On 2-form gauge models of topological phases

We explore various aspects of 2-form topological gauge theories in (3+1)d. These theories can be constructed as sigma models with target space the second classifying space $B^2G$ of the symmetry group $G$, and they are classified by cohomology classes of $B^2G$. Discrete topological gauge theories can typically be embedded into continuous quantum field theories. In the 2-form case, the continuous theory is shown to be a strict 2-group gauge theory. This embedding is studied by carefully constructing the space of $q$-form connections using the technology of Deligne-Beilinson cohomology. The same techniques can then be used to study more general models built from Postnikov towers. For finite symmetry groups, 2-form topological theories have a natural lattice interpretation, which we use to construct a lattice Hamiltonian model in (3+1)d that is exactly solvable. This construction relies on the introduction of a cohomology, dubbed 2-form cohomology, of algebraic cocycles that are identified with the simplicial cocycles of $B^2G$ as provided by the so-called $W$-construction of Eilenberg-MacLane spaces. We show algebraically and geometrically how a 2-form 4-cocycle reduces to the associator and the braiding isomorphisms of a premodular category of $G$-graded vector spaces. This is used to show the correspondence between our 2-form gauge model and the Walker-Wang model.Comment: 78 page

Qub: A Resource Aware Functional Programming Language

Managing resources---file handles, database connections, etc.---is a hard problem. Debugging resource leaks and runtime errors due to resource mismanagement are difficult in evolving production code. Programming languages with static type systems are great tools to ensure erroneous code is detected at compile time. However, modern static type systems do little in the aspect of resource management as resources are treated as normal values. We propose a type system, Qub, based on the logic of bunched implications (BI) which models resources as first class citizens. We distinguish two kinds of program objects---restricted and unrestricted---and two kinds of functions---sharing and separating. Our approach guarantees resource correctness without compromising existing functional abstractions

A Review on Objective-Driven Artificial Intelligence

While advancing rapidly, Artificial Intelligence still falls short of human intelligence in several key aspects due to inherent limitations in current AI technologies and our understanding of cognition. Humans have an innate ability to understand context, nuances, and subtle cues in communication, which allows us to comprehend jokes, sarcasm, and metaphors. Machines struggle to interpret such contextual information accurately. Humans possess a vast repository of common-sense knowledge that helps us make logical inferences and predictions about the world. Machines lack this innate understanding and often struggle with making sense of situations that humans find trivial. In this article, we review the prospective Machine Intelligence candidates, a review from Prof. Yann LeCun, and other work that can help close this gap between human and machine intelligence. Specifically, we talk about what's lacking with the current AI techniques such as supervised learning, reinforcement learning, self-supervised learning, etc. Then we show how Hierarchical planning-based approaches can help us close that gap and deep-dive into energy-based, latent-variable methods and Joint embedding predictive architecture methods.Comment: 5 pages, 5 figures, workshop submissio

Empowering People with Cognitive Disabilities to Live Independently By Supporting Their Self-Management of Food and Related Expenses

People with ADHD (attention deficit hyperactivity disorder) often have difficulty in planning and organization that can impact their eating habits and lifestyle. We have created a novel mobile software application to support choosing meals and making healthy food purchases that meet dietary preferences within a specified budget. The core functions allow 1) Managing user profiles to support personalization 2) Obtaining recipe recommendations to fit profile, budget, and foods-on-hand 3) Planning food purchases, and 4) Reviewing foods-on-hand, budget and the nutritional balance of recent meals and food purchases.The application supports self-introspection to help people with ADHD review their history of food purchases and consumption, using both scrollable inventories and visualizations of their aggregated behavior. These functions allow users to easily see how their choices distribute across different broad categories of food. This information provides a basis for them to make more informed decisions on their future purchases, while being mindful of the most and least frequently discarded foods. A user study was conducted to assess the usability of the app and to determine how different patterns of use correlate with food or shopping related behaviors that might impact the target population. 65% of the subjects found that providing the various types of data requested seemed relevant and easy to do. On the other hand, 84% of the subjects feel that charts helped them to understand how well they were doing at keeping a budget, using foods, and not throwing away much