Nonparametric statistical inference via metric distribution function in metric spaces

The distribution function is essential in statistical inference and connected with samples to form a directed closed loop by the correspondence theorem in measure theory and the Glivenko-Cantelli and Donsker properties. This connection creates a paradigm for statistical inference. However, existing distribution functions are defined in Euclidean spaces and are no longer convenient to use in rapidly evolving data objects of complex nature. It is imperative to develop the concept of the distribution function in a more general space to meet emerging needs. Note that the linearity allows us to use hypercubes to define the distribution function in a Euclidean space. Still, without the linearity in a metric space, we must work with the metric to investigate the probability measure. We introduce a class of metric distribution functions through the metric only. We overcome this challenging step by proving the correspondence theorem and the Glivenko-Cantelli theorem for metric distribution functions in metric spaces, laying the foundation for conducting rational statistical inference for metric space-valued data. Then, we develop a homogeneity test and a mutual independence test for non-Euclidean random objects and present comprehensive empirical evidence to support the performance of our proposed methods. Supplementary materials for this article are available online

Energy-efficient multiuser and multitask computation offloading optimization method

For dynamic application scenarios of Mobile Edge Computing (MEC), an Energy-efficient Multiuser and Multitask Computation Offloading (EMMCO) optimization method is proposed. Under the consideration of multiuser and multitask computation offloading, first, the EMMCO method takes into account the existence of dependencies among different tasks within an implementation, abstracts these dependencies as a Directed Acyclic Graph (DAG), and models the computation offloading problem as a Markov decision process. Subsequently, the task embedding sequence in the DAG is fed to the RNN encoder-decoder neural network with combination of the attention mechanism, the long-term dependencies among different tasks are successfully captured by this scheme. Finally, the Improved Policy Loss Clip-based PPO2 (IPLC-PPO2) algorithm is developed, and the RNN encoder-decoder neural network is trained by the developed algorithm. The loss function in the IPLC-PPO2 algorithm is utilized as a preference for the training process, and the neural network parameters are continuously updated to select the optimal offloading scheduling decisions. Simulation results demonstrate that the proposed EMMCO method can achieve lower latency, reduce energy consumption, and obtain a significant improvement in the Quality of Service (QoS) than the compared algorithms under different situations of mobile edge network

Multi-view 3D Face Reconstruction Based on Flame

At present, face 3D reconstruction has broad application prospects in various fields, but the research on it is still in the development stage. In this paper, we hope to achieve better face 3D reconstruction quality by combining multi-view training framework with face parametric model Flame, propose a multi-view training and testing model MFNet (Multi-view Flame Network). We build a self-supervised training framework and implement constraints such as multi-view optical flow loss function and face landmark loss, and finally obtain a complete MFNet. We propose innovative implementations of multi-view optical flow loss and the covisible mask. We test our model on AFLW and facescape datasets and also take pictures of our faces to reconstruct 3D faces while simulating actual scenarios as much as possible, which achieves good results. Our work mainly addresses the problem of combining parametric models of faces with multi-view face 3D reconstruction and explores the implementation of a Flame based multi-view training and testing framework for contributing to the field of face 3D reconstruction

Trait Mindfulness Is Associated With the Self-Similarity of Heart Rate Variability

Previous studies have linked trait mindfulness with better self-regulation and adaptation. Heart rate variability (HRV) is a good physiological indicator of the capacity for self-regulation and adaptation. The present study explored the relationship between trait mindfulness and HRV from the viewpoint of crosstalking between different HRV parameter pairs, which would reflect the dynamic interactions between each pair of HRV parameters in different processes. We measured the trait mindfulness of seventy-four undergraduate students and recorded nine HRV parameters during the following four consecutive experimental phases: (1) calming phase, (2) mental arithmetic task phase, (3) recovery phase, and (4) mindfulness practice phase. The relationship between trait mindfulness and HRV was explored at the following three levels: (1) the absolute level, i.e., HRV parameters in four different states, (2) the difference-change level, i.e., differences in HRV parameters between different states, and (3) the crosstalking level, i.e., self-similarity of crosstalking HRV parameter pairs. The results supported the following hypothesis: trait mindfulness, as measured by the Mindful Attention Awareness Scale (MAAS), was significantly and positively correlated with the self-similarity of crosstalking HRV parameter pairs but was not significantly correlated with the HRV parameters at the difference-change and absolute levels. These findings indicate that as trait mindfulness increases, the ability to maintain ANS function homeostasis improves.HIGHLIGHTS-Trait mindfulness is associated with better self-regulation and adaptation.-Heart rate variability (HRV) is a good physiological indicator of the capacity for self-regulation and adaptation.-Trait mindfulness is significantly correlated with self-similarity of crosstalking HRV parameter pairs but not with the HRV parameters at the difference-change or absolute levels

