Clustering and visualization of single-cell RNA-seq data using path metrics.

Recent advances in single-cell technologies have enabled high-resolution characterization of tissue and cancer compositions. Although numerous tools for dimension reduction and clustering are available for single-cell data analyses, these methods often fail to simultaneously preserve local cluster structure and global data geometry. To address these challenges, we developed a novel analyses framework, Single-Cell Path Metrics Profiling (scPMP), using power-weighted path metrics, which measure distances between cells in a data-driven way.

On Generalizations of the Nonwindowed Scattering Transform.

In this paper, we generalize finite depth wavelet scattering transforms, which we formulate as norms of a cascade of continuous wavelet transforms (or dyadic wavelet transforms) and contractive nonlinearities. We then provide norms for these operators, prove that these operators are well-defined, and are Lipschitz continuous to the action of diffeomorphisms in specific cases. Lastly, we extend our results to formulate an operator invariant to the action of rotations and an operator that is equivariant to the action of rotations of .

An analysis of classical multidimensional scaling with applications to clustering.

Classical multidimensional scaling is a widely used dimension reduction technique. Yet few theoretical results characterizing its statistical performance exist. This paper provides a theoretical framework for analyzing the quality of embedded samples produced by classical multidimensional scaling.

Wavelet invariants for statistically robust multi-reference alignment.

We propose a nonlinear, wavelet-based signal representation that is translation invariant and robust to both additive noise and random dilations. Motivated by the multi-reference alignment problem and generalizations thereof, we analyze the statistical properties of this representation given a large number of independent corruptions of a target signal. We prove the nonlinear wavelet-based representation uniquely defines the power spectrum but allows for an unbiasing procedure that cannot be directly applied to the power spectrum.

Interpreting measures of risk: Translating evidence into practice.

Advanced practice registered nurses must have a working knowledge of statistical principles in order to provide high-quality, evidence-based care. This article presents basic concepts of risk indexes and case study examples illustrating how these measures can inform practice.

Presurgical promestriene therapy in postmenopausal women with stress urinary incontinence.

Objective: Our study was aimed at evaluating the efficacy of therapy with promestriene, a synthetic diethyl-ether of estradiol with no distal hormonal effects, in patients undergoing surgical correction for stress urinary incontinence (SUI).

Materials And Methods: Ninety-eight healthy, postmenopausal women, non-users of hormone replacement therapy, with a diagnosis of SUI and vulvovaginal dystrophy, were recruited and openly randomized into two main groups. Group I (48 patients) received promestriene 10 mg daily, by vaginal capsule, for 21 days before the operation.