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Jiaqi Liu

Publications and source records attributed to Jiaqi Liu.

212 records · Page 12Linked to original sources
arXiv2019

The Derivative Nonlinear Schrödinger Equation: Global Well-Posedness and Soliton Resolution

We review recent results on global wellposedness and long-time behavior of smooth solutions to the derivative nonlinear Schrödinger (DNLS) equation. Using the integrable character of DNLS, we show how the inverse scattering tools and the method of Zhou for treating spectral singularities lead to global wellposedness for general initial conditions in the weighted Sobolev space $H^{2,2}(\mathbb{R})$. For generic initial data that can support bright solitons but exclude spectral singularities, we prove the soliton resolution conjecture: the solution is asymptotic, at large times, to a sum of localized solitons and a dispersive component, Our results also show that soliton solutions of DNLS are asymptotically stable.

math.AP↗
arXiv2018

Resource Allocation for Cooperative D2D-Enabled Wireless Caching Networks

In this paper, we study the resource allocation problem for a cooperative device-to-device (D2D)-enabled wireless caching network, where each user randomly caches popular contents to its memory and shares the contents with nearby users through D2D links. To enhance the throughput of spectrum sharing D2D links, which may be severely limited by the interference among D2D links, we enable the cooperation among some of the D2D links to eliminate the interference among them. We formulate a joint link scheduling and power allocation problem to maximize the overall throughput of cooperative D2D links (CDLs) and non-cooperative D2D links (NDLs), which is NP-hard. To solve the problem, we decompose it into two subproblems that maximize the sum rates of the CDLs and the NDLs, respectively. For CDL optimization, we propose a semi-orthogonal-based algorithm for joint user scheduling and power allocation. For NDL optimization, we propose a novel low-complexity algorithm to perform link scheduling and develop a Difference of Convex functions (D.C.) programming method to solve the non-convex power allocation problem. Simulation results show that the cooperative transmission can significantly increase both the number of served users and the overall system throughput.

cs.IT↗
arXiv2018

End-to-end Deep Learning from Raw Sensor Data: Atrial Fibrillation Detection using Wearables

We present a convolutional-recurrent neural network architecture with long short-term memory for real-time processing and classification of digital sensor data. The network implicitly performs typical signal processing tasks such as filtering and peak detection, and learns time-resolved embeddings of the input signal. We use a prototype multi-sensor wearable device to collect over 180h of photoplethysmography (PPG) data sampled at 20Hz, of which 36h are during atrial fibrillation (AFib). We use end-to-end learning to achieve state-of-the-art results in detecting AFib from raw PPG data. For classification labels output every 0.8s, we demonstrate an area under ROC curve of 0.9999, with false positive and false negative rates both below $2\times 10^{-3}$. This constitutes a significant improvement on previous results utilising domain-specific feature engineering, such as heart rate extraction, and brings large-scale atrial fibrillation screenings within imminent reach.

stat.ML↗
arXiv2018

Soliton Resolution for the Derivative Nonlinear Schrödinger Equation

We study the Derivative Nonlinear Schrödinger equation for generic initial data in a weighted Sobolev space that can support bright solitons (but exclude spectral singularities). Drawing on previous well-posedness results, we give a full description of the long-time behavior of the solutions in the form of a finite sum of localized solitons and a dispersive component. At leading order and in space-time cones, the solution has the form of a multi-soliton whose parameters are slightly modified from their initial values by soliton-soliton and soliton-radiation interactions. Our analysis provides an explicit expression for the correction dispersive term. We use the nonlinear steepest descent method of Deift and Zhou, revisited by the $\overline{\partial}$-analysis of {McLaughlin-Miller and Dieng-McLaughlin, and complemented by the recent work of Borghese-Jenkins-McLaughlin on soliton resolution for the focusing Nonlinear Schrödinger equation. Our results imply that $N$-soliton solutions of the Derivative Nonlinear Schrödinger equation are asymptotically stable.

math.AP↗
arXiv2017

Splenomegaly Segmentation using Global Convolutional Kernels and Conditional Generative Adversarial Networks

