非侵入式负荷识别可以提供用电信息，帮助用户改善用电习惯，是智能用电的关键技术。现有非侵入式负荷识别方法主要基于负荷的稳态特征进行识别，对稳态特征近似的负荷识别率不高。针对此问题，该文结合各类家用负荷在投切过程中的不同特点，提出了一种基于选择性贝叶斯分类的识别方法。首先，利用模拟退火算法从特征库中依据负荷特点选择出对于各类负荷最具辨识度的特征；然后，根据选择的特征和高斯核密度估计方法建立灵活贝叶斯分类器；最后，通过计算各负荷的后验概率对负荷进行识别。经实测数据检验，该方法具有良好的识别精度和计算速度。  

&nbsp; Non-intrusive load identification can provide information of household loads and improve users' habits, and it is the key technique of smart power utilization. Current non-intrusive load identification methods mainly use steady-state characteristics of loads；usually result in inaccuracy when the loads have similar steady-state characteristics. As various household loads have different peculiarity on switching process, this paper proposes a new identification method based on selected Bayes classifier. Firstly, simulated annealing algorithm is adopted to select the most recognizable characteristics of loads from database for characteristics. Secondly, the flexible Bayes classifier is built on the basis of the selected characteristics and Gaussian kernel density estimation methods. Finally, posterior probability is calculated to identify the load. The measured data shows that the proposed method has high identification accuracy and calculation speed.<div>This work is supported by National Natural Science Foundation of China （No. 51477105 ）.</div><div>&nbsp;</div>

深度探索社会治理角度下电力大数据的应用场景，可为政府数字化开展社会民生工作提供辅助决策。独居老人作为特殊电力用户群体，当前缺乏有效技术识别手段，提出一种基于多维负荷特性挖掘的电力特殊用户用电行为分析方法。首先，基于负荷曲线构建用电行为特征指标，利用互信息值对其增添权重以降低指标设置的主观性，同时结合卷积块注意神经网络模型对独居与非独居老人的负荷数据进行特征提取，获取能表征两类居民用电行为的多维负荷特征向量。其次，利用β-级联森林模型对向量进行自适应表征学习，解决了在分类过程中存在样本不平衡问题，提升模型识别性能。最后，以浙江省某小区居民用户为例验证，并对独居老人进行用电行为监测，结果证明了所提方法样本规模较小且在样本不平衡的数据上具有良好的识别性能。

In this study, we explored the application of big data of power regarding social governance, which can aid decision-making for the government in digitally conducting social livelihood work. Specifically, elderly people who live alone currently lack effective technical identification means； thus, a method for analyzing the electricity consumption behavior of specific power users based on multidimensional load characteristic mining is proposed. First, based on the load curve, a power consumption behavior characteristic index was constructed, incorporating the mutual information value to add weight and reduce the subjectivity of the index setting. Simultaneously, combined with the convolutional block attention neural network model, the load data of elderly residents living alone and not living alone were extracted to obtain multidimensional load feature vectors that can represent the two types of residents power consumption behavior. Next, a β-cascaded forest model was employed for adaptive representation learning of vectors to solve the problem of sample imbalance in the classification process and improve the model recognition performance. Finally, a residential user in a community in Zhejiang Province was considered as an example to verify and monitor the electricity consumption behavior of elderly people living alone. The results prove that the method has good recognition performance on data with a small sample size and sample imbalance.

非侵入负荷监测是全面感知负荷数据及能效优化的有效途径。当前非侵入式负荷监测算法的主要观测对象是具有调控潜力的负荷,但对于其中功率较小、负荷曲线相似的电器辨识准确率还不够理想,算法对先验数据的依赖程度较高。基于此,提出一种基于多特征联合稀疏表达的SOM-K-means非侵入式负荷辨识算法,该算法利用负荷特征训练得出最优字典,结合最优字典与多特征联合稀疏表示构建目标函数,求解多特征联合稀疏矩阵,克服了单类负荷特征限制识别负荷种类的问题;将多特征联合稀疏矩阵作为输入,结合自组织(self-organizing map, SOM)神经网络优化的K-means算法与平均绝对误差值进行快速辨识。最后,利用PLAID数据集进行了实验验证,结果表明,所提算法仅需迭代120次辨识准确率即可达到90%,提高了算法收敛速度,证明了该方法能够准确高效地实现负荷辨识。

Nonintrusive load monitoring is an effective method for comprehensively perceiving load data and optimizing energy efficiency. At present, the main observation object of nonintrusive load monitoring algorithms is the load with a regulation potential; however, the identification accuracy is poor for electrical appliances with small power and similar load curves. Moreover, the algorithm is highly dependent on prior data. Therefore, an SOM-K-means non-intrusive load identification algorithm based on multi-feature joint sparse expression is proposed in this study. The algorithm uses load features to train the optimal dictionary. The objective function is constructed by combining the optimal dictionary and multi-feature joint sparse representation, and the multi-feature joint sparse matrix is solved, which overcomes the problem of identifying load types limited by single-type load characteristics. Considering the multi-feature joint sparse matrix as the input, combined with the K-means algorithm optimized by a self-organizing map (SOM) neural network and the mean absolute error, the load was quickly identified. Finally, experimental verification using the PLAID dataset shows that the identification accuracy of the proposed algorithm can reach 90% with only 120 iterations, improving the convergence speed of the algorithm and proving that the method can realize load identification accurately and efficiently.

