Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Discipline
- Publication Type
Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
Data-Optimized Spatial Field Predictions For Robotic Adaptive Sampling: A Gaussian Process Approach, Zachary Nathan
Data-Optimized Spatial Field Predictions For Robotic Adaptive Sampling: A Gaussian Process Approach, Zachary Nathan
Computer Science Senior Theses
We introduce a framework that combines Gaussian Process models, robotic sensor measurements, and sampling data to predict spatial fields. In this context, a spatial field refers to the distribution of a variable throughout a specific area, such as temperature or pH variations over the surface of a lake. Whereas existing methods tend to analyze only the particular field(s) of interest, our approach optimizes predictions through the effective use of all available data. We validated our framework on several datasets, showing that errors can decline by up to two-thirds through the inclusion of additional colocated measurements. In support of adaptive sampling, …
Orienteering In Knowledge Spaces: The Hyperbolic Geometry Of Wikipedia Mathematics, Gregory Leibon, Daniel N. Rockmore
Orienteering In Knowledge Spaces: The Hyperbolic Geometry Of Wikipedia Mathematics, Gregory Leibon, Daniel N. Rockmore
Dartmouth Scholarship
In this paper we show how the coupling of the notion of a network with directions with the adaptation of the four-point probe from materials testing gives rise to a natural geometry on such networks. This four-point probe geometry shares many of the properties of hyperbolic geometry wherein the network directions take the place of the sphere at infinity, enabling a navigation of the network in terms of pairs of directions: the geodesic through a pair of points is oriented from one direction to another direction, the pair of which are uniquely determined. We illustrate this in the interesting example …
A Classification Of Certain Graphs With Minimal Imperfection Properties, S. H. Whitesides
A Classification Of Certain Graphs With Minimal Imperfection Properties, S. H. Whitesides
Dartmouth Scholarship
The family of (α, ω) graphs are of interest for several reasons. For example, any minimal counter-example to Berge's Strong Perfect Graph Conjecture belongs to this family. This paper accounts for all (4, 3) graphs. One of these is not obtainable by existing techniques for generating (α + 1, ω) graphs from (α, ω) graphs.