lp-Recovery of the Most Significant Subspace among Multiple Subspaces with Outliers

We assume data sampled from a mixture of d-dimensional linear subspaces with spherically symmetric distributions within each subspace and an additional outlier component with spherically symmetric distribution within the ambient space (for simplicity we may assume that all distributions are uniform on their corresponding unit spheres). We also assume mixture weights for the different components. We say that one of the underlying subspaces of the model is most significant if its mixture weight is higher than the sum of the mixture weights of all other subspaces. We study the recovery of the most significant subspace by minimizing the lp-averaged distances of data points from d-dimensional subspaces, where p>0. Unlike other lp minimization problems, this minimization is non-convex for all p>0 and thus requires different methods for its analysis. We show that if 0<p<=1, then for any fraction of outliers the most significant subspace can be recovered by lp minimization with overwhelming probability (which depends on the generating distribution and its parameters). We show that when adding small noise around the underlying subspaces the most significant subspace can be nearly recovered by lp minimization for any 0<p<=1 with an error proportional to the noise level. On the other hand, if p>1 and there is more than one underlying subspace, then with overwhelming probability the most significant subspace cannot be recovered or nearly recovered. This last result does not require spherically symmetric outliers.Comment: This is a revised version of the part of 1002.1994 that deals with single subspace recovery. V3: Improved estimates (in particular for Lemma 3.1 and for estimates relying on it), asymptotic dependence of probabilities and constants on D and d and further clarifications; for simplicity it assumes uniform distributions on spheres. V4: minor revision for the published versio

Exploring the canonical behaviour of long gamma-ray bursts using an intrinsic multiwavelength afterglow correlation

In this paper, we further investigate the relationship, reported by Oates et al., between the optical/UV afterglow luminosity (measured at restframe 200 s) and average afterglow decay rate (measured from restframe 200 s onwards) of long duration gamma-ray bursts (GRBs). We extend the analysis by examining the X-ray light curves, finding a consistent correlation. We therefore explore how the parameters of these correlations relate to the prompt emission phase and, using a Monte Carlo simulation, explore whether these correlations are consistent with predictions of the standard afterglow model. We find significant correlations between: log  LO, 200 s and log  LX, 200 s; αO, >200 s and αX, >200 s, consistent with simulations. The model also predicts relationships between log Eiso and log  L200 s; however, while we find such relationships in the observed sample, the slope of the linear regression is shallower than that simulated and inconsistent at ≳3σ. Simulations also do not agree with correlations observed between log  L200 s and α> 200 s, or logEiso logEiso and α> 200 s. Overall, these observed correlations are consistent with a common underlying physical mechanism producing GRBs and their afterglows regardless of their detailed temporal behaviour. However, a basic afterglow model has difficulty explaining all the observed correlations. This leads us to briefly discuss alternative more complex models

Exploring the canonical behaviour of long gamma-ray bursts with an intrinsic multiwavelength afterglow correlation

In this conference proceeding we examine a correlation between the afterglow luminosity (measured at restframe 200 s; logL200s) and average afterglow decay rate (measured from restframe 200 s onwards; α>200s) found in both the optical/UV and X-ray afterglows of long duration Gamma-ray Bursts (GRBs). Examining the X-ray light curves, we find the correlation does not depend on the presence of specific light curve features. We explore how the parameters in the optical/UV and X-ray bands relate to each other and to the prompt emission phase. We also use a Monte Carlo simulation to explore whether these relationships are consistent with predictions of the standard afterglow model. We conclude that the correlations are consistent with a common underlying physical mechanism producing GRBs and their afterglows regardless of their detailed temporal behaviour. However, a basic afterglow model has difficulty explaining correlations involving α>200s. We therefore briefly discuss alternative more complex models

Electronic Spin Transport in Dual-Gated Bilayer Graphene

The elimination of extrinsic sources of spin relaxation is key in realizing the exceptional intrinsic spin transport performance of graphene. Towards this, we study charge and spin transport in bilayer graphene-based spin valve devices fabricated in a new device architecture which allows us to make a comparative study by separately investigating the roles of substrate and polymer residues on spin relaxation. First, the comparison between spin valves fabricated on SiO2 and BN substrates suggests that substrate-related charged impurities, phonons and roughness do not limit the spin transport in current devices. Next, the observation of a 5-fold enhancement in spin relaxation time in the encapsulated device highlights the significance of polymer residues on spin relaxation. We observe a spin relaxation length of ~ 10 um in the encapsulated bilayer with a charge mobility of 24000 cm2/Vs. The carrier density dependence of spin relaxation time has two distinct regimes; n<4 x 1012 cm-2, where spin relaxation time decreases monotonically as carrier concentration increases, and n>4 x 1012 cm-2, where spin relaxation time exhibits a sudden increase. The sudden increase in the spin relaxation time with no corresponding signature in the charge transport suggests the presence of a magnetic resonance close to the charge neutrality point. We also demonstrate, for the first time, spin transport across bipolar p-n junctions in our dual-gated device architecture that fully integrates a sequence of encapsulated regions in its design. At low temperatures, strong suppression of the spin signal was observed while a transport gap was induced, which is interpreted as a novel manifestation of impedance mismatch within the spin channel

