Characterizations of Super-regularity and its Variants

Convergence of projection-based methods for nonconvex set feasibility problems has been established for sets with ever weaker regularity assumptions. What has not kept pace with these developments is analogous results for convergence of optimization problems with correspondingly weak assumptions on the value functions. Indeed, one of the earliest classes of nonconvex sets for which convergence results were obtainable, the class of so-called super-regular sets introduced by Lewis, Luke and Malick (2009), has no functional counterpart. In this work, we amend this gap in the theory by establishing the equivalence between a property slightly stronger than super-regularity, which we call Clarke super-regularity, and subsmootheness of sets as introduced by Aussel, Daniilidis and Thibault (2004). The bridge to functions shows that approximately convex functions studied by Ngai, Luc and Th\'era (2000) are those which have Clarke super-regular epigraphs. Further classes of regularity of functions based on the corresponding regularity of their epigraph are also discussed.Comment: 15 pages, 2 figure

Impact of disorder on dynamics and ordering in the honeycomb-lattice iridate Na2IrO3

Kitaev's honeycomb spin-liquid model and its proposed realization in materials such as α-RuCl3, Li2IrO3, and Na2IrO3 continue to present open questions about how the dynamics of a spin liquid are modified in the presence of non-Kitaev interactions as well as the presence of inhomogeneities. Here we use Na23 nuclear magnetic resonance to probe both static and dynamical magnetic properties in single-crystal Na2IrO3. We find that the NMR shift follows the bulk susceptibility above 30 K but deviates from it below; moreover below TN the spectra show a broad distribution of internal magnetic fields. Both of these results provide evidence for inequivalent magnetic sites at low temperature, suggesting inhomogeneities are important for the magnetism. The spin-lattice relaxation rate is isotropic and diverges at TN, suggesting that the Kitaev cubic axes may control the critical quantum spin fluctuations. In the ordered state, we observe gapless excitations, which may arise from site substitution, emergent defects from milder disorder, or possibly be associated with nearby quantum paramagnetic states distinct from the Kitaev spin liquid

Activity Identification and Local Linear Convergence of Douglas--Rachford/ADMM under Partial Smoothness

Convex optimization has become ubiquitous in most quantitative disciplines of science, including variational image processing. Proximal splitting algorithms are becoming popular to solve such structured convex optimization problems. Within this class of algorithms, Douglas--Rachford (DR) and alternating direction method of multipliers (ADMM) are designed to minimize the sum of two proper lower semi-continuous convex functions whose proximity operators are easy to compute. The goal of this work is to understand the local convergence behaviour of DR (resp. ADMM) when the involved functions (resp. their Legendre-Fenchel conjugates) are moreover partly smooth. More precisely, when both of the two functions (resp. their conjugates) are partly smooth relative to their respective manifolds, we show that DR (resp. ADMM) identifies these manifolds in finite time. Moreover, when these manifolds are affine or linear, we prove that DR/ADMM is locally linearly convergent. When $J$ and $G$ are locally polyhedral, we show that the optimal convergence radius is given in terms of the cosine of the Friedrichs angle between the tangent spaces of the identified manifolds. This is illustrated by several concrete examples and supported by numerical experiments.Comment: 17 pages, 1 figure, published in the proceedings of the Fifth International Conference on Scale Space and Variational Methods in Computer Visio

Dark Ages Cold Period: A literature review and directions for future research

Several late Quaternary studies have recorded cold and disturbed climates centred during the mid-first millennium AD and discussed these conditions under the term ‘Dark Ages Cold Period’ (DACP). A review of 114 palaeoclimate papers indicated that cold climates were common in the Northern Hemisphere between AD 400 and 765. There are also suggestions that some regions may have been relatively wet during the DACP, while those around the Mediterranean and the China/Tibetan Plateau indicate coinciding droughts. A set of environmental responses, however, indicate a delayed DACP interval (AD 509–865) postdating the actual climate signal. Previously, the DACP has been linked with the North Atlantic ice-rafting event at about 1400 years ago, while some evidence suggests an involvement of the North Atlantic Oscillation and/or El Niño–Southern Oscillation. More recently, another proposed phase of widespread cooling, the ‘Late Antique Little Ice Age’ (LALIA), overlaps with the DACP and has been tentatively linked with volcanic aerosol and solar irradiance variations reinforcing the climatic downturn since AD 536. Importantly, a higher number of proxy records extending over the first millennium AD is required for more rigorous assessments of climate variability and the forcing during these centuries and to disentangle the DACP and LALIA fingerprints in the proxy data, particularly to determine whether the DACP and the LALIA are distinct features. Also a richer network of both climate and environmental proxies is needed to evaluate the human–environment interactions, during the historical Migration Period, and thus through the DACP

