arXiv subjects

Xuemei Chen

Publications and source records attributed to Xuemei Chen.

33 records · Page 2Linked to original sources

arXiv2016

The gap between the null space property and the restricted isometry property

The null space property (NSP) and the restricted isometry property (RIP) are two properties which have received considerable attention in the compressed sensing literature. As the name suggests, NSP is a property that depends solely on the null space of the measurement procedure and as such, any two matrices which have the same null space will have NSP if either one of them does. On the other hand, RIP is a property of the measurement procedure itself, and given an RIP matrix it is straightforward to construct another matrix with the same null space that is not RIP. %Furthermore, RIP is known to imply NSP and therefore RIP is a strictly stronger assumption than NSP. We say a matrix is RIP-NSP if it has the same null space as an RIP matrix. We show that such matrices can provide robust recovery of compressible signals under Basis pursuit which in many applicable settings is comparable to the guarantee that RIP provides. More importantly, we constructively show that the RIP-NSP is stronger than NSP with the aid of this robust recovery result, which shows that RIP is fundamentally stronger than NSP.

cs.IT↗

arXiv2015

Bioinspired interfacial materials with enhanced drop mobility: From fundamentals to multifunctional applications

The development of bio-inspired interfacial materials with enhanced drop mobility that mimic the innate functionalities of nature will have significant impact on the energy, environment and global healthcare. In spite of extensive progress, the state of the art of interfacial materials have not reached the level of maturity sufficient for industrial applications in terms of scalability, stability and reliability, which are complicated by their operating environments and lack of facile approaches to exquisitely control the local structural texture and chemical composition at multiple length scales. In this review, we focus on the recent advances in the fundamental understanding as well as practical applications of bio-inspired interfacial materials, with an emphasis on the drop impact induced bouncing and coalescence induced jumping behaviors. We also suggest our own perspectives on how to catalyze new discoveries and to foster technological adoption to move this exciting area forward.

cond-mat.mtrl-sci↗

arXiv2015

Fusion frames and randomized subspace actions

A randomized subspace action algorithm is investigated for fusion frame signal recovery problems. It is noted that Kaczmarz bounds provide upper bounds on the algorithm's error moments. The main question of which probability distributions on a random fusion frame lead to provably fast convergence is addressed. In particular, it is proven which distributions give minimal Kaczmarz bounds, and hence give best control on error moment upper bounds arising from Kaczmarz bounds. Uniqueness of the optimal distributions is also addressed.

math.NA↗

arXiv2015

A possible formation channel for blue hook stars in globular cluster

The formation mechanism for blue hook (BHk) stars in globular clusters (GCs) is still unclear. Following one of the possible scenario, named late hot flash scenario, we proposed that tidally enhanced stellar wind in binary evolution may provide the huge mass loss on the red giant branch (RGB) and produce BHk stars. Employing the detailed stellar evolution code, Modules for Experiments in Stellar Astrophysics (MESA), we investigated the contributions of tidally enhanced stellar wind as a possible formation channel for BHk stars in GCs. We evolved the primary stars with different initial orbital periods using the binary module in MESA (version 6208) from zero age main-sequence (ZAMS) to post horizontal branch (HB) stage, and obtained their evolution parameters which are compared with the observation. The results are consistent with observation in the color-magnitude diagram (CMD) and the logg-Teff plane for NGC 2808, which is an example GC hosting BHk stars. However, the helium abundance in the surface for our models is higher than the one obtained in BHk stars. This discrepancy between our models and observation is possibly due to the fact that gravitational settling and radiative levitation which are common processes in hot HB stars are not considered in the models as well as the fact that the flash mixing efficiency may be overestimated in the calculations. Our results suggested that tidally enhanced stellar wind in binary evolution is able to naturally provide the huge mass loss on the RGB needed for late hot flash scenario and it is a possible and reasonable formation channel for BHk stars in GCs.

astro-ph.SR↗

arXiv2014

Electrowetting on liquid-infused film (EWOLF): Complete reversibility and controlled droplet oscillation suppression for fast optical imaging

