Weak stability of l_1-minimization methods in sparse data reconstruction

As one of the most plausible convex optimization methods for sparse data reconstruction, l_1-minimization plays a fundamental role in the development of sparse optimization theory. The stability of this method has been addressed in the literature under various assumptions such as the restricted isometry property, null space property, and mutual coherence. In this paper, we propose a unified means to develop the so-called weak stability theory for 1-minimization methods under the condition called the weak range space property of a transposed design matrix, which turns out to be a necessary and sufficient condition for the standard l_1-minimization method to be weakly stable in sparse data reconstruction. The reconstruction error bounds established in this paper are measured by the so-called Robinson’s constant. We also provide a unified weak stability result for standard l_1-minimization under several existing compressed sensing matrix properties. In particular, the weak stability of l_1-minimization under the constant-free range space property of order k of the transposed design matrix is established for the first time in this paper. Different from the existing analysis, we utilize the classic Ho˙man’s lemma concerning the error bound of linear systems as well as Dudley’s theorem concerning the polytope approximation of the unit l_2-ball to show that l_1-minimization is robustly and weakly stable in recovering sparse data from inaccurate measurements

Inverse-free extreme learning machine with optimal information updating

2014-2015 > Academic research: refereed > Publication in refereed journalVersion of RecordPublishe

Characterizing the universal rigidity of generic frameworks

A framework is a graph and a map from its vertices to E^d (for some d). A framework is universally rigid if any framework in any dimension with the same graph and edge lengths is a Euclidean image of it. We show that a generic universally rigid framework has a positive semi-definite stress matrix of maximal rank. Connelly showed that the existence of such a positive semi-definite stress matrix is sufficient for universal rigidity, so this provides a characterization of universal rigidity for generic frameworks. We also extend our argument to give a new result on the genericity of strict complementarity in semidefinite programming.Comment: 18 pages, v2: updates throughout; v3: published versio

Novel Tunable Fiber Optic Edge Filter Based on Modulating Chirp Rate of pi-Phase-Shifted Fiber Bragg Grating

We propose and experimentally demonstrate a novel tunable fiber optic edge filter based on modulating the chirp rate of a pi-phase-shifted fiber Bragg grating (FBG) operated in reflection mode. The phase shift induced notch in the reflection spectrum is utilized as the edge filter. The dependence of the pi-phase-shifted FBG's spectral response on the chirp rate has been numerically studied in detail and experimentally confirmed for the first time. The linear wavelength range of this edge filter can be tuned by changing the chirp rate of FBG. A fiber optic edge filter is further obtained experimentally and tested as a wavelength interrogator, which is in a good agreement with numerical results. The proposed edge filter has advantages of simple-structure, cost-effectiveness, high sensitivity, and flexible tunable, thus opening up some applications, especially as wavelength interrogator in small wavelength range

Spatial housing economics: a survey

This introduction to the Virtual Special Issue surveys the development of spatial housing economics from its roots in neo-classical theory, through more recent developments in social interactions modelling, and touching on the role of institutions, path dependence and economic history. The survey also points to some of the more promising future directions for the subject that are beginning to appear in the literature. The survey covers elements hedonic models, spatial econometrics, neighbourhood models, housing market areas, housing supply, models of segregation, migration, housing tenure, sub-national house price modelling including the so-called ripple effect, and agent-based models. Possible future directions are set in the context of a selection of recent papers that have appeared in Urban Studies. Nevertheless, there are still important gaps in the literature that merit further attention, arising at least partly from emerging policy problems. These include more research on housing and biodiversity, the relationship between housing and civil unrest, the effects of changing age distributions - notably housing for the elderly - and the impact of different international institutional structures. Methodologically, developments in Big Data provide an exciting framework for future work

High power Q-switched thulium doped fibre laser using carbon nanotube polymer composite saturable absorber

We have proposed and demonstrated a Q-switched Thulium doped bre laser (TDFL) with a ‘Yin-Yang’ all- bre cavity scheme based on a combination of nonlinear optical loop mirror (NOLM) and nonlinear ampli ed loop mirror (NALM). Unidirectional lasing operation has been achieved without any intracavity isolator. By using a carbon nanotube polymer composite based saturable absorber (SA), we demonstrated the laser output power of ~197 mW and pulse energy of 1.7 μJ. To the best of our knowledge, this is the highest output power from a nanotube polymer composite SA based Q-switched Thulium doped bre laser

