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Renormalization of networks with weak geometric coupling.
Phys Rev E
September 2024
Departament de Física de la Matèria Condensada, Universitat de Barcelona, Martí i Franquès 1, E-08028 Barcelona, Spain.
The renormalization group is crucial for understanding systems across scales, including complex networks. Renormalizing networks via network geometry, a framework in which their topology is based on the location of nodes in a hidden metric space, is one of the foundational approaches. However, the current methods assume that the geometric coupling is strong, neglecting weak coupling in many real networks.
View Article and Find Full Text PDFEvaluating and Comparing Measures of Aperiodic Neural Activity.
bioRxiv
September 2024
Department of Cognitive Science, University of California, San Diego.
Neuro-electrophysiological recordings contain prominent aperiodic activity - meaning irregular activity, with no characteristic frequency - which has variously been referred to as 1/f (or 1/f-like activity), fractal, or 'scale-free' activity. Previous work has established that aperiodic features of neural activity is dynamic and variable, relating (between subjects) to healthy aging and to clinical diagnoses, and also (within subjects) tracking conscious states and behavioral performance. There are, however, a wide variety of conceptual frameworks and associated methods for the analyses and interpretation of aperiodic activity - for example, time domain measures such as the autocorrelation, fractal measures, and/or various complexity and entropy measures, as well as measures of the aperiodic exponent in the frequency domain.
View Article and Find Full Text PDFFrom individuals to families: design and application of self-similar chiral nanomaterials.
Mater Horiz
August 2024
School of Pharmacy, Changzhou University, Changzhou, Jiangsu 213164, China.
Establishing an intimate relationship between similar individuals is the beginning of self-extension. Various self-similar chiral nanomaterials can be designed using an individual-to-family approach, accomplishing self-extension. This self-similarity facilitates chiral communication, transmission, and amplification of synthons.
View Article and Find Full Text PDF3D hand pose and mesh estimation via a generic Topology-aware Transformer model.
Front Neurorobot
May 2024
Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai, China.
In Human-Robot Interaction (HRI), accurate 3D hand pose and mesh estimation hold critical importance. However, inferring reasonable and accurate poses in severe self-occlusion and high self-similarity remains an inherent challenge. In order to alleviate the ambiguity caused by invisible and similar joints during HRI, we propose a new Topology-aware Transformer network named HandGCNFormer with depth image as input, incorporating prior knowledge of hand kinematic topology into the network while modeling long-range contextual information.
View Article and Find Full Text PDFFractal networks: Topology, dimension, and complexity.
Chaos
April 2024
School of Computing, University of Connecticut, 371 Fairfield Way, Storrs, Connecticut 06269, USA.
Over the past two decades, the study of self-similarity and fractality in discrete structures, particularly complex networks, has gained momentum. This surge of interest is fueled by the theoretical developments within the theory of complex networks and the practical demands of real-world applications. Nonetheless, translating the principles of fractal geometry from the domain of general topology, dealing with continuous or infinite objects, to finite structures in a mathematically rigorous way poses a formidable challenge.
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