Searcharxiv⌕ Search

arXiv subjects

Hua Wang

Publications and source records attributed to Hua Wang.

At least 181 records · Page 10Linked to original sources
arXiv2020

Subtrees and independent subsets in unicyclic graphs and unicyclic graphs with fixed segment sequence

In the study of topological indices two negative correlations are well known: that between the number of subtrees and the Wiener index (sum of distances), and that between the Merrifield-Simmons index (number of independent vertex subsets) and the Hosoya index (number of independent edge subsets). That is, among a certain class of graphs, the extremal graphs that maximize one index usually minimize the other, and vice versa. In this paper, we first study the numbers of subtrees in unicyclic graphs and unicyclic graphs with a given girth, further confirming its opposite behavior to the Wiener index by comparing with known results. We then consider the unicyclic graphs with a given segment sequence and characterize the extremal structure with the maximum number of subtrees. Furthermore, we show that these graphs are not extremal with respect to the Wiener index. We also identify the extremal structures that maximize the number of independent vertex subsets among unicyclic graphs with a given segment sequence, and show that they are not extremal with respect to the number of independent edge subsets. These results may be the first examples where the above negative correlation failed in the extremal structures between these two pairs of indices.

math.CO↗
arXiv2020

Globally optimal dense and sparse spanning trees, and their applications

Finding spanning trees under various constraints is a classic problem with applications in many fields. Recently, a novel notion of "dense" ("sparse") tree, and in particular spanning tree (DST and SST respectively), is introduced as the structure that have a large (small) number of subtrees, or small (large) sum of distances between vertices. We show that finding DST and SST reduces to solving the discrete optimization problems. New and efficient approaches to find such spanning trees is achieved by imposing certain conditions on the vertex degrees which are then used to define an objective function that is minimized over all spanning trees of the graph under consideration. Solving this minimization problem exactly may be prohibitively time consuming for large graphs. Hence, we propose to use genetic algorithm (GA) which is one of well known metaheuristics methods to solve DST and SST approximately. As far as we are aware this is the first time GA has been used in this context. We also demonstrate on a number of applications that GA approach is well suited for these types of problems both in computational efficiency and accuracy of the approximate solution. Furthermore, we improve the efficiency of the proposed method by using Kruskal's algorithm in combination with GA. The application of our methods to several practical large graphs and networks is presented. Computational results show that they perform faster than previously proposed heuristic methods and produce more accurate solutions. Furthermore, the new feature of the proposed approach is that it can be applied recursively to sub-trees or spanning trees with additional constraints in order to further investigate the graphical properties of the graph and/or network. The application of this methodology on the gene network of a cancer cell led to isolating key genes in a network that were not obvious from previous studies.

math.OC↗
arXiv2020

GMD-Based Hybrid Beamforming for Large Reconfigurable Intelligent Surface Assisted Millimeter-Wave Massive MIMO

Reconfigurable intelligent surface (RIS) is considered to be an energy-efficient approach to reshape the wireless environment for improved throughput. Its passive feature greatly reduces the energy consumption, which makes RIS a promising technique for enabling the future smart city. Existing beamforming designs for RIS mainly focus on optimizing the spectral efficiency for single carrier systems. To avoid the complicated bit allocation on different spatial domain subchannels in MIMO systems, in this paper, we propose a geometric mean decomposition-based beamforming for RIS-assisted millimeter wave (mmWave) hybrid MIMO systems so that multiple parallel data streams in the spatial domain can be considered to have the same channel gain. Specifically, by exploiting the common angular-domain sparsity of mmWave massive MIMO channels over different subcarriers, a simultaneous orthogonal match pursuit algorithm is utilized to obtain the optimal multiple beams from an oversampling 2D-DFT codebook. Moreover, by only leveraging the angle of arrival and angle of departure associated with the line of sight (LoS) channels, we further design the phase shifters for RIS by maximizing the array gain for LoS channel. Simulation results show that the proposed scheme can achieve better BER performance than conventional approaches. Our work is an initial attempt to discuss the broadband hybrid beamforming for RIS-assisted mmWave hybrid MIMO systems.