In this paper, we introduce multiscale persistent functions for biomolecular structure characterization. The essential idea is to combine our multiscale rigidity functions (MRFs) with persistent homology analysis, so as to construct a series of multiscale persistent functions, particularly multiscale persistent entropies, for structure characterization. To clarify the fundamental idea of our method, the multiscale persistent entropy (MPE) model is discussed in great detail. Mathematically, unlike the previous persistent entropy (Chintakunta et al. in Pattern Recognit 48(2):391-401, 2015; Merelli et al. in Entropy 17(10):6872-6892, 2015; Rucco et al. in: Proceedings of ECCS 2014, Springer, pp 117-128, 2016), a special resolution parameter is incorporated into our model. Various scales can be achieved by tuning its value. Physically, our MPE can be used in conformational entropy evaluation. More specifically, it is found that our method incorporates in it a natural classification scheme. This is achieved through a density filtration of an MRF built from angular distributions. To further validate our model, a systematical comparison with the traditional entropy evaluation model is done. It is found that our model is able to preserve the intrinsic topological features of biomolecular data much better than traditional approaches, particularly for resolutions in the intermediate range. Moreover, by comparing with traditional entropies from various grid sizes, bond angle-based methods and a persistent homology-based support vector machine method (Cang et al. in Mol Based Math Biol 3:140-162, 2015), we find that our MPE method gives the best results in terms of average true positive rate in a classic protein structure classification test. More interestingly, all-alpha and all-beta protein classes can be clearly separated from each other with zero error only in our model. Finally, a special protein structure index (PSI) is proposed, for the first time, to describe the "regularity" of protein structures. Basically, a protein structure is deemed as regular if it has a consistent and orderly configuration. Our PSI model is tested on a database of 110 proteins; we find that structures with larger portions of loops and intrinsically disorder regions are always associated with larger PSI, meaning an irregular configuration, while proteins with larger portions of secondary structures, i.e., alpha-helix or beta-sheet, have smaller PSI. Essentially, PSI can be used to describe the "regularity" information in any systems.

Tumor segmentation in whole-slide images of histology slides is an important step towards computer-assisted diagnosis. In this work, we propose a tumor segmentation framework based on the novel concept of persistent homology profiles (PHPs). For a given image patch, the homology profiles are derived by efficient computation of persistent homology, which is an algebraic tool from homology theory. We propose an efficient way of computing topological persistence of an image, alternative to simplicial homology. The PHPs are devised to distinguish tumor regions from their normal counterparts by modeling the atypical characteristics of tumor nuclei. We propose two variants of our method for tumor segmentation: one that targets speed without compromising accuracy and the other that targets higher accuracy. The fast version is based on a selection of exemplar image patches from a convolution neural network (CNN) and patch classification by quantifying the divergence between the PHPs of exemplars and the input image patch. Detailed comparative evaluation shows that the proposed algorithm is significantly faster than competing algorithms while achieving comparable results. The accurate version combines the PHPs and high-level CNN features and employs a multi-stage ensemble strategy for image patch labeling. Experimental results demonstrate that the combination of PHPs and CNN features outperform competing algorithms. This study is performed on two independently collected colorectal datasets containing adenoma, adenocarcinoma, signet, and healthy cases. Collectively, the accurate tumor segmentation produces the highest average patch-level F1-score, as compared with competing algorithms, on malignant and healthy cases from both the datasets. Overall the proposed framework highlights the utility of persistent homology for histopathology image analysis.Copyright © 2019 Elsevier B.V. All rights reserved.

We present the performances of our mathematical deep learning (MathDL) models for D3R Grand Challenge 4 (GC4). This challenge involves pose prediction, affinity ranking, and free energy estimation for beta secretase 1 (BACE) as well as affinity ranking and free energy estimation for Cathepsin S (CatS). We have developed advanced mathematics, namely differential geometry, algebraic graph, and/or algebraic topology, to accurately and efficiently encode high dimensional physical/chemical interactions into scalable low-dimensional rotational and translational invariant representations. These representations are integrated with deep learning models, such as generative adversarial networks (GAN) and convolutional neural networks (CNN) for pose prediction and energy evaluation, respectively. Overall, our MathDL models achieved the top place in pose prediction for BACE ligands in Stage 1a. Moreover, our submissions obtained the highest Spearman correlation coefficient on the affinity ranking of 460 CatS compounds, and the smallest centered root mean square error on the free energy set of 39 CatS molecules. It is worthy to mention that our method on docking pose predictions has significantly improved from our previous ones.