A desire for weight loss in season increases disordered eating behaviour risk and energy deficiency in athletes

Objective: The objective was to explore eating behaviour, body image and energy status in female university team sport athletes.Design: This was a cross-sectional, descriptive study design.Setting: The setting was North-West University, Potchefstroom, South Africa.Subjects: Subjects were top university female field hockey and netball player volunteers, aged 18-30 years (n = 22), and recruited during their sport season.Outcome measures: Athletes completed demographic, health and sport, and body weight questionnaires. The Eating Disorder Inventory and the Three-Factor Eating Questionnaire’s cognitive dietary restraint subscale were used to measure disordered eating behaviour. Body composition was measured with dual-energy X-ray absorptiometry. Estimated energy availability (estEA) was determined from a three-day diet and exercise record.Results: Fifteen (68%) athletes were identified with an increased risk of disordered eating. Sixteen (73%) were dieting. A low estEA (24 ± 12 kcal/kg fat-free mass/day) was found in 59% of the athletes, of whom 85% (11/13) had increased risk of disordered eating. A significantly positive (p-value < 0.05) association was found between cognitive dietary restraint and drive for thinness (r = 0.4) and body weight (r = 0.5). A negative association was found between desired weight loss (r = −0.5), energy intake (r = −0.5) and estEA (r = −0.7).Conclusion: Nonlean build athletes who diet in season are at increased risk of disordered eating behaviour and low energy availability. Keywords: disordered eating, body image, nonlean-build sports, female students, energy statu

On Automated Lemma Generation for Separation Logic with Inductive Definitions

Separation Logic with inductive definitions is a well-known approach for deductive verification of programs that manipulate dynamic data structures. Deciding verification conditions in this context is usually based on user-provided lemmas relating the inductive definitions. We propose a novel approach for generating these lemmas automatically which is based on simple syntactic criteria and deterministic strategies for applying them. Our approach focuses on iterative programs, although it can be applied to recursive programs as well, and specifications that describe not only the shape of the data structures, but also their content or their size. Empirically, we find that our approach is powerful enough to deal with sophisticated benchmarks, e.g., iterative procedures for searching, inserting, or deleting elements in sorted lists, binary search tress, red-black trees, and AVL trees, in a very efficient way

Medical audit of the management of cryptococcal meningitis in HIV-positive patients in the Cape Winelands (East) district, Western Cape

Background: Cryptococcal meningitis (CM) has become the most common type of community-acquired meningitis. CM has a poor outcome if the initial in-hospital treatment does not adhere to standard guidelines. The aim of this audit was to improve the quality of the care of human immunodeficiency virus (HIV) positive patients with CM in the Cape Winelands District.Method: Following an initial audit in 2008, the researchers and a new audit team introduced interventions, and planned a second audit cycle. The folders of 25 HIV-positive adults (admitted to three district hospitals, one regional hospital, and one tuberculosis hospital) were audited.Results: Spinal manometry was performed more consistently in the regional hospital, than in the district hospitals. Reasons for failing to reach the 14-day amphotericin B target were in-patient deaths, drug stock problems, and renal impairment. The renal monitoring of amphotericin B treatment was suboptimal. The quality of care at district hospitals appeared to be comparable to that found at the regional hospital. The in-patient referral for antiretroviral treatment (ART) counselling wasbetter in the district hospital setting. However, both levels of care had difficulty in achieving the four-week target between the onset of amphotericin B and onset of ART.Conclusion: Deficiencies in the quality of care remained. Between the prior and current audit cycles, there was no consistent improvement in care at the regional hospital. An integrated care pathway document has been developed, and adopted as policy in the Cape Winelands district. Its impact on the quality of care will be evaluated by a dedicated audit team in the future

Bridge Pile Response to Lateral Soil Movement Induced by Installation of Controlled Modulus Columns

© 2016 The Authors. Published by Elsevier B.V. Controlled modulus columns (CMC) for ground improvement are installed using a hollow stem displacement auger to induce lateral soil displacement effect, followed by grout injection. While the method reduces spoils, the excessive lateral soil displacement may damage adjacent structures. Although there has been growing interest in quantifying such effects, only a handful of studies have been attempted. This paper presents the results of a numerical investigation on the CMC installation effect on an existing bridge pile using the three-dimensional finite difference software package FLAC3D. It has been found that when the CMC is long and the existing bridge pile is slender, the pile bending moment and pile lateral movement, induced by the CMC installation effect, can be significant