arXiv subjects

Wei Xiang

Publications and source records attributed to Wei Xiang.

At least 127 records · Page 7Linked to original sources

arXiv2020

Loss of Regularity of Solutions of the Lighthill Problem for Shock Diffraction for Potential Flow

We are concerned with the suitability of the main models of compressible fluid dynamics for the Lighthill problem for shock diffraction by a convex corned wedge, by studying the regularity of solutions of the problem, which can be formulated as a free boundary problem. In this paper, we prove that there is no regular solution that is subsonic up to the wedge corner for potential flow. This indicates that, if the solution is subsonic at the wedge corner, at least a characteristic discontinuity (vortex sheet or entropy wave) is expected to be generated, which is consistent with the experimental and computational results. Therefore, the potential flow equation is not suitable for the Lighthill problem so that the compressible Euler system must be considered. In order to achieve the non-existence result, a weak maximum principle for the solution is established, and several other mathematical techniques are developed. The methods and techniques developed here are also useful to the other problems with similar difficulties.

math.AP↗

arXiv2020

Anypath Routing Protocol Design via Q-Learning for Underwater Sensor Networks

As a promising technology in the Internet of Underwater Things, underwater sensor networks have drawn a widespread attention from both academia and industry. However, designing a routing protocol for underwater sensor networks is a great challenge due to high energy consumption and large latency in the underwater environment. This paper proposes a Q-learning-based localization-free anypath routing (QLFR) protocol to prolong the lifetime as well as reduce the end-to-end delay for underwater sensor networks. Aiming at optimal routing policies, the Q-value is calculated by jointly considering the residual energy and depth information of sensor nodes throughout the routing process. More specifically, we define two reward functions (i.e., depth-related and energy-related rewards) for Q-learning with the objective of reducing latency and extending network lifetime. In addition, a new holding time mechanism for packet forwarding is designed according to the priority of forwarding candidate nodes. Furthermore, a mathematical analysis is presented to analyze the performance of the proposed routing protocol. Extensive simulation results demonstrate the superiority performance of the proposed routing protocol in terms of the end-to-end delay and the network lifetime.

cs.NI↗

arXiv2020

Training Progressively Binarizing Deep Networks Using FPGAs

While hardware implementations of inference routines for Binarized Neural Networks (BNNs) are plentiful, current realizations of efficient BNN hardware training accelerators, suitable for Internet of Things (IoT) edge devices, leave much to be desired. Conventional BNN hardware training accelerators perform forward and backward propagations with parameters adopting binary representations, and optimization using parameters adopting floating or fixed-point real-valued representations--requiring two distinct sets of network parameters. In this paper, we propose a hardware-friendly training method that, contrary to conventional methods, progressively binarizes a singular set of fixed-point network parameters, yielding notable reductions in power and resource utilizations. We use the Intel FPGA SDK for OpenCL development environment to train our progressively binarizing DNNs on an OpenVINO FPGA. We benchmark our training approach on both GPUs and FPGAs using CIFAR-10 and compare it to conventional BNNs.

cs.CV↗

arXiv2019

Hypersonic Similarity for the Two Dimensional Steady Potential Flow with Large Data

In this paper, we establish the first rigorous mathematical global result on the validation of the hypersonic similarity, which is also called the Mach-number independence principle, for the two dimensional steady potential flow. The hypersonic similarity is equivalent to the Van Dyke's similarity theory, that if the hypersonic similarity parameter $K$ is fixed, the shock solution structures (after scaling) are consistent, when the Mach number of the flow is sufficiently large. One of the difficulty is that after scaling, the solutions are usually of large data since the perturbation of the hypersonic flow is usually not small related to the sonic speed. In order to make it, we first employ the modified Glimm scheme to construct the approximate solutions with large data and find fine structure of the elementary wave curves to obtain the global existence of entropy solutions with large data, for fixed $K$ and sufficiently large Mach number of the incoming flow $M_{\infty}$. Finally, we further show that for a fixed hypersonic similarity parameter $K$, if the Mach number $M_{\infty}\rightarrow\infty$, the solutions obtained above approach to the solution of the corresponding initial-boundary value problem of the hypersonic small-disturbance equations. Therefore, the Van Dyke's similarity theory is first verified rigorously.

math.AP↗

arXiv2019

Uniqueness and Stability for the Shock Reflection-Diffraction Problem for Potential Flow

