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  1. Abstract

    Motivated by an analysis of single molecular experiments in the study of T‐cell signaling, a new model called varying coefficient frailty model with local linear estimation is proposed. Frailty models have been extensively studied, but extensions to nonconstant coefficients are limited to spline‐based methods that tend to produce estimation bias near the boundary. To address this problem, we introduce a local polynomial kernel smoothing technique with a modified expectation‐maximization algorithm to estimate the unknown parameters. Theoretical properties of the estimators, including their unbiased property near the boundary, are derived along with discussions on the asymptotic bias‐variance trade‐off. The finite sample performance is examined by simulation studies, and comparisons with existing spline‐based approaches are conducted to show the potential advantages of the proposed approach. The proposed method is implemented for the analysis of T‐cell signaling. The fitted varying coefficient model provides a rigorous quantification of an early and rapid impact on T‐cell signaling from the accumulation of bond lifetime, which can shed new light on the fundamental understanding of how T cells initiate immune responses.

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  2. Abstract

    Fusion learning methods, developed for the purpose of analyzing datasets from many different sources, have become a popular research topic in recent years. Individualized inference approaches through fusion learning extend fusion learning approaches to individualized inference problems over a heterogeneous population, where similar individuals are fused together to enhance the inference over the target individual. Both classical fusion learning and individualized inference approaches through fusion learning are established based on weighted aggregation of individual information, but the weight used in the latter is localized to thetargetindividual. This article provides a review on two individualized inference methods through fusion learning,iFusion andiGroup, that are developed under different asymptotic settings. Both procedures guarantee optimal asymptotic theoretical performance and computational scalability.

    This article is categorized under:

    Statistical Learning and Exploratory Methods of the Data Sciences > Manifold Learning

    Statistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods

    Statistical and Graphical Methods of Data Analysis > Nonparametric Methods

    Data: Types and Structure > Massive Data

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  3. Free, publicly-accessible full text available April 1, 2024
  4. Free, publicly-accessible full text available February 1, 2024
  5. Abstract In this paper we apply Conley index theory in a covering space of an invariant set S , possibly not isolated, in order to describe the dynamics in S . More specifically, we consider the action of the covering translation group in order to define a topological separation of S which distinguishes the connections between the Morse sets within a Morse decomposition of S . The theory developed herein generalizes the classical connection matrix theory, since one obtains enriched information on the connection maps for non-isolated invariant sets, as well as for isolated invariant sets. Moreover, in the case of an infinite cyclic covering induced by a circle-valued Morse function, one proves that the Novikov differential of f is a particular case of the p -connection matrix defined herein. 
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