Convex recovery of tensors using nuclear norm penalization

The subdifferential of convex functions of the singular spectrum of real matrices has been widely studied in matrix analysis, optimization and automatic control theory. Convex analysis and optimization over spaces of tensors is now gaining much interest due to its potential applications to signal processing, statistics and engineering. The goal of this paper is to present an applications to the problem of low rank tensor recovery based on linear random measurement by extending the results of Tropp to the tensors setting.Comment: To appear in proceedings LVA/ICA 2015 at Czech Republi

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

Evaluating Patient Preferences of Maintenance Therapy for the Treatment of Chronic Obstructive Pulmonary Disease: A Discrete Choice Experiment in the UK, USA and Germany.

Introduction: With increasing availability of different treatments for chronic obstructive pulmonary disease (COPD), we sought to understand patient preferences for COPD treatment in the UK, USA, and Germany using a discrete choice experiment (DCE). Methods: Qualitative research identified six attributes associated with COPD maintenance treatments: ease of inhaler use, exacerbation frequency, frequency of inhaler use, number of different inhalers used, side effect frequency, and out-of-pocket costs. A DCE using these attributes, with three levels each, was designed and tested through cognitive interviews and piloting. It comprised 18 choice sets, selected using a D-efficient experimental design. Demographics and disease history were collected and the final DCE survey was completed online by participants recruited from panels in the UK, USA and Germany. Responses were analyzed using mixed logit models, with results expressed as odds ratios (ORs). Results: Overall, 450 participants (150 per country) completed the DCE; most (UK and Germany, 97.3%; USA, 98.0%) were included in the final analysis. Based on relative attribute importance, avoidance of side effects was found to be most important (UK: OR 11.65; USA: OR 7.17; Germany: OR 11.45; all p<0.0001), followed by the likelihood of fewer exacerbations (UK: OR 2.22; USA: OR 1.63; Germany: OR 2.54; all p<0.0001) and increased ease of use (UK: OR 1.84; USA: OR 1.84; Germany: OR 1.60; all p<0.0001). Number of inhalers, out-of-pocket costs, and frequency of inhaler use were found to be less important. Preferences were relatively consistent across the three countries. All participants required a reduction in exacerbations to accept more frequent inhaler use or use of more inhalers. Conclusion: When selecting COPD treatment, individuals assigned the highest value to the avoidance of side effects, experiencing fewer exacerbations, and ease of inhaler use. Ensuring that patients' preferences are considered may encourage treatment compliance

The Potential of Conductivity, Redox Potential and Dissolved Oxygen in Raw Milk Quality Prediction

Changes in milk quality are associated with changes in dissolved oxygen (DO), redox potential (Eh) and conductivity (Co) reflecting the potential of these parameters in quality prediction. However, limited interpretation of those changes/results limits the application of the same in raw milk quality prediction. The aim of this study was therefore to explore the potential of DO, Eh and Co in milk quality assessment. Raw milk, lactoperoxidase system (LP-s) activated raw milk and LP-s activated Ultra High Temperature (UHT) milk inoculated singly with pure strains were used in this study. The performances of DO, Eh and Co in quality prediction were assessed against the objective methods: pH, titratable acidity (TA), alcohol stability test (AST), clot on boiling (COB), dye reduction tests and total viable counts (TVC). The results showed that any negative Eh value, a Co value greater than the initial Co value and DO around zero or below detection limit all indicated spoilage. These corresponded well with increases in microbial numbers indicative of spoilage recorded at about 7 log cycles of bacterial counts.  Co and Eh were in consistent agreement in quality estimate with AST and TA but more sensitive than COB and pH. On the other hand, DO showed similar sensitivity as COB and pH but was more lenient than AST and TA. The results generally confirmed the suitability of DO and Eh for routine analysis in both normal and LP-s activated milk; however, the use of Co requires a prior knowledge of the initial Co value of milk under test which complicates its use in routine analysis.Key words: Quality prediction, conductivity, redox potential, dissolved oxyge

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

The role of the two splice variants and extranuclear pathway on Ki-67 regulation in non-cancer and cancer cells

Ki-67 is a nuclear protein that has been used in cancer diagnostic because of its specific cell-cycle dependent expression profile. After quantifying and characterising the expression level of Ki-67, as a function of the cell cycle, we found out that the two main splice variants of the protein (i.e. α and β) are differently regulated in non-cancerous and cancerous cells both at mRNA and protein level. We were able to correlate the presence of the α variant of the protein with the progression through the interphase of cell cycle. We also observed that the different expression profiles correspond to different degradation pathways for non-cancerous and cancerous cells. Furthermore, Ki-67 is continuously regulated and degraded via proteasome system in both cell types, suggesting an active control of the protein. However we also observed a putative extranuclear elimination pathway of Ki-67 where it is transported to the Golgi apparatus. Our evidence in the different expression of the splice variants may represent a milestone for the development of new targets for cancer diagnostic and prognostic. Additionally, the unexpected extranuclear elimination of Ki-67 strongly suggests that this protein must be looked at also outside of the "nuclear box", as thought to date

