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A key challenge in analyzing single cell RNA-sequencing data is the large number of false zeros, where genes actually expressed in a given cell are incorrectly measured as unexpressed. We present a method based on low-rank matrix approximation which imputes these values while preserving biologically non-expressed genes (true biological zeros) at zero expression levels. We provide theoretical justification for this denoising approach and demonstrate its advantages relative to other methods on simulated and biological datasets. Missing values in scRNA-seq datasets can bias their analysis. Here, the authors threshold the low rank approximation of the expression matrix, so false zeros can be imputed while true zeros are preserved. [ABSTRACT FROM AUTHOR]

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]

If we pick n random points uniformly in $[0,1]^d$ and connect each point to its $c_d \log{n}$ nearest neighbors, where $d\ge 2$ 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 $\sim n \log\log{n}$ instead of $\sim n \log{n}$ edges that has comparable connectivity properties. This result has non-trivial 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 $k'\ll k$ 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. [ABSTRACT FROM AUTHOR]

Background: We recently developed a classification system to assess skeletal maturity by scoring proximal humeral ossification in a similar way to the canonical Risser sign. The purpose of the present study was to determine whether our system can be used to reliably assess radiographs of the spine for modern patients with idiopathic scoliosis, whether it can be used in combination with the Sanders hand system, and whether the consideration of patient factors such as age, sex, and standing height improves the accuracy of predictions.Methods: We retrospectively reviewed 414 randomized radiographs from 216 modern patients with scoliosis and measured reliability with use of the intraclass correlation coefficient (ICC). We then analyzed 606 proximal humeral radiographs for 70 children from a historical collection to determine the value of integrating multiple classification systems. The age of peak height velocity (PHV) was predicted with use of linear regression models, and performance was evaluated with use of tenfold cross-validation.Results: The proximal humeral ossification system demonstrated excellent reliability in modern patients with scoliosis, with an ICC of 0.97 and 0.92 for intraobserver and interobserver comparisons, respectively. The use of our system in combination with the Sanders hand system yielded 7 categories prior to PHV and demonstrated better results compared with either system alone. Linear regression algorithms showed that integration of the proximal part of the humerus, patient factors, and other classification systems outperformed models based on canonical Risser and triradiate-closure methods.Conclusions: Humeral head ossification can be reliably assessed in modern patients with scoliosis. Furthermore, the system described here can be used in combination with other parameters such as the Sanders hand system, age, sex, and height to predict PHV and percent growth remaining with high accuracy.Clinical Relevance: The proximal humeral ossification system can improve the prediction of PHV in patients with scoliosis on the basis of a standard spine radiograph without a hand radiograph for the determination of bone age. This increased accuracy for predicting maturity will allow physicians to better assess patient maturity relative to PHV and therefore can help to guide treatment decision-making without increasing radiation exposure, time, or cost. The present study demonstrates that assessment of the proximal humeral physis is a viable and valuable aid in the determination of skeletal maturity as obtained from radiographs of the spine that happen to include the shoulder in adolescent patients with idiopathic scoliosis. [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]

Summary: Bimodal patterns of expression have recently been shown to be useful not only in prioritizing genes that distinguish phenotypes, but also in prioritizing network models that correlate with proteomic evidence. In particular, subgroups of strongly coexpressed gene pairs result in an increased variance of the correlation distribution. This variance, a measure of association between sets of genes (or proteins), can be summarized as the bimodality of coexpression (BiC). We developed an online tool to calculate the BiC for user-defined gene lists and associated mRNA expression data. BiC is a comprehensive application that provides researchers with the ability to analyze both publicly available and user-collected array data.Availability: The freely available web service and the documentation can be accessed at http://gurkan.case.edu/software.Contact: gurkan@case.edu [ABSTRACT FROM AUTHOR]