When a plane shock hits a two-dimensional wedge head on, it experiences a reflection-diffraction process, and then a self-similar reflected shock moves outward as the original shock moves forward in time. The experimental, computational, and asymptotic analysis has indicated that various patterns occur, including regular reflection and Mach reflection. The von Neumann conjectures on the transition from regular to Mach reflection involve the existence, uniqueness, and stability of regular shock reflection-diffraction configurations, generated by concave cornered wedges for compressible flow. In this paper, we discuss some recent developments in the study of the von Neumann conjectures. More specifically, we present our recent results of the uniqueness and stability of regular shock reflection-diffraction configurations governed by the potential flow equation in an appropriate class of solutions. We first show that the transonic shocks in the global solutions obtained in Chen-Feldman [19] are convex. Then we establish the uniqueness of global shock reflection-diffraction configurations with convex transonic shocks for any wedge angle larger than the detachment angle or the critical angle. Moreover, the stability of the solutions with respect to the wedge angle is also shown. Our approach also provides an alternative way of proving the existence of the admissible solutions established first in [19].

math.AP↗

arXiv2019

Multi-user Resource Control with Deep Reinforcement Learning in IoT Edge Computing

By leveraging the concept of mobile edge computing (MEC), massive amount of data generated by a large number of Internet of Things (IoT) devices could be offloaded to MEC server at the edge of wireless network for further computational intensive processing. However, due to the resource constraint of IoT devices and wireless network, both the communications and computation resources need to be allocated and scheduled efficiently for better system performance. In this paper, we propose a joint computation offloading and multi-user scheduling algorithm for IoT edge computing system to minimize the long-term average weighted sum of delay and power consumption under stochastic traffic arrival. We formulate the dynamic optimization problem as an infinite-horizon average-reward continuous-time Markov decision process (CTMDP) model. One critical challenge in solving this MDP problem for the multi-user resource control is the curse-of-dimensionality problem, where the state space of the MDP model and the computation complexity increase exponentially with the growing number of users or IoT devices. In order to overcome this challenge, we use the deep reinforcement learning (RL) techniques and propose a neural network architecture to approximate the value functions for the post-decision system states. The designed algorithm to solve the CTMDP problem supports semi-distributed auction-based implementation, where the IoT devices submit bids to the BS to make the resource control decisions centrally. Simulation results show that the proposed algorithm provides significant performance improvement over the baseline algorithms, and also outperforms the RL algorithms based on other neural network architectures.

eess.SP↗

arXiv2019

A Survey of Asynchronous Programming Using Coroutines in the Internet of Things and Embedded Systems

Many Internet of Things and embedded projects are event-driven, and therefore require asynchronous and concurrent programming. Current proposals for C++20 suggest that coroutines will have native language support. It is timely to survey the current use of coroutines in embedded systems development. This paper investigates existing research which uses or describes coroutines on resource-constrained platforms. The existing research is analysed with regard to: software platform, hardware platform and capacity; use cases and intended benefits; and the application programming interface design used for coroutines. A systematic mapping study was performed, to select studies published between 2007 and 2018 which contained original research into the application of coroutines on resource-constrained platforms. An initial set of 566 candidate papers were reduced to only 35 after filters were applied, revealing the following taxonomy. The C & C++ programming languages were used by 22 studies out of 35. As regards hardware, 16 studies used 8- or 16-bit processors while 13 used 32-bit processors. The four most common use cases were concurrency (17 papers), network communication (15), sensor readings (9) and data flow (7). The leading intended benefits were code style and simplicity (12 papers), scheduling (9) and efficiency (8). A wide variety of techniques have been used to implement coroutines, including native macros, additional tool chain steps, new language features and non-portable assembly language. We conclude that there is widespread demand for coroutines on resource-constrained devices. Our findings suggest that there is significant demand for a formalised, stable, well-supported implementation of coroutines in C++, designed with consideration of the special needs of resource-constrained devices, and further that such an implementation would bring benefits specific to such devices.

cs.SE↗

arXiv2019

Accelerating Deterministic and Stochastic Binarized Neural Networks on FPGAs Using OpenCL

Recent technological advances have proliferated the available computing power, memory, and speed of modern Central Processing Units (CPUs), Graphics Processing Units (GPUs), and Field Programmable Gate Arrays (FPGAs). Consequently, the performance and complexity of Artificial Neural Networks (ANNs) is burgeoning. While GPU accelerated Deep Neural Networks (DNNs) currently offer state-of-the-art performance, they consume large amounts of power. Training such networks on CPUs is inefficient, as data throughput and parallel computation is limited. FPGAs are considered a suitable candidate for performance critical, low power systems, e.g. the Internet of Things (IOT) edge devices. Using the Xilinx SDAccel or Intel FPGA SDK for OpenCL development environment, networks described using the high-level OpenCL framework can be accelerated on heterogeneous platforms. Moreover, the resource utilization and power consumption of DNNs can be further enhanced by utilizing regularization techniques that binarize network weights. In this paper, we introduce, to the best of our knowledge, the first FPGA-accelerated stochastically binarized DNN implementations, and compare them to implementations accelerated using both GPUs and FPGAs. Our developed networks are trained and benchmarked using the popular MNIST and CIFAR-10 datasets, and achieve near state-of-the-art performance, while offering a >16-fold improvement in power consumption, compared to conventional GPU-accelerated networks. Both our FPGA-accelerated determinsitic and stochastic BNNs reduce inference times on MNIST and CIFAR-10 by >9.89x and >9.91x, respectively.

