Physical Sciences and Mathematics Commons^™

Vrmovian - An Immersive Data Annotation Tool For Visual Analysis Of Human Interactions In Vr, Isaac Browen

Student Scholar Symposium Abstracts and Posters

Understanding human behavior in virtual reality (VR) is a key component for developing intelligent systems to enhance human focused VR experiences. The ability to annotate human motion data proves to be a very useful way to analyze and understand human behavior. However, due to the complexity and multi-dimensionality of human activity data, it is necessary to develop software that can display the data in a comprehensible way and can support intuitive data annotation for developing machine learning models able recognize and assist human motions in VR (e.g., remote physical therapy). Although past research has been done to improve VR data …

Completeness Of Nominal Props, Samuel Balco, Alexander Kurz

Engineering Faculty Articles and Research

We introduce nominal string diagrams as string diagrams internal in the category of nominal sets. This leads us to define nominal PROPs and nominal monoidal theories. We show that the categories of ordinary PROPs and nominal PROPs are equivalent. This equivalence is then extended to symmetric monoidal theories and nominal monoidal theories, which allows us to transfer completeness results between ordinary and nominal calculi for string diagrams.

Hartree-Fock Implementation For Pedagogical & Research Purposes, Gary Zeri, Jerry Larue

Student Scholar Symposium Abstracts and Posters

Often during the process of innovation and scientific advancement, experimentation is the key to increasing the current knowledge of body. Unfortunately, experimentation can often require extended periods of time as well as monetary resources to perform. The use of computational chemistry can increase the rate of scientific advancement by simulating experimental results, allowing researchers to focus on experiments whose computational counterparts show the greatest promise. Students new to the sciences are often not exposed to these methods due to their complexities. The purpose of this project is to implement the Hartree-Fock method, one type of computational chemistry method, whose programming …

Extending Set Functors To Generalised Metric Spaces, Adriana Balan, Alexander Kurz, Jiří Velebil

Mathematics, Physics, and Computer Science Faculty Articles and Research

For a commutative quantale V, the category V-cat can be perceived as a category of generalised metric spaces and non-expanding maps. We show that any type constructor T (formalised as an endofunctor on sets) can be extended in a canonical way to a type constructor T_V on V-cat. The proof yields methods of explicitly calculating the extension in concrete examples, which cover well-known notions such as the Pompeiu-Hausdorff metric as well as new ones.

Conceptually, this allows us to to solve the same recursive domain equation X ≅ TX in different categories (such as sets and metric spaces) and …