Fiber-optic parametric amplifier and oscillator based on intracavity parametric pump technique

Chinese Government Scholarship of Postgraduates' Oversea Study For Building High-Level UniversityA cost-effective fiber optical parametric amplifier (FOPA) based on the laser intracavity pump technique has been proposed and demonstrated experimentally. The parametric process is realized by inserting a 1 km highly nonlinear dispersion-shifted fiber (HNL-DSF) into a fiber ring-laser cavity that consists of a high-power erbium-doped fiber (EDF) amplifier and two highly reflective fiber Bragg gratings. Compared with the conventional parametric pump schemes, the proposed pumping technique is free from a tunable semiconductor laser as the pump source and also the pump phase modulation. When the oscillating power of 530 mW in the EDF laser cavity is achieved to pump the HNL-DSF, a peak parametric gain of 27.5 dB and a net gain over 45 nm are obtained. Moreover, a widely tunable fiber-optic parametric oscillator is further developed using the FOPA as a gain medium. (C) 2009 Optical Society of Americ

Truncated Inference for Latent Variable Optimization Problems: Application to Robust Estimation and Learning

Optimization problems with an auxiliary latent variable structure in addition to the main model parameters occur frequently in computer vision and machine learning. The additional latent variables make the underlying optimization task expensive, either in terms of memory (by maintaining the latent variables), or in terms of runtime (repeated exact inference of latent variables). We aim to remove the need to maintain the latent variables and propose two formally justified methods, that dynamically adapt the required accuracy of latent variable inference. These methods have applications in large scale robust estimation and in learning energy-based models from labeled data.Comment: 16 page

Three-dimensional micromachining for microsystems by confined etchant layer technique

The micromachining of GaAs with three different truly three-dimensional (3D) molds were performed by the confined etchant layer technique (CELT). The etched patterns were found, approximately, to be the negative copy of the 3D molds. The general comparison of CELT with the existing micromachining techniques, such as two-dimensional (2D) projection lithography and electro-discharge machining, was made. The replication of the complex microstructures down to micrometer scale has been done by CELT in a single step. The photoresist layer, together with the procedures of exposure, developing and removal of resist, could be eliminated. The advantages of CELT over the existing lithography techniques and its potential applications are discussed briefly. It has been shown that CELT could be developed as a complementary technique to the existing micromachining techniques in fabricating microdevices for microsystems. (C) 2001 Elsevier Science Ltd. All rights reserved

Quantum-Dot Light-Emitting Diodes with Nitrogen-Doped Carbon Nanodot Hole Transport and Electronic Energy Transfer Layer

Electroluminescence efficiency is crucial for the application of quantum-dot light-emitting diodes (QD-LEDs) in practical devices. We demonstrate that nitrogen-doped carbon nanodot (N-CD) interlayer improves electrical and luminescent properties of QD-LEDs. The N-CDs were prepared by solution-based bottom up synthesis and were inserted as a hole transport layer (HTL) between other multilayer HTL heterojunction and the red-QD layer. The QD-LEDs with N-CD interlayer represented superior electrical rectification and electroluminescent efficiency than those without the N-CD interlayer. The insertion of N-CD layer was found to provoke the Forster resonance energy transfer (FRET) from N-CD to QD layer, as confirmed by time-integrated and - resolved photoluminescence spectroscopy. Moreover, hole-only devices (HODs) with N-CD interlayer presented high hole transport capability, and ultraviolet photoelectron spectroscopy also revealed that the N-CD interlayer reduced the highest hole barrier height. Thus, more balanced carrier injection with sufficient hole carrier transport feasibly lead to the superior electrical and electroluminescent properties of the QD-LEDs with N-CD interlayer. We further studied effect of N-CD interlayer thickness on electrical and luminescent performances for high-brightness QD-LEDs. The ability of the N-CD interlayer to improve both the electrical and luminescent characteristics of the QD-LEDs would be readily exploited as an emerging photoactive material for high-efficiency optoelectronic devices.ope