arXiv subjects

Wei Luo

Publications and source records attributed to Wei Luo.

At least 199 records · Page 11Linked to original sources

arXiv2018

The polar decomposition for adjointable operators on Hilbert $C^*$-modules and $n$-centered operators

Let $n$ be any natural number. The $n$-centered operator is introduced for adjointable operators on Hilbert $C^*$-modules. Based on the characterizations of the polar decomposition for the product of two adjointable operators, $n$-centered operators, centered operators as well as binormal operators are clarified, and some results known for the Hilbert space operators are improved. It is proved that for an adjointable operator $T$, if $T$ is Moore-Penrose invertible and is $n$-centered, then its Moore-Penrose inverse is also $n$-centered. A Hilbert space operator $T$ is constructed such that $T$ is $n$-centered, whereas it fails to be $(n+1)$-centered.

math.OA↗

arXiv2018

The polar decomposition for adjointable operators on Hilbert $C^*$-modules and centered operators

Let $T$ be an adjointable operator between two Hilbert $C^*$-modules and $T^*$ be the adjoint operator of $T$. The polar decomposition of $T$ is characterized as $T=U(T^*T)^\frac12$ and $\mathcal{R}(U^*)=\overline{\mathcal{R}(T^*)}$, where $U$ is a partial isometry, $\mathcal{R}(U^*)$ and $\overline{\mathcal{R}(T^*)}$ denote the range of $U^*$ and the norm closure of the range of $T^*$, respectively. Based on this new characterization of the polar decomposition, an application to the study of centered operators is carried out.

math.OA↗

arXiv2018

New multiplicative perturbation bounds for the generalized polar decomposition

Some new Frobenius norm bounds of the unique solution to certain structured Sylvester equation are derived. Based on the derived norm upper bounds, new multiplicative perturbation bounds are provided both for subunitary polar factors and positive semi-definite polar factors. Some previous results are then improved.

math.FA↗

arXiv2018

Evolution and spatial distribution of Brillouin backscattering associated to hybrid acoustic modes in sub-wavelength silica microfibers

The spectral evolution and spatial distribution of backscattered Brillouin signals is experimentally investigated in sub-wavelength silica microfibers. The Brillouin spectrum evolution reveals the different dynamics of the various peaks, offering evidence of backscattering signals induced by acoustic waves with phase velocity greater than that of the longitudinal wave. The spatial distribution is found to have significant influence on the response of Brillouin scattering under tensile load, with hybrid acoustic modes providing a smaller response under axial strain. This insight into interactions between optical and hybrid acoustic modes at sub-wavelength confinements could help understand ultrasonic waves in tapered waveguides, and have potential applications in optical sensing and detection.

physics.optics↗

arXiv2018

Perturbation estimation for the parallel sum of Hermitian positive semi-definite matrices

Let $\mathbb{C}^{n\times n}$ be the set of all $n \times n$ complex matrices. For any Hermitian positive semi-definite matrices $A$ and $B$ in $\mathbb{C}^{n\times n}$, their new common upper bound less than $A+B-A:B$ is constructed, where $(A+B)^†$ denotes the Moore-Penrose inverse of $A+B$, and $A:B=A(A+B)^†B$ is the parallel sum of $A$ and $B$. A factorization formula for $(A+X):(B+Y)-A:B-X:Y$ is derived, where $X,Y\in\mathbb{C}^{n\times n}$ are any Hermitian positive semi-definite perturbations of $A$ and $B$, respectively. Based on the derived factorization formula and the constructed common upper bound of $X$ and $Y$, some new and sharp norm upper bounds of $(A+X):(B+Y)-A:B$ are provided. Numerical examples are also provided to illustrate the sharpness of the obtained norm upper bounds.

math.FA↗

arXiv2018

Neutron diffraction study on magnetic structures and transitions in Sr2Cr3As2O2

Sr2Cr3As2O2 is composed of alternating square-lattice CrO2 and Cr2As2 stacking layers, where CrO2 is isostructural to the CuO2 building-block of cuprate high-Tc superconductors and Cr2As2 to Fe2As2 of Fe-based superconductors. Current interest in this material is raised by theoretic prediction of possible superconductivity. In this neutron powder diffraction study, we discovered that magnetic moments of Cr(II) ions in the Cr2As2 sublattice develop a C-type antiferromagnetic structure below 590 K, and the moments of Cr(I) in the CrO2 sublattice form the La2CuO4 -like antiferromagnetic order below 291 K. The staggered magnetic moment 2.19(4)μ B /Cr(II) in the more itinerant Cr2As2 layer is smaller than 3.10(6)μ_B/Cr(I) in the more localized CrO2 layer. Different from previous expectation, a spin-flop transition of the Cr(II) magnetic order observed at 291 K indicates a strong coupling between the CrO2 and Cr2As2 magnetic subsystems.

