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This article presents a novel visualization approach for dynamic graphs, the versinus method, specially useful for real world networks exhibiting free-scale properties. With a simple and fixed layout, and a small set of visual markups, the…
The persistence diagram is an increasingly useful tool from Topological Data Analysis, but its use alongside typical machine learning techniques requires mathematical finesse. The most success to date has come from methods that map…
We propose a snapshots-based method to compute reduction subspaces for physics-based simulations. Our method is applicable to any mesh with some artistic prior knowledge of the solution and only requires a record of existing solutions…
Spatial-temporal Map (STMap)-based methods have shown great potential to process high-angle videos for vehicle trajectory reconstruction, which can meet the needs of various data-driven modeling and imitation learning applications. In this…
In this paper, we consider chaotic dynamics and variational structures of area-preserving maps. There is a lot of study on dynamics of their maps and the works of Poincare and Birkhoff are well-known. To consider variational structures of…
Background subtraction has been a driving engine for many computer vision and video analytics tasks. Although its many variants exist, they all share the underlying assumption that photometric scene properties are either static or exhibit…
Evolutionary algorithms have been frequently used for dynamic optimization problems. With this paper, we contribute to the theoretical understanding of this research area. We present the first computational complexity analysis of…
We introduce the smt toolbox for Matlab. It implements optimized storage and fast arithmetics for circulant and Toeplitz matrices, and is intended to be transparent to the user and easily extensible. It also provides a set of test matrices,…
Currently, high-definition (HD) map construction leans towards a lightweight online generation tendency, which aims to preserve timely and reliable road scene information. However, map elements contain strong shape priors. Subtle and sparse…
We outline an unified introduction to the evolution equations of classical and quantum systems intended for a high school students audience. The attempt consists in circumventing the lack of mathematical knowledge with the use of simplified…
The category of presheaves on a (small) category is a suitable semantic universe to study behaviour of various dynamical systems. In particular, presheaves can be used to record the executions of a system and their morphisms correspond to…
Understanding the lives and interior structures of stellar objects is a fundamental objective of astrophysics. Research in this domain often relies on the visualization of astrophysical data, for instance, the results of theoretical…
The safe deployment of autonomous vehicles relies on their ability to effectively react to environmental changes. This can require maneuvering on varying surfaces which is still a difficult problem, especially for slippery terrains. To…
We define a Markov process on the set of countable graphs with spins. Transitions are local substitutions in the graph. It is proved that the scaling macrodimension is an invariant of such dynamics.
Software libraries for Topological Data Analysis (TDA) offer limited support for interactive visualization. Most libraries only allow to visualize topological descriptors (e.g., persistence diagrams), and lose the connection with the…
Slow-fast dynamics and resonant phenomena can be found in a wide range of physical systems, including problems of celestial mechanics, fluid mechanics, and charged particle dynamics. Important resonant effects that control transport in the…
Gait recognition enables non-intrusive, privacy-preserving identification but suffers in uncontrolled environments due to illumination and motion sensitivity of conventional cameras. In this work, we explore gait recognition using event…
Dynamic data visualizations can convey large amounts of information over time, such as using motion to depict changes in data values for multiple entities. Such dynamic displays put a demand on our visual processing capacities, yet our…
We summarize math search engines and search interfaces produced by the Document and Pattern Recognition Lab in recent years, and in particular the min math search interface and the Tangent search engine. Source code for both systems are…
In the article a technique of the usage of $f$-continuous functions (on mappings) and their families is developed. A proof of the Urysohn's Lemma for mappings is presented and a variant of the Brouwer-Tietze-Urysohn Extension Theorem for…