Exact Matrix Product States for Quantum Hall Wave Functions

We show that the model wave functions used to describe the fractional quantum Hall effect have exact representations as matrix product states (MPS). These MPS can be implemented numerically in the orbital basis of both finite and infinite cylinders, which provides an efficient way of calculating arbitrary observables. We extend this approach to the charged excitations and numerically compute their Berry phases. Finally, we present an algorithm for numerically computing the real-space entanglement spectrum starting from an arbitrary orbital basis MPS, which allows us to study the scaling properties of the real-space entanglement spectra on infinite cylinders. The real-space entanglement spectrum obeys a scaling form dictated by the edge conformal field theory, allowing us to accurately extract the two entanglement velocities of the Moore-Read state. In contrast, the orbital space spectrum is observed to scale according to a complex set of power laws that rule out a similar collapse.Comment: 10 pages and Appendix, v3 published versio

Search for 2νββ decay of ^(136)Xe to the 0^+^1 excited state of ^(136)Ba with the EXO-200 liquid xenon detector

EXO-200 is a single phase liquid xenon detector designed to search for neutrinoless ββ decay of ^(136)Xe to the ground state of ^(136)Ba. We report here on a search for the two-neutrino ββ decay of 136Xe to the first 0+ excited state, 0^+_1, of ^(136)Ba based on a 100 kg yr exposure of ^(136)Xe. Using a specialized analysis employing a machine learning algorithm, we obtain a 90% CL half-life sensitivity of 1.7 × 10^(24) yr. We find no statistically significant evidence for the 2νββ decay to the excited state resulting in a lower limit of T^(2ν)_(1/2)(0^+ → 0^+_1) > 6.9 ×10^(23) yr at 90% CL. This observed limit is consistent with the estimated half-life of 2.5 × 10^(25) yr

A simple proof of the Markoff conjecture for prime powers

We give a simple and independent proof of the result of Jack Button and Paul Schmutz that the Markoff conjecture on the uniqueness of the Markoff triples (a,b,c), where a, b, and c are in increasing order, holds whenever $c$ is a prime power.Comment: 5 pages, no figure

Improving the diagnosis management and outcomes of children with pneumonia where are the gaps

Pneumonia is the greatest contributor to childhood mortality and morbidity in resource poor regions, while in high-income countries it is one of the most common reasons for clinic attendance and hospitalization in this age group. Furthermore, pneumonia in children increases the risk of developing chronic pulmonary disorders in later adult life. While substantial advances in managing childhood pneumonia have been made, many issues remain, some of which are highlighted in this perspective. Multiple studies are required as many factors that influence outcomes, such as etiology, patient characteristics, and prevention strategies can vary between and within countries and regions. Also, outside of vaccine studies, most randomized controlled trials (RCTs) on pneumonia have been based in resource-poor countries where the primary aim is usually prevention of mortality. Few RCTs have focused on medium to long-term outcomes or prevention. We propose different tiers of primary outcomes, where in resource-rich countries medium to long-term sequelae should also be included and not just the length of hospitalization and readmission rates

Metabolic labelling of cholesteryl glucosides in Helicobacter pylori reveals how the uptake of human lipids enhances bacterial virulence.

Helicobacter pylori infects approximately half of the human population and is the main cause of various gastric diseases. This pathogen is auxotrophic for cholesterol, which it converts upon uptake to various cholesteryl α-glucoside derivatives, including cholesteryl 6'-acyl and 6'-phosphatidyl α-glucosides (CAGs and CPGs). Owing to a lack of sensitive analytical methods, it is not known if CAGs and CPGs play distinct physiological roles or how the acyl chain component affects function. Herein we established a metabolite-labelling method for characterising these derivatives qualitatively and quantitatively with a femtomolar detection limit. The development generated an MS/MS database of CGds, allowing for profiling of all the cholesterol-derived metabolites. The subsequent analysis led to the unprecedented information that these bacteria acquire phospholipids from the membrane of epithelial cells for CAG biosynthesis. The resulting increase in longer or/and unsaturated CAG acyl chains helps to promote lipid raft formation and thus delivery of the virulence factor CagA into the host cell, supporting the idea that the host/pathogen interplay enhances bacterial virulence. These findings demonstrate an important connection between the chain length of CAGs and the bacterial pathogenicity

Competing Abelian and non-Abelian topological orders in ν=1/3+1/3 quantum Hall bilayers

Bilayer quantum Hall systems, realized either in two separated wells or in the lowest two subbands of a wide quantum well, provide an experimentally realizable way to tune between competing quantum orders at the same filling fraction. Using newly developed density matrix renormalization group techniques combined with exact diagonalization, we return to the problem of quantum Hall bilayers at filling ν=1/3+1/3. We first consider the Coulomb interaction at bilayer separation d, bilayer tunneling energy ΔSAS, and individual layer width w, where we find a phase diagram which includes three competing Abelian phases: a bilayer Laughlin phase (two nearly decoupled ν=1/3 layers), a bilayer spin-singlet phase, and a bilayer symmetric phase. We also study the order of the transitions between these phases. A variety of non-Abelian phases has also been proposed for these systems. While absent in the simplest phase diagram, by slightly modifying the interlayer repulsion we find a robust non-Abelian phase which we identify as the "interlayer-Pfaffian" phase. In addition to non-Abelian statistics similar to the Moore-Read state, it exhibits a novel form of bilayer-spin charge separation. Our results suggest that ν=1/3+1/3 systems merit further experimental study

CheXpert: A Large Chest Radiograph Dataset with Uncertainty Labels and Expert Comparison

Large, labeled datasets have driven deep learning methods to achieve expert-level performance on a variety of medical imaging tasks. We present CheXpert, a large dataset that contains 224,316 chest radiographs of 65,240 patients. We design a labeler to automatically detect the presence of 14 observations in radiology reports, capturing uncertainties inherent in radiograph interpretation. We investigate different approaches to using the uncertainty labels for training convolutional neural networks that output the probability of these observations given the available frontal and lateral radiographs. On a validation set of 200 chest radiographic studies which were manually annotated by 3 board-certified radiologists, we find that different uncertainty approaches are useful for different pathologies. We then evaluate our best model on a test set composed of 500 chest radiographic studies annotated by a consensus of 5 board-certified radiologists, and compare the performance of our model to that of 3 additional radiologists in the detection of 5 selected pathologies. On Cardiomegaly, Edema, and Pleural Effusion, the model ROC and PR curves lie above all 3 radiologist operating points. We release the dataset to the public as a standard benchmark to evaluate performance of chest radiograph interpretation models. The dataset is freely available at https://stanfordmlgroup.github.io/competitions/chexpert .Comment: Published in AAAI 201