cs.IT↗
arXiv2019

An Efficient Pre-processing Method to Eliminate Adversarial Effects

Deep Neural Networks (DNNs) are vulnerable to adversarial examples generated by imposing subtle perturbations to inputs that lead a model to predict incorrect outputs. Currently, a large number of researches on defending adversarial examples pay little attention to the real-world applications, either with high computational complexity or poor defensive effects. Motivated by this observation, we develop an efficient preprocessing method to defend adversarial images. Specifically, before an adversarial example is fed into the model, we perform two image transformations: WebP compression, which is utilized to remove the small adversarial noises. Flip operation, which flips the image once along one side of the image to destroy the specific structure of adversarial perturbations. Finally, a de-perturbed sample is obtained and can be correctly classified by DNNs. Experimental results on ImageNet show that our method outperforms the state-of-the-art defense methods. It can effectively defend adversarial attacks while ensure only very small accuracy drop on normal images.

cs.CV↗
arXiv2019

Deformable Non-local Network for Video Super-Resolution

The video super-resolution (VSR) task aims to restore a high-resolution (HR) video frame by using its corresponding low-resolution (LR) frame and multiple neighboring frames. At present, many deep learning-based VSR methods rely on optical flow to perform frame alignment. The final recovery results will be greatly affected by the accuracy of optical flow. However, optical flow estimation cannot be completely accurate, and there are always some errors. In this paper, we propose a novel deformable non-local network (DNLN) which is a non-optical-flow-based method. Specifically, we apply the deformable convolution and improve its ability of adaptive alignment at the feature level. Furthermore, we utilize a non-local structure to capture the global correlation between the reference frame and the aligned neighboring frames, and simultaneously enhance desired fine details in the aligned frames. To reconstruct the final high-quality HR video frames, we use residual in residual dense blocks to take full advantage of the hierarchical features. Experimental results on benchmark datasets demonstrate that the proposed DNLN can achieve state-of-the-art performance on VSR task.

eess.IV↗
arXiv2019

ACSEE: Antagonistic Crowd Simulation Model with Emotional Contagion and Evolutionary Game Theory

Antagonistic crowd behaviors are often observed in cases of serious conflict. Antagonistic emotions, which is the typical psychological state of agents in different roles (i.e. cops, activists, and civilians) in crowd violent scenes, and the way they spread through contagion in a crowd are important causes of crowd antagonistic behaviors. Moreover, games, which refers to the interaction between opposing groups adopting different strategies to obtain higher benefits and less casualties, determine the level of crowd violence. We present an antagonistic crowd simulation model, ACSEE, which is integrated with antagonistic emotional contagion and evolutionary game theories. Our approach models the antagonistic emotions between agents in different roles using two components: mental emotion and external emotion. We combine enhanced susceptible-infectious-susceptible (SIS) and game approaches to evaluate the role of antagonistic emotional contagion in crowd violence. Our evolutionary game theoretic approach incorporates antagonistic emotional contagion through deterrent force, which is modelled by a mixture of emotional forces and physical forces defeating the opponents. Antagonistic emotional contagion and evolutionary game theories influence each other to determine antagonistic crowd behaviors. We evaluate our approach on real-world scenarios consisting of different kinds of agents. We also compare the simulated crowd behaviors with real-world crowd videos and use our approach to predict the trends of crowd movements in violence incidents. We investigate the impact of various factors (number of agents, emotion, strategy, etc.) on the outcome of crowd violence. We present results from user studies suggesting that our model can simulate antagonistic crowd behaviors similar to those seen in real-world scenarios.

cs.MA↗
arXiv2019

Closed-Loop Sparse Channel Estimation for Wideband Millimeter-Wave Full-Dimensional MIMO Systems

This paper proposes a closed-loop sparse channel estimation (CE) scheme for wideband millimeter-wave hybrid full-dimensional multiple-input multiple-output and time division duplexing based systems, which exploits the channel sparsity in both angle and delay domains. At the downlink CE stage, random transmit precoder is designed at base station (BS) for channel sounding, and receive combiners at user devices (UDs) are designed to visualize hybrid array as a low-dimensional digital array for facilitating the multi-dimensional unitary ESPRIT (MDU-ESPRIT) algorithm to estimate respective angle-of-arrivals (AoAs). At the uplink CE stage, the estimated downlink AoAs, namely, uplink angle-of-departures (AoDs), are exploited to design multi-beam transmit precoder at UDs to enable BS to estimate the uplink AoAs, i.e., the downlink AoDs, and delays of different UDs using the MDU-ESPRIT algorithm based on the designed receive combiners at BS. Furthermore, a maximum likelihood approach is proposed to pair the channel parameters acquired at the two stages, and the path gains are then obtained using least squares estimator. According to spectrum estimation theory, our solution can acquire the super-resolution estimations of the AoAs/AoDs and delays of sparse multipath components with low training overhead. Simulation results verify the better CE performance and lower computational complexity of our solution over existing state-of-the-art approaches.