Spleen volume estimation using automated image segmentation technique may be used to detect splenomegaly (abnormally enlarged spleen) on Magnetic Resonance Imaging (MRI) scans. In recent years, Deep Convolutional Neural Networks (DCNN) segmentation methods have demonstrated advantages for abdominal organ segmentation. However, variations in both size and shape of the spleen on MRI images may result in large false positive and false negative labeling when deploying DCNN based methods. In this paper, we propose the Splenomegaly Segmentation Network (SSNet) to address spatial variations when segmenting extraordinarily large spleens. SSNet was designed based on the framework of image-to-image conditional generative adversarial networks (cGAN). Specifically, the Global Convolutional Network (GCN) was used as the generator to reduce false negatives, while the Markovian discriminator (PatchGAN) was used to alleviate false positives. A cohort of clinically acquired 3D MRI scans (both T1 weighted and T2 weighted) from patients with splenomegaly were used to train and test the networks. The experimental results demonstrated that a mean Dice coefficient of 0.9260 and a median Dice coefficient of 0.9262 using SSNet on independently tested MRI volumes of patients with splenomegaly.

cs.CV↗
arXiv2017

Global Well-Posesedness for the Derivative Nonlinear Schrodinger Equation

We study the Derivative Nonlinear Schrödinger (DNLS). equation for general initial conditions in weighted Sobolev spaces that can support bright solitons (but exclude spectral singularities corresponding to algebraic solitons). We show that the set of such initial data is open and dense in a weighted Sobolev space, and includes data of arbitrarily large $L^2$-norm. We prove global well-posedness on this open and dense set. In a subsequent paper, we will use these results and a steepest descent analysis to prove the soliton resolution conjecture for the DNLS equation with the initial data considered here and asymptotic stability of $N-$soliton solutions.

math.AP↗
arXiv2017

Global Well-posedness and soliton resolution for the Derivative Nonlinear Schrödinger equation

We study the Derivative Nonlinear Schrödinger equation for general initial conditions in weighted Sobolev spaces that can support bright solitons (but excluding spectral singularities). We prove global well-posedness and give a full description of the long- time behavior of the solutions in the form of a finite sum of localized solitons and a dispersive component. At leading order and in space-time cones, the solution has the form of a multi-soliton whose parameters are slightly modified from their initial values by soliton-soliton and soliton-radiation interactions. Our analysis provides an explicit expression for the correction dispersive term. We use the nonlinear steepest descent method of Deift and Zhou revisited by the $\bar{\partial}$-analysis of Dieng-McLaughlin and complemented by the recent work of Borghese-Jenkins-McLaughlin on soliton resolution for the focusing nonlinear Schrödinger equation.

math.AP↗
arXiv2017

Enhanced betatron radiation by steering a low-energy-spread electron beam in a deflected laser-driven plasma wiggler

Laser wakefield accelerators (LWFA) hold great potential to produce high-quality high-energy electron beams (e beams) and simultaneously bright x-ray sources via betatron radiation, which are very promising for pump-probe study in ultrafast science. However, in order to obtain a high-quality e beam, electron injection and acceleration should be carefully manipulated, where a large oscillation amplitude has to be avoided and thus the emitted x-ray yield is limited. Here, we report a new scheme to experimentally enhance betatron radiation significantly both in photon yield and photon energy by separating electron injection and acceleration from manipulation of the e-beam transverse oscillation in the wake via introducing a slanted thin plasma refraction slab. Particle-in-cell simulations indicate that the e-beam transverse oscillation amplitude can be increased by more than 10 folds, after being steered into the deflected laser-driven wakefield due to refraction at the slab's boundaries. Spectral broadening of the x-rays can be suppressed owing to the small variation in the peak energy of the low-energy-spread e beam in a plasma wiggler regime. We demonstrate that the high-quality e-beam generation, refracting and wiggling can act as a whole to realize the concurrence of monoenergetic e beam and bright x-rays in a compact LWFA.

physics.plasm-ph↗
arXiv2016

Deep Recurrent Convolutional Neural Network: Improving Performance For Speech Recognition

A deep learning approach has been widely applied in sequence modeling problems. In terms of automatic speech recognition (ASR), its performance has significantly been improved by increasing large speech corpus and deeper neural network. Especially, recurrent neural network and deep convolutional neural network have been applied in ASR successfully. Given the arising problem of training speed, we build a novel deep recurrent convolutional network for acoustic modeling and then apply deep residual learning to it. Our experiments show that it has not only faster convergence speed but better recognition accuracy over traditional deep convolutional recurrent network. In the experiments, we compare the convergence speed of our novel deep recurrent convolutional networks and traditional deep convolutional recurrent networks. With faster convergence speed, our novel deep recurrent convolutional networks can reach the comparable performance. We further show that applying deep residual learning can boost the convergence speed of our novel deep recurret convolutional networks. Finally, we evaluate all our experimental networks by phoneme error rate (PER) with our proposed bidirectional statistical n-gram language model. Our evaluation results show that our newly proposed deep recurrent convolutional network applied with deep residual learning can reach the best PER of 17.33\% with the fastest convergence speed on TIMIT database. The outstanding performance of our novel deep recurrent convolutional neural network with deep residual learning indicates that it can be potentially adopted in other sequential problems.