cond-mat.str-el↗

arXiv2018

Local bifurcation of steady almost periodic water waves with constant vorticity

In this paper we mainly investigate the traveling wave solution of the two dimensional Euler equations with gravity at the free surface over a flat bed. We assume that the free surface is almost periodic in the horizontal direction. Using conformal mappings, one can change the free boundary problem into a fixed boundary problem with some unknown functions in the boundary condition. By virtue of the Hilbert transform, the problem is equivalent to a quasilinear pseudodifferential equation for a almost periodic function of one variable. The bifurcation theory ensures us to obtain a existence result. Our existence result generalizes and covers the recent result in \cite{Constantin2011v}. Moreover, our result implies a non-uniqueness result at the same bifurcation point.

math.AP↗

arXiv2018

Global existence and well-posedness for the Doi-Edwards polymer model

In this paper we mainly investigate the Cauchy problem of the Doi-Edwards polymer model with dimension $d\geq2$. The model was derived in the late 1970s to describe the dynamics of polymers in melts. The system contain a Navier-Stokes equation with an additional stress tensor which depend on the deformation gradient tensor and the memory function. The deformation gradient tensor satisfies a transport equation and the memory function satisfies a degenerate parabolic equation. We first proved the local well-posedness for the Doi-Edwards polymer model in Besov spaces by using the Littlewood-Paley theory. Moreover, if the initial velocity and the initial memory is small enough, we obtain a global existence result.

math.AP↗

arXiv2017

Two-Dimensional Hyperferroelectric Metals: a Different Route to Ferromagnetic-Ferroelectric Multiferroics

Recently, two-dimensional (2D) multiferroics have attracted numerous attention due to their fascinating properties and promising applications. Although the ferroelectric (FE)-ferroelastic and ferromagnetic (FM)-ferroelastic multiferroics have been observed/predicted in 2D systems, 2D ferromagnetic-ferroelectric (FM-FE) multiferroics remain to be discovered since FM insulators are very rare. Here, we proposed for the first time the concept of 2D hyperferroelectric metals, with which the insulating prerequisite for the FM-FE multiferroic is no longer required in 2D systems. We validate the concept of 2D hyperferroelectric metals and 2D metallic FM-FE multiferroics by performing first-principle calculations on 2D CrN and CrB2 systems. The 2D buckled monolayer CrN is found to be a hyperferroelectic metal with the FM ground state, i.e., a 2D FM-FE multiferroic. With the global optimization approach, we find the 2D CrB2 system has an antiferromagnetic (AFM)/planar ground state and a FM/FE metastable state, suggesting that it can be used to realize electric field control of magnetism. Our analysis demonstrates that the spin-phonon coupling and metal-metal interaction are two new mechanisms for stabilizing the out-of-plane electric polarization in 2D systems. Our work not only extends the concept of FE to metallic systems, but also paves a new way to search the long-sought high temperature FM-FE multiferroics.

cond-mat.mtrl-sci↗

arXiv2017

The $L^2$ decay for the 2D co-rotation FENE dumbbell model of polymeric flows

In this paper we mainly study the long time behaviour of solutions to the finite extensible nonlinear elastic (FENE) dumbbell model with dimension two in the co-rotation case. Firstly, we obtain the $L^2$ decay rate of the velocity of the 2D co-rotation FENE model is $(1+t)^{-\frac{1}{2}}$ with small data. Then, by virtue of the Littlewood-Paley theory, we can remove the small condition. Our obtained sharp result improves considerably the recent results in \cite{Luo-Yin,Schonbek}.

math.AP↗

arXiv2017

Prediction of High Temperature Quantum Anomalous Hall Effect in Two Dimensional Transition-Metal Oxides

Quantum anomalous Hall (QAH) insulator is a topological phase which exhibits chiral edge states in the absence of magnetic field. The celebrated Haldane model is the first example of QAH effect, but difficult to realize. Here, we predict the two-dimensional single-atomic-layer V2O3 with a honeycomb-Kagome structure is a QAH insulator with a large band gap (large than 0.1 eV) and a high ferromagnetic Curie temperature (about 900 K). Combining the first-principle calculations with the effective Hamiltonian analysis, we find that the spin-majority dxy and dyz orbitals of V atoms on the honeycomb lattice form a massless Dirac cone near the Fermi level which becomes massive when the on-site spin-orbit coupling is included. Interestingly, we find that the large band gap is caused by a cooperative effect of electron correlation and spin-orbit coupling. Both first-principle calculations and the effective Hamiltonian analysis confirm that 2D V2O3 has a non-zero Chern number (i.e., one). Our work paves a new direction towards realizing the QAH effect at room temperature.

