arXiv subjects
Publications and source records attributed to Hua Wang.
The fibbinary numbers are positive integers whose binary representation contains no consecutive ones. We prove the following result: If the $j$th odd fibbinary is the $n$th \emph{odd} fibbinary number, then $j = \lfloor nϕ^2 \rfloor - 1.$
In this paper, we consider a 3d cubic focusing nonlinear Schrödinger equation (NLS) with slowing decaying potentials. Adopting the variational method of Ibrahim-Masmoudi-Nakanishi \cite{IMN}, we obtain a condition for scattering. It is actually sharp in some sense since the solution will blow up if it's false. The proof of blow-up part relies on the method of Du-Wu-Zhang \cite{DWZ}
Nonlinear optical responses to external electromagnetic field, characterized by second and higher order susceptibilities, play crucial roles in nonlinear optical devices and novel optoelectronics. Herein we present a quantum nonlinear ferroic optical Hall effect (QNFOHE) in multiferroics - a Hall-like direct photocurrent originated from the second order current response to intense electromagnetic field whose direction can be controlled by both internal ferroic orders and external light polarization. QNFOHE consists of two types of nonlinear photocurrent responses - shift current and circular photocurrent under linearly and circularly polarized light irradiation dominated by topological shift vector and Berry curvature, respectively. We elucidate the microscopic mechanism of QNFOHE in a representative class of 2D multiferroic materials using group theoretical analyses and first-principles electronic structure theory. The complex interplay of crystalline, permutation, gauge, and time reversal symmetries as well as inherent causality governs the symmetry properties of shift current and circular photocurrent. QNFOHE combined with rich ferroic degrees of freedom in multiferroic materials will open up a variety of new avenues for realizing tunable and configurable nonlinear optoelectronics etc.
We mainly consider the focusing biharmonic Schrödinger equation with a large radial repulsive potential $V(x)$: \begin{equation*} \left\{ \begin{aligned} iu_{t}+(Δ^2+V)u-|u|^{p-1}u=0,\;\;(t,x) \in {\bf{R}\times{\bf{R}}^{N}}, u(0, x)=u_{0}(x)\in H^{2}({\bf{R}}^{N}), \end{aligned}\right. \end{equation*} If $N>8$, \ $1+\frac{8}{N} N+4$, then we firstly prove a global well-posedness and scattering result for the radial data $u_0\in H^2({\bf R}^N)$ which satisfies that $$ M(u_0)^{\frac{2-s_c}{s_c}}E(u_0) \|Q\|^{\frac{2-s_c}{s_c}}_{L^{2}}\|ΔQ\|_{L^{2}}. $$
Millimeter-wave (mmWave) communication is considered as an indispensable technique for the next-generation backhaul/fronthaul network thanks to its large transmission bandwidth. Especially for heterogeneous network (HetNet), the mmWave full-dimension (FD)-MIMO is exploited to establish the backhaul/fronthaul link between phantom-cell base stations (BSs) and macro-cell BSs, where an efficient precoding is prerequisite. Against this background, this paper proposes a principle component analysis (PCA)-based hybrid precoding for wideband mmWave MIMO backhaul/fronthaul channels. We first propose an optimal hybrid precoder by exploiting principal component analysis (PCA), whereby the optimal high dimensional frequency-selective precoder are projected to the low-dimensional frequency-flat precoder. Moreover, the combiner is designed by leveraging the weighted PCA, where the covariance of received signal is taken into account as weight to the optimal minimum mean square error (MMSE) fully-digital combiner for further improved performance. Simulations have confirmed that the proposed scheme outperforms conventional schemes in spectral efficiency (SE) and bit-error-rate (BER) performance.
