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A general theory of efficient estimation for ergodic diffusion processes sampled at high frequency with an infinite time horizon is presented. High frequency sampling is common in many applications, with finance as a prominent example. The theory is formulated in term of approximate martingale estimating functions and covers a large class of estimators including most of the previously proposed estimators for diffusion processes. Easily checked conditions ensuring that an estimating function is an approximate martingale are derived, and general conditions ensuring consistency and asymptotic normality of estimators are given. Most importantly, simple conditions are given that ensure rate optimality and efficiency. Rate optimal estimators of parameters in the diffusion coefficient converge faster than estimators of drift coefficient parameters because they take advantage of the information in the quadratic variation. The conditions facilitate the choice among the multitude of estimators that have been proposed for diffusion models. Optimal martingale estimating functions in the sense of Godambe and Heyde and their high frequency approximations are, under weak conditions, shown to satisfy the conditions for rate optimality and efficiency. This provides a natural feasible method of constructing explicit rate optimal and efficient estimating functions by solving a linear equation.

Supercomputers have revolutionized how industries and scientific fields process large amounts of data. These machines group hundreds or thousands of computing nodes working together to execute time-consuming programs that require a large amount of computational resources. Over the years, supercomputers have expanded to include new and different technologies characterizing them as heterogeneous. However, executing a program in a heterogeneous environment requires attention to a specific aspect of performance degradation: load imbalance. In this research, we address the challenges associated with load imbalance when scheduling many homogeneous tasks in a heterogeneous environment. To address this issue, we introduce the concept of adaptive asynchronous work-stealing. This approach collects information about the nodes and utilizes it to improve work-stealing aspects, such as victim selection and task offloading. Additionally, the proposed approach eliminates the need for extra threads to communicate information, thereby reducing overhead when implementing a fully asynchronous approach. Our experimental results demonstrate a performance improvement of approximately 10.1\% compared to other conventional and state-of-the-art implementations.

Occlusion presents a significant challenge in human pose estimation. The challenges posed by occlusion can be attributed to the following factors: 1) Data: The collection and annotation of occluded human pose samples are relatively challenging. 2) Feature: Occlusion can cause feature confusion due to the high similarity between the target person and interfering individuals. 3) Inference: Robust inference becomes challenging due to the loss of complete body structural information. The existing methods designed for occluded human pose estimation usually focus on addressing only one of these factors. In this paper, we propose a comprehensive framework DAG (Data, Attention, Graph) to address the performance degradation caused by occlusion. Specifically, we introduce the mask joints with instance paste data augmentation technique to simulate occlusion scenarios. Additionally, an Adaptive Discriminative Attention Module (ADAM) is proposed to effectively enhance the features of target individuals. Furthermore, we present the Feature-Guided Multi-Hop GCN (FGMP-GCN) to fully explore the prior knowledge of body structure and improve pose estimation results. Through extensive experiments conducted on three benchmark datasets for occluded human pose estimation, we demonstrate that the proposed method outperforms existing methods. Code and data will be publicly available.

Gesture recognition is an indispensable component of natural and efficient human-computer interaction technology, particularly in desktop-level applications, where it can significantly enhance people's productivity. However, the current gesture recognition community lacks a suitable desktop-level (top-view perspective) dataset for lightweight gesture capture devices. In this study, we have established a dataset named GR4DHCI. What distinguishes this dataset is its inherent naturalness, intuitive characteristics, and diversity. Its primary purpose is to serve as a valuable resource for the development of desktop-level portable applications. GR4DHCI comprises over 7,000 gesture samples and a total of 382,447 frames for both Stereo IR and skeletal modalities. We also address the variances in hand positioning during desktop interactions by incorporating 27 different hand positions into the dataset. Building upon the GR4DHCI dataset, we conducted a series of experimental studies, the results of which demonstrate that the fine-grained classification blocks proposed in this paper can enhance the model's recognition accuracy. Our dataset and experimental findings presented in this paper are anticipated to propel advancements in desktop-level gesture recognition research.

Ning Cai and the author jointly studied secure network codes over adaptive and active attacks, which were rarely studied until these seminal papers. This paper reviews the result for secure network code over adaptive and active attacks. We focus on two typical network models, a one-hop relay network and a unicast relay network.

Fiber-reinforced composites (FRC) provide structural systems with unique features that appeal to various civilian and military sectors. Often, one needs to modulate the temperature field to achieve the intended functionalities (e.g., self-healing) in these lightweight structures. Vascular-based active cooling offers one efficient way of thermal regulation in such material systems. However, the thermophysical properties (e.g., thermal conductivity, specific heat capacity) of FRC and their base constituents depend on temperature, and such structures are often subject to a broad spectrum of temperatures. Notably, prior active cooling modeling studies did not account for such temperature dependence. Thus, the primary aim of this paper is to reveal the effect of temperature-dependent material properties -- obtained via material characterization -- on the qualitative and quantitative behaviors of active cooling. By applying mathematical analysis and conducting numerical simulations, we show this dependence does not affect qualitative attributes, such as minimum and maximum principles (in the same spirit as \textsc{Hopf}'s results for elliptic partial differential equations). However, the dependence slightly affects quantitative results, such as the mean surface temperature and thermal efficiency. The import of our study is that it provides a deeper understanding of thermal regulation systems under practical scenarios and can guide researchers and practitioners in perfecting associated designs.

