17 citations · 36 across the 14 of their papers we have counts for
14 papers
Clearing Sections of Lattice Liability Networks
Robert Ghrist, Julian Gould, Miguel Lopez +1
Modern financial networks involve complex obligations that transcend simple monetary debts: multiple currencies, prioritized claims, supply chain dependencies, and more. We present…
Categorical Diffusion of Weighted Lattices
Robert Ghrist, Miguel Lopez, Paige Randall North +1
We introduce a categorical formalization of diffusion processes for network-structured data, motivated by applications in data science and information dynamics. At the heart of our…
Network Preference Dynamics using Lattice Theory
Hans Riess, Gregory Henselman-Petrusek, Michael C. Munger +3
Preferences, fundamental in all forms of strategic behavior and collective decision-making, in their raw form, are an abstract ordering on a set of alternatives. Agents, we assume,…
Lattice Theory in Multi-Agent Systems
Hans Riess
In this thesis, we argue that (order-) lattice-based multi-agent information systems constitute a broad class of networked multi-agent systems in which relational data is passed be…
Max-Plus Synchronization in Decentralized Trading Systems
Hans Riess, Michael Munger, Michael M. Zavlanos
We introduce a decentralized mechanism for pricing and exchanging alternatives constrained by transaction costs. We characterize the time-invariant solutions of a heat equation inv…
Tangent Bundle Convolutional Learning: from Manifolds to Cellular Sheaves and Back
Claudio Battiloro, Zhiyang Wang, Hans Riess +2
In this work we introduce a convolution operation over the tangent bundle of Riemann manifolds in terms of exponentials of the Connection Laplacian operator. We define tangent bund…
Stable and Transferable Hyper-Graph Neural Networks
Mikhail Hayhoe, Hans Riess, Victor M. Preciado +1
We introduce an architecture for processing signals supported on hypergraphs via graph neural networks (GNNs), which we call a Hyper-graph Expansion Neural Network (HENN), and prov…
Tangent Bundle Filters and Neural Networks: from Manifolds to Cellular Sheaves and Back
Claudio Battiloro, Zhiyang Wang, Hans Riess +2
In this work we introduce a convolution operation over the tangent bundle of Riemannian manifolds exploiting the Connection Laplacian operator. We use the convolution to define tan…
Diffusion of Information on Networked Lattices by Gossip
Hans Riess, Robert Ghrist
We study time-dependent dynamics on a network of order lattices, where structure-preserving lattice maps are used to fuse lattice-valued data over vertices and edges. The principal…
Multidimensional Persistence Module Classification via Lattice-Theoretic Convolutions
Hans Riess, Jakob Hansen, Robert Ghrist
Multiparameter persistent homology has been largely neglected as an input to machine learning algorithms. We consider the use of lattice-based convolutional neural network layers a…
Quiver Signal Processing (QSP)
Alejandro Parada-Mayorga, Hans Riess, Alejandro Ribeiro +1
In this paper we state the basics for a signal processing framework on quiver representations. A quiver is a directed graph and a quiver representation is an assignment of vector s…
A Temporal Logic-Based Hierarchical Network Connectivity Controller
Hans Riess, Yiannis Kantaros, George Pappas +1
In this paper, we consider networks of static sensors with integrated sensing and communication capabilities. The goal of the sensors is to propagate their collected information to…
Cellular Sheaves of Lattices and the Tarski Laplacian
Robert Ghrist, Hans Riess
This paper initiates a discrete Hodge theory for cellular sheaves taking values in a category of lattices and Galois connections. The key development is the Tarski Laplacian, an en…
Moduli Spaces of Morse Functions for Persistence
Michael J. Catanzaro, Justin Curry, Brittany Terese Fasy +5
We consider different notions of equivalence for Morse functions on the sphere in the context of persistent homology, and introduce new invariants to study these equivalence classe…