Related papers: Topological data analysis of C. elegans locomotion…
We use topological data analysis and machine learning to study a seminal model of collective motion in biology [D'Orsogna et al., Phys. Rev. Lett. 96 (2006)]. This model describes agents interacting nonlinearly via attractive-repulsive…
We use topological data analysis as a tool to analyze the fit of mathematical models to experimental data. This study is built on data obtained from motion tracking groups of aphids in [Nilsen et al., PLOS One, 2013] and two random walk…
The 1mm roundworm C. elegans is a model organism used in many sub-areas of biology to investigate different types of biological processes. In order to complement the n-vivo analysis with computer-based investigations, several methods have…
An organism's ability to move freely is a fundamental behaviour in the animal kingdom. To understand animal locomotion requires a characterisation of the material properties, as well as the biomechanics and physiology. We present a…
We perform topological data analysis on the internal states of convolutional deep neural networks to develop an understanding of the computations that they perform. We apply this understanding to modify the computations so as to (a) speed…
Topological Data Analysis has grown in popularity in recent years as a way to apply tools from algebraic topology to large data sets. One of the main tools in topological data analysis is persistent homology. This paper uses undergraduate…
We experimentally studied the locomotion of the nematode C. elegans in both fluidic and granular media. In this fluid dynamics video, we show the motility gaits of the nematode in these two environments. The motility of the nematode C.…
Topological data analysis refers to approaches for systematically and reliably computing abstract ``shapes'' of complex data sets. There are various applications of topological data analysis in life and data sciences, with growing interest…
Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we…
Animal behavior is often quantified through subjective, incomplete variables that may mask essential dynamics. Here, we develop a behavioral state space in which the full instantaneous state is smoothly unfolded as a combination of…
Computational topologists recently developed a method, called persistent homology to analyze data presented in terms of similarity or dissimilarity. Indeed, persistent homology studies the evolution of topological features in terms of a…
Statistical analysis on object data presents many challenges. Basic summaries such as means and variances are difficult to compute. We apply ideas from topology to study object data. We present a framework for using persistence landscapes…
Topological data analysis (TDA) is a tool from data science and mathematics that is beginning to make waves in environmental science. In this work, we seek to provide an intuitive and understandable introduction to a tool from TDA that is…
Natural data offer a hard challenge to data analysis. One set of tools is being developed by several teams to face this difficult task: Persistent topology. After a brief introduction to this theory, some applications to the analysis and…
Living systems exhibit complex yet organized behavior on multiple spatiotemporal scales. To investigate the nature of multiscale coordination in living systems, one needs a meaningful and systematic way to quantify the complex dynamics, a…
We introduce the first unified theory for target tracking using Multiple Hypothesis Tracking, Topological Data Analysis, and machine learning. Our string of innovations are 1) robust topological features are used to encode behavioral…
Many multi-variate time series obtained in the natural sciences and engineering possess a repetitive behavior, as for instance state-space trajectories of industrial machines in discrete automation. Recovering the times of recurrence from…
Animal locomotion is often subject to constraints arising from anatomical/physiological asymmetries. We use the nematode C.~elegans as a minimal model system to ask whether such constraints might shape locomotion patterns optimized during…
C. elegans is commonly used in neuroscience for behaviour analysis because of it's compact nervous system with well-described connectivity. Localizing the animal and distinguishing between its head and tail are important tasks to track the…
Interacting, self-propelled particles such as epithelial cells can dynamically self-organize into complex multicellular patterns, which are challenging to classify without a priori information. Classically, different phases and phase…