Related papers: Forman-Ricci flow for change detection in large dy…
Understanding and interacting with everyday physical scenes requires rich knowledge about the structure of the world, represented either implicitly in a value or policy function, or explicitly in a transition model. Here we introduce a new…
Algorithms for search of communities in networks usually consist discrete variations of links. Here we discuss a flow method, driven by a set of differential equations. Two examples are demonstrated in detail. First is a partition of a…
We review the main aspects of Ricci flows as they arise in physics and mathematics. In field theory they describe the renormalization group equations of the target space metric of two dimensional sigma models to lowest order in the…
The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…
While Graph Neural Networks (GNNs) have been successfully leveraged for learning on graph-structured data across domains, several potential pitfalls have been described recently. Those include the inability to accurately leverage…
Complex heterogeneous dynamic networks like knowledge graphs are powerful constructs that can be used in modeling data provenance from computer systems. From a security perspective, these attributed graphs enable causality analysis and…
This works explores and illustrates recent results developed by the author in field of dynamical network analysis. The considered approach is blind, i.e., no a priori assumptions on the interconnected systems are available. Moreover, the…
Graph Machine Learning often involves the clustering of nodes based on similarity structure encoded in the graph's topology and the nodes' attributes. On homophilous graphs, the integration of pooling layers has been shown to enhance the…
Many complex networks, ranging from social to biological systems, exhibit structural patterns consistent with an underlying hyperbolic geometry. Revealing the dimensionality of this latent space can disentangle the structural complexity of…
We propose a new graph kernel for graph classification and comparison using Ollivier Ricci curvature. The Ricci curvature of an edge in a graph describes the connectivity in the local neighborhood. An edge in a densely connected…
Discrete forms of the scalar, sectional and Ricci curvatures are constructed on simplicial piecewise flat triangulations of smooth manifolds, depending directly on the simplicial structure and a choice of dual tessellation. This is done by…
Graph representations offer powerful and intuitive ways to describe data in a multitude of application domains. Here, we consider stochastic processes generating graphs and propose a methodology for detecting changes in stationarity of such…
We design strategies in nonlinear geometric analysis to temper the effects of adversarial learning for sufficiently smooth data of numerical method-type dynamics in encoder-decoder methods, variational and deterministic, through the use of…
In this work, we use the Ricci flow approach to study the gap phenomenon of Riemannian manifolds with non-negative curvature and sub-critical scaling invariant curvature decay. The first main result is a quantitative Ricci flow existence…
This paper presents a new look at the neural network (NN) robustness problem, from the point of view of graph theory analysis, specifically graph curvature. Graph curvature (e.g., Ricci curvature) has been used to analyze system dynamics…
Community detection remains an important problem in data mining, owing to the lack of scalable algorithms that exploit all aspects of available data - namely the directionality of flow of information and the dynamics thereof. Most existing…
We present in this paper a general approach to study the Ricci flow on homogeneous manifolds. Our main tool is a dynamical system defined on a subset H(q,n) of the variety of (q+n)-dimensional Lie algebras, parameterizing the space of all…
Detecting and visualizing what are the most relevant changes in an evolving network is an open challenge in several domains. We present a fast algorithm that filters subsets of the strongest nodes and edges representing an evolving weighted…
We implement methods from computational homology to obtain a topological signal of singularity formation in a selection of geometries evolved numerically by Ricci flow. Our approach, based on persistent homology, produces precise,…
An efficient and relatively fast algorithm for the detection of communities in complex networks is introduced. The method exploits spectral properties of the graph Laplacian-matrix combined with hierarchical-clustering techniques, and…