The road to deterministic matrices with the restricted isometry property

The restricted isometry property (RIP) is a well-known matrix condition that provides state-of-the-art reconstruction guarantees for compressed sensing. While random matrices are known to satisfy this property with high probability, deterministic constructions have found less success. In this paper, we consider various techniques for demonstrating RIP deterministically, some popular and some novel, and we evaluate their performance. In evaluating some techniques, we apply random matrix theory and inadvertently find a simple alternative proof that certain random matrices are RIP. Later, we propose a particular class of matrices as candidates for being RIP, namely, equiangular tight frames (ETFs). Using the known correspondence between real ETFs and strongly regular graphs, we investigate certain combinatorial implications of a real ETF being RIP. Specifically, we give probabilistic intuition for a new bound on the clique number of Paley graphs of prime order, and we conjecture that the corresponding ETFs are RIP in a manner similar to random matrices.Comment: 24 page

Continuum emission around AGB stars at 1.2 mm

It is generally acknowledged that the mass loss of Asymptotic Giant Branch (AGB) stars undergoes variations on different time scales. We constructed models for the dust envelopes for a sample of AGB stars to assess whether mass-loss variations influence the spectral energy distribution (SED). To constrain the variability, extra observations at millimetre wavelengths (1.2 mm) were acquired. From the analysis of the dust models, two indications for the presence of mass-loss variations can be found, being (1) a dust temperature at the inner boundary of the dust envelope that is far below the dust condensation temperature and (2) an altered density distribution with respect to rho(r) \propto r^{-2} resulting from a constant mass-loss rate. For 5 out of the 18 studied sources a two-component model of the envelope is required, consisting of an inner region with a constant mass-loss rate and an outer region with a less steep density distribution. For one source an outer region with a steeper density distribution was found. Moreover, in a search for time variability in our data set at 1.2 mm, we found that WX Psc shows a large relative time variation of 34% which might partially be caused by variable molecular line emission.Comment: Accepted for publication in MNRAS; 16 pages, 19 figure

Synthetic photometry for carbon-rich giants II. The effects of pulsation and circumstellar dust

By using self-consistent dynamic model atmospheres which simulate pulsation-enhanced dust-driven winds of AGB stars we studied in detail the influence of (i) pulsations of the stellar interiors, and (ii) the development of dusty stellar winds on the spectral appearance of long period variables with carbon-rich atmospheric chemistry. While the pulsations lead to large-amplitude photometric variability, the dusty envelopes cause pronounced circumstellar reddening. Based on one selected dynamical model which is representative of C-type Mira variables with intermediate mass loss rates, we calculated synthetic spectra and photometry for standard broad-band filters from the visual to the near-infrared. Our modelling allows to investigate in detail the substantial effect of circumstellar dust on the resultant photometry. The pronounced absorption of amorphous carbon dust grains leads to colour indices which are significantly redder than the corresponding ones based on hydrostatic dust-free models. Only if we account for this circumstellar reddening we get synthetic colours that are comparable to observations of evolved AGB stars. The photometric variations of the dynamical model were compared to observed lightcurves of the C-type Mira RU_Vir which appears to be quite similar to the model. We found good agreement concerning the principal behaviour of the BVRIJHKL lightcurves and also quantitatively fitting details. The analysed model is able to reproduce the variations of RU_Vir and other Miras in (J-H) vs. (H-K) diagrams throughout the light cycle. Contrasting the model photometry with observational data for a variety of galactic C-rich giants in such colour-colour diagrams proved that the chosen atmospheric model fits well into a sequence of objects with increasing mass loss rates, i.e., redder colour indices.Comment: Accepted for publication in A&

Is Arcturus a well-understood K giant? Test of model atmospheres and potential companion detection by near-infrared interferometry

We present near-IR interferometric measurements of the K1.5 giant Arcturus (alpha Bootis), obtained at the IOTA interferometer with the FLUOR instrument, in four narrow filters with central wavelengths ranging from 2.03 to 2.39 micron. These observations were expected to allow us to quantify the wavelength dependence of the diameter of a typical K giant. They are compared to predictions from both plane-parallel and spherical model atmospheres. Unexpectedly, neither can explain the observed visibilities. We show how these data suggest the presence of a companion, in accordance with the Hipparcos data on this star, and discuss this solution with respect to Arcturus' single star status.Comment: 15 pages, 14 figures, accepted for publication by Astronomy & Astrophysic

A phase I study of the oral gamma secretase inhibitor R04929097 in combination with gemcitabine in patients with advanced solid tumors (PHL-078/CTEP 8575)