cs.IT↗
arXiv2019

Ferroelectric nonlinear anomalous Hall effect in few-layer WTe$_2$

Under broken time reversal symmetry such as in the presence of external magnetic field or internal magnetization, a transverse voltage can be established in materials perpendicular to both longitudinal current and applied magnetic field, known as classical Hall effect. However, this symmetry constraint can be relaxed in the nonlinear regime, thereby enabling nonlinear anomalous Hall current in time-reversal invariant materials - an underexplored realm with exciting new opportunities beyond classical linear Hall effect. Here, using group theory and first-principles theory, we demonstrate a remarkable ferroelectric nonlinear anomalous Hall effect in time-reversal invariant few-layer WTe$_2$ where nonlinear anomalous Hall current switches in odd-layer WTe$_2$ while remaining invariant in even-layer WTe$_2$ upon ferroelectric transition. This even-odd oscillation of ferroelectric nonlinear anomalous Hall effect was found to originate from the absence and presence of Berry curvature dipole reversal and shift dipole reversal due to distinct ferroelectric transformation in even and odd-layer WTe$_2$. Our work not only treats Berry curvature dipole and shift dipole on an equal footing to account for intraband and interband contributions to nonlinear anomalous Hall effect, but also establishes Berry curvature dipole and shift dipole as new order parameters for noncentrosymmetric materials. The present findings, therefore, suggest that ferroelectric metals and Weyl semimetals may offer unprecedented opportunities for the development of nonlinear quantum electronics.

cond-mat.mtrl-sci↗
arXiv2019

The normality and sum of normalities of trees

The eccentricity of a vertex $v$ in a graph $G$ is the maximum distance from $v$ to any other vertex. The vertices whose eccentricity are equal to the diameter (the maximum eccentricity) of $G$ are called peripheral vertices. In trees the eccentricity at $v$ can always be achieved by the distance from $v$ to a peripheral vertex. From this observation we are motivated to introduce normality of a vertex $v$ as the minimum distance from $v$ to any peripheral vertex. We consider the properties of the normality as well as the middle part of a tree with respect to this concept. Various related observations are discussed and compared with those related to the eccentricity. Then, analogous to the sum of eccentricities we consider the sum of normalities. After briefly discussing the extremal problems in general graphs we focus on trees and trees under various constraints. As opposed to the path and star in numerous extremal problems, we present several interesting and unexpected extremal structures. Lastly we consider the difference between eccentricity and normality, and the sum of these differences. We also introduce some unsolved problems in the context.

math.CO↗
arXiv2019

Morrey spaces for Schrödinger operators with certain nonnegative potentials, Littlewood-Paley and Lusin functions on the Heisenberg groups

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 sublaplacian on $\mathbb H^n$ and the nonnegative potential $V$ belongs to the reverse Hölder class $RH_q$ with $q\geq Q/2$. Here $Q=2n+2$ is the homogeneous dimension of $\mathbb H^n$. Assume that $\{e^{-s\mathcal L}\}_{s>0}$ is the heat semigroup generated by $\mathcal L$. The Littlewood-Paley function $\mathfrak{g}_{\mathcal L}$ and the Lusin area integral $\mathcal{S}_{\mathcal L}$ associated with the Schrödinger operator $\mathcal L$ are defined, respectively, by \begin{equation*} \mathfrak{g}_{\mathcal L}(f)(u) := \bigg(\int_0^{\infty}\bigg|s\frac{d}{ds} e^{-s\mathcal L}f(u) \bigg|^2\frac{ds}{s}\bigg)^{1/2} \end{equation*} and \begin{equation*} \mathcal{S}_{\mathcal L}(f)(u) := \bigg(\iint_{Γ(u)} \bigg|s\frac{d}{ds} e^{-s\mathcal L}f(v) \bigg|^2 \frac{dvds}{s^{Q/2+1}}\bigg)^{1/2}, \end{equation*} where \begin{equation*} Γ(u) := \big\{(v,s)\in\mathbb H^n\times(0,\infty): |u^{-1}v| < \sqrt{s\,}\big\}. \end{equation*} In this paper the author first introduces a class of Morrey spaces associated with the Schrödinger operator $\mathcal L$ on $\mathbb H^n$. Then by using some pointwise estimates of the kernels related to the nonnegative potential $V$, the author establishes the boundedness properties of these two operators $\mathfrak{g}_{\mathcal L}$ and $\mathcal{S}_{\mathcal L}$ acting on the Morrey spaces. It can be shown that the same conclusions also hold for the operators $\mathfrak{g}_{\sqrt{\mathcal L}}$ and $\mathcal{S}_{\sqrt{\mathcal L}}$ with respect to the Poisson semigroup $\{e^{-s\sqrt{\mathcal L}}\}_{s>0}$.

