Related papers: A Sheaf Theoretical Approach to Uncertainty Quanti…

Consider the case of many sensors, each returning very different types of data (e.g., a camera returning images, a thermometer returning probability distributions, a newspaper returning articles, a traffic counter returning numbers).…

As data grows in size and complexity, finding frameworks which aid in interpretation and analysis has become critical. This is particularly true when data comes from complex systems where extensive structure is available, but must be drawn…

Multi-agent target tracking in the presence of nonlinear dynamics and agent heterogeneity, where state-space dimensions may differ, is a challenging problem that traditional graph Laplacian methods cannot easily address. This work leverages…

Many complicated network problems can be easily understood on small networks. Difficulties arise when small networks are combined into larger ones. Fortunately, the mathematical theory of sheaves was constructed to address just this kind of…

There is an interplay between models, specified by variables and equations, and their connections to one another. This dichotomy should be reflected in the abstract as well. Without referring to the models directly -- only that a model…

This paper provides an overview of the applications of sheaf theory in deep learning, data science, and computer science in general. The primary text of this work serves as a friendly introduction to applied and computational sheaf theory…

Sheaf theory, which is a complex but powerful tool supported by topological theory, offers more flexibility and precision than traditional graph theory when it comes to modeling relationships between multiple features. In the realm of air…

We consider the problem of tracking multiple, unknown, and time-varying numbers of objects using a distributed network of heterogeneous sensors. In an effort to derive a formulation for practical settings, we consider limited and unknown…

A sensor integration framework should be sufficiently general to accurately represent all information sources, and also be able to summarize information in a faithful way that emphasizes important, actionable information. Few approaches…

Conventional multimodal alignment methods assume mutual redundancy across all modalities, an assumption that fails in real-world distributed scenarios. We propose SheafAlign, a sheaf-theoretic framework for decentralized multimodal…

Bearing measurements,as the most common modality in nature, have recently gained traction in multi-robot systems to enhance mutual localization and swarm collaboration. Despite their advantages, challenges such as sensory noise, obstacle…

This document develops general concepts useful for extracting knowledge embedded in large graphs or datasets that have pair-wise relationships, such as cause-effect-type relations. Almost no underlying assumptions are made, other than that…

Collaborative object localization aims to collaboratively estimate locations of objects observed from multiple views or perspectives, which is a critical ability for multi-agent systems such as connected vehicles. To enable collaborative…

In this paper, sensor selection problems for target tracking in large sensor networks with linear equality or inequality constraints are considered. First, we derive an equivalent Kalman filter for sensor selection, i.e., generalized…

We propose that the sheaf condition on a presheaf of design spaces provides a mathematical model for multi-view consistency in the architecture of cyber-physical systems (CPS). In model-based systems engineering, multiple engineering views…

We introduce a sheaf-theoretic characterization of task solvability in general distributed computing models, unifying distinct approaches to message-passing models. We establish cellular sheaves as a natural mathematical framework for…

Many structured systems admit locally consistent descriptions that nevertheless fail to globalize when constrained by an ambient reference or feasibility condition. Diagnosing such failures is naturally an evaluative problem: given a fixed…

Machine Learning algorithms are ubiquitous in key decision-making contexts such as justice, healthcare and finance, which has spawned a great demand for fairness in these procedures. However, the theoretical properties of such models in…

We introduce a graph-theoretic framework based on discrete sheaves to diagnose and localize inconsistencies in preference aggregation. Unlike traditional linearization methods (e.g., HodgeRank), this approach preserves the discrete…

To ensure safety in confined environments such as mines or subway tunnels, a (wireless) sensor network can be deployed to monitor various environmental conditions. One of its most important applications is to track personnel, mobile…