Alternating Projections and Douglas-Rachford for Sparse Affine Feasibility

The problem of finding a vector with the fewest nonzero elements that satisfies an underdetermined system of linear equations is an NP-complete problem that is typically solved numerically via convex heuristics or nicely-behaved nonconvex relaxations. In this work we consider elementary methods based on projections for solving a sparse feasibility problem without employing convex heuristics. In a recent paper Bauschke, Luke, Phan and Wang (2014) showed that, locally, the fundamental method of alternating projections must converge linearly to a solution to the sparse feasibility problem with an affine constraint. In this paper we apply different analytical tools that allow us to show global linear convergence of alternating projections under familiar constraint qualifications. These analytical tools can also be applied to other algorithms. This is demonstrated with the prominent Douglas-Rachford algorithm where we establish local linear convergence of this method applied to the sparse affine feasibility problem.Comment: 29 pages, 2 figures, 37 references. Much expanded version from last submission. Title changed to reflect new development

Brahms, Opus 32: The Forgotten Cycles

A song cycle may be loosely defined as a set of works for solo voice and piano intended for performance as a whole, and in a predetermined order. Established by such composers as Beethoven, Schubert and Schumann, cycles are typically characterized by a deliberate structure, the texts of which are almost without exception by the same author. So conventional is the practice of containing the settings of a single poet, it may be considered a prerequisite. Song cycles are also distinguished, therefore, by one or more unifying elements originating in the poetry, such as literary themes or narration. It is thus inherent that a composer takes a deliberate approach to writing a cycle, both in his selection and setting of the texts. The result is a cohesive musical form with an obvious structure dependent on the aforementioned elements, the musical expression of which is influenced by the text

Preschool children's proto-episodic memory assessed by deferred imitation.

This is the author accepted manuscript. The final version is available from Taylor & Francis via http://dx.doi.org/10.1080/09658211.2014.963625In two experiments, both employing deferred imitation, we studied the developmental origins of episodic memory in two- to three-year-old children by adopting a "minimalist" view of episodic memory based on its What-When-Where ("WWW": spatiotemporal plus semantic) content. We argued that the temporal element within spatiotemporal should be the order/simultaneity of the event elements, but that it is not clear whether the spatial content should be egocentric or allocentric. We also argued that episodic recollection should be configural (tending towards all-or-nothing recall of the WWW elements). Our first deferred imitation experiment, using a two-dimensional (2D) display, produced superior-to-chance performance after 2.5 years but no evidence of configural memory. Moreover, performance did not differ from that on a What-What-What control task. Our second deferred imitation study required the children to reproduce actions on an object in a room, thereby affording layout-based spatial cues. In this case, not only was there superior-to-chance performance after 2.5 years but memory was also configural at both ages. We discuss the importance of allocentric spatial cues in episodic recall in early proto-episodic memory and reflect on the possible role of hippocampal development in this process

Visualizing the Historic Landscape of Montserrat: Social Justice Through Community Mapping in a Post-Colonial Environment

Scholars across the disciplines of geography, archaeology, and history argue for need to reconceptualize representations of history in post-colonial environments and to actively orientate scholarly research towards increasing the inclusion of local knowledge with \u27expert\u27 academic knowledge through participative methods. This thesis will show that the landscape surrounding the Little Bay Plantation contains cultural associations vital to a socially just interpretation of Montserrat culture that is not captured by existing archaeological research centered on ruins of the plantation infrastructure and European historical discourse. Through a participatory research methodology this thesis shows that there are many memories inscribed within and upon the landscape of Little Bay; the Cpt. Wm. Carr story is but one of them. To provide an alternative narrative this study incorporates qualitative and participatory methods to focus on geographic issues related to the non-elite community, their associative landscapes, and how the drama of human activity has been recorded in the landscape. The results of the study provide an example of how GIScience and geographic theory can be employed to include the knowledge and associations of local people intimately familiar with the landscape, thereby creating a richer, more nuanced representation of Montserrat cultural heritage at the Little Bay Plantation

The At-Risk Mental State (ARMS) for Psychosis in Children and Adolescents.

