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Time-delay distance measurements from strongly lensed quasars provide a robust, independent method for determining the Hubble constant ($H_0$). This approach cross-checks $H_0$ estimates from the distance ladder in the late universe and the…
Characterization of medium-range order in amorphous materials and its relation to short-range order is discussed. A new topological approach is presented here to extract a hierarchical structure of amorphous materials, which is robust…
Persistent Homology is a widely used topological data analysis tool that creates a concise description of the topological properties of a point cloud based on a specified filtration. Most filtrations used for persistent homology depend…
The quest for simplification in physics drives the exploration of concise mathematical representations for complex systems. This Dissertation focuses on the concept of dimensionality reduction as a means to obtain low-dimensional…
Previous video-based human pose estimation methods have shown promising results by leveraging aggregated features of consecutive frames. However, most approaches compromise accuracy to mitigate jitter or do not sufficiently comprehend the…
Modern business and economic datasets often exhibit nonlinear, multi-scale structures that traditional linear tools under-represent. Topological Data Analysis (TDA) offers a geometric lens for uncovering robust patterns, such as connected…
In this paper, we leverage the properties of non-Euclidean Geometry to define the Geodesic distance (GD) on the space of statistical manifolds. The Geodesic distance is a real and intuitive similarity measure that is a good alternative to…
Data-driven modeling of human motions is ubiquitous in computer graphics and computer vision applications, such as synthesizing realistic motions or recognizing actions. Recent research has shown that such problems can be approached by…
A comprehensive numerical solution is developed for the transient thermo-elasto-hydrodynamic (TEHD) characteristics of mechanical face seals. Transient lubrication features of the fluid film, transient thermal deformation features of the…
Network or physical attacks on industrial equipment or computer systems may cause massive losses. Therefore, a quick and accurate anomaly detection (AD) based on monitoring data, especially the multivariate time-series (MTS) data, is of…
Geometric consistency, i.e. the preservation of neighbourhoods, is a natural and strong prior in 3D shape matching. Geometrically consistent matchings are crucial for many downstream applications, such as texture transfer or statistical…
In high-density crowds, close proximity between pedestrians makes the steady state highly vulnerable to disruption by pushing behaviours, potentially leading to serious accidents. However, the scarcity of experimental data has hindered…
We experimentally observe the nonlinear dynamics of an optoelectronic time-delayed feedback loop designed for chaotic communication using commercial fiber optic links, and we simulate the system using delay differential equations. We show…
Symmetry is an implicit objective in structural form-finding that often reconciles efficiency and aesthetics. This paper identifies the symmetry of polyhedral diagrams in three-dimensional graphic statics (3DGS) as point groups and…
Persistent homology is a powerful tool for characterizing the topology of a data set at various geometric scales. When applied to the description of molecular structures, persistent homology can capture the multiscale geometric features and…
Nonlinear dynamical systems are complex and typically only simple systems can be analytically studied. In applications, these systems are usually defined with a set of tunable parameters and as the parameters are varied the system response…
This work presents a novel framework for time series analysis using entropic measures based on the kernel density estimate (KDE) of the time series' Takens' embeddings. Using this framework we introduce two distinct analytical tools: (1) a…
This paper proposes a geodesic-distance-based feature that encodes global information for improved video segmentation algorithms. The feature is a joint histogram of intensity and geodesic distances, where the geodesic distances are…
Hamiltonian dynamics describe a wide range of physical systems. As such, data-driven simulations of Hamiltonian systems are important for many scientific and engineering problems. In this work, we propose kernel-based methods for…
Emerging processor architectures such as GPUs and Intel MICs provide a huge performance potential for high performance computing. However developing software using these hardware accelerators introduces additional challenges for the…