The effect of ethnicity and genetic ancestry on the epidemiology, clinical features and outcome of systemic lupus erythematosus

Arthritis Research U

One-step generation of high-quality squeezed and EPR states in cavity QED

We show how to generate bilinear (quadratic) Hamiltonians in cavity quantum electrodynamics (QED) through the interaction of a single driven three-level atom with two (one) cavity modes. With this scheme it is possible to generate one-mode mesoscopic squeezed superpositions, two-mode entanglements, and two-mode squeezed vacuum states (such the original EPR state), without the need for Ramsey zones and external parametric amplification. The degree of squeezing achieved is up to 99% with currently feasible experimental parameters and the errors due to dissipative mechanisms become practically negligible

Observational study of the association of first insulin type in uncontrolled type 2 diabetes with macrovascular and microvascular disease

&lt;p&gt;Aims: To compare the risk of vascular disease, HbA1c and weight change, between first prescribed insulins in people with type 2 diabetes.&lt;/p&gt; &lt;p&gt;Methods: People included in THIN United Kingdom primary care record database who began insulin (2000–2007) after poor control on oral glucose-lowering agents (OGLD) were grouped by the number of OGLDs in their treatment regimen immediately before starting insulin (n = 3,485). Within OGLD group, Cox regression compared macrovascular (all-cause mortality, myocardial infarction, acute coronary syndrome and stroke) and microvascular disease (peripheral neuropathy, nephropathy, and retinopathy) between insulin type (basal, pre-mix or Neutral Protamine Hagedorn, NPH) while ANCOVAs compared haemoglobin A1c (HbA1c) and weight change.&lt;/p&gt; &lt;p&gt;Results: Mean follow-up was 3.6 years. Rates of incident macrovascular events were similar when basal insulin was compared to pre-mix or NPH, adjusted hazard ratio versus basal: pre-mix 1.08 (95% CI 0.73, 1.59); NPH 1.00 (0.63, 1.58) after two OGLDs, and pre-mix 0.97 (0.46, 2.02); NPH 0.77 (0.32, 1.86) after three OGLDs. An increased risk of microvascular disease in NPH versus basal after 3 OGLDs, adjusted hazard ratio1.87 (1.04, 3.36), was not seen after two agents or in comparisons of basal and pre-mix. At one year, after two OGLDs, weight increase was less with basal compared with pre-mix. After three OGLDs, mean HbA1c had reduced less in basal versus pre-mix or NPH at 6–8 and at 9–11 months, and versus pre-mix at 12–14 months.&lt;/p&gt; &lt;p&gt;Conclusion: We found no difference in the risk of macrovascular events between first insulins in the medium term when started during poor glycaemia control. The increased risk of microvascular events with NPH warrants further study. In certain groups, first use of basal insulin was associated with less gain in weight and decrease in HbA1c compared to other insulins.&lt;/p&gt

The effect of moving to East Village, the former London 2012 Olympic and Paralympic Games Athletes' Village, on mode of travel (ENABLE London study, a natural experiment)

Background Interventions to encourage active modes of travel (walking, cycling) may improve physical activity levels, but longitudinal evidence is limited and major change in the built environment / travel infrastructure may be needed. East Village (the former London 2012 Olympic Games Athletes Village) has been repurposed on active design principles with improved walkability, open space and public transport and restrictions on residential car parking. We examined the effect of moving to East Village on adult travel patterns. Methods One thousand two hundred seventy-eight adults (16+ years) seeking to move into social, intermediate, and market-rent East Village accommodation were recruited in 2013–2015, and followed up after 2 years. Individual objective measures of physical activity using accelerometry (ActiGraph GT3X+) and geographic location using GPS travel recorders (QStarz) were time-matched and a validated algorithm assigned four travel modes (walking, cycling, motorised vehicle, train). We examined change in time spent in different travel modes, using multilevel linear regresssion models adjusting for sex, age group, ethnicity, housing group (fixed effects) and household (random effect), comparing those who had moved to East Village at follow-up with those who did not. Results Of 877 adults (69%) followed-up, 578 (66%) provided valid accelerometry and GPS data for at least 1 day (≥540 min) at both time points; half had moved to East Village. Despite no overall effects on physical activity levels, sizeable improvements in walkability and access to public transport in East Village resulted in decreased daily vehicle travel (8.3 mins, 95%CI 2.5,14.0), particularly in the intermediate housing group (9.6 mins, 95%CI 2.2,16.9), and increased underground travel (3.9 mins, 95%CI 1.2,6.5), more so in the market-rent group (11.5 mins, 95%CI 4.4,18.6). However, there were no effects on time spent walking or cycling