Recently, a semidefinite programming (SDP) relaxation approach has been proposed to solve the sensor network localization problem. Although it achieves high accuracy in estimating the sensor locations, the speed of the SDP approach is not satisfactory for practical applications. In this paper we propose methods to further relax the SDP relaxation, more precisely, to relax the single semidefinite matrix cone into a set of small-size semidefinite submatrix cones, which we call a sub-SDP (SSDP) approach. We present two such relaxations. Although they are weaker than the original SDP relaxation, they retain the key theoretical property, and numerical experiments show that they are both efficient and accurate. The speed of the SSDP is even faster than that of other approaches based on weaker relaxations. The SSDP approach may also pave a way to efficiently solving general SDP problems without sacrificing the solution quality.

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Parkinson’s disease (PD) is one of the most common progressive degenerative diseases, and its diagnosis is challenging on clinical grounds. Clinically, effective and quantifiable biomarkers to detect PD are urgently needed. In our study, we analyzed data from two centers, the primary set was used to train the model, and the independent external validation set was used to validate our model. We applied amplitude of low-frequency fluctuation (ALFF)-based radiomics method to extract radiomics features (including first- and high-order features). Subsequently, t-test and least absolute shrinkage and selection operator (LASSO) were harnessed for feature selection and data dimensionality reduction, and grid search method and nested 10-fold cross-validation were applied to determine the optimal hyper-parameter λ of LASSO and evaluate the performance of the model, in which a support vector machine was used to construct the classification model to classify patients with PD and healthy controls (HCs). We found that our model achieved good performance [accuracy = 81.45% and area under the curve (AUC) = 0.850] in the primary set and good generalization in the external validation set (accuracy = 67.44% and AUC = 0.667). Most of the discriminative features were high-order radiomics features, and the identified brain regions were mainly located in the sensorimotor network and lateral parietal cortex. Our study indicated that our proposed method can effectively classify patients with PD and HCs, ALFF-based radiomics features that might be potential biomarkers of PD, and provided further support for the pathological mechanism of PD, that is, PD may be related to abnormal brain activity in the sensorimotor network and lateral parietal cortex.

Electrophysiological Monitoring A multifunctional ionic hydrogel based on dual physical cross‐linked networks helps build a highly compliant and gapless interface with the skin, as described by Tailang Yin, Zhou Li, and co‐workers in article number 2200653. When applied as the epidermal electrode, it shows good capability to record multifarious electrophysiological signals with high signal‐to‐noise ratio and ultra‐low detection limit.

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