Introduction In the last decade it has been proposed that individuals who are at an elevated future risk of developing psychosis compared to the general population can be identified using operationalised criteria. Those who fulfil these criteria are labelled as having an At-Risk Mental State (ARMS) for psychosis. Research in working-age adults has reported a lowering of the short-term rate of transition of such individuals to psychosis over successive cohorts. Nevertheless, such individuals report poor psychosocial functioning and high distress levels. To date, there has been a dearth of research specifically focussed on the concept of the ARMS in adolescents. Thus it is not established how these young people present to mental health services, what mental health diagnostic categories, if any, they would fulfil and what their short-term outcomes are in terms of mental health and psychosocial functioning. Moreover, it is unknown how this group may experience the label of being ‘at-risk’ and whether these individuals would benefit from the ARMS criteria being made an official diagnostic category. The aim of this study was to investigate how young people fulfilling the ARMS criteria present to services, to characterise them and report the short-term outcomes, in terms of mental health and functioning. The views and experiences of young people with the ARMS label and mental health professionals potentially working with this client group were also explored. Methods Two separate projects were completed: Project 1; The Follow-up of the At-Risk Mental State (FARMS) project and Project 2; The Professional Attitudes towards the At-Risk Mental State (PAARMS) project. Study 1 of the FARMS project involved a prospective longitudinal cohort study and investigated how adolescents categorised as having an ARMS initially present to mental health services and fared over a six month follow-up period. Study 2 involved recruiting a purposive sample of participants fulfilling the ARMS criteria from Study 1, into a qualitative study. An Interpretative Phenomenological Analysis (IPA) framework was then used to explore the personal understanding and experiences of these young people in relation to the ARMS concept. The PAARMS project used a mixed methods approach in order to evaluate the attitudes and experience of Child and Adolescent Mental Health Service (CAMHS) professionals in relation to the ARMS concept. Firstly, in-depth interviews were conducted with a purposive sample of six CAMHS clinicians who work in Early Intervention in Psychosis (EIP) services regarding their experience and attitudes in relation to working with young mental health service-users who have the ARMS label. Secondly, a survey involving 180 CAMHS clinicians was conducted. Results Study 1 of the FARMS project confirmed that adolescents fulfilling the ARMS criteria present to services with significant levels of reported psychopathology and functional impairment. Auditory perceptual disturbance was the most frequently reported ‘positive’ symptom whilst 70% of participants met the threshold for at least one current ICD-10 Axis I psychiatric diagnosis. In terms of short term outcomes, transition rates to psychosis were low (1/29; 3%) with a handful of individuals (7/29; 24%) demonstrating significant remission of symptoms and/or significant improvements in psychosocial functioning. The findings from Study 2 indicate that young people wish to be told about their condition upon identification and do not report experiencing significantly negative or distressing instances of stigma, though this was a voiced initial concern. Talking to mental health professionals and possibly peers, who also experience similar symptoms, are perceived as the most beneficial elements of support offered by services. Finally, CAMHS professionals participating in the PAARMS project reported being reluctant to recommend medication as a first-line treatment strategy. However, monitoring, psycho-education and psychological therapies were widely endorsed. Identification and management of adolescents with the ARMS label was viewed as challenging and complicated by a variety of factors including maturational process and a lack of official guidelines and protocols. Discussion The results of this study not only characterise how adolescents fulfilling the ARMS criteria present to services but also inform future debates regarding the ARMS concept as a distinct diagnosis. These findings should therefore facilitate the development of new policies for the identification and management of the condition in young people and address areas of clinical practice that require immediate attention. Future research is required to establish whether these initial findings are generalisable to services elsewhere and to evaluate plausible interventional approaches that target distressing symptoms and functioning

The keys to unlock Northern Australia have already been cut

[Extract] Ignoring history can lead to a futile repetition of past mistakes. In the new wave of enthusiasm to "unlock" northern Australia, the federal government has overlooked the past and espoused an extraordinarily rosy vision of the future