Related papers: Topological signature for periodic motion recognit…
We study one-component fermions in chain lattices with proximity-induced superconducting gap and interparticle short-range interaction, capable of hosting Majorana fermions. By systematically tracking various physical quantities, we show…
Using software UDEC to simulate the instability failure process of slope under seismic load, studing the dynamic response of slope failure, obtaining the deformation characteristics and displacement cloud map of slope, then analyzing the…
Protein-ligand binding is a fundamental biological process that is paramount to many other biological processes, such as signal transduction, metabolic pathways, enzyme construction, cell secretion, gene expression, etc. Accurate prediction…
Existing Graph Convolutional Networks to achieve human motion prediction largely adopt a one-step scheme, which output the prediction straight from history input, failing to exploit human motion patterns. We observe that human motions have…
In a system of many similar self-propelled entities such as flocks of birds, fish school, cells and molecules, the interactions with neighbors can lead to a "coherent state", meaning the formation of visually compelling aggregation patterns…
Persistent homology is a powerful mathematical tool that summarizes useful information about the shape of data allowing one to detect persistent topological features while one adjusts the resolution. However, the computation of such…
The aim of this article is to provide a simple sampling procedure to reconstruct any monotone path from its signature. For every N, we sample a lattice path of N steps with weights given by the coefficient of the corresponding word in the…
The appearance of topological effects in systems exhibiting a non-trivial topological band structure strongly relies on the coherent wave nature of the equations of motion. Here, we reveal topological dynamics in a classical stochastic…
Objective: In this paper, we demonstrate the applicability of radar for gait classification with application to home security, medical diagnosis, rehabilitation and assisted living. Aiming at identifying changes in gait patterns based on…
The human ability to detect and segment moving objects works in the presence of multiple objects, complex background geometry, motion of the observer, and even camouflage. In addition to all of this, the ability to detect motion is nearly…
Persistent homology is a multiscale method for analyzing the shape of sets and functions from point cloud data arising from an unknown distribution supported on those sets. When the size of the sample is large, direct computation of the…
The present paper aims at analyzing the topological content of the complex trajectories that weeder-autonomous robots follow in operation. We will prove that the topological descriptors of these trajectories are affected by the robot…
A topological theory initiated recently by the author uses methods of algebraic topology to estimate numerically the character of instabilities arising in motion planning algorithms. The present paper studies random motion planning…
We design a motion planning algorithm to coordinate the movements of two robots along a figure eight track, in such a way that no collisions occur. We use a topological approach to robot motion planning that relates instabilities in motion…
Topological data analysis is a relatively new branch of machine learning that excels in studying high dimensional data, and is theoretically known to be robust against noise. Meanwhile, data objects with mixed numeric and categorical…
The signature of a path \gamma is a sequence whose n-th term is the order-n iterated integrals of \gamma. It arises from solving multidimensional linear differential equations driven by \gamma. We are interested in relating the path…
Variations of human body skeletons may be considered as dynamic graphs, which are generic data representation for numerous real-world applications. In this paper, we propose a spatio-temporal graph convolution (STGC) approach for assembling…
The signature of a parametric curve is a sequence of tensors whose entries are iterated integrals. This construction is central to the theory of rough paths in stochastic analysis. It is here examined through the lens of algebraic geometry.…
Detecting and segmenting individual objects, regardless of their category, is crucial for many applications such as action detection or robotic interaction. While this problem has been well-studied under the classic formulation of…
This article introduces an algorithm to compute the persistent homology of a filtered complex with various coefficient fields in a single matrix reduction. The algorithm is output-sensitive in the total number of distinct persistent…