in individuals’ attitudes and behaviours, but also in social norms, contexts and practices. Despite the social nature of the challenge, perhaps the most fundamental social medium – social interaction - remains under-theorised in this area. To address this gap, this paper applies Erving Goffman’s understandings of social interaction to an ethnographic case study of a pro- environmental change initiative called Environment Champions. The analysis shows that social interaction plays a crucially important role in shaping responses to pro-environmental change processes that has the potential to both help and hinder the spread of pro-environmental action. The paper concludes by exploring how Goffman’s ideas develop and extend current debates about pro- environmental behaviour change

M31 Pixel Lensing PLAN Campaign: MACHO Lensing and Self Lensing Signals

We present the final analysis of the observational campaign carried out by the PLAN (Pixel Lensing Andromeda) collaboration to detect a dark matter signal in form of MACHOs through the microlensing effect. The campaign consists of about 1 month/year observations carried out during 4 years (2007-2010) at the 1.5m Cassini telescope in Loiano ("Astronomical Observatory of BOLOGNA", OAB) plus 10 days of data taken in 2010 at the 2m Himalayan Chandra Telescope (HCT) monitoring the central part of M31 (two fields of about 13'x12.6'). We establish a fully automated pipeline for the search and the characterization of microlensing flux variations: as a result we detect 3 microlensing candidates. We evaluate the expected signal through a full Monte Carlo simulation of the experiment completed by an analysis of the detection efficiency of our pipeline. We consider both "self lensing" and "MACHO lensing" lens populations, given by M31 stars and dark matter halo MACHOs, in the M31 and the Milky Way (MW), respectively. The total number of events is compatible with the expected self-lensing rate. Specifically, we evaluate an expected signal of about 2 self-lensing events. As for MACHO lensing, for full 0.5 (0.01) solar mass MACHO halos, our prediction is for about 4 (7) events. The comparatively small number of expected MACHO versus self lensing events, together with the small number statistics at disposal, do not enable us to put strong constraints on that population. Rather, the hypothesis, suggested by a previous analysis, on the MACHO nature of OAB-07-N2, one of the microlensing candidates, translates into a sizeable lower limit for the halo mass fraction in form of the would be MACHO population, f, of about 15% for 0.5 solar mass MACHOs.Comment: ApJ accepted, 13 pages, 5 figures, 2 table

Quantization and Compressive Sensing

Quantization is an essential step in digitizing signals, and, therefore, an indispensable component of any modern acquisition system. This book chapter explores the interaction of quantization and compressive sensing and examines practical quantization strategies for compressive acquisition systems. Specifically, we first provide a brief overview of quantization and examine fundamental performance bounds applicable to any quantization approach. Next, we consider several forms of scalar quantizers, namely uniform, non-uniform, and 1-bit. We provide performance bounds and fundamental analysis, as well as practical quantizer designs and reconstruction algorithms that account for quantization. Furthermore, we provide an overview of Sigma-Delta ($\Sigma\Delta$) quantization in the compressed sensing context, and also discuss implementation issues, recovery algorithms and performance bounds. As we demonstrate, proper accounting for quantization and careful quantizer design has significant impact in the performance of a compressive acquisition system.Comment: 35 pages, 20 figures, to appear in Springer book "Compressed Sensing and Its Applications", 201

Correspondence to William Barrett Taylor, date unknown or unclear

Correspondence to William Barrett Taylor, date unknown or unclear. Box 3, folder 7.https://digitalcommons.wofford.edu/littlejohnboggs/1022/thumbnail.jp

Efficient and feasible state tomography of quantum many-body systems

We present a novel method to perform quantum state tomography for many-particle systems which are particularly suitable for estimating states in lattice systems such as of ultra-cold atoms in optical lattices. We show that the need for measuring a tomographically complete set of observables can be overcome by letting the state evolve under some suitably chosen random circuits followed by the measurement of a single observable. We generalize known results about the approximation of unitary 2-designs, i.e., certain classes of random unitary matrices, by random quantum circuits and connect our findings to the theory of quantum compressed sensing. We show that for ultra-cold atoms in optical lattices established techniques like optical super-lattices, laser speckles, and time-of-flight measurements are sufficient to perform fully certified, assumption-free tomography. Combining our approach with tensor network methods - in particular the theory of matrix-product states - we identify situations where the effort of reconstruction is even constant in the number of lattice sites, allowing in principle to perform tomography on large-scale systems readily available in present experiments.Comment: 10 pages, 3 figures, minor corrections, discussion added, emphasizing that no single-site addressing is needed at any stage of the scheme when implemented in optical lattice system

A Typology of Child Sponsorship Activity

Framing the debate over child sponsorship in terms of legitimacy and changing perceptions of credible international humanitarian interventions, this chapter takes exception to the tendency of child sponsorship critics to assume that sponsorship funded activity is much the same everywhere and similar today when compared to sponsorship practice in the past. Mindful of ongoing critique of child sponsorship, this chapter seeks to position those international non-governmental organisations that utilise child sponsorship to fund interventions, in a landscape of contested ideas. It argues that informed critique of child sponsorship is best achieved through a typology of funded interventions. Four key types of sponsorship funded activity are identified as emerging over time, some of which are currently deemed to be less legitimate in terms of poverty reduction and are best seen as welfare measures aimed at individual children rather than community development or advocacy activities

Social support for and through exercise and sport in a sample of men with serious mental illness.

Social support is important for people experiencing serious mental illness and is also important during the initiation and maintenance of exercise. In this article we draw on interpretive research into the experiences of 11 men with serious mental illness to explore four dimensions of social support both for and through exercise. Our findings suggest that informational, tangible, esteem, and emotional support were both provided for and given by participants through exercise. We conclude that experiences of both receiving and giving diverse forms of support in this way are significant for some people living with and recovering from serious mental illness

Youth Savings Groups in Africa: They’re a Family Affair

Based on fieldwork in Tanzania, Zambia, Uganda, and Ghana, in the paper we provide new evidence that young people’s engagement with savings groups in Africa is deeply embedded in networks of family and social relations. Savings group members rely on money that is given to them by partners and family members to make savings contributions to the groups, while they also transfer some of their share-outs and loans to family members and friends. This is particularly true for younger members. As such we argue that the socially embedded nature of young people's engagement with savings group needs to be taken into account. The tension between the primary focus on the individual within youth saving programming, and the socially embedded nature of their engagement, has important implications for programme design, implementation and evaluation