Codes in the sum-rank metric have received many attentions in recent years, since they have wide applications in the multishot network coding, the space-time coding and the distributed storage. Fundamental bounds, some explicit or probabilistic constructions of sum-rank codes and their decoding algorithms have been developed in previous papers. In this paper, we construct covering codes in the sum-rank metric from covering codes in the Hamming metric. Then some upper bounds on sizes of covering codes in the sum-rank metric are presented. Block length functions of covering codes in the sum-rank metric are also introduced and studied. As applications of our upper bounds on covering codes in the sum-rank metric and block length functions, several strong Singleton-like bounds on sum-rank codes are proposed and proved. These strong Singleton-like bounds are much stronger than the Singleton-like bound for sum-rank codes, when block lengths are larger and minimum sum-rank distances are small. An upper bound on sizes of list-decodable codes in the sum-rank metric is also given, which leads to an asymptotic bound on list-decodability of sum-rank codes. We also give upper bounds on block lengths of general MSRD codes.
Patients with atrial fibrillation have a 5-7 fold increased risk of having an ischemic stroke. In these cases, the most common site of thrombus localization is inside the left atrial appendage (LAA) and studies have shown a correlation between the LAA shape and the risk of ischemic stroke. These studies make use of manual measurement and qualitative assessment of shape and are therefore prone to large inter-observer discrepancies, which may explain the contradictions between the conclusions in different studies. We argue that quantitative shape descriptors are necessary to robustly characterize LAA morphology and relate to other functional parameters and stroke risk. Deep Learning methods are becoming standardly available for segmenting cardiovascular structures from high resolution images such as computed tomography (CT), but only few have been tested for LAA segmentation. Furthermore, the majority of segmentation algorithms produces non-smooth 3D models that are not ideal for further processing, such as statistical shape analysis or computational fluid modelling. In this paper we present a fully automatic pipeline for image segmentation, mesh model creation and statistical shape modelling of the LAA. The LAA anatomy is implicitly represented as a signed distance field (SDF), which is directly regressed from the CT image using Deep Learning. The SDF is further used for registering the LAA shapes to a common template and build a statistical shape model (SSM). Based on 106 automatically segmented LAAs, the built SSM reveals that the LAA shape can be quantified using approximately 5 PCA modes and allows the identification of two distinct shape clusters corresponding to the so-called chicken-wing and non-chicken-wing morphologies.
Conventional distributed approaches to coverage control may suffer from lack of convergence and poor performance, due to the fact that agents have limited information, especially in non-convex discrete environments. To address this issue, we extend the approach of [Marden 2016] which demonstrates how a limited degree of inter-agent communication can be exploited to overcome such pitfalls in one-dimensional discrete environments. The focus of this paper is on extending such results to general dimensional settings. We show that the extension is convergent and keeps the approximation ratio of 2, meaning that any stable solution is guaranteed to have a performance within 50% of the optimal one. The experimental results exhibit that our algorithm outperforms several state-of-the-art algorithms, and also that the runtime is scalable.
Hypergraphs are marked by complex topology, expressing higher-order interactions among multiple entities with hyperedges. Lately, hypergraph-based deep learning methods to learn informative data representations for the problem of node classification on text-attributed hypergraphs have garnered increasing research attention. However, existing methods struggle to simultaneously capture the full extent of hypergraph structural information and the rich linguistic attributes inherent in the nodes attributes, which largely hampers their effectiveness and generalizability. To overcome these challenges, we explore ways to further augment a pretrained BERT model with specialized hypergraph-aware layers for the task of node classification. Such layers introduce higher-order structural inductive bias into the language model, thus improving the model's capacity to harness both higher-order context information from the hypergraph structure and semantic information present in text. In this paper, we propose a new architecture, HyperBERT, a mixed text-hypergraph model which simultaneously models hypergraph relational structure while maintaining the high-quality text encoding capabilities of a pre-trained BERT. Notably, HyperBERT presents results that achieve a new state-of-the-art on 5 challenging text-attributed hypergraph node classification benchmarks.
Identification of optimal dose combinations in early phase dose-finding trials is challenging, due to the trade-off between precisely estimating the many parameters required to flexibly model the possibly non-monotonic dose-response surface, and the small sample sizes in early phase trials. This difficulty is even more pertinent in the context of personalized dose-finding, where patient characteristics are used to identify tailored optimal dose combinations. To overcome these challenges, we propose the use of Bayesian optimization for finding optimal dose combinations in standard ("one size fits all") and personalized multi-agent dose-finding trials. Bayesian optimization is a method for estimating the global optima of expensive-to-evaluate objective functions. The objective function is approximated by a surrogate model, commonly a Gaussian process, paired with a sequential design strategy to select the next point via an acquisition function. This work is motivated by an industry-sponsored problem, where focus is on optimizing a dual-agent therapy in a setting featuring minimal toxicity. To compare the performance of the standard and personalized methods under this setting, simulation studies are performed for a variety of scenarios. Our study concludes that taking a personalized approach is highly beneficial in the presence of heterogeneity.
An open scientific challenge is how to classify events with reliable measures of uncertainty, when we have a mechanistic model of the data-generating process but the distribution over both labels and latent nuisance parameters is different between train and target data. We refer to this type of distributional shift as generalized label shift (GLS). Direct classification using observed data $\mathbf{X}$ as covariates leads to biased predictions and invalid uncertainty estimates of labels $Y$. We overcome these biases by proposing a new method for robust uncertainty quantification that casts classification as a hypothesis testing problem under nuisance parameters. The key idea is to estimate the classifier's receiver operating characteristic (ROC) across the entire nuisance parameter space, which allows us to devise cutoffs that are invariant under GLS. Our method effectively endows a pre-trained classifier with domain adaptation capabilities and returns valid prediction sets while maintaining high power. We demonstrate its performance on two challenging scientific problems in biology and astroparticle physics with data from realistic mechanistic models.
