Bi-stochastically normalized graph Laplacian: convergence to manifold Laplacian and robustness to outlier noise.

Bi-stochastic normalization provides an alternative normalization of graph Laplacians in graph-based data analysis and can be computed efficiently by Sinkhorn-Knopp (SK) iterations. This paper proves the convergence of bi-stochastically normalized graph Laplacian to manifold (weighted-)Laplacian with rates, when [Formula: see text] data points are i.i.

Gene trajectory inference for single-cell data by optimal transport metrics.

Single-cell RNA sequencing has been widely used to investigate cell state transitions and gene dynamics of biological processes. Current strategies to infer the sequential dynamics of genes in a process typically rely on constructing cell pseudotime through cell trajectory inference. However, the presence of concurrent gene processes in the same group of cells and technical noise can obscure the true progression of the processes studied.

Spatiotemporally heterogeneous coordination of cholinergic and neocortical activity.

Variation in an animal's behavioral state is linked to fluctuations in brain activity and cognitive ability. In the neocortex, state-dependent circuit dynamics may reflect neuromodulatory influences such as that of acetylcholine (ACh). Although early literature suggested that ACh exerts broad, homogeneous control over cortical function, recent evidence indicates potential anatomical and functional segregation of cholinergic signaling.

Decomposing a deterministic path to mesenchymal niche formation by two intersecting morphogen gradients.

Organ formation requires integrating signals to coordinate proliferation, specify cell fates, and shape tissue. Tracing these events and signals remains a challenge, as intermediate states across many critical transitions are unresolvable over real time and space. Here, we designed a unique computational approach to decompose a non-linear differentiation process into key components to resolve the signals and cell behaviors that drive a rapid transition, using the hair follicle dermal condensate as a model.

Biwhitening Reveals the Rank of a Count Matrix.

Estimating the rank of a corrupted data matrix is an important task in data analysis, most notably for choosing the number of components in PCA. Significant progress on this task was achieved using random matrix theory by characterizing the spectral properties of large noise matrices. However, utilizing such tools is not straightforward when the data matrix consists of count random variables, e.

Doubly Stochastic Normalization of the Gaussian Kernel Is Robust to Heteroskedastic Noise.

A fundamental step in many data-analysis techniques is the construction of an affinity matrix describing similarities between data points. When the data points reside in Euclidean space, a widespread approach is to from an affinity matrix by the Gaussian kernel with pairwise distances, and to follow with a certain normalization (e.g.

KLT picker: Particle picking using data-driven optimal templates.

Particle picking is currently a critical step in the cryo-EM single particle reconstruction pipeline. Despite extensive work on this problem, for many data sets it is still challenging, especially for low SNR micrographs. We present the KLT (Karhunen Loeve Transform) picker, which is fully automatic and requires as an input only the approximated particle size.

Steerable Principal Components for Space-Frequency Localized Images.

As modern scientific image datasets typically consist of a large number of images of high resolution, devising methods for their accurate and efficient processing is a central research task. In this paper, we consider the problem of obtaining the steerable principal components of a dataset, a procedure termed "steerable PCA" (steerable principal component analysis). The output of the procedure is the set of orthonormal basis functions which best approximate the images in the dataset and all of their planar rotations.