• Korean Journal of Mathematics
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• v.30 no.1
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• pp.131-146
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• 2022

This is an expository article about the gradients in deep neural network. It is hard to find a place where gradients in a deep neural network are dealt in details in a systematic and mathematical way. We review and compute the gradients and Jacobians to derive formulas for gradients which appear in the backpropagation and implement them in vectorized forms in Python.

• The korean journal of orthodontics
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• v.52 no.4
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• pp.268-277
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• 2022

Objective: Poor experience with Invisalign treatment affects patient compliance and, thus, treatment outcome. Knowing the potential discomfort level in advance can help orthodontists better prepare the patient to overcome the difficult stage. This study aimed to construct artificial neural networks (ANNs) to predict patient experience in the early stages of Invisalign treatment. Methods: In total, 196 patients were enrolled. Data collection included questionnaires on pain, anxiety, and quality of life (QoL). A four-layer fully connected multilayer perception with three backpropagations was constructed to predict patient experience of the treatment. The input data comprised 17 clinical features. The partial derivative method was used to calculate the relative contributions of each input in the ANNs. Results: The predictive success rates for pain, anxiety, and QoL were 87.7%, 93.4%, and 92.4%, respectively. ANNs for predicting pain, anxiety, and QoL yielded areas under the curve of 0.963, 0.992, and 0.982, respectively. The number of teeth with lingual attachments was the most important factor affecting the outcome of negative experience, followed by the number of lingual buttons and upper incisors with attachments. Conclusions: The constructed ANNs in this preliminary study show good accuracy in predicting patient experience (i.e., pain, anxiety, and QoL) of Invisalign treatment. Artificial intelligence system developed for predicting patient comfort has potential for clinical application to enhance patient compliance.