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

Pathways to Care: Duration of Untreated Psychosis from Karachi, Pakistan

Background: Substantial amount of time is lost before initiation of treatment in Schizophrenia. The delay in treatment is labelled as Duration of Untreated Psychosis (DUP). Most of these estimates come from western countries, where health systems are relatively better developed. There is dearth of information on pathway to care from developing countries. Methods And Results: Patients with ICD-10 based diagnosis of Schizophrenia were enrolled by convenient method of sampling. The pathway to care was explored through a semi-structured questionnaire. Onset, course and symptoms of psychosis were assessed using Interview for the Retrospective Assessment of the Onset of Schizophrenia (IRAOS). Ethical approval of the project was taken from The Aga Khan University, Ethics Review Committee. Of the enrolled 93 subjects, 55 (59%) were males and 38 (41%) were females. In our sample, 1.56 mean (median, 2) attempts were made prior to successful help seeking. The duration of untreated psychosis was 14.8 months (St. Deviation, 29.4). DUP was 16.8 months (St. Deviation, 34.9) for males and 11.8 months (St. Deviation, 18.9) for females. In the pathway to care, psychiatrists featured prominently as initial care providers. In the first attempt at help-seeking, 43% Patients were initially taken to psychiatrists. After the initial consultation, 45% were prescribed psychotropic medication while 7% were hospitalized. Only 9% subjects were given the diagnosis of schizophrenia initially. When participants were inquired about the reasons for delay, 29% reported financial difficulties as the barrier to care. Positive symptoms of psychosis were present in 57% subjects while negative symptoms were present in 30% subjects. There was a statistically significant difference (Chi-square, 7.928, df: 1, Sig 0.005) between DUP and the positive and negative symptoms category. Conclusion: In the absence of well developed primary care health system in Pakistan, majority of Patients present to psychiatrists as a first contact. DUP, as a measurement of help seeking behaviour, tends to be shorter with positive symptoms of Schizophrenia. Substantial amount of time is lost due to non recognition of disease and subsequently, inadequate treatment. Secondary prevention strategies should focus on families, which play an important role in the treatment-seeking process of psychotic Patients

Separation of Oligosaccharides from Lotus Seeds via Medium-pressure Liquid Chromatography Coupled with ELSD and DAD

peer-reviewedLotus seeds were identified by the Ministry of Public Health of China as both food and medicine. One general function of lotus seeds is to improve intestinal health. However, to date, studies evaluating the relationship between bioactive compounds in lotus seeds and the physiological activity of the intestine are limited. In the present study, by using medium pressure liquid chromatography coupled with evaporative light-scattering detector and diode-array detector, five oligosaccharides were isolated and their structures were further characterized by electrospray ionization-mass spectrometry and gas chromatography-mass spectrometry. In vitro testing determined that LOS3-1 and LOS4 elicited relatively good proliferative effects on Lactobacillus delbrueckii subsp. bulgaricus. These results indicated a structure-function relationship between the physiological activity of oligosaccharides in lotus seeds and the number of probiotics applied, thus providing room for improvement of this particular feature. Intestinal probiotics may potentially become a new effective drug target for the regulation of immunity

An Adaptive Sublinear-Time Block Sparse Fourier Transform

The problem of approximately computing the $k$ dominant Fourier coefficients of a vector $X$ quickly, and using few samples in time domain, is known as the Sparse Fourier Transform (sparse FFT) problem. A long line of work on the sparse FFT has resulted in algorithms with $O(k\log n\log (n/k))$ runtime [Hassanieh \emph{et al.}, STOC'12] and $O(k\log n)$ sample complexity [Indyk \emph{et al.}, FOCS'14]. These results are proved using non-adaptive algorithms, and the latter $O(k\log n)$ sample complexity result is essentially the best possible under the sparsity assumption alone: It is known that even adaptive algorithms must use $\Omega((k\log(n/k))/\log\log n)$ samples [Hassanieh \emph{et al.}, STOC'12]. By {\em adaptive}, we mean being able to exploit previous samples in guiding the selection of further samples. This paper revisits the sparse FFT problem with the added twist that the sparse coefficients approximately obey a $(k_0,k_1)$-block sparse model. In this model, signal frequencies are clustered in $k_0$ intervals with width $k_1$ in Fourier space, and $k= k_0k_1$ is the total sparsity. Signals arising in applications are often well approximated by this model with $k_0\ll k$. Our main result is the first sparse FFT algorithm for $(k_0, k_1)$-block sparse signals with a sample complexity of $O^*(k_0k_1 + k_0\log(1+ k_0)\log n)$ at constant signal-to-noise ratios, and sublinear runtime. A similar sample complexity was previously achieved in the works on {\em model-based compressive sensing} using random Gaussian measurements, but used $\Omega(n)$ runtime. To the best of our knowledge, our result is the first sublinear-time algorithm for model based compressed sensing, and the first sparse FFT result that goes below the $O(k\log n)$ sample complexity bound. Interestingly, the aforementioned model-based compressive sensing result that relies on Gaussian measurements is non-adaptive, whereas our algorithm crucially uses {\em adaptivity} to achieve the improved sample complexity bound. We prove that adaptivity is in fact necessary in the Fourier setting: Any {\em non-adaptive} algorithm must use $\Omega(k_0k_1\log \frac{n}{k_0k_1})$ samples for the $(k_0,k_1$)-block sparse model, ruling out improvements over the vanilla sparsity assumption. Our main technical innovation for adaptivity is a new randomized energy-based importance sampling technique that may be of independent interest

