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1. The Efficacy of Computerized Cognitive Behavioral Therapy for Depressive and Anxiety Symptoms in Patients With COVID-19: Randomized Controlled Trial

Author

Liu, Zhifen, Qiao, Dan, Xu, Yifan, Zhao, Wentao, Yang, Yang, Wen, Dan, Li, Xinrong, Nie, Xiaoping, Dong, Yongkang, Tang, Shiyou, Jiang, Yi, Wang, Ying, Zhao, Juan, and Xu, Yong

Subjects
Computer applications to medicine. Medical informatics, R858-859.7, Public aspects of medicine, RA1-1270
Abstract

BackgroundThe prevalence of depressive and anxiety symptoms in patients with COVID-19 is higher than usual. Previous studies have shown that there are drug-to-drug interactions between antiretroviral drugs and antidepressants. Therefore, an effective and safe treatment method was needed. Cognitive behavioral therapy (CBT) is the first-line psychological therapy in clinical treatment. Computerized CBT (cCBT) was proven to be an effective alternative to CBT and does not require face-to-face therapy between a therapist and the patient, which suited the COVID-19 pandemic response. ObjectiveThis study aims to evaluate the efficacy of the cCBT program we developed in improving depressive and anxiety symptoms among patients with COVID-19. MethodsWe customized a cCBT program focused on improving depressive and anxiety symptoms among patients with COVID-19, and then, we assessed its effectiveness. Screening was based on symptoms of depression or anxiety for patients who scored ≥7 on the Hamilton Depression Rating Scale (HAMD17) or the Hamilton Anxiety Scale (HAMA). A total of 252 patients with COVID-19 at five sites were randomized into two groups: cCBT + treatment as usual (TAU; n=126) and TAU without cCBT (n=126). The cCBT + TAU group received the cCBT intervention program for 1 week. The primary efficacy measures were the HAMD17 and HAMA scores. The secondary outcome measures were the Self-Rating Depression Scale (SDS), Self-Rating Anxiety Scale (SAS), and Athens Insomnia Scale (AIS). Assessments were carried out pre- and postintervention. The patients’ symptoms of anxiety and depression in one of the centers were assessed again within 1 month after the postintervention assessment. ResultsThe cCBT + TAU group displayed a significantly decreased score on the HAMD17, HAMA, SDS, SAS, and AIS after the intervention compared to the TAU group (all P

Published
2021
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11. Normal Cones Intersection Rule and Optimality Analysis for Low-Rank Matrix Optimization with Affine Manifolds

Author

Li, Xinrong and Luo, Ziyan

Subjects
Mathematics - Optimization and Control
Abstract

The low-rank matrix optimization with affine manifold (rank-MOA) aims to minimize a continuously differentiable function over a low-rank set intersecting with an affine manifold. This paper is devoted to the optimality analysis for rank-MOA. As a cornerstone, the intersection rule of the Fr\'{e}chet normal cone to the feasible set of the rank-MOA is established under some mild linear independence assumptions. Aided with the resulting explicit formulae of the underlying normal cone, the so-called F-stationary point and the \alpha-stationary point of rank-MOA are investigated and the relationship with local/global minimizers are then revealed in terms of first-order optimality conditions. Furthermore, the second-order optimality analysis, including the necessary and the sufficient conditions, is proposed based on the second-order differentiation information of the model. All these results will enrich the theory of low-rank matrix optimization and give potential clues to designing efficient numerical algorithms for seeking low rank solutions. Meanwhile, two specific applications of the rank-MOA are discussed to illustrate our proposed optimality analysis., Comment: arXiv admin note: text overlap with arXiv:1912.03029

Published
2022

43. Low-Rank Matrix Optimization Over Affine Set

Author

Li, Xinrong, Xiu, Naihua, and Luo, Ziyan

Subjects
Mathematics - Spectral Theory, Mathematics - Optimization and Control
Abstract

The low-rank matrix optimization with affine set (rank-MOA) is to minimize a continuously differentiable function over a low-rank set intersecting with an affine set. Under some suitable assumptions, the intersection rule of the Fr\'{e}chet normal cone to the feasible set of the rank-MOA is established. This allows us to propose the first-order optimality conditions for the rank-MOA in terms of the so-called F-stationary point and the $\alpha$-stationary point. Furthermore, the second-order optimality analysis, including the necessary condition and the sufficient one, is proposed as well. All these results will enrich the theory of low-rank matrix optimization and give potential clues to designing efficient numerical algorithms for seeking low-rank solutions. Meanwhile, we illustrate our proposed optimality analysis for several specific applications of the rank-MOA including the Hankel matrix approximation problem in system identification and the low-rank representation on linear manifold in signal processing.

Published
2019

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