cs.LG↗

arXiv2019

Steady Euler Flows with Large Vorticity and Characteristic Discontinuities in Arbitrary Infinitely Long Nozzles

We establish the existence and uniqueness of smooth solutions with large vorticity and weak solutions with vortex sheets/entropy waves for the steady Euler equations for both compressible and incompressible fluids in arbitrary infinitely long nozzles. We first develop a new approach to establish the existence of smooth solutions without assumptions on the sign of the second derivatives of the horizontal velocity, or the Bernoulli and entropy functions, at the inlet for the smooth case. Then the existence for the smooth case can be applied to construct approximate solutions to establish the existence of weak solutions with vortex sheets/entropy waves by nonlinear arguments. This is the first result on the global existence of solutions of the multidimensional steady compressible full Euler equations with free boundaries, which are not necessarily small perturbations of piecewise constant background solutions. The subsonic-sonic limit of the solutions is also shown. Finally, through the incompressible limit, we establish the existence and uniqueness of incompressible Euler flows in arbitrary infinitely long nozzles for both the smooth solutions with large vorticity and the weak solutions with vortex sheets. The methods and techniques developed here will be useful for solving other problems involving similar difficulties.

math.AP↗

arXiv2019

Regularity of solutions to time-harmonic Maxwell's system with various lower than Lipschitz coefficients

In this paper, we study the regularity of the solutions of Maxwell's equations in a bounded domain. We consider several different types of low regularity assumptions to the coefficients which are all less than Lipschitz. We first develop a new approach by giving $\mathcal{H}^1$ estimate when the coefficients are $\mathcal{L}^{\infty}$ bounded; and then we derive $\mathcal{W}^{1,p}$ estimates for every $p > 2$ when one of the leading coefficients is simply continuous; Finally, we extend the result to $\mathcal{C}^{1,α}$ almost everywhere for the solution of the homogeneous Maxwell's equations when the coefficients are $\mathcal{W}^{1,p}, \, p>3$ and close to the identity matrix in the sense of $\mathcal{L}^{\infty}$ norm. The last two estimates are new, and the techniques and methods developed here can also be applied to other problems with similar difficulties.

math.AP↗

arXiv2019

Low Mach Number Limit of Multidimensional Steady Flows on the Airfoil Problem

In this paper, we justify the low Mach number limit of the steady irrotational Euler flows for the airfoil problem, which is the first result for the low Mach number limit of the steady Euler flows in an exterior domain. The uniform estimates on the compressibility parameter $\varepsilon$, which is singular for the flows, are established via a variational approach based on the compressible-incompressible difference functions. The limit is on the Hölder space and is unique. Moreover, the convergence rate is of order $\varepsilon^2$. It is noticeable that, due to the feature of the airfoil problem, the extra force dominates the asymptotic decay rate of the compressible flow to the infinity. And the effect of extra force vanishes in the limiting process from compressible flows to the incompressible ones, as the Mach number goes to zero.

math.AP↗

arXiv2019

Low Mach Number Limit of Steady Euler Flows in Multi-Dimensional Nozzles

In this paper, we consider the steady irrotational Euler flows in multidimensional nozzles. The first rigorous proof on the existence and uniqueness of the incompressible flow is provided. Then, we justify the corresponding low Mach number limit, which is the first result of the low Mach number limit on the steady Euler flows. We establish several uniform estimates, which does not depend on the Mach number, to validate the convergence of the compressible flow with extra force to the corresponding incompressible flow, which is free from the extra force effect, as the Mach number goes to zero. The limit is on the Holder space and is unique. Moreover, the convergence rate is of order $\varepsilon^2$, which is higher than the ones in the previous results on the low Mach number limit for the unsteady flow.

math.AP↗

arXiv2018

Heter-Sim: Heterogeneous multi-agent systems simulation by interactive data-driven optimization

Interactive multi-agent simulation algorithms are used to compute the trajectories and behaviors of different entities in virtual reality scenarios. However, current methods involve considerable parameter tweaking to generate plausible behaviors. We introduce a novel approach (Heter-Sim) that combines physics-based simulation methods with data-driven techniques using an optimization-based formulation. Our approach is general and can simulate heterogeneous agents corresponding to human crowds, traffic, vehicles, or combinations of different agents with varying dynamics. We estimate motion states from real-world datasets that include information about position, velocity, and control direction. Our optimization algorithm considers several constraints, including velocity continuity, collision avoidance, attraction, and direction control. To accelerate the computations, we reduce the search space for both collision avoidance and optimal solution computation. Heter-Sim can simulate tens or hundreds of agents at interactive rates and we compare its accuracy with real-world datasets and prior algorithms. We also perform user studies that evaluate the plausible behaviors generated by our algorithm and a user study that evaluates the plausibility of our algorithm via VR.

