Related papers: The Geometry of Synchronization (Long Version)
In order to gain a better understanding of the state space of programs, with the aim of making their verification more tractable, models based on directed topological spaces have been introduced, allowing to take in account equivalence…
We have previously defined synchronization (Gomez, E. and K. Schubert 2011) as a relation between the times at which a pair of events can happen, and introduced an algebra that covers all possible relations for such pairs. In this work we…
A new approach to analysis of the synchronization of chaotic oscillations in two (or more) coupled oscillators is described that makes it possible to reveal changes in the structure of attractors and detect the appearance of intermittency.…
Inter-layer synchronization is a distinctive process of multiplex networks whereby each node in a given layer undergoes a synchronous evolution with all its replicas in other layers, irrespective of whether or not it is synchronized with…
Zero-shot graph machine learning, especially with graph neural networks (GNNs), has garnered significant interest due to the challenge of scarce labeled data. While methods like self-supervised learning and graph prompt learning have been…
Real-world systems in epidemiology, social sciences, power transportation, economics and engineering are often described as multilayer networks. Here we first define and compute the symmetries of multilayer networks, and then study the…
We study the grokking phenomenon through the lens of topology. Using persistent homology on point clouds derived from the embedding matrices of a range of models trained on modular arithmetic with varying primes, we identify a clear and…
The phenomenon of synchronization, where entities exhibit stable oscillations with aligned frequencies and phases, has been detected in diverse areas of natural science. It plays a crucial role in achieving frequency locking in multiple…
The geometric evolution of token representations in large language models (LLMs) presents a fundamental paradox: while human language inherently organizes semantic information in low-dimensional spaces ($\sim 10^1$ dimensions), modern LLMs…
Synchronization of coupled oscillators on a $d$-dimensional lattice with the power-law coupling $G(r) = g_0/r^\alpha$ and randomly distributed intrinsic frequency is analyzed. A systematic perturbation theory is developed to calculate the…
An approach based on the kernel methods for capturing the nonlinear interdependence between two signals is introduced. It is demonstrated that the proposed approach is useful for characterizing generalized synchronization with a successful…
In this paper, the investigation is first motivated by showing two examples of simple regular symmetrical graphs, which have the same structural parameters, such as average distance, degree distribution and node betweenness centrality, but…
Teleparallel gravity theories employ a tetrad and a Lorentz spin connection as independent variables in their covariant formulation. In order to solve their field equations, it is helpful to search for solutions which exhibit certain…
Symmetry -- invariance to certain operators -- is a fundamental concept in many branches of physics. We propose ways to measure symmetric properties of vertices, and their surroundings, in networks. To be stable to the randomness inherent…
Most real-world networks are embedded in latent geometries. If a node in a network is found in the vicinity of another node in the latent geometry, the two nodes have a disproportionately high probability of being connected by a link. The…
Linear logic has provided new perspectives on proof-theory, denotational semantics and the study of programming languages. One of its main successes are proof-nets, canonical representations of proofs that lie at the intersection between…
Synchronization is one of the paradigmatic phenomena in the study of complex systems. It has been explored theoretically and experimentally mostly to understand natural phenomena, but also in view of technological applications. Although…
We consider molecule generation in 3D space using language models (LMs), which requires discrete tokenization of 3D molecular geometries. Although tokenization of molecular graphs exists, that for 3D geometries is largely unexplored. Here,…
We study a network of finitely many interacting clusters where each cluster is a collection of globally coupled circle maps in the thermodynamic (or mean field) limit. The state of each cluster is described by a probability measure, and its…
Combining multiple knowledge graphs (KGs) across linguistic boundaries is a persistent challenge due to semantic heterogeneity and the complexity of graph environments. We propose a framework for cross-lingual graph fusion, leveraging the…