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t-distributed stochastic neighborhood embedding (t-SNE), a clustering and visualization method proposed by van der Maaten and Hinton in 2008, has rapidly become a standard tool in the natural sciences. Despite its overwhelming success, it has a distinct lack of mathematical foundations and the inner workings of the algorithm are not well understood. The purpose of this paper is to prove that t-SNE is able to recover well-separated clusters. As a by-product, the proof suggests that t-SNE is merely one of many possible algorithms of a large family of methods generated by dynamical systems--this perspective suggests new questions and problems, some of which we discuss. [ABSTRACT FROM AUTHOR]

Let G = (V,E,w) be a finite, connected graph with weighted edges. We are interested in the problem of finding a subset W ⊂ V of vertices and weights aw such that 1/|V| ∑v∈Vƒ(v)~ ∑w∈Waw ƒ(w) for functions ƒ : V → R that are ''smooth'' with respect to the geometry of the graph; here ~ indicates that we want the right-hand side to be as close to the left-hand side as possible. The main application comprises problems where ƒ is known to vary smoothly over the underlying graph but is expensive to evaluate on even a single vertex. We prove an inequality showing that the integration problem can be rewritten as a geometric problem (''the optimal packing of heat balls''). We discuss how one would construct approximate solutions of the heat ball packing problem; numerical examples demonstrate the efficiency of the method. [ABSTRACT FROM AUTHOR]

Worldwide, many hundreds of thousands of stents are implanted each year to revascularize occlusions in coronary arteries. Intravascular optical coherence tomography is an important emerging imaging technique, which has the resolution and contrast necessary to quantitatively analyze stent deployment and tissue coverage following stent implantation. Automation is needed, as current, it takes up to 16 h to manually analyze hundreds of images and thousands of stent struts from a single pullback. For automated strut detection, we used image formation physics and machine learning via a Bayesian network, and 3-D knowledge of stent structure via graph search. Graph search was done on en face projections using minimum spanning tree algorithms. Depths of all struts in a pullback were simultaneously determined using graph cut. To assess the method, we employed the largest validation data set used so far, involving more than 8000 clinical images from 103 pullbacks from 72 patients. Automated strut detection achieved a 0.91\pm 0.04 recall, and 0.84\pm 0.08 precision. Performance was robust in images of varying quality. This method can improve the workflow for analysis of stent clinical trial data, and can potentially be used in the clinic to facilitate real-time stent analysis and visualization, aiding stent implantation. [ABSTRACT FROM AUTHOR]

Background: Hypertension is common in China and its prevalence is rising, yet it remains inadequately controlled. Few studies have the capacity to characterise the epidemiology and management of hypertension across many heterogeneous subgroups. We did a study of the prevalence, awareness, treatment, and control of hypertension in China and assessed their variations across many subpopulations.Methods: We made use of data generated in the China Patient-Centered Evaluative Assessment of Cardiac Events (PEACE) Million Persons Project from Sept 15, 2014, to June 20, 2017, a population-based screening project that enrolled around 1·7 million community-dwelling adults aged 35-75 years from all 31 provinces in mainland China. In this population, we defined hypertension as systolic blood pressure of at least 140 mm Hg, or diastolic blood pressure of at least 90 mm Hg, or self-reported antihypertensive medication use in the previous 2 weeks. Hypertension awareness, treatment, and control were defined, respectively, among hypertensive adults as a self-reported diagnosis of hypertension, current use of antihypertensive medication, and blood pressure of less than 140/90 mm Hg. We assessed awareness, treatment, and control in 264 475 population subgroups-defined a priori by all possible combinations of 11 demographic and clinical factors (age [35-44, 45-54, 55-64, and 65-75 years], sex [men and women], geographical region [western, central, and eastern China], urbanity [urban vs rural], ethnic origin [Han and non-Han], occupation [farmer and non-farmer], annual household income [< ¥10 000, ¥10 000-50 000, and ≥¥50 000], education [primary school and below, middle school, high school, and college and above], previous cardiovascular events [yes or no], current smoker [yes or no], and diabetes [yes or no]), and their associations with individual and primary health-care site characteristics, using mixed models.Findings: The sample contained 1 738 886 participants with a mean age of 55·6 years (SD 9·7), 59·5% of whom were women. 44·7% (95% CI 44·6-44·8) of the sample had hypertension, of whom 44·7% (44·6-44·8) were aware of their diagnosis, 30·1% (30·0-30·2) were taking prescribed antihypertensive medications, and 7·2% (7·1-7·2) had achieved control. The age-standardised and sex-standardised rates of hypertension prevalence, awareness, treatment, and control were 37·2% (37·1-37·3), 36·0% (35·8-36·2), 22·9% (22·7-23·0), and 5·7% (5·6-5·7), respectively. The most commonly used medication class was calcium-channel blockers (55·2%, 55·0-55·4). Among individuals whose hypertension was treated but not controlled, 81·5% (81·3-81·6) were using only one medication. The proportion of participants who were aware of their hypertension and were receiving treatment varied significantly across subpopulations; lower likelihoods of awareness and treatment were associated with male sex, younger age, lower income, and an absence of previous cardiovascular events, diabetes, obesity, or alcohol use (all p<0·01). By contrast, control rate was universally low across all subgroups (<30·0%).Interpretation: Among Chinese adults aged 35-75 years, nearly half have hypertension, fewer than a third are being treated, and fewer than one in twelve are in control of their blood pressure. The low number of people in control is ubiquitous in all subgroups of the Chinese population and warrants broad-based, global strategy, such as greater efforts in prevention, as well as better screening and more effective and affordable treatment.Funding: Ministry of Finance and National Health and Family Planning Commission, China. [ABSTRACT FROM AUTHOR]