A Randomized Trial of Intravenous Iron Supplementation and Exercise on Exercise Capacity in Iron-Deficient Nonanemic Patients With CKD

Introduction: Patients with chronic kidney disease (CKD) are often iron deficient, even when not anemic. This trial evaluated whether iron supplementation enhances exercise capacity of nonanemic patients with CKD who have iron-deficiency. Methods: Prospective, multicenter double-blind randomized controlled trial of nondialysis patients with CKD and iron-deficiency but without anemia (Hemoglobin [Hb] >110 g/l). Patients were assigned 1:1 to intravenous (IV) iron therapy, or placebo. An 8-week exercise program commenced at week 4. The primary outcome was the mean between-group difference in 6-minute walk test (6MWT) at 4 weeks. Secondary outcomes included 6MWT at 12 weeks, transferrin saturation (TSAT), serum ferritin (SF), Hb, renal function, muscle strength, functional capacity, quality of life, and adverse events at baseline, 4 weeks, and at 12 weeks. Mean between-group differences were analyzed using analysis of covariance models. Results: Among 75 randomized patients, mean (SD) age for iron therapy (n = 37) versus placebo (n = 38) was 54 (16) versus 61 (12) years; estimated glomerular filtration rate (eGFR) (34 [12] vs. 35 [11] ml/min per 1.73 m2], TSAT (23 [12] vs. 21 [6])%; SF (57 [64] vs. 62 [33]) μg/l; Hb (122.4 [9.2] vs. 127 [13.2] g/l); 6MWT (384 [95] vs. 469 [142] meters) at baseline, respectively. No significant mean between-group difference was observed in 6MWT distance at 4 weeks. There were significant increases in SF and TSAT at 4 and 12 weeks (P < 0.02), and Hb at 12 weeks (P = 0.009). There were no between-group differences in other secondary outcomes and no adverse events attributable to iron therapy. Conclusion: This trial did not demonstrate beneficial effects of IV iron therapy on exercise capacity at 4 weeks. A larger study is needed to confirm if IV iron is beneficial in nondialysis patients with CKD who are iron-deficient

Production of π0 and η mesons in Cu+Au collisions at sNN =200 GeV

Production of π0 and η mesons has been measured at midrapidity in Cu+Au collisions at sNN=200GeV. Measurements were performed in π0(η)→γγ decay channel in the 1(2)-20GeV/c transverse momentum range. A strong suppression is observed for π0 and η meson production at high transverse momentum in central Cu+Au collisions relative to the p+p results scaled by the number of nucleon-nucleon collisions. In central collisions the suppression is similar to Au+Au with comparable nuclear overlap. The η/π0 ratio measured as a function of transverse momentum is consistent with mT-scaling parametrization down to pT=2GeV/c, its asymptotic value is constant and consistent with Au+Au and p+p and does not show any significant dependence on collision centrality. Similar results were obtained in hadron-hadron, hadron-nucleus, and nucleus-nucleus collisions as well as in e+e- collisions in a range of collision energies sNN=3-1800 GeV. This suggests that the quark-gluon-plasma medium produced in Cu+Cu collisions either does not affect the jet fragmentation into light mesons or it affects the π0 and η the same way

Common risk factor approach to address socioeconomic inequality in the oral health of preschool children – a prospective cohort study

Background: Dental caries remains the most prevalent chronic condition in children and a major contributor to poor general health. There is ample evidence of a skewed distribution of oral health, with a small proportion of children in the population bearing the majority of the burden of the disease. This minority group is comprised disproportionately of socioeconomically disadvantaged children. An in-depth longitudinal study is needed to better understand the determinants of child oral health, in order to support effective evidence-based policies and interventions in improving child oral health. The aim of the Study of Mothers’ and Infants’ Life Events Affecting Oral Health (SMILE) project is to identify and evaluate the relative importance and timing of critical factors that shape the oral health of young children and then to seek to evaluate those factors in their inter-relationship with socioeconomic influences.Methods/Design: This investigation will apply an observational prospective study design to a cohort ofsocioeconomically-diverse South Australian newborns and their mothers, intensively following these dyads as the children grow to toddler age. Mothers of newborn children will be invited to participate in the study in the early post-partum period. At enrolment, data will be collected on parental socioeconomic status, mothers’ general and dental health conditions, details of the pregnancy, infant feeding practice and parental health behaviours and practices. Data on diet and feeding practices, oral health behaviours and practices, and dental visiting patterns will be collected at 3, 6, 12 and 24 months of age. When children turn 24-30 months, the children and their mothers/primary care givers will be invited to an oral examination to record oral health status. Anthropometric assessment will also be conducted.Discussion: This prospective cohort study will examine a wide range of determinants influencing child oral health and related general conditions such as overweight. It will lead to the evaluation of the inter-relationship among main influences and their relative effect on child oral health. The study findings will provide high level evidence of pathways through which socio-environmental factors impact child oral health. It will also provide an opportunity to examine the relationship between oral health and childhood overweight.Discussion: This prospective cohort study will examine a wide range of determinants influencing child oral health and related general conditions such as overweight. It will lead to the evaluation of the inter-relationship among main influences and their relative effect on child oral health. The study findings will provide high level evidence of pathways through which socio-environmental factors impact child oral health. It will also provide an to examine the relationship between oral health and childhood overweight