Super-resolution, Extremal Functions and the Condition Number of Vandermonde Matrices

Super-resolution is a fundamental task in imaging, where the goal is to extract fine-grained structure from coarse-grained measurements. Here we are interested in a popular mathematical abstraction of this problem that has been widely studied in the statistics, signal processing and machine learning communities. We exactly resolve the threshold at which noisy super-resolution is possible. In particular, we establish a sharp phase transition for the relationship between the cutoff frequency ($m$) and the separation ($\Delta$). If $m > 1/\Delta + 1$, our estimator converges to the true values at an inverse polynomial rate in terms of the magnitude of the noise. And when $m < (1-\epsilon) /\Delta$ no estimator can distinguish between a particular pair of $\Delta$-separated signals even if the magnitude of the noise is exponentially small. Our results involve making novel connections between {\em extremal functions} and the spectral properties of Vandermonde matrices. We establish a sharp phase transition for their condition number which in turn allows us to give the first noise tolerance bounds for the matrix pencil method. Moreover we show that our methods can be interpreted as giving preconditioners for Vandermonde matrices, and we use this observation to design faster algorithms for super-resolution. We believe that these ideas may have other applications in designing faster algorithms for other basic tasks in signal processing.Comment: 19 page

Is hazard perception ability culturally specific? A cross-cultural comparison between China, Spain and the UK

Hazard perception refers to a driver’s ability to spot hazards on the road in time to make a safe manoeuvre to avoid collision. Such a test is now part of the formal licencing procedure in the UK and in parts of Australia. But can such tests be successfully exported to other countries to reduce traffic fatalities? The aim of this project is to study whether hazard perception skill is culturally specific by comparing UK, Spanish and Chinese drivers across clips filmed in all three countries. Data collection was set-up in the respective countries in collaboration with the University of Granada (Spain) and Tsinghua University (China). Participants had to watch 30 video clips filmed from the driver’s perspective (10 filmed in each of the three countries). Two variants of the test were created: a typical hazard perception test (with full clips requiring speeded responses to hazards), and a hazard prediction task (or 'What Happens Next?' task), where the film ends immediately prior to the hazard onset. This latter test removes the confound of individual hazard thresholds, as participants could successfully report 'what happens next' without judging whether it posed a hazard to them. All videos contained a variety of hazardous situations (or precursors to hazards) reflecting the particular driving environment of each country. Three hundred participants across the 3 countries were tested, evenly divided between learner and experienced drivers. The differences between the culturally-specific tests in their ability to discriminate between driver groups will be discussed in regards to the potential for employing hazard perception testing in diverse geographical locations and cultures

Effects of trade barriers on development and growth

A basic definition of trade barriers could be ‘all factors that influence the amount of goods and services shipped across international borders’ (Feenstra and Taylor, 2017a). This definition is quite neutral, and it needs to be understood that the word ‘barrier’ has a negative connotation, which means that a trade barrier would be any instrument that limits or restrict trade between countries, as opposed to free trade. It is generally accepted that free trade is good for productivity and economic growth, but it is also true that most countries apply some sort of trade restriction, for different reasons

Mindfulness-based stress reduction in Parkinson’s disease: a systematic review

Background: Mindfulness based stress reduction (MBSR) is increasingly being used to improve outcomes such as stress and depression in a range of long-term conditions (LTCs). While systematic reviews on MBSR have taken place for a number of conditions there remains limited information on its impact on individuals with Parkinson’s disease (PD). Methods: Medline, Central, Embase, Amed, CINAHAL were searched in March 2016. These databases were searched using a combination of MeSH subject headings where available and keywords in the title and abstracts. We also searched the reference lists of related reviews. Study quality was assessed based on questions from the Cochrane Collaboration risk of bias tool. Results: Two interventions and three papers with a total of 66 participants were included. The interventions were undertaken in Belgium (n = 27) and the USA (n = 39). One study reported significantly increased grey matter density (GMD) in the brains of the MBSR group compared to the usual care group. Significant improvements were reported in one study for a number of outcomes including PD outcomes, depression, mindfulness, and quality of life indicators. Only one intervention was of reasonable quality and both interventions failed to control for potential confounders in the analysis. Adverse events and reasons for drop-outs were not reported. There was also no reporting on the costs/benefits of the intervention or how they affected health service utilisation. Conclusion: This systematic review found limited and inconclusive evidence of the effectiveness of MBSR for PD patients. Both of the included interventions claimed positive effects for PD patients but significant outcomes were often contradicted by other results. Further trials with larger sample sizes, control groups and longer follow-ups are needed before the evidence for MBSR in PD can be conclusively judged

