arXiv subjects

Rui Zhu

Publications and source records attributed to Rui Zhu.

At least 181 records · Page 10Linked to original sources

arXiv2017

On The Time Constant for Last Passage Percolation on Complete Graph

This paper focuses on the time constant for last passage percolation on complete graph. Let $G_n=([n],E_n)$ be the complete graph on vertex set $[n]=\{1,2,\ldots,n\}$, and i.i.d. sequence $\{X_e:e\in E_n\}$ be the passage times of edges. Denote by $W_n$ the largest passage time among all self-avoiding paths from 1 to $n$. First, it is proved that $W_n/n$ converges to constant $μ$, where $μ$ is called the time constant and coincides with the essential supremum of $X_e$. Second, when $μ<\infty$, it is proved that the deviation probability $P(W_n/n\leq μ-x)$ decays as fast as $e^{-Θ(n^2)}$, and as a corollary, an upper bound for the variance of $W_n$ is obtained. Finally, when $μ=\infty$, lower and upper bounds for $W_n/n$ are given.

math.PR↗

arXiv2017

Object-Centric Photometric Bundle Adjustment with Deep Shape Prior

Reconstructing 3D shapes from a sequence of images has long been a problem of interest in computer vision. Classical Structure from Motion (SfM) methods have attempted to solve this problem through projected point displacement \& bundle adjustment. More recently, deep methods have attempted to solve this problem by directly learning a relationship between geometry and appearance. There is, however, a significant gap between these two strategies. SfM tackles the problem from purely a geometric perspective, taking no account of the object shape prior. Modern deep methods more often throw away geometric constraints altogether, rendering the results unreliable. In this paper we make an effort to bring these two seemingly disparate strategies together. We introduce learned shape prior in the form of deep shape generators into Photometric Bundle Adjustment (PBA) and propose to accommodate full 3D shape generated by the shape prior within the optimization-based inference framework, demonstrating impressive results.

cs.CV↗

arXiv2017

Rethinking Reprojection: Closing the Loop for Pose-aware ShapeReconstruction from a Single Image

An emerging problem in computer vision is the reconstruction of 3D shape and pose of an object from a single image. Hitherto, the problem has been addressed through the application of canonical deep learning methods to regress from the image directly to the 3D shape and pose labels. These approaches, however, are problematic from two perspectives. First, they are minimizing the error between 3D shapes and pose labels - with little thought about the nature of this label error when reprojecting the shape back onto the image. Second, they rely on the onerous and ill-posed task of hand labeling natural images with respect to 3D shape and pose. In this paper we define the new task of pose-aware shape reconstruction from a single image, and we advocate that cheaper 2D annotations of objects silhouettes in natural images can be utilized. We design architectures of pose-aware shape reconstruction which re-project the predicted shape back on to the image using the predicted pose. Our evaluation on several object categories demonstrates the superiority of our method for predicting pose-aware 3D shapes from natural images.

cs.CV↗

arXiv2017

Fano resonance via bonding and antibonding states in nonadiabatically-pumped double-quantum-well systems

In this work, transport properties of the nonadiabatically pumped double-quantum-well (DQW) structure are studied. Different from a single quantum well, band mixing in the DQW generates bonding and antibonding states, whose wave functions have different spatial symmetry. By applying a time-dependent electric potential to the two well regions simultaneously, Floquet sidebands are formed, which constitutes additional quantum tunneling paths. When one of the Floquet sidebands coincides with the bonding or antibonding quasibound states within the DQW structure, sharp Fano resonances are found in the transmission coefficients as well as in the differential shot noise spectra. While such Fano resonances originate from quantum interference, their shapes are strikingly different for transport via the bonding state and via the antibonding state. The Fano resonance via the even-parity bonding state shows a perfect transmission followed by a total reflection and the Fano resonance via the odd-parity antibonding state has a reversed symmetry and shows a total reflection before a perfect transmission.

cond-mat.mes-hall↗

arXiv2017

On The Modified Newman-Watts Small World and Its Random Walk

It is well known that adding "long edges (shortcuts)" to a regularly constructed graph will make the resulted model a small world. Recently, \cite{W} indicated that, among all long edges, those edges with length proportional to the diameter of the regularly constructed graph may play the key role. In this paper, we modify the original Newman-Watts small world by adding only long special edges to the $d$-dimensional lattice torus (with size $n^d$) according to \cite{W}, and show that the diameter of the modified model and the mixing time of random walk on it grow polynomially fast in $\ln n$.

