Daily Papers

In material sciences, characterizing faults in periodic structures is vital for understanding material properties. To characterize magnetic labyrinthine patterns, it is necessary to accurately identify junctions and terminals, often featuring over a thousand closely packed defects per image. This study introduces a new technique called TM-CNN (Template Matching - Convolutional Neural Network) designed to detect a multitude of small objects in images, such as defects in magnetic labyrinthine patterns. TM-CNN was used to identify these structures in 444 experimental images, and the results were explored to deepen the understanding of magnetic materials. It employs a two-stage detection approach combining template matching, used in initial detection, with a convolutional neural network, used to eliminate incorrect identifications. To train a CNN classifier, it is necessary to create a large number of training images. This difficulty prevents the use of CNN in many practical applications. TM-CNN significantly reduces the manual workload for creating training images by automatically making most of the annotations and leaving only a small number of corrections to human reviewers. In testing, TM-CNN achieved an impressive F1 score of 0.988, far outperforming traditional template matching and CNN-based object detection algorithms.

In this paper, we consider a varying terminal time structure for the stochastic optimal control problem under state constraints, in which the terminal time varies with the mean value of the state. In this new stochastic optimal control system, the control domain does not need to be convex and the diffusion coefficient contains the control variable. To overcome the difficulty in the proof of the related Pontryagin's stochastic maximum principle, we develop asymptotic first- and second-order adjoint equations for the varying terminal time, and then establish its variational equation. In the end, two examples are given to verify the main results of this study.