Hybrid precoding design can be challenging for broadband millimeter-wave (mmWave) massive MIMO due to the frequency-flat analog precoder in radio frequency (RF). Prior broadband hybrid precoding work usually focuses on fully-connected array (FCA), while seldom considers the energy-efficient partially-connected subarray (PCS) including the fixed subarray (FS) and dynamic subarray (DS). Against this background, this paper proposes a machine learning based broadband hybrid precoding for mmWave massive MIMO with DS. Specifically, we first propose an optimal hybrid precoder based on principal component analysis (PCA) for the FS, whereby the frequency-flat RF precoder for each subarray is extracted from the principle component of the optimal frequency-selective precoders for fully-digital MIMO. Moreover, we extend the PCA-based hybrid precoding to DS, where a shared agglomerative hierarchical clustering (AHC) algorithm developed from machine learning is proposed to group the DS for improved spectral efficiency (SE). Finally, we investigate the energy efficiency (EE) of the proposed scheme for both passive and active antennas. Simulations have confirmed that the proposed scheme outperforms conventional schemes in both SE and EE.
We participated the Task 1: Lesion Segmentation. The paper describes our algorithm and the final result of validation set for the ISIC Challenge 2018 - Skin Lesion Analysis Towards Melanoma Detection.
Low-dimensional multiferroicity, though highly scarce in nature, has attracted great attention due to both fundamental and technological interests. Using first-principles density functional theory, we show that ferromagnetism and ferroelectricity can coexist in monolayer transition metal phosphorus chalcogenides (TMPCs) - CuMP$_2$X$_6$ (M=Cr, V; X=S, Se). These van der Waals layered materials represent a class of 2D multiferroic semiconductors that simultaneously possess ferroelectric and ferromagnetic orders. In these monolayer materials, Cu atoms spontaneously move away from the center atomic plane, giving rise to nontrivial electric dipole moment along the plane normal. In addition, their ferromagnetism originates from indirect exchange interaction between Cr/V atoms, while their out-of-plane ferroelectricity suggests the possibility of controlling electric polarization by external vertical electric field. Monolayer semiconducting TMPCs thus provide a solid-state 2D materials platform for realizing 2D nanoscale switches and memory devices patterned with top and bottom electrodes.
Domestic Violence against women is now recognized to be a serious and widespread problem worldwide. Domestic Violence and Abuse is at the root of so many issues in society and considered as the societal tabooed topic. Fortunately, with the popularity of social media, social welfare communities and victim support groups facilitate the victims to share their abusive stories and allow others to give advice and help victims. Hence, in order to offer the immediate resources for those needs, the specific messages from the victims need to be alarmed from other messages. In this paper, we regard intention mining as a binary classification problem (abuse or advice) with the usecase of abuse discourse. To address this problem, we extract rich feature sets from the raw corpus, using psycholinguistic clues and textual features by term-class interaction method. Machine learning algorithms are used to predict the accuracy of the classifiers between two different feature sets. Our experimental results with high classification accuracy give a promising solution to understand a big social problem through big social media and its use in serving information needs of various community welfare organizations.
Let $\mathcal L=-Δ_{\mathbb H^n}+V$ be a Schrödinger operator on the Heisenberg group $\mathbb H^n$, where $Δ_{\mathbb H^n}$ is the sub-Laplacian on $\mathbb H^n$ and the nonnegative potential $V$ belongs to the reverse Hölder class $RH_s$ with $s\geq Q/2$. Here $Q=2n+2$ is the homogeneous dimension of $\mathbb H^n$. For given $α\in(0,Q)$, the fractional integrals associated to the Schrödinger operator $\mathcal L$ is defined by $\mathcal I_α={\mathcal L}^{-α/2}$. In this article, we first introduce the Morrey space $L^{p,κ}_{ρ,\infty}(\mathbb H^n)$ and weak Morrey space $WL^{p,κ}_{ρ,\infty}(\mathbb H^n)$ related to the nonnegative potential $V$. Then we establish the boundedness of fractional integrals ${\mathcal L}^{-α/2}$ on these new spaces. Furthermore, in order to deal with certain extreme cases, we also introduce the spaces $\mathrm{BMO}_{ρ,\infty}(\mathbb H^n)$ and $\mathcal{C}^β_{ρ,\infty}(\mathbb H^n)$ with exponent $β\in(0,1]$.
