Related papers: Sheaves are the canonical datastructure for sensor…
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…
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).…
We employ techniques from topological data analysis to model sensor networks. Our approach to sensor integration uses the topological method of sheaves over cell complexes. The internal consistency of data from individual sensors is…
Integration of heterogeneous sensors is a challenging problem across a range of applications. Prominent among these are multi-target tracking, where one must combine observations from different sensor types in a meaningful way to track…
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 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…
This chapter explores dynamical structural equation models (DSEMs) and their nonlinear generalizations into sheaves of dynamical systems. It demonstrates these two disciplines on part of the food web in the Bering Sea. The translation from…
A compositional sheaf-theoretic framework for the modeling of complex event-based systems is presented. We show that event-based systems are machines, with inputs and outputs, and that they can be composed with machines of different types,…
A compositional sheaf-theoretic framework for the modeling of complex event-based systems is presented. We show that event-based systems are machines, with inputs and outputs, and that they can be composed with machines of different types,…
Machine learning (ML) is becoming prevalent in embedded AI sensing systems. These "ML sensors" enable context-sensitive, real-time data collection and decision-making across diverse applications ranging from anomaly detection in industrial…
Knowledge graph embedding involves learning representations of entities -- the vertices of the graph -- and relations -- the edges of the graph -- such that the resulting representations encode the known factual information represented by…
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…
Data heterogeneity hampers the effort to integrate and infer knowledge from vast heterogeneous data sources. An application case study is described, in which the objective was to semantically represent and integrate structured data from…
This is a preliminary version of visual interpretation integrating multiple sensors in SUCCESSOR, an intelligent, model-based vision system. We pursue a thorough integration of hierarchical Bayesian inference with comprehensive physical…
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…
Scientific codes are increasingly being used in compositional settings, especially problem solving environments (PSEs). Typical compositional modeling frameworks require significant buy-in, in the form of commitment to a particular style of…
In this paper, we identify some categorical structures in which one can model predicative formal systems: in other words, predicative analogues of the notion of a topos, with the aim of using sheaf models to interprete predicative formal…
Neural networks organize information according to the hierarchical, multi-scale structure of natural data. Methods to interpret model internals should be similarly scale-aware, explicitly tracking how features compose across resolutions and…
Essentials of sheaves are briefly presented, followed by related comments on presheaves, bundles, manifolds and singularities, aiming to point to their differences not only in their different formal mathematical structures, but also in the…
We introduce and develop the theory of metric sheaves. A metric sheaf $\A$ is defined on a topological space $X$ such that each fiber is a metric model. We describe the construction of the generic model as the quotient space of the sheaf…