Discontinuous Galerkin methods and their adaptivity for the tempered fractional (convection) diffusion equations

This paper focuses on the adaptive discontinuous Galerkin (DG) methods for the tempered fractional (convection) diffusion equations. The DG schemes with interior penalty for the diffusion term and numerical flux for the convection term are used to solve the equations, and the detailed stability and convergence analyses are provided. Based on the derived posteriori error estimates, the local error indicator is designed. The theoretical results and the effectiveness of the adaptive DG methods are respectively verified and displayed by the extensive numerical experiments. The strategy of designing adaptive schemes presented in this paper works for the general PDEs with fractional operators.Comment: 31 pages, 5 figure

A++ Random Access for Two-way Relaying in Wireless Networks

Two-way relaying can significantly improve performance of next generation wireless networks. However, due to its dependence on multi-node cooperation and transmission coordination, applying this technique to a wireless network in an effective and scalable manner poses a challenging problem. To tackle this problem without relying on complicated scheduling or network optimization algorithms, we propose a scalable random access scheme that takes measures in both the physical layer and the medium access control layer. Specifically, we propose a two-way relaying technique that supports fully asynchronous transmission and is modulation-independent. It also assumes no priori knowledge of channel conditions. On the top of this new physical layer technique, a random access MAC protocol is designed to dynamically form two-way relaying cooperation in a wireless network. To evaluate the scalable random access scheme, both theoretical analysis and simulations are carried out. Performance results illustrate that our scheme has achieved the goal of scalable two-way relaying in a wireless network and significantly outperforms CSMA/CA protocol

Cross-Layer Scheduling in Multi-user System with Delay and Secrecy Constraints

Recently, physical layer security based approaches have drawn considerable attentions and are envisaged to provide secure communications in the wireless networks. However, most existing literatures only focus on the physical layer. Thus, how to design an effective transmission scheme which also considers the requirements from the upper layers is still an unsolved problem. We consider such cross-layer resource allocation problem in the multi-user downlink environment for both having instantaneous and partial eavesdropping channel information scenarios. The problem is first formulated in a new security framework. Then, the control scheme is designed to maximize the average admission rate of the data, incorporating delay, power, and secrecy as constraints, for both non-colluding and colluding eavesdropping cases in each scenario. Performance analysis is given based on the stochastic optimization theory and the simulations are carried out to validate the effectiveness of our scheme.Comment: 22 page

L\'{e}vy-walk-like Langevin dynamics

Continuous time random walks and Langevin equations are two classes of stochastic models for describing the dynamics of particles in the natural world. While some of the processes can be conveniently characterized by both of them, more often one model has significant advantages (or has to be used) compared with the other one. In this paper, we consider the weakly damped Langevin system coupled with a new subordinator|$\alpha$-dependent subordinator with $1<\alpha<2$. We pay attention to the diffusion behaviour of the stochastic process described by this coupled Langevin system, and find the super-ballistic diffusion phenomena for the system with an unconfined potential on velocity but sub-ballistic superdiffusion phenomenon with a confined potential, which is like L\'{e}vy walk for long times. One can further note that the two-point distribution of inverse subordinator affects mean square displacement of this coupled weakly damped Langevin system in essential.Comment: 24 pages, 4 figure

Localization and ballistic diffusion for the tempered fractional Brownian-Langevin motion

This paper further discusses the tempered fractional Brownian motion, its ergodicity, and the derivation of the corresponding Fokker-Planck equation. Then we introduce the generalized Langevin equation with the tempered fractional Gaussian noise for a free particle, called tempered fractional Langevin equation (tfLe). While the tempered fractional Brownian motion displays localization diffusion for the long time limit and for the short time its mean squared displacement has the asymptotic form $t^{2H}$, we show that the asymptotic form of the mean squared displacement of the tfLe transits from $t^2$ (ballistic diffusion for short time) to $t^{2-2H}$, and then to $t^2$ (again ballistic diffusion for long time). On the other hand, the overdamped tfLe has the transition of the diffusion type from $t^{2-2H}$ to $t^2$ (ballistic diffusion). The tfLe with harmonic potential is also considered.Comment: 19 pages, 9 figure

Langevin dynamics for L\'evy walk with memory

Memory effects, sometimes, can not be neglected. In the framework of continuous time random walk, memory effect is modeled by the correlated waiting times. In this paper, we derive the two-point probability distribution of the stochastic process with correlated increments as well as the one of its inverse process, and present the Langevin description of L\'evy walk with memory, i.e., correlated waiting times. Based on the built Langevin picture, the properties of aging and nonstationary are discussed. The Langevin system exhibits sub-ballistic superdiffusion if the friction force is involved, while it displays super-ballistic diffusion or hyperdiffusion if there is no friction. It is discovered that the correlation of waiting times suppresses the diffusion behavior whether there is friction or not, and the stronger the correlation of waiting times becomes, the slower the diffusion is. In particular, the correlation function, correlation coefficient, ergodicity, and scaling property of the corresponding stochastic process are also investigated.Comment: 11 pages, 4 figure

