Dataset Information

On the Construction of Group Equivariant Non-Expansive Operators via Permutants and Symmetric Functions.

ABSTRACT: Group Equivariant Operators (GEOs) are a fundamental tool in the research on neural networks, since they make available a new kind of geometric knowledge engineering for deep learning, which can exploit symmetries in artificial intelligence and reduce the number of parameters required in the learning process. In this paper we introduce a new method to build non-linear GEOs and non-linear Group Equivariant Non-Expansive Operators (GENEOs), based on the concepts of symmetric function and permutant. This method is particularly interesting because of the good theoretical properties of GENEOs and the ease of use of permutants to build equivariant operators, compared to the direct use of the equivariance groups we are interested in. In our paper, we prove that the technique we propose works for any symmetric function, and benefits from the approximability of continuous symmetric functions by symmetric polynomials. A possible use in Topological Data Analysis of the GENEOs obtained by this new method is illustrated.

SUBMITTER: Conti F

PROVIDER: S-EPMC8887714 | biostudies-literature | 2022

REPOSITORIES: biostudies-literature

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On the Construction of Group Equivariant Non-Expansive Operators <i>via</i> Permutants and Symmetric Functions.

Conti Francesco F Frosini Patrizio P Quercioli Nicola N

Frontiers in artificial intelligence 20220215

Group Equivariant Operators (GEOs) are a fundamental tool in the research on neural networks, since they make available a new kind of geometric knowledge engineering for deep learning, which can exploit symmetries in artificial intelligence and reduce the number of parameters required in the learning process. In this paper we introduce a new method to build non-linear GEOs and non-linear Group Equivariant Non-Expansive Operators (GENEOs), based on the concepts of symmetric function and permutant ...[more]

PMID: 35243336

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Project description:Lung ultrasound is a growing modality in clinics for diagnosing and monitoring acute and chronic lung diseases due to its low cost and accessibility. Lung ultrasound works by emitting diagnostic pulses, receiving pressure waves and converting them into radio frequency (RF) data, which are then processed into B-mode images with beamformers for radiologists to interpret. However, unlike conventional ultrasound for soft tissue anatomical imaging, lung ultrasound interpretation is complicated by complex reverberations from the pleural interface caused by the inability of ultrasound to penetrate air. The indirect B-mode images make interpretation highly dependent on reader expertise, requiring years of training, which limits its widespread use despite its potential for high accuracy in skilled hands. To address these challenges and democratize ultrasound lung imaging as a reliable diagnostic tool, we propose Luna (the Lung Ultrasound Neural operator for Aeration), an AI model that directly reconstructs lung aeration maps from RF data, bypassing the need for traditional beamformers and indirect interpretation of B-mode images. Luna uses a Fourier neural operator, which processes RF data efficiently in Fourier space, enabling accurate reconstruction of lung aeration maps. From reconstructed aeration maps, we calculate lung percent aeration, a key clinical metric, offering a quantitative, reader-independent alternative to traditional semi-quantitative lung ultrasound scoring methods. The development of Luna involves synthetic and real data: We simulate synthetic data with an experimentally validated approach and scan ex vivo swine lungs as real data. Trained on abundant simulated data and fine-tuned with a small amount of real-world data, Luna achieves robust performance, demonstrated by an aeration estimation error of 9% in ex-vivo swine lung scans. We demonstrate the potential of directly reconstructing lung aeration maps from RF data, providing a foundation for improving lung ultrasound interpretability, reproducibility and diagnostic utility.

Project description:BackgroundCognitive ability refers to the ability to receive, process, store, and extract information. It is the most important psychological condition for people to successfully complete activities. Previous studies have shown that the design of the human-computer interface of the command and control system cannot exceed the cognitive ability of the operator of the command and control system, and it must match the cognitive ability of the operator in order to reduce the mental load intensity, and improve the accuracy, timeliness and work efficiency. However, previous researchers in the field of cognitive science have not put forward a core index system that can represent the cognitive ability of ship command and control system operators and the importance of each index, and there are few achievements that can be used for reference.ObjectiveTo explore the core index system of cognitive ability that affecting the cognitive process of command and control system operators, and to verify the index system.MethodsBased on the classic O*NET questionnaire, two indexes of O*NET were revised, three indexes of response ability were added, and then a questionnaire on the importance evaluation of cognitive abilities index was formed. The questionnaire includes 24 indexes in six aspects: verbal abilities, idea generation and reasoning abilities, quantitative abilities, visual perception abilities, mnemonic and attentive abilities, and response abilities. The cognitive ability importance evaluation data of 202 people from different positions in the ship command and control system were collected. These data reflect the overall level of cognitive ability of operators in the whole ship command and control field.ResultsThe data analysis results show that: firstly, the most important cognitive abilities affecting command and control system operators were visual perception abilities, mnemonic and attentive abilities, and response abilities. Secondly, the results of confirmatory factor analysis show that CMIN/DF, GFI, CFI, TLI, RMSEA, RMR and other indicators used in the model test all meet the requirements. The model has a good fitting degree, and the overall index extraction method is feasible. Thirdly, the independence T test results show that for beginners and experienced experts, there is a significant difference in the important evaluation of mnemonic and attentive abilities, while there is no significant difference in the important evaluation of response and visual perception abilities. Fourthly, the results of Bi-group confirmatory factor analysis experiment show that the structural model has good stability and factor invariance.ConclusionsThrough the research of this paper, the index system which can express the core cognitive ability of the commander of command and control system is successfully constructed, and the index system has been fully verified by mathematics. The 3 abilities and 10 indexes in the index system are closely related to the work tasks of operators, which also reflects the correctness of our construction results to a certain extent. According to the results of data analysis, there are differences between assistant commanders and professional commanders in the evaluation of the importance of some indexes, which reflects the importance of working age and experience to the promotion of position skills. The results of this research are of great significance for the subsequent acquisition of cognitive ability data and assessment of post cognitive ability of command and control system operators.

Dataset Information

On the Construction of Group Equivariant Non-Expansive Operators via Permutants and Symmetric Functions.

Publications

On the Construction of Group Equivariant Non-Expansive Operators <i>via</i> Permutants and Symmetric Functions.

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