Related papers: Feigenbaum graphs: a complex network perspective o…
The limited penetrable horizontal visibility algorithm is a new time analysis tool and is a further development of the horizontal visibility algorithm. We present some exact results on the topological properties of the limited penetrable…
What is a time-varying graph, a time-varying topological space, or, more generally, a mathematical structure that evolves over time? In this work, we lay the foundations for a general theory of temporal data by introducing categories of…
We analyze complexity in spatial network ensembles through the lens of graph entropy. Mathematically, we model a spatial network as a soft random geometric graph, i.e., a graph with two sources of randomness, namely nodes located randomly…
Understanding the training dynamics of deep neural networks (DNNs) is important as it can lead to improved training efficiency and task performance. Recent works have demonstrated that representing the wirings of static graph cannot capture…
Complex networks are universal, arising in fields as disparate as sociology, physics, and biology. In the past decade, extensive research into the properties and behaviors of complex systems has uncovered surprising commonalities among the…
There have been several recent efforts towards developing representations for multivariate time-series in an unsupervised learning framework. Such representations can prove beneficial in tasks such as activity recognition, health…
A link stream is a set of possibly weighted triplets (t, u, v) modeling that u and v interacted at time t. Link streams offer an effective model for datasets containing both temporal and relational information, making their proper analysis…
Transitions to chaos in archetypal low-dimensional nonlinear maps offer real and precise model systems in which to assess proposed generalizations of statistical mechanics. The known association of chaotic dynamics with the structure of…
Sequences of correlated binary patterns can represent many time-series data including text, movies, and biological signals. These patterns may be described by weighted combinations of a few dominant structures that underpin specific…
We study dynamical systems composed of a set of linearly coupled quadratic maps which, if uncoupled, would be on the Feigenbaum accumulation point. For two units we prove the existence of an infinite number of sinks for an open set of…
The concept of time series irreversibility -- the degree by which the statistics of signals are not invariant under time reversal -- naturally appears in non-equilibrium physics in stationary systems which operate away from equilibrium and…
Some of the basic properties of any dynamical system can be summarized by a graph. The dynamical systems in our theory run from maps like the logistic map to ordinary differential equations to dissipative partial differential equations. Our…
This paper presents graph theoretic conditions for the controllability and accessibility of bilinear systems over the special orthogonal group, the special linear group and the general linear group, respectively, in the presence of drift…
Inspired by "quantum graphity" models for spacetime, a statistical model of graphs is proposed to explore possible realizations of emergent manifolds. Graphs with given numbers of vertices and edges are considered, governed by a very…
Graph Neural Networks (GNNs) have recently become increasingly popular due to their ability to learn complex systems of relations or interactions arising in a broad spectrum of problems ranging from biology and particle physics to social…
These lecture notes have been written for a short introductory course on universality and renormalization group techniques given at the VIII Modave School in Mathematical Physics by the author, intended for PhD students and researchers new…
Many real-world networks of interest are embedded in physical space. We present a new random graph model aiming to reflect the interplay between the geometries of the graph and of the underlying space. The model favors configurations with…
The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a…
Chaotic attractors, chaotic saddles and periodic orbits are examples of chain-recurrent sets. Using arbitrary small controls, a trajectory starting from any point in a chain-recurrent set can be steered to any other in that set. The…
Despite the celebrated popularity of Graph Neural Networks (GNNs) across numerous applications, the ability of GNNs to generalize remains less explored. In this work, we propose to study the generalization of GNNs through a novel…