Constructions of distance-optimal codes and quasi-perfect codes are challenging problems and have attracted many attentions. In this paper, we give the following three results. 1) If $\lambda|q^{sm}-1$ and $\lambda <\sqrt{\frac{(q^s-1)}{2(q-1)^2(1+\epsilon)}}$, an infinite family of distance-optimal $q$-ary cyclic sum-rank codes with the block length $t=\frac{q^{sm}-1}{\lambda}$, the matrix size $s \times s$, the cardinality $q^{s^2t-s(2m+3)}$ and the minimum sum-rank distance four is constructed. 2) Block length $q^4-1$ and the matrix size $2 \times 2$ distance-optimal sum-rank codes with the minimum sum-rank distance four and the Singleton defect four are constructed. These sum-rank codes are close to the sphere packing bound , the Singleton-like bound and have much larger block length $q^4-1>>q-1$. 3) For given positive integers $m$ satisfying $2 \leq m$, an infinite family of quasi-perfect sum-rank codes with the matrix size $2 \times m$, and the minimum sum-rank distance three is also constructed. Quasi-perfect binary sum-rank codes with the minimum sum-rank distance four are also given. Almost MSRD $q$-ary codes with the block lengths up to $q^2$ are given. We show that more distance-optimal binary sum-rank codes can be obtained from the Plotkin sum.
Africa has a high student-to-teacher ratio which limits students' access to teachers for learning support such as educational question answering. In this work, we extended Kwame, a bilingual AI teaching assistant for coding education, adapted it for science education, and deployed it as a web app. Kwame for Science provides passages from well-curated knowledge sources and related past national exam questions as answers to questions from students based on the Integrated Science subject of the West African Senior Secondary Certificate Examination (WASSCE). Furthermore, students can view past national exam questions along with their answers and filter by year, question type, and topics that were automatically categorized by a topic detection model which we developed (91% unweighted average recall). We deployed Kwame for Science in the real world over 8 months and had 750 users across 32 countries (15 in Africa) and 1.5K questions asked. Our evaluation showed an 87.2% top 3 accuracy (n=109 questions) implying that Kwame for Science has a high chance of giving at least one useful answer among the 3 displayed. We categorized the reasons the model incorrectly answered questions to provide insights for future improvements. We also share challenges and lessons with the development, deployment, and human-computer interaction component of such a tool to enable other researchers to deploy similar tools. With a first-of-its-kind tool within the African context, Kwame for Science has the potential to enable the delivery of scalable, cost-effective, and quality remote education to millions of people across Africa.
Deep neural models in recent years have been successful in almost every field, including extremely complex problem statements. However, these models are huge in size, with millions (and even billions) of parameters, thus demanding more heavy computation power and failing to be deployed on edge devices. Besides, the performance boost is highly dependent on redundant labeled data. To achieve faster speeds and to handle the problems caused by the lack of data, knowledge distillation (KD) has been proposed to transfer information learned from one model to another. KD is often characterized by the so-called `Student-Teacher' (S-T) learning framework and has been broadly applied in model compression and knowledge transfer. This paper is about KD and S-T learning, which are being actively studied in recent years. First, we aim to provide explanations of what KD is and how/why it works. Then, we provide a comprehensive survey on the recent progress of KD methods together with S-T frameworks typically for vision tasks. In general, we consider some fundamental questions that have been driving this research area and thoroughly generalize the research progress and technical details. Additionally, we systematically analyze the research status of KD in vision applications. Finally, we discuss the potentials and open challenges of existing methods and prospect the future directions of KD and S-T learning.
Deep neural networks have revolutionized many machine learning tasks in power systems, ranging from pattern recognition to signal processing. The data in these tasks is typically represented in Euclidean domains. Nevertheless, there is an increasing number of applications in power systems, where data are collected from non-Euclidean domains and represented as the graph-structured data with high dimensional features and interdependency among nodes. The complexity of graph-structured data has brought significant challenges to the existing deep neural networks defined in Euclidean domains. Recently, many studies on extending deep neural networks for graph-structured data in power systems have emerged. In this paper, a comprehensive overview of graph neural networks (GNNs) in power systems is proposed. Specifically, several classical paradigms of GNNs structures (e.g., graph convolutional networks, graph recurrent neural networks, graph attention networks, graph generative networks, spatial-temporal graph convolutional networks, and hybrid forms of GNNs) are summarized, and key applications in power systems such as fault diagnosis, power prediction, power flow calculation, and data generation are reviewed in detail. Furthermore, main issues and some research trends about the applications of GNNs in power systems are discussed.
Object detection typically assumes that training and test data are drawn from an identical distribution, which, however, does not always hold in practice. Such a distribution mismatch will lead to a significant performance drop. In this work, we aim to improve the cross-domain robustness of object detection. We tackle the domain shift on two levels: 1) the image-level shift, such as image style, illumination, etc, and 2) the instance-level shift, such as object appearance, size, etc. We build our approach based on the recent state-of-the-art Faster R-CNN model, and design two domain adaptation components, on image level and instance level, to reduce the domain discrepancy. The two domain adaptation components are based on H-divergence theory, and are implemented by learning a domain classifier in adversarial training manner. The domain classifiers on different levels are further reinforced with a consistency regularization to learn a domain-invariant region proposal network (RPN) in the Faster R-CNN model. We evaluate our newly proposed approach using multiple datasets including Cityscapes, KITTI, SIM10K, etc. The results demonstrate the effectiveness of our proposed approach for robust object detection in various domain shift scenarios.