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07/16/2022
Rewiring Networks for Graph Neural Network Training Using Discrete Geometry
Information over-squashing is a phenomenon of inefficient information pr...
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10/07/2021
Curved Markov Chain Monte Carlo for Network Learning
We present a geometrically enhanced Markov chain Monte Carlo sampler for...
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01/16/2021
Hypernetworks: From Posets to Geometry
We show that hypernetworks can be regarded as posets which, in their tur...
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10/28/2020
Geometric Sampling of Networks
Motivated by the methods and results of manifold sampling based on Ricci...
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06/26/2020
Ricci Curvature Based Volumetric Segmentation of the Auditory Ossicles
The auditory ossicles that are located in the middle ear are the smalles...
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03/08/2020
Discrete Morse Theory, Persistent Homology and Forman-Ricci Curvature
Using Banchoff's discrete Morse Theory, in tandem with Bloch's result on...
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10/14/2019
A Simple Differential Geometry for Networks and its Generalizations
Based on two classical notions of curvature for curves in general metric...
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02/09/2019
Metric Curvatures and their Applications 2: Metric Ricci Curvature and Flow
In this second part of our overview of the different metric curvatures a...
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01/02/2019
Persistent homology of unweighted complex networks via discrete Morse theory
We present a new method based on discrete Morse theory to study topologi...
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10/17/2018
Forman's Ricci curvature - From networks to hypernetworks
Networks and their higher order generalizations, such as hypernetworks o...
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12/20/2017
Comparative analysis of two discretizations of Ricci curvature for complex networks
We have performed an empirical comparison of two distinct notions of dis...
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08/17/2011
Fat Triangulations and Differential Geometry
We study the differential geometric consequences of our previous result ...
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04/29/2010
Isometric Embeddings in Imaging and Vision: Facts and Fiction
We explore the practicability of Nash's Embedding Theorem in vision and ...
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02/15/2010
Geometric approach to sampling and communication
Relationships that exist between the classical, Shannon-type, and geomet...
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03/23/2009
Combinatorial Ricci Curvature and Laplacians for Image Processing
A new Combinatorial Ricci curvature and Laplacian operators for grayscal...
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01/26/2004