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We introduce a path-dependent hamiltonian representation (the path representation) for SU(2) with fermions in 3 + 1 dimensions. The gauge-invariant operators and hamiltonian are realized in a Hilbert space of open path and loop functionals.…
As urban environments manifest high levels of complexity it is of vital importance that safety systems embedded within autonomous vehicles (AVs) are able to accurately anticipate short-term future motion of nearby agents. This problem can…
Unsupervised learning enables modeling complex images without the need for annotations. The representation learned by such models can facilitate any subsequent analysis of large image datasets. However, some generative factors that cause…
We study the class $HQ(\mathbb{D})$, the set of harmonic quasiconformal automorphisms of the unit disk $\mathbb{D}$ in the complex plane, endowed with the topology of uniform convergence. Several important topological properties of this…
In this thesis we investigate proposed duals to QCD. Duals to QCD fall into two categories: `top-down' and `bottom-up'. We take inspiration from both by truncating a consistent solution to the type IIB supergravity equations of motion…
We introduce Guided Harmonic Path-Integral Diffusion (GH-PID), a linearly-solvable framework for guided Stochastic Optimal Transport (SOT) with a hard terminal distribution and soft, application-driven path costs. A low-dimensional guidance…
In production rendering systems, caustics are typically rendered via photon mapping and gathering, a process often hindered by insufficient photon density. In this paper, we propose a novel photon guiding method to improve the photon…
This invention addresses fixed-point representations of convolutional neural networks (CNN) in integrated circuits. When quantizing a CNN for a practical implementation there is a trade-off between the precision used for operations between…
Dimensionality reduction represents a crucial step in extracting meaningful insights from Molecular Dynamics (MD) simulations. Conventional approaches, including linear methods such as principal component analysis as well as various…
A new method to represent and approximate rotation matrices is introduced. The method represents approximations of a rotation matrix $Q$ with linearithmic complexity, i.e. with $\frac{1}{2}n\lg(n)$ rotations over pairs of coordinates,…
Computational models are quantitative representations of systems. By analyzing and comparing the outputs of such models, it is possible to gain a better understanding of the system itself. Though as the complexity of model outputs…
In this paper we present a new approach to the solution to a generalized version of Hughes' models for pedestrian movements based on a follow-the-leader many particle approximation. In particular, we provide a rigorous global existence…
We present a new learning-based framework to recover vehicle pose in SO(3) from a single RGB image. In contrast to previous works that map from local appearance to observation angles, we explore a progressive approach by extracting…
Let G be a connected semisimple Lie group such that the associated symmetric space X is Hermitian and let Gamma be the fundamental group of a compact orientable surface of genus at least 2. We survey the study of maximal representations,…
The representation of a Configuration Space C plays a vital role in accelerating the finding of a collision-free path for sampling-based motion planners where the majority of computation time is spent in collision checking of states.…
We propose a new hologram representation based on structured complex-valued 2D Gaussian primitives, which replaces per-pixel information storage and reduces the parameter search space by up to 10:1. To enable end-to-end training, we develop…
In this work, we utilize discrete geometric mechanics to derive a 2nd-order variational integrator so as to simulate rigid body dynamics. The developed integrator is to simulate the motion of a free rigid body and a quad-rotor. We…
We present a representation learning algorithm that learns a low-dimensional latent dynamical system from high-dimensional \textit{sequential} raw data, e.g., video. The framework builds upon recent advances in amortized inference methods…
We present a small autonomous vehicle, with the purpose of aiding teachers and researchers to easily deploy different approaches to guidance, control and positioning systems, without the hassle to develop the entire modules required for…
We present a framework for dynamic trajectory generation for autonomous navigation, which does not rely on HD maps as the underlying representation. High Definition (HD) maps have become a key component in most autonomous driving…