Scattering Transform for Classification in Non-Intrusive Load Monitoring

Nonintrusive Load Monitoring (NILM) uses computational methods to disaggregate and classify electrical appliances signals. The classification is usually based on the power signatures of the appliances obtained by a feature extractor. State-of-the-art results were obtained extracting NILM features with convolutional neural networks (CNN). However, it depends on the training process with large datasets or data augmentation strategies. In this paper, we propose a feature extraction strategy for NILM using the Scattering Transform (ST). The ST is a convolutional network analogous to CNN. Nevertheless, it does not need a training process in the feature extraction stage, and the filter coefficients are analytically determined (not empirically, like CNN). We perform tests with the proposed method on different publicly available datasets and compare the results with state-of-the-art deep learning-based and traditional approaches (including wavelet transform and V-I representations). The results show that ST classification accuracy is more robust in terms of waveform parameters, such as signal length, sampling frequency, and event location. Besides, ST overcame the state-of-the-art techniques for single and aggregated loads (accuracies above 99% for all evaluated datasets), in different training scenarios with single and aggregated loads, indicating its feasibility in practical NILM scenarios.

Tissue-wide coordination of calcium signaling regulates the epithelial stem cell pool during homeostasis

Regenerative processes in the mammalian skin require coordinated cell-cell communication. Ca2+ signaling can coordinate tissue-level responses in developing and wounded epithelia in tissue explants and invertebrates. However, its role in the homeostatic, regenerative basal layer of the skin epithelium is unknown due to significant challenges in studying signaling dynamics in a spatially complex tissue context in live mice. Here we combine in vivo imaging of dynamic Ca2+ signaling at the single cell level across thousands of cells with a novel computational approach, Geometric Scattering Trajectory Homology (GSTH). GSTH models Ca2+ as signals over a cell adjacency graph and uses a multi-level wavelet-like transform (called a scattering transform) to extract signaling patterns from our high dimensional in vivo datasets. We discover local Ca2+ signaling patterns are orchestrated so that signals flow in a coordinated and directed manner across the tissue, distinct from topographically uncoordinated Ca2+ signaling in excitatory tissues. Directed Ca2+ signaling is regulated by the major gap junction protein in the epidermal stem cell layer, Connexin 43 (Cx43). Cx43 gap junctions are dissociated as cells progress through the cell cycle out of G1 and play an essential role in the progression of stem cells from G2 towards mitosis. Finally, G2 cells display related signaling patterns and are essential for tissue-level signaling coordination. Together, our results provide insight into how such a ubiquitous signaling pathway regulates highly specific behaviors and outcomes at a tissue-wide level to maintain proper homeostasis.

The multi-triple-pole solitons for the focusing mKdV hierarchy with nonzero boundary conditions

In this paper, the general triple-pole multi-soliton solutions are proposed for the focusing modified Korteweg–de Vries (mKdV) equation with both nonzero boundary conditions (NZBCs) and triple zeros of analytical scattering coefficients by means of the inverse scattering transform. Furthermore, we also give the corresponding trace formulae and theta conditions. Particularly, we analyze some representative reflectionless potentials containing the triple-pole multi-dark-anti-dark solitons and breathers. The idea can also be extended to the whole mKdV hierarchy (e.g. the fifth-order mKdV equation, and third-fifth-order mKdV equation) with NZBCs and triple zeros of analytical scattering coefficients. Moreover, these obtained triple-pole solutions can also be degenerated to the triple-pole soliton solutions with zero boundary conditions.