On Schr\"odinger equations involving the regional fractional Laplacian in a ball with the zero boundary condition

Our purpose in this article to show the existence of positive classical solutions of $$( - \Delta )_{B_1}^s u +u=h_1 u^p+\epsilon h_2 \quad {\rm in} \ \, B_1,\qquad u = 0 \quad {\rm on}\ \partial B_1$$ for $\epsilon>0$ small enough, where $( - \Delta )_{B_1}^s$ is the regional fractional Laplacian, $p>1$, $h_i$ with $i=1,2$ are H\"older continuous and satisfy some additional conditions. Our existence is based on the solution of $$( - \Delta )_{B_1}^s u +u=1 \quad {\rm in} \ \, B_1,\qquad u = 0 \quad {\rm on}\ \partial B_1.$$Comment: 2

Detecting Energy Theft in Different Regions Based on Convolutional and Joint Distribution Adaptation

© 2023 IEEE. This is the accepted manuscript version of an article which has been published in final form at https://doi.org/10.1109/TIM.2023.3291769Electricity theft has been a major concern all over the world. There are great differences in electricity consumption among residents from different regions. However, existing supervised methods of machine learning are not in detecting electricity theft from different regions, while the development of transfer learning provides a new view for solving the problem. Hence, an electricity-theft detection method based on Convolutional and Joint Distribution Adaptation(CJDA) is proposed. In particular, the model consists of three components: convolutional component (Conv), Marginal Distribution Adaptation(MDA) and Conditional Distribution Adaptation(CDA). The convolutional component can efficiently extract the customer’s electricity characteristics. The Marginal Distribution Adaptation can match marginal probability distributions and solve the discrepancies of residents from different regions while Conditional Distribution Adaptation can reduce the difference of the conditional probability distributions and enhance the discrimination of features between energy thieves and normal residents. As a result, the model can find a matrix to adapt the electricity residents in different regions to achieve electricity theft detection. The experiments are conducted on electricity consumption data from the Irish Smart Energy Trial and State Grid Corporation of China and metrics including ACC, Recall, FPR, AUC and F1Score are used for evaluation. Compared with other methods including some machine learning methods such as DT, RF and XGBoost, some deep learning methods such as RNN, CNN and Wide & Deep CNN and some up-to-date methods such as BDA, WBDA, ROCKET and MiniROCKET, our proposed method has a better effect on identifying electricity theft from different regions.Peer reviewe

A New Comparative Definition of Community and Corresponding Identifying Algorithm

In this paper, a new comparative definition for community in networks is proposed and the corresponding detecting algorithm is given. A community is defined as a set of nodes, which satisfy that each node's degree inside the community should not be smaller than the node's degree toward any other community. In the algorithm, the attractive force of a community to a node is defined as the connections between them. Then employing attractive force based self-organizing process, without any extra parameter, the best communities can be detected. Several artificial and real-world networks, including Zachary Karate club network and College football network are analyzed. The algorithm works well in detecting communities and it also gives a nice description for network division and group formation.Comment: 11 pages, 4 fihure

Product Quality Modeling and Optimizing Control of Soft Capsule Dropping Pills Based on LSSVM and PSO

Soft capsule dropping pills product quality control system is a multi-input and multi-output complex system. First of all, the process parameters and a two-level hierarchy index system of soft capsule pills product quality were proposed based on the analysis to the production process. Then the model was established based on least squares support vector machine (LSSVM), whose inputs are the process parameters and outputs are the secondary quality indexes. Analysis hierarchy process (AHP) was used to determine the weights of the secondary quality indexes. On this basis, particle swarm optimization (PSO) algorithm was used to optimize the process parameters in order to improve the yield of soft capsule pills, which is a multi-objective optimization problem. The nominal values of the process parameters corresponding to the highest yield can be obtained. The yield increases by 2.7% when the optimizing parameters are used to the soft capsule dropping pills process

Experimental Observation of Efficient Nonreciprocal Mode Transitions via Spatiotemporally-Modulated Acoustic Metamaterials

In lossless acoustic systems, mode transitions are always time-reversible, consistent with Lorentz reciprocity, giving rise to symmetric sound manipulation in space-time. To overcome this fundamental limitation and break space-time symmetry, nonreciprocal sound steering is realized by designing and experimentally implementing spatiotemporally-modulated acoustic metamaterials. Relying on no slow mechanical parts, unstable and noisy airflow or complicated piezoelectric array, our mechanism uses the coupling between an ultrathin membrane and external electromagnetic field to realize programmable, dynamic control of acoustic impedance in a motionless and noiseless manner. The fast and flexible impedance modulation at the deeply subwavelength scale enabled by our compact metamaterials provides an effective unidirectional momentum in space-time to realize irreversible transition in k-{\omega} space between different diffraction modes. The nonreciprocal wave-steering functionality of the proposed metamaterial is elucidated by theoretically deriving the time-varying acoustic response and demonstrated both numerically and experimentally via two distinctive examples of unidirectional evanescent wave conversion and nonreciprocal blue-shift focusing. This work can be further extended into the paradigm of Bloch waves and impact other vibrant domains, such as non-Hermitian topological acoustics and parity-time-symmetric acoustics.Comment: 15 pages, 4 figure