Dimensionality reduction is a crucial step in essentially every single-cell RNA-sequencing (scRNA-seq) analysis. In this chapter, we describe the typical dimensionality reduction workflow that is used for scRNA-seq datasets, specifically highlighting the roles of principal component analysis, t-distributed stochastic neighborhood embedding, and uniform manifold approximation and projection in this setting. We particularly emphasize efficient computation; the software implementations used in this chapter can scale to datasets with millions of cells.

Introduction: Improving postoperative patient recovery after cardiac surgery is a priority, but our current understanding of individual variations in recovery and factors associated with poor recovery is limited. We are using a health-information exchange platform to collect patient-reported outcome measures (PROMs) and wearable device data to phenotype recovery patterns in the 30-day period after cardiac surgery hospital discharge, to identify factors associated with these phenotypes and to investigate phenotype associations with clinical outcomes., Methods and Analysis: We designed a prospective cohort study to enrol 200 patients undergoing valve, coronary artery bypass graft or aortic surgery at a tertiary centre in the USA. We are enrolling patients postoperatively after the intensive care unit discharge and delivering electronic surveys directly to patients every 3 days for 30 days after hospital discharge. We will conduct medical record reviews to collect patient demographics, comorbidity, operative details and hospital course using the Society of Thoracic Surgeons data definitions. We will use phone interview and medical record review data for adjudication of survival, readmission and complications. We will apply group-based trajectory modelling to the time-series PROM and device data to classify patients into distinct categories of recovery trajectories. We will evaluate whether certain recovery pattern predicts death or hospital readmissions, as well as whether clinical factors predict a patient having poor recovery trajectories. We will evaluate whether early recovery patterns predict the overall trajectory at the patient-level., Ethics and Dissemination: The Yale Institutional Review Board approved this study. Following the description of the study procedure, we obtain written informed consent from all study participants. The consent form states that all personal information, survey response and any medical records are confidential, will not be shared and are stored in an encrypted database. We plan to publish our study findings in peer-reviewed journals., Competing Interests: Competing interests: SC is a paid reviewer for the CVS Caremark State of CT Clinical Pharmacy Program. BJM is supported in part by the Center for Remote Health Technologies and Systems and Texas A&M University, as well as awards 1R01EB028106-01 and 1R21EB028486-01 from the National Institute for Biomedical Imaging and Bioengineering (NIBIB) for work employing machine learning on health data. Dr Mortazavi reported having a patent US10201746B1 approved for 'Near-realistic sports motion analysis and activity monitoring' and a patent to US20180315507A1 is pending. HMK works under contract with the Centers for Medicare & Medicaid Services to support quality measurement programs; was a recipient of a research grant, through Yale, from Medtronic and the U.S. Food and Drug Administration to develop methods for post-market surveillance of medical devices; was a recipient of a research grant with Medtronic and is the recipient of a research grant from Johnson & Johnson, through Yale University, to support clinical trial data sharing; was a recipient of a research agreement, through Yale University, from the Shenzhen Center for Health Information for work to advance intelligent disease prevention and health promotion; collaborates with the National Center for Cardiovascular Diseases in Beijing; receives payment from the Arnold & Porter Law Firm for work related to the Sanofi clopidogrel litigation, from the Martin/Baughman Law Firm for work related to the Cook Celect IVC filter litigation, and from the Siegfried and Jensen Law Firm for work related to Vioxx litigation; is a venture partner for F-Prime; chairs a Cardiac Scientific Advisory Board for UnitedHealth; was a participant/participant representative of the IBM Watson Health Life Sciences Board; is a member of the Advisory Board for Element Science, the Advisory Board for Facebook, and the Physician Advisory Board for Aetna; and is the co-founder of HugoHealth, a personal health information platform, and co-founder of Refactor Health, an enterprise healthcare AI-augmented data management company., (© Author(s) (or their employer(s)) 2020. Re-use permitted under CC BY-NC. No commercial re-use. See rights and permissions. Published by BMJ.)