PURPOSE: To establish the recommended phase II dose of the oral γ-secretase inhibitor RO4929097 (RO) in combination with gemcitabine; secondary objectives include the evaluation of safety, tolerability, pharmacokinetics, biomarkers of Notch signaling and preliminary anti-tumor activity. METHODS: Patients with advanced solid tumors were enrolled in cohorts of escalating RO dose levels (DLs). Tested RO DLs were 20 mg, 30 mg, 45 mg and 90 mg. RO was administered orally, once daily on days 1-3, 8-10, 15-17, 22-24. Gemcitabine was administered at 1,000 mg/m(2) on d1, 8, and 15 in 28 d cycles. Dose limiting toxicities (DLTs) were assessed by CTCAE v4. Serial plasma was collected for RO (total and unbound) and gemcitabine pharmacokinetic analysis. Biomarkers of Notch signaling were assessed by immunohistochemistry in archival tissue. Antitumor activity was evaluated (RECIST 1.1). RESULTS: A total of 18 patients were enrolled to establish the recommended phase II dose. Of these, 3 patients received 20 mg RO, 7 patients received 30 mg RO, 6 patients received 45 mg RO and 2 patients received 90 mg RO. DLTs were grade 3 transaminitis (30 mg RO), grade 3 transaminitis and maculopapular rash (45 mg RO), and grade 3 transaminitis and failure to receive 75 % of planned RO doses secondary to prolonged neutropenia (90 mg); all were reversible. The maximum tolerated dose was exceeded at 90 mg RO. Pharmacokinetic analysis of both total and free RO confirmed the presence of autoinduction at 45 and 90 mg. Median levels of Notch3 staining were higher in individuals who received fewer than 4 cycles (p = 0.029). Circulating angiogenic factor levels did not correlate with time to progression or ≥ grade 3 adverse events. Best response (RECIST 1.1) was partial response (nasopharyngeal cancer) and stable disease > 4 months was observed in 3 patients (pancreas, tracheal, and breast primary cancers). CONCLUSIONS: RO and gemcitabine can be safely combined. The recommended phase II dose of RO was 30 mg in combination with gemcitabine 1,000 mg/m(2). Although RO exposure was limited by the presence of autoinduction, RO levels achieved exceeded the area under the concentration-time curve for 0-24 h (AUC(0-24)) predicted for efficacy in preclinical models using daily dosing. Evidence of clinical antitumor activity and prolonged stable disease were identified

The Impact of Advocacy Organizations on Low-Income Housing Policy in U.S. Cities

Financial support for affordable housing competes with many other municipal priorities. This work seeks to explain the variation in support for affordable housing among U.S. cities with populations of 100,000 or more. Using multivariate statistical analysis, this research investigates political explanations for the level of city expenditures on housing and community with a particular interest in the influence of housing advocacy organizations (AOs). Data for the model were gathered from secondary sources, including the U.S. Census and the National Center for Charitable Statistics. Among other results, the analysis indicates that, on average, the political maturity of AOs has a statistically significant, positive effect on local housing and community development expenditures

Neurodevelopmental and psychosocial risk factors in serial killers and mass murderers

Multiple and serial murders are rare events that have a very profound societal impact. We have conducted a systematic review, following PRISMA guidelines, of both the peer reviewed literature and of journalistic and legal sources regarding mass and serial killings. Our findings tentatively indicate that these extreme forms of violence may be a result of a highly complex interaction of biological, psychological and sociological factors and that, potentially, a significant proportion of mass or serial killers may have had neurodevelopmental disorders such as autism spectrum disorder or head injury. Research into multiple and serial murders is in its infancy: there is a lack of rigorous studies and most of the literature is anecdotal and speculative. Specific future study of the potential role of neurodevelopmental disorders in multiple and serial murders is warranted and, due to the rarity of these events, innovative research techniques may be required

The Changing Landscape for Stroke\ua0Prevention in AF: Findings From the GLORIA-AF Registry Phase 2

Background GLORIA-AF (Global Registry on Long-Term Oral Antithrombotic Treatment in Patients with Atrial Fibrillation) is a prospective, global registry program describing antithrombotic treatment patterns in patients with newly diagnosed nonvalvular atrial fibrillation at risk of stroke. Phase 2 began when dabigatran, the first non\u2013vitamin K antagonist oral anticoagulant (NOAC), became available. Objectives This study sought to describe phase 2 baseline data and compare these with the pre-NOAC era collected during phase 1. Methods During phase 2, 15,641 consenting patients were enrolled (November 2011 to December 2014); 15,092 were eligible. This pre-specified cross-sectional analysis describes eligible patients\u2019 baseline characteristics. Atrial fibrillation disease characteristics, medical outcomes, and concomitant diseases and medications were collected. Data were analyzed using descriptive statistics. Results Of the total patients, 45.5% were female; median age was 71 (interquartile range: 64, 78) years. Patients were from Europe (47.1%), North America (22.5%), Asia (20.3%), Latin America (6.0%), and the Middle East/Africa (4.0%). Most had high stroke risk (CHA2DS2-VASc [Congestive heart failure, Hypertension, Age  6575 years, Diabetes mellitus, previous Stroke, Vascular disease, Age 65 to 74 years, Sex category] score  652; 86.1%); 13.9% had moderate risk (CHA2DS2-VASc = 1). Overall, 79.9% received oral anticoagulants, of whom 47.6% received NOAC and 32.3% vitamin K antagonists (VKA); 12.1% received antiplatelet agents; 7.8% received no antithrombotic treatment. For comparison, the proportion of phase 1 patients (of N = 1,063 all eligible) prescribed VKA was 32.8%, acetylsalicylic acid 41.7%, and no therapy 20.2%. In Europe in phase 2, treatment with NOAC was more common than VKA (52.3% and 37.8%, respectively); 6.0% of patients received antiplatelet treatment; and 3.8% received no antithrombotic treatment. In North America, 52.1%, 26.2%, and 14.0% of patients received NOAC, VKA, and antiplatelet drugs, respectively; 7.5% received no antithrombotic treatment. NOAC use was less common in Asia (27.7%), where 27.5% of patients received VKA, 25.0% antiplatelet drugs, and 19.8% no antithrombotic treatment. Conclusions The baseline data from GLORIA-AF phase 2 demonstrate that in newly diagnosed nonvalvular atrial fibrillation patients, NOAC have been highly adopted into practice, becoming more frequently prescribed than VKA in Europe and North America. Worldwide, however, a large proportion of patients remain undertreated, particularly in Asia and North America. (Global Registry on Long-Term Oral Antithrombotic Treatment in Patients With Atrial Fibrillation [GLORIA-AF]; NCT01468701