Electrowetting on dielectric (EWOD) has emerged as a powerful tool to electrically manipulate tiny individual droplets in a controlled manner. Despite tremendous progress over the past two decades, current EWOD operating in ambient conditions has limited functionalities posing challenges for its applications, including electronic display, energy generation, and microfluidic systems. Here, we demonstrate a new paradigm of electrowetting on liquid-infused film (EWOLF) that allows for complete reversibility and tunable transient response simultaneously. We determine that these functionalities in EWOLF are attributed to its novel configuration, which allows for the formation of viscous liquid-liquid interfaces as well as additional wetting ridges, thereby suppressing the contact line pinning and severe droplet oscillation encountered in the conventional EWOD. Finally, by harnessing these functionalities demonstrated in EWOLF, we also explore its application as liquid lens for fast optical focusing.

cond-mat.mtrl-sci↗

arXiv2014

The Hildreth's Algorithm with Applications to Soft Constraints for User Interface Layout

The Hildreth's algorithm is a row action method for solving large systems of inequalities. This algorithm is efficient for problems with sparse matrices, as opposed to direct methods such as Gaussian elimination or QR-factorization. We apply the Hildreth's algorithm, as well as a randomized version, along with prioritized selection of the inequalities, to efficiently detect the highest priority feasible subsystem of equations. We prove convergence results and feasibility criteria for both cyclic and randomized Hildreth's algorithm, as well as a mixed algorithm which uses Hildreth's algorithm for inequalities and Kaczmarz algorithm for equalities. These prioritized, sparse systems of inequalities commonly appear in constraint-based user interface (UI) layout specifications. The performance and convergence of these proposed algorithms are evaluated empirically using randomly generated UI layout specifications of various sizes. The results show that these methods offer improvements in performance over standard methods like Matlab's LINPROG, a well-known efficient linear programming solver, and the recent developed Kaczmarz algorithm with prioritized IIS detection.

math.NA↗

arXiv2014

Effect of Binary Fraction on Horizontal Branch Morphology under Tidally Enhanced Stellar Wind

Tidally enhanced stellar wind may affect horizontal branch (HB) morphology in globular clusters (GCs) by enhancing the mass loss of primary star during binary evolution. Lei et al. (2013a, 2013b) studied the effect of this kind of wind on HB morphology in details, and their results indicated that binary is a possible secondparameter (2P) candidate in GCs. Binary fraction is an very important fact in the tidally-enhanced-stellar-wind model. In this paper, we studied the effect of binary fraction on HB morphology by removing the effects of metallicity and age. Five different binary fractions (i.e., 10%, 15%, 20%, 30% and 50%) are adopted in our model calculations. The synthetic HB morphologies with different binary fractions are obtained at different metallicities and ages. We found that, due to the great influence of metallicity and age, the effect of binary fraction on HB morphology may be masked by these two parameters. However, when the effects of metallicity and age are removed, the tendency that HB morphologies become bluer with increasing of binary fractions is clearly presented. Furthermore, we compared our results with the observation by Milone et al. (2012). Our results are consistent well with the observation at metalrich and metal-poor GCs. For the GCs with intermediate metallicity, when the effect of age on HB morphology is removed, a weak tendency that HB morphologies become bluer with increasing of binary fractions is presented in all regions of GCs, which is consistent with our results obtained in this metallicity range.

astro-ph.SR↗

arXiv2014

Measures of scalability

Scalable frames are frames with the property that the frame vectors can be rescaled resulting in tight frames. However, if a frame is not scalable, one has to aim for an approximate procedure. For this, in this paper we introduce three novel quantitative measures of the closeness to scalability for frames in finite dimensional real Euclidean spaces. Besides the natural measure of scalability given by the distance of a frame to the set of scalable frames, another measure is obtained by optimizing a quadratic functional, while the third is given by the volume of the ellipsoid of minimal volume containing the symmetrized frame. After proving that these measures are equivalent in a certain sense, we establish bounds on the probability of a randomly selected frame to be scalable. In the process, we also derive new necessary and sufficient conditions for a frame to be scalable.

math.FA↗

arXiv2013

A null space property approach to compressed sensing with frames

An interesting topic in compressive sensing concerns problems of sensing and recovering signals with sparse representations in a dictionary. In this note, we study conditions of sensing matrices A for the L1-synthesis method to accurately recover sparse, or nearly sparse signals in a given dictionary D. In particular, we propose a dictionary based null space property (D-NSP) which, to the best of our knowledge, is the first sufficient and necessary condition for the success of the L1 recovery. This new property is then utilized to detect some of those dictionaries whose sparse families cannot be compressed universally. Moreover, when the dictionary is full spark, we show that AD being NSP, which is well-known to be only sufficient for stable recovery via L1-synthesis method, is indeed necessary as well.