The proximal gradient method is a generic technique introduced to tackle the non-smoothness in optimization problems, wherein the objective function is expressed as the sum of a differentiable convex part and a non-differentiable regularization term. Such problems with tensor format are of interest in many fields of applied mathematics such as image and video processing. Our goal in this paper is to address the solution of such problems with a more general form of the regularization term. An adapted iterative proximal gradient method is introduced for this purpose. Due to the slowness of the proposed algorithm, we use new tensor extrapolation methods to enhance its convergence. Numerical experiments on color image deblurring are conducted to illustrate the efficiency of our approach.

For the past 30 years or so, machine learning has stimulated a great deal of research in the study of approximation capabilities (expressive power) of a multitude of processes, such as approximation by shallow or deep neural networks, radial basis function networks, and a variety of kernel based methods. Motivated by applications such as invariant learning, transfer learning, and synthetic aperture radar imaging, we initiate in this paper a general approach to study the approximation capabilities of kernel based networks using non-symmetric kernels. While singular value decomposition is a natural instinct to study such kernels, we consider a more general approach to include the use of a family of kernels, such as generalized translation networks (which include neural networks and translation invariant kernels as special cases) and rotated zonal function kernels. Naturally, unlike traditional kernel based approximation, we cannot require the kernels to be positive definite. In particular, we obtain estimates on the accuracy of uniform approximation of functions in a ($L^2$)-Sobolev class by ReLU$^r$ networks when $r$ is not necessarily an integer. Our general results apply to the approximation of functions with small smoothness compared to the dimension of the input space.

This work, in a pioneering approach, attempts to build a biometric system that works purely based on the fluid mechanics governing exhaled breath. We test the hypothesis that the structure of turbulence in exhaled human breath can be exploited to build biometric algorithms. This work relies on the idea that the extrathoracic airway is unique for every individual, making the exhaled breath a biomarker. Methods including classical multi-dimensional hypothesis testing approach and machine learning models are employed in building user authentication algorithms, namely user confirmation and user identification. A user confirmation algorithm tries to verify whether a user is the person they claim to be. A user identification algorithm tries to identify a user's identity with no prior information available. A dataset of exhaled breath time series samples from 94 human subjects was used to evaluate the performance of these algorithms. The user confirmation algorithms performed exceedingly well for the given dataset with over $97\%$ true confirmation rate. The machine learning based algorithm achieved a good true confirmation rate, reiterating our understanding of why machine learning based algorithms typically outperform classical hypothesis test based algorithms. The user identification algorithm performs reasonably well with the provided dataset with over $50\%$ of the users identified as being within two possible suspects. We show surprisingly unique turbulent signatures in the exhaled breath that have not been discovered before. In addition to discussions on a novel biometric system, we make arguments to utilise this idea as a tool to gain insights into the morphometric variation of extrathoracic airway across individuals. Such tools are expected to have future potential in the area of personalised medicines.

Recent advances in 3D fully convolutional networks (FCN) have made it feasible to produce dense voxel-wise predictions of volumetric images. In this work, we show that a multi-class 3D FCN trained on manually labeled CT scans of several anatomical structures (ranging from the large organs to thin vessels) can achieve competitive segmentation results, while avoiding the need for handcrafting features or training class-specific models. To this end, we propose a two-stage, coarse-to-fine approach that will first use a 3D FCN to roughly define a candidate region, which will then be used as input to a second 3D FCN. This reduces the number of voxels the second FCN has to classify to ~10% and allows it to focus on more detailed segmentation of the organs and vessels. We utilize training and validation sets consisting of 331 clinical CT images and test our models on a completely unseen data collection acquired at a different hospital that includes 150 CT scans, targeting three anatomical organs (liver, spleen, and pancreas). In challenging organs such as the pancreas, our cascaded approach improves the mean Dice score from 68.5 to 82.2%, achieving the highest reported average score on this dataset. We compare with a 2D FCN method on a separate dataset of 240 CT scans with 18 classes and achieve a significantly higher performance in small organs and vessels. Furthermore, we explore fine-tuning our models to different datasets. Our experiments illustrate the promise and robustness of current 3D FCN based semantic segmentation of medical images, achieving state-of-the-art results. Our code and trained models are available for download: //github.com/holgerroth/3Dunet_abdomen_cascade.