Let $\mathcal L=-Δ+V$ be a Schrödinger operator on $\mathbb R^d$, $d\geq3$, where $Δ$ is the Laplacian operator on $\mathbb R^d$ and the nonnegative potential $V$ belongs to the reverse Hölder class $RH_s$ for $s\geq d/2$. For given $0<α<d$, the fractional integrals associated to the Schrödinger operator $\mathcal L$ is defined by $\mathcal I_α={\mathcal L}^{-α/2}$.Suppose that $b$ is a locally integrable function on $\mathbb R^d$, the commutator generated by $b$ and $\mathcal I_α$ is defined by $[b,\mathcal I_α]f(x)=b(x)\cdot \mathcal I_αf(x)-\mathcal I_α(bf)(x)$. In this paper, we first introduce some kinds of weighted Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder class $RH_s$ for $s\geq d/2$. Then we will establish the boundedness properties of the fractional integrals $\mathcal I_α$ on these new spaces. Furthermore, weighted strong-type estimate for the corresponding commutator $[b,\mathcal I_α]$ in the framework of Morrey spaces is also obtained. The classes of weights, the classes of symbol functions as well as weighted Morrey spaces discussed in this paper are larger than $A_{p,q}$, $\mathrm{BMO}(\mathbb R^d)$ and $L^{p,κ}(μ,ν)$ corresponding to the classical case (that is $V\equiv0$).
As a consequence of the huge advancement of the Electronic Health Record (EHR) in healthcare settings, the My Health Record (MHR) is introduced in Australia. However security and privacy of the MHR system have been encumbering the development of the system. Even though the MHR system is claimed as patient-cenred and patient-controlled, there are several instances where healthcare providers (other than the usual provider) and system operators who maintain the system can easily access the system and these unauthorised accesses can lead to a breach of the privacy of the patients. This is one of the main concerns of the consumers that affect the uptake of the system. In this paper, we propose a patient centred MHR framework which requests authorisation from the patient to access their sensitive health information. The proposed model increases the involvement and satisfaction of the patients in their healthcare and also suggests mobile security system to give an online permission to access the MHR system.
The personalized health care service utilizes the relational patient data and big data analytics to tailor the medication recommendations. However, most of the health care data are in unstructured form and it consumes a lot of time and effort to pull them into relational form. This study proposes a novel data lake architecture to reduce the data ingestion time and improve the precision of healthcare analytics. It also removes the data silos and enhances the analytics by allowing the connectivity to the third-party data providers (such as clinical lab results, chemist, insurance company,etc.). The data lake architecture uses the Hadoop Distributed File System (HDFS) to provide the storage for both structured and unstructured data. This study uses K-means clustering algorithm to find the patient clusters with similar health conditions. Subsequently, it employs a support vector machine to find the most successful healthcare recommendations for the each cluster. Our experiment results demonstrate the ability of data lake to reduce the time for ingesting data from various data vendors regardless of its format. Moreover, it is evident that the data lake poses the potential to generate clusters of patients more precisely than the existing approaches. It is obvious that the data lake provides a unified storage location for the data in its native format. It can also improve the personalized healthcare medication recommendations by removing the data silos.
Let $\mathcal L=-Δ+V$ be a Schrödinger operator, where $Δ$ is the Laplacian on $\mathbb R^d$ and the nonnegative potential $V$ belongs to the reverse Hölder class $RH_q$ for $q\geq d$. The Riesz transform associated with the operator $\mathcal L=-Δ+V$ is denoted by $\mathcal R=\nabla{(-Δ+V)}^{-1/2}$ and the dual Riesz transform is denoted by $\mathcal R^{\ast}=(-Δ+V)^{-1/2}\nabla$. In this paper, we first introduce some kinds of weighted Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder class $RH_q$ for $q\geq d$. Then we will establish the boundedness properties of the operators $\mathcal R$ and its adjoint $\mathcal R^{\ast}$ on these new spaces. Furthermore, weighted strong-type estimate and weighted endpoint estimate for the corresponding commutators $[b,\mathcal R]$ and $[b,\mathcal R^{\ast}]$ are also obtained. The classes of weights, the classes of symbol functions as well as weighted Morrey spaces discussed in this paper are larger than $A_p$, $\mathrm{BMO}(\mathbb R^d)$ and $L^{p,κ}(w)$ corresponding to the classical Riesz transforms ($V\equiv0$).