cs.IT↗

arXiv2013

A null space analysis of the L1 synthesis method in dictionary-based compressed sensing

An interesting topic in compressed sensing aims to recover signals with sparse representations in a dictionary. Recently the performance of the L1-analysis method has been a focus, while some fundamental problems for the L1-synthesis method are still unsolved. For example, what are the conditions for it to stably recover compressible signals under noise? Whether coherent dictionaries allow the existence of sensing matrices that guarantee good performances of the L1-synthesis method? To answer these questions, we build up a framework for the L1-synthesis method. In particular, we propose a dictionary-based null space property DNSP which, to the best of our knowledge, is the first sufficient and necessary condition for the success of L1-synthesis without measurement noise. With this new property, we show that when the dictionary D is full spark, it cannot be too coherent otherwise the method fails for all sensing matrices. We also prove that in the real case, DNSP is equivalent to the stability of L1-synthesis under noise.

cs.IT↗

arXiv2013

A note on scalable frames

We study the problem of determining whether a given frame is scalable, and when it is, understanding the set of all possible scalings. We show that for most frames this is a relatively simple task in that the frame is either not scalable or is scalable in a unique way, and to find this scaling we just have to solve a linear system. We also provide some insight into the set of all scalings when there is not a unique scaling. In particular, we show that this set is a convex polytope whose vertices correspond to minimal scalings.

math.FA↗

arXiv2012

New Existence Theorems about the Solutions of Some Stochastic Integral Equations

Picard's iteration has been used to prove the existence and uniqueness of the solution for stochastic integral equations, here we use Schauder's fixed point theorem to give a new existence theorem about the solution of a stochastic integral equation, our theorem can weak some conditions gotten by applying Banach's fixed point theorem.

math.FA↗

arXiv2011

Preparation and ferroelectric properties of (124)-oriented SrBi4Ti4O15 ferroelectric thin film on (110)-oriented LaNiO3 electrode

A (124)-oriented SrBi4Ti4O15 (SBTi) ferroelectric thin film with high volume fraction of αSBTi(124)=97% was obtained using a metal organic decomposition process on SiO2/Si substrate coated by (110)-oriented LaNiO3 (LNO) thin film. The remanent polarization and coercive field for (124)-oriented SBTi film are 12.1 μC/cm2 and 74 kV/cm, respectively. No evident fatigue of (124)-oriented SBTi thin film can be observed after 1{\times}10e9 switching cycles. Besides, the (124)-oriented SBTi film can be uniformly polarized over large areas using a piezoelectric-mode atomic force microscope. Considering that the annealing temperature was 650°C and the thickness of each deposited layer was merely 30 nm, a long-range epitaxial relationship between SBTi(124) and LNO(110) facets was proposed. The epitaxial relationship was demonstrated based on the crystal structures of SBTi and LNO.

cond-mat.mtrl-sci↗

arXiv2008

Unambiguous unitary quantum channels

Unambiguous unitary maps and unambiguous unitary quantum channels are introduced and some of their properties are derived. These properties ensure certain simple form for the measurements involved in realizing an unambiguous unitary quantum channel. Error correction and unambiguous error correction with nonzero probability are discussed in terms of unambiguous unitary quantum channels. We not only re-derive the well-known condition for a set of errors to be correctable with certainty, but also obtain a necessary and sufficient condition for the errors caused by a noisy channel to be correctable with any nonzero probability. Dense coding with a partially entangled state can also be viewed as an unambiguous unitary quantum channel when all messages are required to be transmitted with equal probability of success, the maximal achievable probability of success is derived and the optimum protocol is also obtained.

quant-ph↗

arXiv2000

A necessary and sufficient criterion for multipartite separable states

We present a necessary and sufficient condition for the separability of multipartite quantum states, this criterion also tells us how to write a multipartite separable state as a convex sum of separable pure states. To work out this criterion, we need to solve a set of equations, actually it is easy to solve these quations analytically if the density matrix of the given quantum state has few nonzero eigenvalues.

quant-ph↗