If we pick n random points uniformly in [0, 1] d and connect each point to its c d log n -nearest neighbors, where d ≥ 2 is the dimension and c d is a constant depending on the dimension, then it is well known that the graph is connected with high probability. We prove that it suffices to connect every point to c d ,1 log log n points chosen randomly among its c d ,2 log n -nearest neighbors to ensure a giant component of size n - o ( n ) with high probability. This construction yields a much sparser random graph with ~ n log log n instead of ~ n log n edges that has comparable connectivity properties. This result has nontrivial implications for problems in data science where an affinity matrix is constructed: instead of connecting each point to its k nearest neighbors, one can often pick k ' ≪ k random points out of the k nearest neighbors and only connect to those without sacrificing quality of results. This approach can simplify and accelerate computation; we illustrate this with experimental results in spectral clustering of large-scale datasets.

t-distributed Stochastic Neighborhood Embedding (t-SNE), a clustering and visualization method proposed by van der Maaten & Hinton in 2008, has rapidly become a standard tool in a number of natural sciences. Despite its overwhelming success, there is a distinct lack of mathematical foundations and the inner workings of the algorithm are not well understood. The purpose of this paper is to prove that t-SNE is able to recover well-separated clusters; more precisely, we prove that t-SNE in the 'early exaggeration' phase, an optimization technique proposed by van der Maaten & Hinton (2008) and van der Maaten (2014), can be rigorously analyzed. As a byproduct, the proof suggests novel ways for setting the exaggeration parameter α and step size h . Numerical examples illustrate the effectiveness of these rules: in particular, the quality of embedding of topological structures (e.g. the swiss roll) improves. We also discuss a connection to spectral clustering methods.

Importance: Body mass index (BMI) is positively associated with blood pressure (BP); this association has critical implications for countries like China, where hypertension is highly prevalent and obesity is increasing. A greater understanding of the association between BMI and BP is required to determine its effect and develop strategies to mitigate it., Objective: To assess the heterogeneity in the association between BMI and BP across a wide variety of subgroups of the Chinese population., Design, Setting, and Participants: In this cross-sectional study, data were collected at 1 time point from 1.7 million adults (aged 35-80 years) from 141 primary health care sites (53 urban districts and 88 rural counties) from all 31 provinces in mainland China who were enrolled in the China PEACE (Patient-Centered Evaluative Assessment of Cardiac Events) Million Persons Project, conducted between September 15, 2014, and June 20, 2017. A comprehensive subgroup analysis was performed by defining more than 22 000 subgroups of individuals based on covariates, and within each subgroup, linearly regressing BMI to BP., Main Outcomes and Measures: Systolic BP was measured twice with the participant in a seated position, using an electronic BP monitor., Results: The study included 1 727 411 participants (1 027 711 women and 699 700 men; mean [SD] age, 55.7 [9.8] years). Among the study sample, the mean (SD) BMI was 24.7 (3.5), the mean (SD) systolic BP was 136.5 (20.4) mm Hg, and the mean (SD) diastolic BP was 81.1 (11.2) mm Hg. The increase of BP per unit BMI ranged from 0.8 to 1.7 mm Hg/(kg/m2) for 95% of the subgroups not taking antihypertensive medication. The association between BMI and BP was substantially weaker in subgroups of patients taking antihypertensive medication compared with those who were untreated. In untreated subgroups, 95% of the coefficients varied by less than 1 mm Hg/(kg/m2)., Conclusions and Relevance: The association between BMI and BP is positive across tens of thousands of individuals in population subgroups, and, if causal, given its magnitude, would have significant implications for public health.

Recent years have witnessed intense development of randomized methods for low-rank approximation. These methods target principal component analysis and the calculation of truncated singular value decompositions. The present article presents an essentially black-box, foolproof implementation for Mathworks' MATLAB, a popular software platform for numerical computation. As illustrated via several tests, the randomized algorithms for low-rank approximation outperform or at least match the classical deterministic techniques (such as Lanczos iterations run to convergence) in basically all respects: accuracy, computational efficiency (both speed and memory usage), ease-of-use, parallelizability, and reliability. However, the classical procedures remain the methods of choice for estimating spectral norms and are far superior for calculating the least singular values and corresponding singular vectors (or singular subspaces).

Worldwide, many hundreds of thousands of stents are implanted each year to revascularize occlusions in coronary arteries. Intravascular optical coherence tomography is an important emerging imaging technique, which has the resolution and contrast necessary to quantitatively analyze stent deployment and tissue coverage following stent implantation. Automation is needed, as current, it takes up to 16 h to manually analyze hundreds of images and thousands of stent struts from a single pullback. For automated strut detection, we used image formation physics and machine learning via a Bayesian network, and 3-D knowledge of stent structure via graph search. Graph search was done on en face projections using minimum spanning tree algorithms. Depths of all struts in a pullback were simultaneously determined using graph cut. To assess the method, we employed the largest validation data set used so far, involving more than 8000 clinical images from 103 pullbacks from 72 patients. Automated strut detection achieved a 0.91±0.04 recall, and 0.84±0.08 precision. Performance was robust in images of varying quality. This method can improve the workflow for analysis of stent clinical trial data, and can potentially be used in the clinic to facilitate real-time stent analysis and visualization, aiding stent implantation.