Charles Truong

All viruses on Earth rely on host cell machinery for replication, a process that involves a complex self-assembly mechanism. Our aim here is to scrutinize in real time the growth of icosahedral viral nucleocapsids with single-molecule precision. Using total internal reflection fluorescence microscopy, we probed the binding and unbinding dynamics of fluorescently labeled capsid subunits on hundreds of immobilized viral RNA molecules simultaneously at each time point. A step-detection algorithm combined with statistical analysis allowed us to estimate microscopic quantities such as the equilibrium binding rate and mean residence time, which are otherwise inaccessible through traditional ensemble-averaging techniques. Additionally, we could estimate a set of rate constants modeling the growth kinetics from nonequilibrium measurements, and we observed an acceleration in growth caused by the electrostatic screening effect of monovalent salts. Single-molecule fluorescence imaging will be crucial for elucidating virus self-assembly at the molecular level, particularly in crowded, cell-like environments.

Identifying characteristic patterns in time series, such as heartbeats or brain responses to a stimulus, is critical to understanding the physical or physiological phenomena monitored with sensors. Convolutional sparse coding (CSC) methods, which aim to approximate signals by a sparse combination of short signal templates (also called atoms), are well-suited for this task. However, enforcing sparsity leads to non-convex and untractable optimization problems. This article proposes finding the optimal solution to the original and non-convex CSC problem when the atoms do not overlap. Specifically, we show that the reconstruction error satisfies a simple recursive relationship in this setting, which leads to an efficient detection algorithm. We prove that our method correctly estimates the number of patterns and their localization, up to a detection margin that depends on a certain measure of the signal-to-noise ratio. In a thorough empirical study, with simulated and real-world physiological data sets, our method is shown to be more accurate than existing algorithms at detecting the patterns’ onsets.

TL;DR: This paper introduces an unsupervised representation learning algorithm for time series tailored to biomedical inter-individual studies using tools from shape analysis.

Abstract: Analyzing inter-individual variability of physiological functions is particularly appealing in medical and biological contexts to describe or quantify health conditions. Such analysis can be done by comparing individuals to a reference one with time series as biomedical data. This paper introduces an unsupervised representation learning (URL) algorithm for time series tailored to inter-individual studies. The idea is to represent time series as deformations of a reference time series. The deformations are diffeomorphisms parameterized and learned by our method called TS-LDDMM. Once the deformations and the reference time series are learned, the vector representations of individual time series are given by the parametrization of their corresponding deformation. At the crossroads between URL for time series and shape analysis, the proposed algorithm handles irregularly sampled multivariate time series of variable lengths and provides shape-based representations of temporal data. In this work, we establish a representation theorem for the graph of a time series and derive its consequences on the LDDMM framework. We showcase the advantages of our representation compared to existing methods using synthetic data and real-world examples motivated by biomedical applications.

Change-point detection, also known as signal segmentation, is an essential preprocessing step in many applications, ranging from industrial monitoring to bioinformatics. In short, it consists in finding the temporal boundaries of homogeneous regimes in long and non-stationary time series. While this area of research is active, most existing methods are designed for Euclidean data. However, in many practical scenarios, the collected time series are compositional, meaning that each observation belongs to the probability simplex (the set of non-negative vectors whose components sum to one). In this work, we propose an algorithm detecting change-points in large compositional signals with an underlying piecewise stationary model. We cast the change-point detection task as a discrete optimization problem, whose solution is shown to converge to the true change-points. We introduce a new and time-efficient dynamic programming algorithm that solves exactly this problem. To limit the number of operations, we describe a novel pruning rule that allows us to reduce the set of candidate change-point indices. Our method is tested on a thorough simulation study, which confirms its efficiency. Additionally, we apply our method to a human activity segmentation task, highlighting the necessity for such novel techniques compared to standard algorithms.

This article presents a selective survey of algorithms for the offline detection of multiple change points in multivariate time series. A general yet structuring methodological strategy is adopted to organize this vast body of work. More precisely, detection algorithms considered in this review are characterized by three elements: a cost function, a search method and a constraint on the number of changes. Each of those elements is described, reviewed and discussed separately. Implementations of the main algorithms described in this article are provided within a Python package called ruptures.