cs.CL↗
arXiv2016

Composing Music with Grammar Argumented Neural Networks and Note-Level Encoding

Creating aesthetically pleasing pieces of art, including music, has been a long-term goal for artificial intelligence research. Despite recent successes of long-short term memory (LSTM) recurrent neural networks (RNNs) in sequential learning, LSTM neural networks have not, by themselves, been able to generate natural-sounding music conforming to music theory. To transcend this inadequacy, we put forward a novel method for music composition that combines the LSTM with Grammars motivated by music theory. The main tenets of music theory are encoded as grammar argumented (GA) filters on the training data, such that the machine can be trained to generate music inheriting the naturalness of human-composed pieces from the original dataset while adhering to the rules of music theory. Unlike previous approaches, pitches and durations are encoded as one semantic entity, which we refer to as note-level encoding. This allows easy implementation of music theory grammars, as well as closer emulation of the thinking pattern of a musician. Although the GA rules are applied to the training data and never directly to the LSTM music generation, our machine still composes music that possess high incidences of diatonic scale notes, small pitch intervals and chords, in deference to music theory.

cs.LG↗
arXiv2016

Long-Time Behavior of Solutions to the Derivative Nonlinear Schrödinger Equation for Soliton-Free Initial Data

The large-time behavior of solutions to the derivative nonlinear Schrödinger equation is established for initial conditions in some weighted Sobolev spaces under the assumption that the initial conditions do not support solitons. Our approach uses the inverse scattering setting and the nonlinear steepest descent method of Deift and Zhou as recast by Dieng and McLaughlin.

math.AP↗
arXiv2016

Global Existence for the Derivative Nonlinear Schrodinger Equation by the Method of Inverse Scattering

We develop inverse scattering for the derivative nonlinear Schrodinger equation (DNLS) on the line using its gauge equivalence with a related nonlinear dispersive equation. We prove Lipschitz continuity of the direct and inverse scattering maps from the weighted Sobolev spaces $H^{2,2}(\mathbb{R})$ to itself. These results immediately imply global existence of solutions to the DNLS for initial data in a spectrally determined (open) subset of $H^{2,2}(\mathbb{R})$ containing a neighborhood of 0.

math.AP↗
arXiv2012

MPO: An Efficient and Low-cost Peer-to-Peer Overlay for Autonomic Communications

The term Autonomic Communication (AC) refers to self-managing systems which are capable of supporting self-configuration, self-healing and self-optimization. However, information reflection and collection, lack of centralized control, non-cooperation and so on are just some of the challenges within AC systems. We have considered these problems in theory and practice and reached the following conclusion; in order to build an ideal system for autonomic communication, there are three key problems to be solved. Motivated by the need for AC, we have designed an efficient and low-cost Peer-to-Peer (P2P) overlay called Maya-Pyramid overlay (MPO) and combined merits of unstructured P2P with those of structured P2P overlays. Differing from the traditional hierarchical P2P (i.e. tree-like structure) overlay, (1) MPO is composed of levels and layers, which uses small world characteristic to improve efficiency, and the maintenance cost is decreased because update and backup only take place in two neighboring levels or layers instead of recursively perform in higher levels. (2) Unlike normal redundant mechanisms for solving the single fault problem: Tri-Information Center (Tri-IC) mechanism is presented in order to improve robustness by alleviating the load of cluster heads in a hierarchical P2P overlay. (3) A source ranking mechanism is proposed in order to discourage free riding and whitewashing and to encourage frequent information exchanges between peers. (4) Inspired by Pastry's ID structure for a structured DHT algorithm, a 3D unique ID structure is presented in the unstructured P2P overlay. This will guarantee anonymity in routing, and will be, not only more efficient because it applies the DHT-like routing algorithm in the unstructured P2P overlay, but also more adaptive to suit AC. Evaluation proved that MPO is robust, highly efficient and of a low-cost.

cs.DC↗