Lipschitz equivalence of a class of self-similar sets

We consider a class of homogeneous self-similar sets with complete overlaps and give a sufficient condition for the Lipschitz equivalence between members in this class.Comment: A remark was added. To appear in Ann. Acad. Sci. Fenn. Mat

Application of Artificial Neural Networks in Predicting Abrasion Resistance of Solution Polymerized Styrene-Butadiene Rubber Based Composites

Abrasion resistance of solution polymerized styrene-butadiene rubber (SSBR) based composites is a typical and crucial property in practical applications. Previous studies show that the abrasion resistance can be calculated by the multiple linear regression model. In our study, considering this relationship can also be described into the non-linear conditions, a Multilayer Feed-forward Neural Networks model with 3 nodes (MLFN-3) was successfully established to describe the relationship between the abrasion resistance and other properties, using 23 groups of data, with the RMS error 0.07. Our studies have proved that Artificial Neural Networks (ANN) model can be used to predict the SSBR-based composites, which is an accurate and robust process

Deep Descriptor Transforming for Image Co-Localization

Reusable model design becomes desirable with the rapid expansion of machine learning applications. In this paper, we focus on the reusability of pre-trained deep convolutional models. Specifically, different from treating pre-trained models as feature extractors, we reveal more treasures beneath convolutional layers, i.e., the convolutional activations could act as a detector for the common object in the image co-localization problem. We propose a simple but effective method, named Deep Descriptor Transforming (DDT), for evaluating the correlations of descriptors and then obtaining the category-consistent regions, which can accurately locate the common object in a set of images. Empirical studies validate the effectiveness of the proposed DDT method. On benchmark image co-localization datasets, DDT consistently outperforms existing state-of-the-art methods by a large margin. Moreover, DDT also demonstrates good generalization ability for unseen categories and robustness for dealing with noisy data.Comment: Accepted by IJCAI 201

Neural Architecture Search for Compressed Sensing Magnetic Resonance Image Reconstruction

Recent works have demonstrated that deep learning (DL) based compressed sensing (CS) implementation can accelerate Magnetic Resonance (MR) Imaging by reconstructing MR images from sub-sampled k-space data. However, network architectures adopted in previous methods are all designed by handcraft. Neural Architecture Search (NAS) algorithms can automatically build neural network architectures which have outperformed human designed ones in several vision tasks. Inspired by this, here we proposed a novel and efficient network for the MR image reconstruction problem via NAS instead of manual attempts. Particularly, a specific cell structure, which was integrated into the model-driven MR reconstruction pipeline, was automatically searched from a flexible pre-defined operation search space in a differentiable manner. Experimental results show that our searched network can produce better reconstruction results compared to previous state-of-the-art methods in terms of PSNR and SSIM with 4-6 times fewer computation resources. Extensive experiments were conducted to analyze how hyper-parameters affect reconstruction performance and the searched structures. The generalizability of the searched architecture was also evaluated on different organ MR datasets. Our proposed method can reach a better trade-off between computation cost and reconstruction performance for MR reconstruction problem with good generalizability and offer insights to design neural networks for other medical image applications. The evaluation code will be available at https://github.com/yjump/NAS-for-CSMRI.Comment: To be appear in Computerized Medical Imaging and Graphic