cond-mat.mtrl-sci↗

arXiv2017

Matching Using Sufficient Dimension Reduction for Causal Inference

To estimate casual treatment effects, we propose a new matching approach based on the reduced covariates obtained from sufficient dimension reduction. Compared to the original covariates and the propensity score, which are commonly used for matching in the literature, the reduced covariates are estimable nonparametrically under a mild assumption on the original covariates, and are sufficient and effective in imputing the missing potential outcomes. Under the ignorability assumption, the consistency of the proposed approach requires a weaker common support condition. In addition, the researchers are allowed to use different reduced covariates to find matched subjects for different treatment groups. We develop relative asymptotic results, and conduct simulation studies as well as real data analysis to illustrate the usefulness of the proposed approach.

stat.ME↗

arXiv2017

Inverse Edelstein effect of the surface states of a topological insulator

The surface states of three-dimensional topological insulators posses the unique property of spin-momentum interlocking. This property gives rise to the interesting inverse Edelstein effect (IEE), in which an applied spin bias $μ$ is converted to a measurable charge voltage difference $V$. We develop a semiclassical theory for the IEE of the surface states of $\text{Bi}_2\text{Se}_3$ thin films, which is applicable from the ballistic regime to diffusive regime. We find that the IEE efficiency ratio $γ=V/μ$ exhibits universal dependence on sample size, and approaches $π/4$ in the ballistic limit and $1$ in the diffusive limit.

cond-mat.mes-hall↗

arXiv2016

Integrality structures in topological strings I: framed unknot

We study the open string integrality invariants (LMOV invariants) for toric Calabi-Yau 3-folds with Aganagic-Vafa brane (AV-brane). In this paper, we focus on the case of the resolved conifold with one out AV-brane in any integer framing $τ$, which is the large $N$ duality of the Chern-Simons theory for a framed unknot with integer framing $τ$ in $S^3$. We compute the explicit formulas for the LMOV invariants in genus $g=0$ with any number of holes, and prove their integrality. For the higher genus LMOV invariants with one hole, they are reformulated into a generating function $g_{m}(q,a)$, and we prove that $g_{m}(q,a)\in (q^{1/2}-q^{-1/2})^{-2}\mathbb{Z}[(q^{1/2}-q^{-1/2})^2,a^{\pm 1/2}]$ for any integer $m\geq 1$. As a by product, we compute the reduced open string partition function of $\mathbb{C}^3$ with one AV-brane in framing $τ$. We find that, for $τ\leq -1$, this open string partition function is equivalent to the Hilbert-Poincaré series of the Cohomological Hall algebra of the $|τ|$-loop quiver. It gives an open string GW/DT correspondence.

math.AG↗

arXiv2016

Control Matching via Discharge Code Sequences

In this paper, we consider the patient similarity matching problem over a cancer cohort of more than 220,000 patients. Our approach first leverages on Word2Vec framework to embed ICD codes into vector-valued representation. We then propose a sequential algorithm for case-control matching on this representation space of diagnosis codes. The novel practice of applying the sequential matching on the vector representation lifted the matching accuracy measured through multiple clinical outcomes. We reported the results on a large-scale dataset to demonstrate the effectiveness of our method. For such a large dataset where most clinical information has been codified, the new method is particularly relevant.

cs.LG↗

arXiv2016

Global conservative solution for the periodic $μ$-Camassa-Holm equation

In this paper we mainly investigate the periodic $μ$-Camassa-Holm equation. We show the existence of global conservative solutions to the Cauchy problem of the periodic $μ$-Camassa-Holm equation. The result is obtained by introducing a coordinate transformation into Lagrangian coordinates. Our solutions depend continuously on the initial data and has a semigroup property.

math.AP↗

arXiv2016

Preterm Birth Prediction: Deriving Stable and Interpretable Rules from High Dimensional Data

Preterm births occur at an alarming rate of 10-15%. Preemies have a higher risk of infant mortality, developmental retardation and long-term disabilities. Predicting preterm birth is difficult, even for the most experienced clinicians. The most well-designed clinical study thus far reaches a modest sensitivity of 18.2-24.2% at specificity of 28.6-33.3%. We take a different approach by exploiting databases of normal hospital operations. We aims are twofold: (i) to derive an easy-to-use, interpretable prediction rule with quantified uncertainties, and (ii) to construct accurate classifiers for preterm birth prediction. Our approach is to automatically generate and select from hundreds (if not thousands) of possible predictors using stability-aware techniques. Derived from a large database of 15,814 women, our simplified prediction rule with only 10 items has sensitivity of 62.3% at specificity of 81.5%.

stat.ML↗

arXiv2016

Robust AC Quantum Spin Hall Effect without Participation of Edge States

The quantum spin Hall (QSH) effect in the DC regime, which has been intensively researched, relies on the existence of symmetry-protected edge states. Here, we demonstrate that a QSH system behaves quite differently in response to an applied AC electric field, and put forward the idea of AC QSH effect. The AC QSH effect can occur in the bulk without involving the fragile edge states, hence being robust against time-reversal symmetry breaking and disorder. It lays a more solid foundation for practical applications of the two-dimensional topological insulators, in the emerging field of AC spintronics.

cond-mat.mes-hall↗