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Given that fingerprint localization methods can be effectively modeled as supervised learning problems, machine learning has been employed for indoor localization tasks based on fingerprint methods. However, it is often challenging for popular machine learning models to effectively capture the unstructured data features inherent in fingerprint data that are generated in diverse propagation environments. In this paper, we propose an indoor localization algorithm based on a high-order graph neural network (HoGNNLoc) to enhance the accuracy of indoor localization and improve localization stability in dynamic environments. The algorithm first designs an adjacency matrix based on the spatial relative locations of access points (APs) to obtain a graph structure; on this basis, a high-order graph neural network is constructed to extract and aggregate the features; finally, the designed fully connected network is used to achieve the regression prediction of the location of the target to be located. The experimental results on our self-built dataset show that the proposed algorithm achieves localization accuracy within 1.29 m at 80% of the cumulative distribution function (CDF) points. The improvements are 59.2%, 51.3%, 36.1%, and 22.7% compared to the K-nearest neighbors (KNN), deep neural network (DNN), simple graph convolutional network (SGC), and graph attention network (GAT). Moreover, even with a 30% reduction in fingerprint data, the proposed algorithm exhibits stable localization performance. On a public dataset, our proposed localization algorithm can also show better performance. [ABSTRACT FROM AUTHOR]

To meet the increased customer demands, microgrid evolved. The structure of microgrid changes dynamically due to the intermittent nature of renewable-based generation, status of the distributed generator and opening of breakers for fault/maintenance. Hence, the magnitude of fault current is dynamic in nature. In order to deal with these dynamic changes, this paper addresses an adaptive central microgrid controller-based protection and relay coordination scheme, which revises the relay settings dynamically (both radial and looped configuration) for every change in topology. In the proposed algorithm, the primary relay responds to a fault immediately since the individual relays are given with fault level setting. For any abnormality in the network, the fault location is determined both via local relay and microgrid central controller (MCC). Hence, even though the local relay fails to identify the fault due to high fault impedance, the MCC locates the fault accurately and isolates the minimum faulty part. The coordination between relays is carried out by MCC in a time-graded manner based on microgrid central protection and relay coordination algorithm. The proposed algorithm is tested using Matlab in a microgrid built based on the IEEE 33 bus distribution network. [ABSTRACT FROM AUTHOR]

This paper presents a novel theory and method to calculate the canonical labelings of digraphs whose definition is entirely different from the traditional definition of Nauty. It indicates the mutual relationships that exist between the canonical labeling of a digraph and the canonical labeling of its complement graph. It systematically examines the link between computing the canonical labeling of a digraph and the k-neighborhood and k-mix-neighborhood subdigraphs. To facilitate the presentation, it introduces several concepts including mix diffusion outdegree sequence and entire mix diffusion outdegree sequences. For each node in a digraph G, it assigns an attribute m_NearestNode to enhance the accuracy of calculating canonical labeling. The four theorems proved here demonstrate how to determine the first nodes added into MaxQ(G). Further, the other two theorems stated below deal with identifying the second nodes added into MaxQ(G). When computing Cmax(G), if MaxQ(G) already contains the first i vertices u1, u2, ..., ui, Diffusion Theorem provides a guideline on how to choose the subsequent node of MaxQ(G). Besides, the Mix Diffusion Theorem shows that the selection of the (i + 1)th vertex of MaxQ(G) for computing Cmax(G) is from the open mix-neighborhood subdigraph N++(Q) of the nodes set Q = {u1, u2, ..., ui}. It also offers two theorems to calculate the Cmax(G) of the disconnected digraphs. The four algorithms implemented in it illustrate how to calculate MaxQ(G) of a digraph. Through software testing, the correctness of our algorithms is preliminarily verified. Our method can be utilized to mine the frequent subdigraph. We also guess that if there exists a vertex v ∈ S+(G) satisfying conditions Cmax(G - v) ≤ Cmax(G - w) for each w ∈ S+(G) ^ w ≠ v, then u1 = v for MaxQ(G). [ABSTRACT FROM AUTHOR]

This paper puts forward an innovative theory and method to calculate the canonical labelings of graphs that are distinct to N a u t y 's. It shows the correlation between the canonical labeling of a graph and the canonical labeling of its complement graph. It regularly examines the link between computing the canonical labeling of a graph and the canonical labeling of its o p e n k- n e i g h b o r h o o d s u b g r a p h . It defines d i f f u s i o n d e g r e e s e q u e n c e s and e n t i r e d i f f u s i o n d e g r e e s e q u e n c e . For each node of a graph G, it designs a characteristic m _ N e a r e s t N o d e to improve the precision for calculating canonical labeling. Two theorems established here display how to compute the first nodes of M a x Q (G) . Another theorem presents how to determine the second nodes of M a x Q (G) . When computing C m a x (G) , if M a x Q (G) already holds the first i nodes u 1 , u 2 , ⋯ , u i , Diffusion and Nearest Node theorems provide skill on how to pick the succeeding node of M a x Q (G) . Further, it also establishes two theorems to determine the C m a x (G) of disconnected graphs. Four algorithms implemented here demonstrate how to compute M a x Q (G) of a graph. From the results of the software experiment, the accuracy of our algorithms is preliminarily confirmed. Our method can be employed to mine the frequent subgraph. We also conjecture that if there is a node v ∈ S (G) meeting conditions C m a x (G − v) ⩽ C m a x (G − w) for each w ∈ S (G) ∧ w ≠ v , then u 1 = v for M a x Q (G) . [ABSTRACT FROM AUTHOR]