Diffusion microscopic MRI of the mouse embryo: Protocol and practical implementation in the splotch mouse model

Advanced methodologies for visualizing novel tissue contrast are essential for phenotyping the ever-increasing number of mutant mouse embryos being generated. Although diffusion microscopic MRI (μMRI) has been used to phenotype embryos, widespread routine use is limited by extended scanning times, and there is no established experimental procedure ensuring optimal data acquisition

Simple models of the chemical field around swimming plankton

Background. Cervical cancer is the fourth most common cancer in women, and we recently reported human leukocyte antigen (HLA) alleles showing strong associations with cervical neoplasia risk and protection. HLA ligands are recognized by killer immunoglobulin-like receptors (KIRs) expressed on a range of immune cell subsets, governing their proinflammatory activity. We hypothesized that the inheritance of particular HLA-KIR combinations would increase cervical neoplasia risk. Methods. Here, we used HLA and KIR dosages imputed from single-nucleotide polymorphism genotype data from 2143 cervical neoplasia cases and 13 858 healthy controls of European decent. Results. The following 4 novel HLA alleles were identified in association with cervical neoplasia, owing to their linkage disequilibrium with known cervical neoplasia-associated HLA-DRB1 alleles: HLA-DRB3*9901 (odds ratio [OR], 1.24; P = 2.49 × 10−9), HLA-DRB5*0101 (OR, 1.29; P = 2.26 × 10−8), HLA-DRB5*9901 (OR, 0.77; P = 1.90 × 10−9), and HLA-DRB3*0301 (OR, 0.63; P = 4.06 × 10−5). We also found that homozygosity of HLA-C1 group alleles is a protective factor for human papillomavirus type 16 (HPV16)-related cervical neoplasia (C1/C1; OR, 0.79; P = .005). This protective association was restricted to carriers of either KIR2DL2 (OR, 0.67; P = .00045) or KIR2DS2 (OR, 0.69; P = .0006). Conclusions. Our findings suggest that HLA-C1 group alleles play a role in protecting against HPV16-related cervical neoplasia, mainly through a KIR-mediated mechanism

Entropy of three-dimensional asymptotically flat cosmological solutions

The thermodynamics of three-dimensional asymptotically flat cosmological solutions that play the same role than the BTZ black holes in the anti-de Sitter case is derived and explained from holographic properties of flat space. It is shown to coincide with the flat-space limit of the thermodynamics of the inner black hole horizon on the one hand and the semi-classical approximation to the gravitational partition function associated to the entropy of the outer horizon on the other. This leads to the insight that it is the Massieu function that is universal in the sense that it can be computed at either horizon.Comment: 16 pages Latex file, v2: references added, cosmetic changes, v3: 1 reference adde

Investigating the impact of poverty on colonization and infection with drug-resistant organisms in humans: a systematic review

Background Poverty increases the risk of contracting infectious diseases and therefore exposure to antibiotics. Yet there is lacking evidence on the relationship between income and non-income dimensions of poverty and antimicrobial resistance. Investigating such relationship would strengthen antimicrobial stewardship interventions. Methods A systematic review was conducted following Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines. PubMed, Ovid, MEDLINE, EMBASE, Scopus, CINAHL, PsychINFO, EBSCO, HMIC, and Web of Science databases were searched in October 2016. Prospective and retrospective studies reporting on income or non-income dimensions of poverty and their influence on colonisation or infection with antimicrobial-resistant organisms were retrieved. Study quality was assessed with the Integrated quality criteria for review of multiple study designs (ICROMS) tool. Results Nineteen articles were reviewed. Crowding and homelessness were associated with antimicrobial resistance in community and hospital patients. In high-income countries, low income was associated with Streptococcus pneumoniae and Acinetobacter baumannii resistance and a seven-fold higher infection rate. In low-income countries the findings on this relation were contradictory. Lack of education was linked to resistant S. pneumoniae and Escherichia coli. Two papers explored the relation between water and sanitation and antimicrobial resistance in low-income settings. Conclusions Despite methodological limitations, the results suggest that addressing social determinants of poverty worldwide remains a crucial yet neglected step towards preventing antimicrobial resistance