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Principal Component Analysis (PCA) is a workhorse of modern data science. While PCA assumes the data conforms to Euclidean geometry, for specific data types, such as hierarchical and cyclic data structures, other spaces are more…
We pursue a novel morphometric analysis to detect sources in very-high-energy gamma-ray counts maps by structural deviations from the background noise. Because the Minkowski functionals from integral geometry quantify the shape of the…
Sparse Principal Component Analysis (sPCA) is a cardinal technique for obtaining combinations of features, or principal components (PCs), that explain the variance of high-dimensional datasets in an interpretable manner. This involves…
We consider the problem of estimating multiple principal components using the recently-proposed Sparse and Functional Principal Components Analysis (SFPCA) estimator. We first propose an extension of SFPCA which estimates several principal…
This paper presents an algebro-geometric solution to the problem of segmenting an unknown number of subspaces of unknown and varying dimensions from sample data points. We represent the subspaces with a set of homogeneous polynomials whose…
A set of discrete individual points located in an embedding continuum space can be seen as percolating or non-percolating, depending on the radius of the discs/spheres associated with each of them. This problem is relevant in theoretical…
We propose generalized conditional functional principal components analysis (GC-FPCA) for the joint modeling of the fixed and random effects of non-Gaussian functional outcomes. The method scales up to very large functional data sets by…
We consider the simultaneous movement of finitely many colored points in space, calling it a spatial sorting process. The name suggests a purpose that drives the collection to a configuration of increased or decreased order. Mapping such a…
The scalar difference equation $x_{n+1}=f_{n}(x_{n},x_{n-1},...,x_{n-k})$ may exhibit symmetries in its form that allow for reduction of order through substitution or a change of variables. Such form symmetries can be defined generally…
Super-resolution imaging techniques have largely improved our capabilities to visualize nanometric structures in biological systems. Their application further enables one to potentially quantitate relevant parameters to determine the…
We develop a theory of aggregation using statistical mechanical methods. An example of a complicated aggregation system with several levels of structures is peptide/protein self-assembly. The problem of protein aggregation is important for…
Complex systems are usually represented as an intricate set of relations between their components forming a complex graph or network. The understanding of their functioning and emergent properties are strongly related to their structural…
Identifying local structural motifs and packing patterns of molecular solids is a challenging task for both simulation and experiment. We demonstrate two novel approaches to characterize local environments in different polymorphs of…
Two existing approaches to functional principal components analysis (FPCA) are due to Rice and Silverman (1991) and Silverman (1996), both based on maximizing variance but introducing penalization in different ways. In this article we…
Living organisms rely on molecular networks, such as gene circuits and signaling pathways, for information processing and robust decision-making in crowded, noisy environments. Recent advances show that interacting biomolecules…
This paper studies a discrepancy-sensitive approach to dynamic fractional cascading. We provide an efficient data structure for dominated maxima searching in a dynamic set of points in the plane, which in turn leads to an efficient dynamic…
This paper reviews developments in statistics for spatial point processes obtained within roughly the last decade. These developments include new classes of spatial point process models such as determinantal point processes, models…
Inspired by biology's most sophisticated computer, the brain, neural networks constitute a profound reformulation of computational principles. Remarkably, analogous high-dimensional, highly-interconnected computational architectures also…
Cell sorting, the segregation of cells with different properties into distinct domains, is a key phenomenon in biological processes such as embryogenesis. We use a phase-field model of a confluent cell layer to study the role of activity in…
Regularized variants of Principal Components Analysis, especially Sparse PCA and Functional PCA, are among the most useful tools for the analysis of complex high-dimensional data. Many examples of massive data, have both sparse and…