cs.GR↗

arXiv2018

Non-coherent Massive SIMO Systems in ISI Channels: Constellation Design and Performance Analysis

A massive single-input multiple-output (SIMO) system with a single transmit antenna and a large number of receive antennas in intersymbol interference (ISI) channels is considered. Contrast to existing energy detection (ED)-based non-coherent receiver where conventional pulse amplitude modulation (PAM) is employed, we propose a constellation design which minimizes the symbol-error rate (SER) with the knowledge of channel statistics. To make a comparison, we derive the SERs of the ED-based receiver with both the proposed constellation and PAM, namely $P_{e\_opt}$ and $P_{e\_pam}$. Specifically, asymptotic behaviors of the SER in regimes of a large number of receive antennas and high signal-to-noise ratio (SNR) are investigated. Analytical results demonstrate that the logarithms of both $P_{e\_opt}$ and $P_{e\_pam}$ decrease approximately linearly with the number of receive antennas, while $P_{e\_opt}$ degrades faster. It is also shown that the proposed design is of less cost, because compared with PAM, less antennas are required to achieve the same error rate.

eess.SP↗

arXiv2018

Global Instability of the Multi-dimensional Plane Shocks for the isothermal flow

In this paper, we are concerned with the long time behavior of the piecewise smooth solutions to the generalized Riemann problem governed by the compressible isothermal Euler equations in two and three dimensions. Non-existence result is established for the fan-shaped wave structure solution, including two shocks and one contact discontinuity and which is a perturbation of plane waves. Therefore, unlike the one-dimensional case, the multi-dimensional plane shocks are not stable globally. What is more, the sharp lifespan estimate is established which is the same as the lifespan estimate for the nonlinear wave equations in both two and three space dimensions.

math.AP↗

arXiv2018

Stability of supersonic contact discontinuity for two-dimensional steady compressible Euler flows in a finite nozzle

In this paper, we study the stability of supersonic contact discontinuity for the two-dimensional steady compressible Euler flows in a finitely long nozzle of varying cross-sections. We formulate the problem as an initial-boundary value problem with the contact discontinuity as a free boundary. To deal with the free boundary value problem, we employ the Lagrangian transformation to straighten the contact discontinuity and then the free boundary value problem becomes a fixed boundary value problem. We develop an iteration scheme and establish some novel estimates of solutions for the first order of hyperbolic equations on a cornered domain. Finally, by using the inverse Lagrangian transformation and under the assumption that the incoming flows and the nozzle walls are smooth perturbations of the background state, we prove that the original free boundary problem admits a unique weak solution which is a small perturbation of the background state and the solution consists of two smooth supersonic flows separated by a smooth contact discontinuity.

math.AP↗

arXiv2018

Context-Aware Single-Shot Detector

SSD is one of the state-of-the-art object detection algorithms, and it combines high detection accuracy with real-time speed. However, it is widely recognized that SSD is less accurate in detecting small objects compared to large objects, because it ignores the context from outside the proposal boxes. In this paper, we present CSSD--a shorthand for context-aware single-shot multibox object detector. CSSD is built on top of SSD, with additional layers modeling multi-scale contexts. We describe two variants of CSSD, which differ in their context layers, using dilated convolution layers (DiCSSD) and deconvolution layers (DeCSSD) respectively. The experimental results show that the multi-scale context modeling significantly improves the detection accuracy. In addition, we study the relationship between effective receptive fields (ERFs) and the theoretical receptive fields (TRFs), particularly on a VGGNet. The empirical results further strengthen our conclusion that SSD coupled with context layers achieves better detection results especially for small objects ($+3.2\% {\rm AP}_{@0.5}$ on MS-COCO compared to the newest SSD), while maintaining comparable runtime performance.

cs.CV↗

arXiv2017

Reliable Energy-Efficient Routing Algorithm for Vehicle-Assisted Wireless Ad-Hoc Networks

We investigate the design of the optimal routing path in a moving vehicles involved the internet of things (IoT). In our model, jammers exist that may interfere with the information exchange between wireless nodes, leading to worsened quality of service (QoS) in communications. In addition, the transmit power of each battery-equipped node is constrained to save energy. We propose a three-step optimal routing path algorithm for reliable and energy-efficient communications. Moreover, results show that with the assistance of moving vehicles, the total energy consumed can be reduced to a large extend. We also study the impact on the optimal routing path design and energy consumption which is caused by path loss, maximum transmit power constrain, QoS requirement, etc.

cs.NI↗