11 papers
Adjoint-Based Calibration and Optimal Control of Stochastic Multiscale Bioprocess Digital Twins
Keilung Choy, Wei Xie
We develop a bias-aware digital-twin calibration and control framework for multiscale bioprocess models within a biological systems-of-systems (Bio-SoS) paradigm. The digital twin…
Optimal Transport on Graphs and Stochastically Evolving Trees
Fan Chung, Sawyer Jack Robertson
We give an effective algorithm for determining the transportation distance between two given probability density functions defined on the vertices of a graph by analyzing…
Distance Exceptional Graphs and the Curvature Index
Sawyer Jack Robertson, Finn Southerland, Erlang Surya
A graph on vertices is said to be \emph{distance exceptional} if the equation admits no solution , where $D\in\mathbb{R…
Discrete Curvatures and Convex Polytopes
Jesús A. De Loera, Jillian Eddy, Sawyer Jack Robertson +1
We study Forman--Ricci and effective resistance curvatures on the skeleta of convex polytopes. Our guiding questions are: how frequently do polytopal graphs exhibit everywhere posi…
Stochastically Evolving Graphs via Edit Semigroups
Fan Chung, Sawyer Jack Robertson
We investigate a randomly evolving process of subgraphs in an underlying host graph using the spectral theory of semigroups related to the Tsetlin library and hyperplane arrangemen…
Matrix Concentration for Random Signed Graphs and Community Recovery in the Signed Stochastic Block Model
Sawyer Jack Robertson
We consider graphs where edges and their signs are added independently at random from among all pairs of nodes. We establish strong concentration inequalities for adjacency and Lap…
A Comparative Study of Curvature on Trees
Sawyer Jack Robertson
There are several interrelated notions of discrete curvature on graphs. Many approaches utilize the optimal transportation metric on its probability simplex or the distance matrix…
Random Walks, Conductance, and Resistance for the Connection Graph Laplacian
Alexander Cloninger, Gal Mishne, Andreas Oslandsbotn +3
We investigate the concept of effective resistance in connection graphs, expanding its traditional application from undirected graphs. We propose a robust definition of effective r…
Harnack Inequality for Magnetic Graphs
Sawyer Jack Robertson
For magnetic graphs satisfying connection curvature dimension inequality , we prove a Harnack-type inequality for eigenfunctions of the graph magnetic Laplace operator i…
Topics in Hilbert Spaces, Spectral Theory, and Harmonic Analysis
Sawyer Jack Robertson
General expository paper concerning topics in Hilbert spaces, spectral theory, and harmonic analysis. The preliminary section includes basic Banach algebra and Hilbert space theory…
Kantorovich Duality and Optimal Transport Problems on Magnetic Graphs
Sawyer Jack Robertson
We consider Lipschitz- and Arens-Eells-type function spaces constructed for magnetic graphs, which are adapted to this setting from the area of optimal transport on discrete spaces…