RESUMO
Graph neural networks (GNNs) excel in modeling relational data such as biological, social, and transportation networks, but the underpinnings of their success are not well understood. Traditional complexity measures from statistical learning theory fail to account for observed phenomena like the double descent or the impact of relational semantics on generalization error. Motivated by experimental observations of "transductive" double descent in key networks and datasets, we use analytical tools from statistical physics and random matrix theory to precisely characterize generalization in simple graph convolution networks on the contextual stochastic block model. Our results illuminate the nuances of learning on homophilic versus heterophilic data and predict double descent whose existence in GNNs has been questioned by recent work. We show how risk is shaped by the interplay between the graph noise, feature noise, and the number of training labels. Our findings apply beyond stylized models, capturing qualitative trends in real-world GNNs and datasets. As a case in point, we use our analytic insights to improve performance of state-of-the-art graph convolution networks on heterophilic datasets.
RESUMO
Brain-computer interfaces have seen extraordinary surges in developments in recent years, and a significant discrepancy now exists between the abundance of available data and the limited headway made in achieving a unified theoretical framework. This discrepancy becomes particularly pronounced when examining the collective neural activity at the micro and meso scale, where a coherent formalization that adequately describes neural interactions is still lacking. Here, we introduce a mathematical framework to analyze systems of natural neurons and interpret the related empirical observations in terms of lattice field theory, an established paradigm from theoretical particle physics and statistical mechanics. Our methods are tailored to interpret data from chronic neural interfaces, especially spike rasters from measurements of single neuron activity, and generalize the maximum entropy model for neural networks so that the time evolution of the system is also taken into account. This is obtained by bridging particle physics and neuroscience, paving the way for particle physics-inspired models of the neocortex.
RESUMO
Objective: In order to address the issues of inconvenience, high medical costs, and lack of universality associated with traditional knee rehabilitation equipment, a portable intelligent wheelchair for knee rehabilitation was designed in this study. Methods: Based on the analysis of the knee joint's structure and rehabilitation mechanisms, an electric pushrod-driven rehabilitation institution was developed. A multi-functional module was designed with a modular approach, and the control of the wheelchair body and each functional module was implemented using an STM32 single-chip microcomputer. A three-dimensional model was established using SolidWorks software. In conjunction with Adams and Ansys simulation software, kinematic and static analyses were conducted on the knee joint rehabilitation institution and its core components. A prototype was constructed to verify the equipment's actual performance. Results: According to the prototype testing, the actual range of motion for the knee joint swing rod is 15.1°~88.9°, the angular speed of the swing rod ranges from -7.9 to 8.1°/s, the angular acceleration of the swing rod varies from -4.2 to 1.6°/s², the thrust range of the electric pushrod is -82.6 to 153.1 N, and the maximum displacement of the load pedal is approximately 1.7 mm, with the leg support exhibiting a maximum deformation of about 1.5 mm. Conclusion: The intelligent knee joint rehabilitation wheelchair meets the designed functions and its actual performance aligns with the design criteria, thus validating the rationality and feasibility of the structural design.