math.CA↗
arXiv2019

Morrey spaces for Schrödinger operators with nonnegative potentials, fractional integral operators and the Adams inequality on the Heisenberg groups

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 sublaplacian on $\mathbb H^n$ and the nonnegative potential $V$ belongs to the reverse Hölder class $RH_s$ with $s\in[Q/2,\infty)$. Here $Q=2n+2$ is the homogeneous dimension of $\mathbb H^n$. For given $α\in(0,Q)$, the fractional integral operator associated with the Schrödinger operator $\mathcal L$ is defined by $\mathcal I_α={\mathcal L}^{-α/2}$. In this article, the author introduces the Morrey space $L^{p,κ}_{ρ,\infty}(\mathbb H^n)$ and weak Morrey space $WL^{p,κ}_{ρ,\infty}(\mathbb H^n)$ associated with $\mathcal L$, where $(p,κ)\in[1,\infty)\times[0,1)$ and $ρ(\cdot)$ is an auxiliary function related to the nonnegative potential $V$. The relation between the fractional integral operator and the maximal operator on the Heisenberg group is established. From this, the author further obtains the Adams (Morrey-Sobolev) inequality on these new spaces. It is shown that the fractional integral operator $\mathcal I_α={\mathcal L}^{-α/2}$ is bounded from $L^{p,κ}_{ρ,\infty}(\mathbb H^n)$ to $L^{q,κ}_{ρ,\infty}(\mathbb H^n)$ with $0<α<Q$, $1<p<Q/α$, $0<κ<1-{(αp)}/Q$ and $1/q=1/p-α/{Q(1-κ)}$, and bounded from $L^{1,κ}_{ρ,\infty}(\mathbb H^n)$ to $WL^{q,κ}_{ρ,\infty}(\mathbb H^n)$ with $0<α<Q$, $0<κ<1-α/Q$ and $1/q=1-α/{Q(1-κ)}$. Moreover, in order to deal with the extreme cases $κ\geq 1-{(αp)}/Q$, the author also introduces the spaces $\mathrm{BMO}_{ρ,\infty}(\mathbb H^n)$ and $\mathcal{C}^β_{ρ,\infty}(\mathbb H^n)$, $β\in(0,1]$ associated with $\mathcal L$.

math.CA↗
arXiv2019

Robust Linear Discriminant Analysis Using Ratio Minimization of L1,2-Norms

As one of the most popular linear subspace learning methods, the Linear Discriminant Analysis (LDA) method has been widely studied in machine learning community and applied to many scientific applications. Traditional LDA minimizes the ratio of squared L2-norms, which is sensitive to outliers. In recent research, many L1-norm based robust Principle Component Analysis methods were proposed to improve the robustness to outliers. However, due to the difficulty of L1-norm ratio optimization, so far there is no existing work to utilize sparsity-inducing norms for LDA objective. In this paper, we propose a novel robust linear discriminant analysis method based on the L1,2-norm ratio minimization. Minimizing the L1,2-norm ratio is a much more challenging problem than the traditional methods, and there is no existing optimization algorithm to solve such non-smooth terms ratio problem. We derive a new efficient algorithm to solve this challenging problem, and provide a theoretical analysis on the convergence of our algorithm. The proposed algorithm is easy to implement, and converges fast in practice. Extensive experiments on both synthetic data and nine real benchmark data sets show the effectiveness of the proposed robust LDA method.

cs.LG↗
arXiv2019

A 28/37/39GHz Multiband Linear Doherty Power Amplifier in Silicon for 5G Applications

