On the Absolute-Value Integral of a Brownian Motion with Drift: Exact and Asymptotic Formulae

The present paper is concerned with the integral of the absolute value of a Brownian motion with drift. By establishing an asymptotic expansion of the space Laplace transform, we obtain series representations for the probability density function and cumulative distribution function of the integral, making use of Meijer's G-function. A functional recursive formula is derived for the moments, which is shown to yield only exponentials and Gauss' error function up to arbitrary orders, permitting exact computations. To obtain sharp asymptotic estimates for small- and large-deviation probabilities, we employ a marginal space-time Laplace transform and apply a newly developed generalization of Laplace's method to exponential Airy integrals. The impact of drift on the complete distribution of the integral is explored in depth. The resultant new formulae complement existing ones in the standard Brownian motion case to great extent in terms of both theoretical generality and modeling capacity and have been presented for easy implementation, which numerical experiments demonstrate.Comment: 35 pages, 4 tables, 5 figures; added reference

Ranking comments: An Entropy-based Method with Word Embedding Clustering

Automatically ranking comments by their relevance plays an important role in text mining and text summarization area. In this thesis, firstly, we introduce a new text digitalization method: the bag of word clusters model. Unlike the traditional bag of words model that treats each word as an independent item, we group semantic-related words as clusters using pre-trained word2vec word embeddings and represent each comment as a distribution of word clusters. This method can extract both semantic and statistical information from texts. Next, we propose an unsupervised ranking algorithm that identifies relevant comments by their distance to the “ideal” comment. The “ideal” comment is the maximum general entropy comment with respect to the global word cluster distribution. The intuition is that the “ideal” comment highlights aspects of a product that many other comments frequently mention. Therefore, it can be regarded as a standard to judge a comment’s relevance to this product. At last, we analyze our algorithm’s performance on a real Amazon product

Computational fluid dynamics-based hull form optimization using approximation method

With the rapid development of the computational technology, computational fluid dynamics (CFD) tools have been widely used to evaluate the ship hydrodynamic performances in the hull forms optimization. However, it is very time consuming since a great number of the CFD simulations need to be performed for one single optimization. It is of great importance to find a high-effective method to replace the calculation of the CFD tools. In this study, a CFD-based hull form optimization loop has been developed by integrating an approximate method to optimize hull form for reducing the total resistance in calm water. In order to improve the optimization accuracy of particle swarm optimization (PSO) algorithm, an improved PSO (IPSO) algorithm is presented where the inertia weight coefficient and search method are designed based on random inertia weight and convergence evaluation, respectively. To improve the prediction accuracy of total resistance, a data prediction method based on IPSO-Elman neural network (NN) is proposed. Herein, IPSO algorithm is used to train the weight coefficients and self-feedback gain coefficient of ElmanNN. In order to build IPSO-ElmanNN model, optimal Latin hypercube design (Opt LHD) is used to design the sampling hull forms, and the total resistance (objective function) of these hull forms are calculated by Reynolds averaged Navier–Stokes (RANS) method. For the purpose of this paper, this optimization framework has been employed to optimize two ships, namely, the DTMB5512 and WIGLEY III ships, and these hull forms are changed by arbitrary shape deformation (ASD) technique. The results show that the optimization framework developed in this study can be used to optimize hull forms with significantly reduced computational effort

Efficient Task Offloading Algorithm for Digital Twin in Edge/Cloud Computing Environment

In the era of Internet of Things (IoT), Digital Twin (DT) is envisioned to empower various areas as a bridge between physical objects and the digital world. Through virtualization and simulation techniques, multiple functions can be achieved by leveraging computing resources. In this process, Mobile Cloud Computing (MCC) and Mobile Edge Computing (MEC) have become two of the key factors to achieve real-time feedback. However, current works only considered edge servers or cloud servers in the DT system models. Besides, The models ignore the DT with not only one data resource. In this paper, we propose a new DT system model considering a heterogeneous MEC/MCC environment. Each DT in the model is maintained in one of the servers via multiple data collection devices. The offloading decision-making problem is also considered and a new offloading scheme is proposed based on Distributed Deep Learning (DDL). Simulation results demonstrate that our proposed algorithm can effectively and efficiently decrease the system's average latency and energy consumption. Significant improvement is achieved compared with the baselines under the dynamic environment of DTs

A Spatio-Temporal Graph Convolutional Network for Gesture Recognition from High-Density Electromyography

Accurate hand gesture prediction is crucial for effective upper-limb prosthetic limbs control. As the high flexibility and multiple degrees of freedom exhibited by human hands, there has been a growing interest in integrating deep networks with high-density surface electromyography (HD-sEMG) grids to enhance gesture recognition capabilities. However, many existing methods fall short in fully exploit the specific spatial topology and temporal dependencies present in HD-sEMG data. Additionally, these studies are often limited number of gestures and lack generality. Hence, this study introduces a novel gesture recognition method, named STGCN-GR, which leverages spatio-temporal graph convolution networks for HD-sEMG-based human-machine interfaces. Firstly, we construct muscle networks based on functional connectivity between channels, creating a graph representation of HD-sEMG recordings. Subsequently, a temporal convolution module is applied to capture the temporal dependences in the HD-sEMG series and a spatial graph convolution module is employed to effectively learn the intrinsic spatial topology information among distinct HD-sEMG channels. We evaluate our proposed model on a public HD-sEMG dataset comprising a substantial number of gestures (i.e., 65). Our results demonstrate the remarkable capability of the STGCN-GR method, achieving an impressive accuracy of 91.07% in predicting gestures, which surpasses state-of-the-art deep learning methods applied to the same dataset