In this paper, we address the issue of congestion in future Unmanned Aerial Vehicle (UAVs) traffic system in uncertain weather. We treat the traffic of UAVs as fluid queues, and introduce models for traffic dynamics at three basic traffic components: single link, tandem link, and merge link. The impact of weather uncertainty is captured as fluctuation of the saturation rate of fluid queue discharge (capacity). The uncertainty is assumed to follow a continuous-time Markov process. We define the resilience of the UAV traffic system as the long-run stability of the traffic queues and the optimal throughput strategy under uncertainties. We derive the necessary and sufficient conditions for the stabilities of the traffic queues in the three basic traffic components. Both conditions can be easily verified in practice. The optimal throughput can be calculated via the stability conditions. Our results offer strong insight and tool for designing flows in the UAV traffic system that is resilient against weather uncertainty.

Single cell RNA-sequencing (scRNA-seq) technology enables comprehensive transcriptomic profiling of thousands of cells with distinct phenotypic and physiological states in a complex tissue. Substantial efforts have been made to characterize single cells of distinct identities from scRNA-seq data, including various cell clustering techniques. While existing approaches can handle single cells in terms of different cell (sub)types at a high resolution, identification of the functional variability within the same cell type remains unsolved. In addition, there is a lack of robust method to handle the inter-subject variation that often brings severe confounding effects for the functional clustering of single cells. In this study, we developed a novel data denoising and cell clustering approach, namely CIBS, to provide biologically explainable functional classification for scRNA-seq data. CIBS is based on a systems biology model of transcriptional regulation that assumes a multi-modality distribution of the cells' activation status, and it utilizes a Boolean matrix factorization approach on the discretized expression status to robustly derive functional modules. CIBS is empowered by a novel fast Boolean Matrix Factorization method, namely PFAST, to increase the computational feasibility on large scale scRNA-seq data. Application of CIBS on two scRNA-seq datasets collected from cancer tumor micro-environment successfully identified subgroups of cancer cells with distinct expression patterns of epithelial-mesenchymal transition and extracellular matrix marker genes, which was not revealed by the existing cell clustering analysis tools. The identified cell groups were significantly associated with the clinically confirmed lymph-node invasion and metastasis events across different patients.

Cross-lingual document search is an information retrieval task in which the queries' language differs from the documents' language.In this paper, we study the instability of neural document search models and propose a novel end-to-end robust framework that achieves improved performance in cross-lingual search with different documents' languages.This framework includes a novel measure of the relevance, smooth cosine similarity, between queries and documents, and a novel loss function, Smooth Ordinal Search Loss, as the objective.We further provide theoretical guarantee on the generalization error bound for the proposed framework.We conduct experiments to compare our approach with other document search models, and observe significant gains under commonly used ranking metrics on the cross-lingual document retrieval task in a variety of languages.

This paper presents a framework for norm-based capacity control with respect to an lp,q-norm in weight-normalized Residual Neural Networks (ResNets). We first formulate the representation of each residual block. For the regression problem, we analyze the Rademacher Complexity of the ResNets family. We also establish a tighter generalization upper bound for weight-normalized ResNets. in a more general sight. Using the lp,q-norm weight normalization in which 1/p+1/q >=1, we discuss the properties of a width-independent capacity control, which only relies on the depth according to a square root term. Several comparisons suggest that our result is tighter than previous work. Parallel results for Deep Neural Networks (DNN) and Convolutional Neural Networks (CNN) are included by introducing the lp,q-norm weight normalization for DNN and the lp,q-norm kernel normalization for CNN. Numerical experiments also verify that ResNet structures contribute to better generalization properties.

In this paper, we propose a compositional nonparametric method in which a model is expressed as a labeled binary tree of $2k+1$ nodes, where each node is either a summation, a multiplication, or the application of one of the $q$ basis functions to one of the $p$ covariates. We show that in order to recover a labeled binary tree from a given dataset, the sufficient number of samples is $O(k\log(pq)+\log(k!))$, and the necessary number of samples is $Ω(k\log (pq)-\log(k!))$. We further propose a greedy algorithm for regression in order to validate our theoretical findings through synthetic experiments.

This paper presents a general framework for norm-based capacity control for $L_{p,q}$ weight normalized deep neural networks. We establish the upper bound on the Rademacher complexities of this family. With an $L_{p,q}$ normalization where $q\le p^*$ and $1/p+1/p^{*}=1$, we discuss properties of a width-independent capacity control, which only depends on the depth by a square root term. We further analyze the approximation properties of $L_{p,q}$ weight normalized deep neural networks. In particular, for an $L_{1,\infty}$ weight normalized network, the approximation error can be controlled by the $L_1$ norm of the output layer, and the corresponding generalization error only depends on the architecture by the square root of the depth.