A Class of Embedded DG Methods for Dirichlet Boundary Control of Convection Diffusion PDEs

We investigated an hybridizable discontinuous Galerkin (HDG) method for a convection diffusion Dirichlet boundary control problem in our earlier work [SIAM J. Numer. Anal. 56 (2018) 2262-2287] and obtained an optimal convergence rate for the control under some assumptions on the desired state and the domain. In this work, we obtain the same convergence rate for the control using a class of embedded DG methods proposed by Nguyen, Peraire and Cockburn [J. Comput. Phys. vol. 302 (2015), pp. 674-692] for simulating fluid flows. Since the global system for embedded DG methods uses continuous elements, the number of degrees of freedom for the embedded DG methods are smaller than the HDG method, which uses discontinuous elements for the global system. Moreover, we introduce a new simpler numerical analysis technique to handle low regularity solutions of the boundary control problem. We present some numerical experiments to confirm our theoretical results

Few-shot Open-set Recognition Using Background as Unknowns

Few-shot open-set recognition aims to classify both seen and novel images given only limited training data of seen classes. The challenge of this task is that the model is required not only to learn a discriminative classifier to classify the pre-defined classes with few training data but also to reject inputs from unseen classes that never appear at training time. In this paper, we propose to solve the problem from two novel aspects. First, instead of learning the decision boundaries between seen classes, as is done in standard close-set classification, we reserve space for unseen classes, such that images located in these areas are recognized as the unseen classes. Second, to effectively learn such decision boundaries, we propose to utilize the background features from seen classes. As these background regions do not significantly contribute to the decision of close-set classification, it is natural to use them as the pseudo unseen classes for classifier learning. Our extensive experiments show that our proposed method not only outperforms multiple baselines but also sets new state-of-the-art results on three popular benchmarks, namely tieredImageNet, miniImageNet, and Caltech-USCD Birds-200-2011 (CUB).Comment: Accpeted to ACM MM 202

Bioinformatics Tools for Exploring Regulatory Mechanisms

Gene expression is the fundamental initial step in the flow of genetic information in biological systems and it is controlled by multiple precisely coordinated regulatory mechanisms, such as structural and epigenetic regulations. Dysregulation of gene expression plays important roles in the development of a broad range of diseases. Modern high-throughput technologies provide unprecedented opportunities to investigate these diverse regulatory mechanisms on a genome-wide scale. Here we develop several methods to analyze these omics profiles. First, Hi-C experiments generate genome-wide contact frequencies between pairs of loci by sequencing DNA segments ligated from loci in close spatial proximity. To detect biologically meaningful interactions between loci, we propose a hidden Markov random field (HMRF) based Bayesian method to rigorously model interaction probabilities in the two-dimensional space based on the contact frequency matrix. By borrowing information from neighboring loci pairs, our method demonstrates superior reproducibility and statistical power in both simulation studies and real data analysis. Second, DNA methylation is a key epigenetic mark involved in both normal development and disease progression. To facilitate joint analysis of methylation data from multiple platforms with varying resolution, we propose a penalized functional regression model to impute missing methylation data. By incorporating functional predictors, our model utilizes information from non-local probes to improve imputation quality. We compared the performance of our functional model to linear regression and the best single probe surrogate in real data and via simulations, and our method showed higher imputation accuracy. The simulated association study further demonstrated that our method substantially improves the statistical power to identify trait- associated methylation loci in epigenome-wide association study (EWAS). Finally, we applied an integrative analysis to characterize molecular systems associated with hepatocellular carcinoma (HCC). Dysregulaton of inflammation-related genes plays a pivotal role in the development of HCC. We performed array-based analyses to comprehensively investigate the contributions of DNA methylation and somatic copy number aberration (SCNA) to the aberrant expression of inflammation-related genes in 30 HCCs and paired non-tumor tissues. The results were validated in public datasets and an additional sample set of 47 paired HCCs and non-tumor tissues. We found that DNA methylation and SCNA together contributed to less than 30% aberrant expression of inflammation-related genes, suggesting that other molecular mechanisms might play major role in the dysregulation in HCCs.Doctor of Philosoph

CRNet: Cross-Reference Networks for Few-Shot Segmentation

Over the past few years, state-of-the-art image segmentation algorithms are based on deep convolutional neural networks. To render a deep network with the ability to understand a concept, humans need to collect a large amount of pixel-level annotated data to train the models, which is time-consuming and tedious. Recently, few-shot segmentation is proposed to solve this problem. Few-shot segmentation aims to learn a segmentation model that can be generalized to novel classes with only a few training images. In this paper, we propose a cross-reference network (CRNet) for few-shot segmentation. Unlike previous works which only predict the mask in the query image, our proposed model concurrently make predictions for both the support image and the query image. With a cross-reference mechanism, our network can better find the co-occurrent objects in the two images, thus helping the few-shot segmentation task. We also develop a mask refinement module to recurrently refine the prediction of the foreground regions. For the $k$-shot learning, we propose to finetune parts of networks to take advantage of multiple labeled support images. Experiments on the PASCAL VOC 2012 dataset show that our network achieves state-of-the-art performance

DeepEMD: Differentiable Earth Mover's Distance for Few-Shot Learning

Deep learning has proved to be very effective in learning with a large amount of labelled data. Few-shot learning in contrast attempts to learn with only a few labelled data. In this work, we develop methods for few-shot image classification from a new perspective of optimal matching between image regions. We employ the Earth Mover's Distance (EMD) as a metric to compute a structural distance between dense image representations to determine image relevance. The EMD generates the optimal matching flows between structural elements that have the minimum matching cost, which is used to calculate the image distance for classification. To generate the important weights of elements in the EMD formulation, we design a cross-reference mechanism, which can effectively alleviate the adverse impact caused by the cluttered background and large intra-class appearance variations. To handle $k$-shot classification, we propose to learn a structured fully connected layer that can directly classify dense image representations with the proposed EMD. Based on the implicit function theorem, the EMD can be inserted as a layer into the network for end-to-end training. Our extensive experiments validate the effectiveness of our algorithm which outperforms state-of-the-art methods by a significant margin on four widely used few-shot classification benchmarks, namely, miniImageNet, tieredImageNet, Fewshot-CIFAR100 (FC100) and Caltech-UCSD Birds-200-2011 (CUB).Comment: Extended version of DeepEMD in CVPR2020 (oral