A New Look at the Scalar Meson f0(500)f_0(500) via D+→π+π−ℓ+νℓD^+\to \pi^+\pi^-\ell^+\nu_\ell Decays

Using $2.93~\mathrm{fb}^{-1}$ of $e^+e^-$ collision data collected with the BESIII detector at the center-of-mass energy of 3.773 GeV, we investigate the semileptonic decays $D^+\to \pi^+\pi^- \ell^+\nu_\ell$ ($\ell=e$ and $\mu$). The $D^+\to f_0(500)\mu^+\nu_\mu$ decay is observed for the first time. By analyzing simultaneously the differential decay rates of $D^+\to f_0(500) \mu^+\nu_\mu$ and $D^+\to f_0(500) e^+\nu_e$ in different $\ell^+\nu_\ell$ four-momentum transfer intervals, the product of the relevant hadronic form factor $f^{f_0}_{+}(0)$ and the magnitude of the $c\to d$ Cabibbo-Kobayashi-Maskawa matrix element $|V_{cd}|$ is determined to be $f_{+}^{f_0} (0)|V_{cd}|=0.0787\pm0.0060_{\rm stat}\pm0.0033_{\rm syst}$ for the first time. With the input of $|V_{cd}|$ from the global fit in the standard model, we determine $f_{+}^{f_0} (0)=0.350\pm0.027_{\rm stat}\pm0.015_{\rm syst}$. The absolute branching fractions of $D^+\to f_0(500)_{(\pi^+\pi^-)}\mu^+\nu_\mu$ and $D^+\to \rho^0_{(\pi^+\pi^-)} \mu^+\nu_\mu$ are determined as $(0.72\pm0.13_{\rm stat}\pm0.10_{\rm syst})\times10^{-3}$ and $(1.64\pm0.13_{\rm stat}\pm0.11_{\rm syst})\times 10^{-3}$. Combining these results with those of previous BESIII measurements on their semielectronic counterparts from the same data sample, we test lepton flavor universality by measuring the branching fraction ratios ${\mathcal B}_{D^+\to \rho^0 \mu^+\nu_\mu}/{\mathcal B}_{D^+\to \rho^0 e^+\nu_e}=0.88\pm0.10$ and ${\mathcal B}_{D^+\to f_0(500) \mu^+\nu_\mu}/{\mathcal B}_{D^+\to f_0(500) e^+\nu_e}=1.14\pm0.28$, which are compatible with the standard model expectation.Comment: Supplemental Materials added in this versio

A method for faster non-unit stride convolution in deep neural networks

Since computer vision and machine learning target increasingly complicated and challenging goals, the complexity of the computation models rises rapidly as the magnitude of the datasets multiplies. Deep convolutional neural networks are implemented to many realtime applications for which faster progressing time is crucial. Thus, with the rising demand for more rapid responses from data processing, there is an urgent need for further optimized convolution algorithms. For unit stride convolutions, we use FFT-based methods and Winograd algorithms, which significantly reduce the computing complexity under some specific conditions. For non-unit stride convolutions, nevertheless, we usually cannot directly apply the algorithm mentioned above but instead use conventional direct multiplications. In this thesis, we propose an algorithm which works as an extension to both FFT and Winograd algorithms to speed up convolutions with non-unit stride. The algorithm first computes the output map as if we were performing unit stride convolution and then down-samples the calculated output map to generate the final output for non-unit stride convolution. We also present a proof of the down- sampling stage of the algorithm to confirm its accuracy. Finally, we perform tests on the method under different configurations. The results confirms that the proposed method promises accelerated processing time compared to the direct-multiplying method when computing non-unit stride convolution.U of I Onlyundergraduate senior thesis not recommended for open acces

A method for faster non-unit stride convolution in deep neural networks

Since computer vision and machine learning target increasingly complicated and challenging goals, the complexity of the computation models rises rapidly as the magnitude of the datasets multiplies. Deep convolutional neural networks are implemented to many realtime applications for which faster progressing time is crucial. Thus, with the rising demand for more rapid responses from data processing, there is an urgent need for further optimized convolution algorithms. For unit stride convolutions, we use FFT-based methods and Winograd algorithms, which significantly reduce the computing complexity under some specific conditions. For non-unit stride convolutions, nevertheless, we usually cannot directly apply the algorithm mentioned above but instead use conventional direct multiplications. In this thesis, we propose an algorithm which works as an extension to both FFT and Winograd algorithms to speed up convolutions with non-unit stride. The algorithm first computes the output map as if we were performing unit stride convolution and then down-samples the calculated output map to generate the final output for non-unit stride convolution. We also present a proof of the down- sampling stage of the algorithm to confirm its accuracy. Finally, we perform tests on the method under different configurations. The results confirms that the proposed method promises accelerated processing time compared to the direct-multiplying method when computing non-unit stride convolution.U of I Onlyundergraduate senior thesis not recommended for open acces