Distribution of Capillary Transit Times in Isolated Lungs of Oxygen-Tolerant Rats

Rats pre-exposed to 85% O2 for 5–7 days tolerate the otherwise lethal effects of 100% O2. The objective was to evaluate the effect of rat exposure to 85% O2 for 7 days on lung capillary mean transit time (t¯c) and distribution of capillary transit times (h c(t)). This information is important for subsequent evaluation of the effect of this hyperoxia model on the redox metabolic functions of the pulmonary capillary endothelium. The venous concentration vs. time outflow curves of fluorescein isothiocyanate labeled dextran (FITC-dex), an intravascular indicator, and coenzyme Q1 hydroquinone (CoQ1H2), a compound which rapidly equilibrates between blood and tissue on passage through the pulmonary circulation, were measured following their bolus injection into the pulmonary artery of isolated perfused lungs from rats exposed to room air (normoxic) or 85% O2 for 7 days (hyperoxic). The moments (mean transit time and variance) of the measured FITC-dex and CoQ1H2 outflow curves were determined for each lung, and were then used in a mathematical model [Audi et al. J. Appl. Physiol. 77: 332–351, 1994] to estimate t¯c and the relative dispersion (RDc) of h c(t). Data analysis reveals that exposure to hyperoxia decreases lung t¯c by 42% and increases RDc, a measure h c(t) heterogeneity, by 40%

Phenotypic spectrum associated with de novo and inherited deletions and duplications at 16p11.2 in individuals ascertained for diagnosis of autism spectrum disorder

Background Recurrent microdeletions and microduplications of w555 kb at 16p11.2 confer susceptibility to autism spectrum disorder (ASD) in up to 1% of ASD patients. No physical or behavioural features have been identified that distinguish these individuals as having a distinct ASD subtype, but clinical data are limited. Methods We report five autistic probands identified by microarray analysis with copy number variation (CNV) of 16p11.2 (three deletions, two duplications). Each patient was assessed for ASD and dysmorphic features. We also describe a deletion positive 26-month-old female who has developmental delay (DD) and autistic features. Results Proband 1 (female with ASD, de novo deletion) is not dysmorphic. Proband 2 (male with autism, de novo deletion) and proband 3 and his brother (males with autism, inherited deletions) are dysmorphic, but the two probands do not resemble one another. The mother of proband 3 has mild mental retardation (MR), minor dysmorphism and meets the criteria for ASD. Proband 4 (dysmorphic autistic male, de novo duplication) had a congenital diaphragmatic hernia. Proband 5 (nondysmorphic ASD female with a duplication) has two apparently healthy duplication positive relatives. Probands 1 and 2 have deletion negative siblings with ASD and Asperger syndrome, respectively. Proband 6 (a female with DD and an inherited duplication) is dysmorphic, but has oligohydramnios sequence. Conclusions The phenotypic spectrum associated with CNV at 16p11.2 includes ASD, MR/DD and/or possibly other primary psychiatric disorders. Compared with the microduplications, the reciprocal microdeletions are more likely to be penetrant and to be associated with nonspecific major or minor dysmorphism. There are deletion positive ASD probands with a less severe phenotype than deletion negative ASD siblings underscoring the significant phenotypic heterogeneity.published_or_final_versio

Clostridium perfringens epsilon toxin increases the small intestinal permeability in mice and rats

Epsilon toxin is a potent neurotoxin produced by Clostridium perfringens types B and D, an anaerobic bacterium that causes enterotoxaemia in ruminants. In the affected animal, it causes oedema of the lungs and brain by damaging the endothelial cells, inducing physiological and morphological changes. Although it is believed to compromise the intestinal barrier, thus entering the gut vasculature, little is known about the mechanism underlying this process. This study characterizes the effects of epsilon toxin on fluid transport and bioelectrical parameters in the small intestine of mice and rats. The enteropooling and the intestinal loop tests, together with the single-pass perfusion assay and in vitro and ex vivo analysis in Ussing's chamber, were all used in combination with histological and ultrastructural analysis of mice and rat small intestine, challenged with or without C. perfringens epsilon toxin. Luminal epsilon toxin induced a time and concentration dependent intestinal fluid accumulation and fall of the transepithelial resistance. Although no evident histological changes were observed, opening of the mucosa tight junction in combination with apoptotic changes in the lamina propria were seen with transmission electron microscopy. These results indicate that C. perfringens epsilon toxin alters the intestinal permeability, predominantly by opening the mucosa tight junction, increasing its permeability to macromolecules, and inducing further degenerative changes in the lamina propria of the bowel. © 2009 Goldstein et al