Let $0<γ<n$ and $I_γ$ be the fractional integral operator of order $γ$, $I_γf(x)=\int_{\mathbb R^n}|x-y|^{γ-n}f(y)\,dy$, and let $[b,I_γ]$ be the linear commutator generated by a symbol function $b$ and $I_γ$, $[b,I_γ]f(x)=b(x)\cdot I_γf(x)-I_γ(bf)(x)$. This paper is concerned with two-weight, weak type norm estimates for such operators on the weighted Morrey and amalgam spaces. Based on weak-type norm inequalities on weighted Lebesgue spaces and certain $A_p$-type conditions on pairs of weights, we can establish the weak-type norm inequalities for fractional integral operator $I_γ$ as well as the corresponding commutator in the framework of weighted Morrey and amalgam spaces. Furthermore, some estimates for the extreme case are also obtained on these weighted spaces.
Among many topological indices of trees the sum of distances $σ(T)$ and the number of subtrees $F(T)$ have been a long standing pair of graph invariants that are well known for their negative correlation. That is, among various given classes of trees, the extremal structures maximizing one usually minimize the other, and vice versa. By introducing the "local" versions of these invariants, $σ_T(v)$ for the sum of distance from $v$ to all other vertices and $F_T(v)$ for the number of subtrees containing $v$, extremal problems can be raised and studied for vertices within a tree. This leads to the concept of "middle parts" of a tree with respect to different indices. A challenging problem is to find extremal values of the ratios between graph indices and corresponding local functions at middle parts or leaves. This problem also provides new opportunities to further verify the the correlation between different indices such as $σ(T)$ and $F(T)$. Such extremal ratios, along with the extremal structures, were studied and compared for the distance and subtree problems for general trees In this paper this study is extended to binary trees, a class of trees with numerous practical applications in which the extremal ratio problems appear to be even more complicated. After justifying some basic properties on the distance and subtree problems in trees and binary trees, characterizations are provided for the extremal structures achieving two extremal ratios in binary trees of given order. The generalization of this work to $k$-ary trees is also briefly discussed. The findings are compared with the previous established extremal structures in general trees. Lastly some potential future work is mentioned.
Let $\mathcal T_α~(0\leqα<n)$ be a class of sublinear operators satisfying certain size conditions introduced by Soria and Weiss, and let $[b,\mathcal T_α]~(0\leqα<n)$ be the commutators generated by $\mathrm{BMO}(\mathbb R^n)$ functions and $\mathcal T_α$. This paper is concerned with two-weight, weak type norm estimates for these sublinear operators and their commutators on the weighted Morrey and amalgam spaces. Some boundedness criterions for such operators are given, under the assumptions that weak-type norm inequalities on weighted Lebesgue spaces are satisfied. As applications of our main results, we can obtain the weak-type norm inequalities for several integral operators as well as the corresponding commutators in the framework of weighted Morrey and amalgam spaces.
In this paper, we first introduce some new classes of weighted amalgam spaces. Then we give the weighted strong-type and weak-type estimates for fractional integral operators $I_γ$ on these new function spaces. Furthermore, the weighted strong-type estimate and endpoint estimate of linear commutators $[b,I_γ]$ generated by $b$ and $I_γ$ are established as well. In addition, we are going to study related problems about two-weight, weak type inequalities for $I_γ$ and $[b,I_γ]$ on the weighted amalgam spaces and give some results. Based on these results and pointwise domination, we can prove norm inequalities involving fractional maximal operator $M_γ$ and generalized fractional integrals $\mathcal L^{-γ/2}$ in the context of weighted amalgam spaces, where $0<γ<n$ and $\mathcal L$ is the infinitesimal generator of an analytic semigroup on $L^2(\mathbb R^n)$ with Gaussian kernel bounds.