Estimation of Markov Chain via Rank-Constrained Likelihood

This paper studies the estimation of low-rank Markov chains from empirical trajectories. We propose a non-convex estimator based on rank-constrained likelihood maximization. Statistical upper bounds are provided for the Kullback-Leiber divergence and the $\ell_2$ risk between the estimator and the true transition matrix. The estimator reveals a compressed state space of the Markov chain. We also develop a novel DC (difference of convex function) programming algorithm to tackle the rank-constrained non-smooth optimization problem. Convergence results are established. Experiments show that the proposed estimator achieves better empirical performance than other popular approaches.Comment: Accepted at ICML 201

Towards Universal Object Detection by Domain Attention

Despite increasing efforts on universal representations for visual recognition, few have addressed object detection. In this paper, we develop an effective and efficient universal object detection system that is capable of working on various image domains, from human faces and traffic signs to medical CT images. Unlike multi-domain models, this universal model does not require prior knowledge of the domain of interest. This is achieved by the introduction of a new family of adaptation layers, based on the principles of squeeze and excitation, and a new domain-attention mechanism. In the proposed universal detector, all parameters and computations are shared across domains, and a single network processes all domains all the time. Experiments, on a newly established universal object detection benchmark of 11 diverse datasets, show that the proposed detector outperforms a bank of individual detectors, a multi-domain detector, and a baseline universal detector, with a 1.3x parameter increase over a single-domain baseline detector. The code and benchmark will be released at http://www.svcl.ucsd.edu/projects/universal-detection/.Comment: 11 pages, 6 figures. Accepted to CVPR 201

Semiconductor Nanocrystals: Synthesis, Optical Properties and Environmental Impact

The study in this dissertation mainly focused on semiconductor nanocrystals ranging from controllable synthesis of II-VI quantum dots in both organic phase and aqueous phase, to their optical property and potential environmental impact. Besides, our study of fluorescent nanomaterials was extended from semiconductor nanocrystals to another system, carbon dots. In the first project, an unconventional method to induce anisotropic growth of CdS arms on CdSe/CdS seeds was developed to form nanotetrapods. Our control experiments suggested the key role of CdS shell thickness of CdSe/CdS seeds and concentration of precursor for CdS growth in the growth of nanotetrapods. Our results show that the branching came from a zinc blende phase formation at the slow growing end of c-axis of wurtzite CdSe/CdS seeds due to the enrichment of stacking fault. The second work focused on the study of blinking properties of CdSe/CdS core/shell QDs with various morphology, surface capping ligands, and shell growth chemistry. Outstanding blinking suppression has been observed with hexagonal pyramid and bipyramid QDs, especially the bipyramid QDs. Besides, there are more off-state events observed with QDs coated with hydrophilic ligands, while the quantum yield was slightly decreased after ligand exchange reaction. Additionally, QDs prepared with the newly developed shell growth chemistry have been observed with lower on time fraction and an effect of core size on the blinking properties. The third work focused on the study on how Hg interacts with nanoparticles using aqueous CdSe nanoparticles capped with l-cysteine as a model system. The fluorescent nature of CdSe nanoparticles allows us to study the interaction of Hg ion with CdSe nanoparticles via photoluminescence spectra and photoluminescence decay. Results of ICP-MS measurements of CdSe NPs and the separated solution obtained after addition of Hg ions excluded the cation exchange of Cd2+ by Hg2+ except at very high Hg to Cd ratio. XPS further suggested that the Hg was bound to the amine and carboxylate group of l-cysteine capping agent on the nanoparticle surface. The fourth project is an experimental study of fluorescent carbon nanodots on their photoluminescence response to external electric field. Fluorescent carbon dots were synthesized using procedures modified from oil phase synthesis of QDs with citric acid as the reactants. The carbon nanodots showed remarkable excitation dependent emission properties. After encapsulated in artificial lipid bilayers, the carbon dots showed competitive sensitivity of voltage compared to the most used commercial membrane potential sensing dyes, which indicates great potential of carbon dots as alternative voltage sensing probes

Smart Pilot Assignment for Massive MIMO

A massive multiple-input multiple-output (MIMO) system, which utilizes a large number of antennas at the base station (BS) to serve multiple users, suffers from pilot contamination due to inter-cell interference. A smart pilot assignment (SPA) scheme is proposed in this letter to improve the performance of users with severe pilot contamination. Specifically, by exploiting the large-scale characteristics of fading channels, the BS firstly measures the inter-cell interference of each pilot sequence caused by the users with the same pilot sequence in other adjacent cells. Then, in contrast to the conventional schemes which assign the pilot sequences to the users randomly, the proposed SPA method assigns the pilot sequence with the smallest inter-cell interference to the user having the worst channel quality in a sequential way to improve its performance. Simulation results verify the performance gain of the proposed scheme in typical massive MIMO systems.Comment: 4 pages, 3 figure