This paper presents the first multiband mm-wave linear Doherty PA in silicon for broadband 5G applications. We introduce a new transformer-based on-chip Doherty power combiner, which can reduce the impedance transformation ratio in power back-off (PBO) and thus improve the bandwidth and power-combining efficiency. We also devise a "driver-PA co-design" method, which creates power-dependent uneven feeding in the Doherty PA and enhances the Doherty operation without any hardware overhead or bandwidth compromise. For the proof of concept, we implement a 28/37/39-GHz PA fully integrated in a standard 130-nm SiGe BiCMOS process, which occupies 1.8mm2. The PA achieves a 52% -3-dB small-signal S21 bandwidth and a 40% -1-dB large-signal saturated output power (Psat) bandwidth. At 28/37/39GHz, the PA achieves +16.8/+17.1/+17-dBm Psat, +15.2/+15.5/+15.4-dBm P1dB, and superior 1.72/1.92/1.62 times efficiency enhancement over class-B operation at 5.9/6/6.7-dB PBO. Moreover, the PA demonstrates multi-Gb/s data rates with excellent efficiency and linearity for 64QAM in all the three 5G bands. This PA advances the state of the art for Doherty, wideband, and 5G silicon PAs in mm-wave bands. It supports drop-in upgrade for current PAs in existing mm-wave systems and opens doors to compact system solutions for future multiband 5G massive MIMO and phased-array platforms.

eess.SP↗
arXiv2019

Spherical Principal Component Analysis

Principal Component Analysis (PCA) is one of the most important methods to handle high dimensional data. However, most of the studies on PCA aim to minimize the loss after projection, which usually measures the Euclidean distance, though in some fields, angle distance is known to be more important and critical for analysis. In this paper, we propose a method by adding constraints on factors to unify the Euclidean distance and angle distance. However, due to the nonconvexity of the objective and constraints, the optimized solution is not easy to obtain. We propose an alternating linearized minimization method to solve it with provable convergence rate and guarantee. Experiments on synthetic data and real-world datasets have validated the effectiveness of our method and demonstrated its advantages over state-of-art clustering methods.

cs.LG↗
arXiv2019

Crowd Behavior Simulation with Emotional Contagion in Unexpected Multi-hazard Situations

In this paper we present a novel crowd simulation method by modeling the generation and contagion of panic emotion under multi-hazard circumstances. Specifically, we first classify hazards into different types (transient and persistent, concurrent and non-concurrent, static and dynamic ) based on their inherent characteristics. Then, we introduce the concept of perilous field for each hazard and further transform the critical level of the field to its invoked-panic emotion. After that, we propose an emotional contagion model to simulate the evolving process of panic emotion caused by multiple hazards in these situations. Finally, we introduce an Emotional Reciprocal Velocity Obstacles (ERVO) model to simulate the crowd behaviors by augmenting the traditional RVO model with emotional contagion, which combines the emotional impact and local avoidance together for the first time. Our experimental results show that this method can soundly generate realistic group behaviors as well as panic emotion dynamics in a crowd in multi-hazard environments.

cs.MA↗
arXiv2019

Variations of the eccentricity and their properties in trees

Motivated from the study of eccentricity, center, and sum of eccentricities in graphs and trees, we introduce several new distance-based global and local functions based on the smallest distance from a vertex to some leaf (called the `uniformity' at that vertex). Some natural extremal problems on trees are considered. Then the middle parts of a tree is discussed and compared with the well-known center of a tree. The values of the global functions are also compared with the sum of eccentricities and some sharp bounds are established. Last but not the least, we show that the difference between the eccentricity and the uniformity, when considered as a local function, behaves in a very similar way as the eccentricity itself.

math.CO↗
arXiv2019

Scattering and blow-up criteria for 3D cubic focusing nonlinear inhomogeneous NLS with a potential

In this paper, we consider the 3d cubic focusing inhomogeneous nonlinear Schrödinger equation with a potential $$ iu_{t}+Δu-Vu+|x|^{-b}|u|^{2}u=0,\;\;(t,x) \in {\bf{R}\times{\bf{R}}^{3}}, $$ where $0 \mathcal{K}$ if $V$ satisfies some additional assumptions.0}\|_{L^{2}}^{2(1-s_{c})}\|H^{\frac{1}{2}}u_{0}\|_{L^{2}}^{2s_{c}}>\mathcal{K}$ if $V$ satisfies some additional assumptions.

math.AP↗