math.PR↗

arXiv2017

Expectile Matrix Factorization for Skewed Data Analysis

Matrix factorization is a popular approach to solving matrix estimation problems based on partial observations. Existing matrix factorization is based on least squares and aims to yield a low-rank matrix to interpret the conditional sample means given the observations. However, in many real applications with skewed and extreme data, least squares cannot explain their central tendency or tail distributions, yielding undesired estimates. In this paper, we propose \emph{expectile matrix factorization} by introducing asymmetric least squares, a key concept in expectile regression analysis, into the matrix factorization framework. We propose an efficient algorithm to solve the new problem based on alternating minimization and quadratic programming. We prove that our algorithm converges to a global optimum and exactly recovers the true underlying low-rank matrices when noise is zero. For synthetic data with skewed noise and a real-world dataset containing web service response times, the proposed scheme achieves lower recovery errors than the existing matrix factorization method based on least squares in a wide range of settings.

stat.ML↗

arXiv2016

Skyrmion dynamics in a chiral magnet driven by periodically varying spin currents

In this work, we investigated the spin dynamics in a slab of chiral magnets induced by an alternating (ac) spin current. Periodic trajectories of the skyrmion in real space are discovered under the ac current as a result of the Magnus and viscous forces, which originate from the Gilbert damping, the spin transfer torque, and the $ β$-nonadiabatic torque effects. The results are obtained by numerically solving the Landau-Lifshitz-Gilbert equation and can be explained by the Thiele equation characterizing the skyrmion core motion.

cond-mat.mes-hall↗

arXiv2016

Tailoring the topological details of the magnetic skyrmion by the spin configuration at the edges

The magnetic skyrmion structure can be formed in the chiral magnets (CMs) with strong Dzyaloshinskii-Moriya interactions. In this work, we propose a way of artificially tailoring the topological details of the skyrmion such as its radial and whirling symmetric patterns by external magnetic fields besieging the CM slab. As long as the boundary magnetic fields are strong enough to fix the boundary ferromagnetism, the attained skyrmion profile is stable over time. The dynamics of spins is considered by numerically solving the non-equilibrium Landau-Lifshitz-Gilbert equation.

cond-mat.mes-hall↗

arXiv2016

The Conditional Lucas & Kanade Algorithm

The Lucas & Kanade (LK) algorithm is the method of choice for efficient dense image and object alignment. The approach is efficient as it attempts to model the connection between appearance and geometric displacement through a linear relationship that assumes independence across pixel coordinates. A drawback of the approach, however, is its generative nature. Specifically, its performance is tightly coupled with how well the linear model can synthesize appearance from geometric displacement, even though the alignment task itself is associated with the inverse problem. In this paper, we present a new approach, referred to as the Conditional LK algorithm, which: (i) directly learns linear models that predict geometric displacement as a function of appearance, and (ii) employs a novel strategy for ensuring that the generative pixel independence assumption can still be taken advantage of. We demonstrate that our approach exhibits superior performance to classical generative forms of the LK algorithm. Furthermore, we demonstrate its comparable performance to state-of-the-art methods such as the Supervised Descent Method with substantially less training examples, as well as the unique ability to "swap" geometric warp functions without having to retrain from scratch. Finally, from a theoretical perspective, our approach hints at possible redundancies that exist in current state-of-the-art methods for alignment that could be leveraged in vision systems of the future.

cs.CV↗

arXiv2015

Resonance in the nonadiabatic quantum pumping of the time-dependent Josephson junction

In this work, we investigated the nonadiabatic transport properties of the one-dimensional time-dependent superconductor-normal metal-superconductor (SNS) Josephson junction biased by a current source and driven by a high-frequency-ac-gate-potential applied to the normal-metal layer. BCS superconductors are considered and treated with the time-dependent Bogoliubov-de Gennes equation. Using Floquet theory, we compute the transmission coefficients and the Wigner-Smith delay times as a function of the incident energy and find that they display resonances when one of the electron or hole Floquet wavevectors coincides with the bound quasiparticle state within the superconducting energy gap. The resonance varies with the phase difference between the two superconductors as a result of the bound quasiparticle level displacement. The supercurrent flowing through the SNS junction is dramatically enhanced by the resonances.

cond-mat.supr-con↗

arXiv2015

Conductance and shot noise in the helimagnet tunnel junction

As a result of sinusoidal spatial modulation, helimagnet induces spin-dependent diffracted transmission. In this work, we propose a general scattering matrix treatment to the transport properties in helimagnets with arbitrary helical structures. Multiferroic properties can be considered by taking electric polarization and magnetic helix together into account. A monolayer magnetic helix can be treated as a $δ$-barrier by diffraction theory. The conductance and shot noise properties of the normal metal/helimagnet/normal metal toy model are investigated. It is found that the shot noise is suppressed and demonstrates rise-and-fall variations as a result of interference between different diffracted channels. Sharp change of the shot noise occurs when one and both diffracted beams disappear into evanescent modes at the helimagnet spiral wave vector equal to one and two times the electron Fermi wave vector $q=k_F$ and $2 k_F$. We also considered the conductance and shot noise properties in a real multiferroic helimagnet $\rm{TbMnO_3}$ with ferroelectric and helimagnetism coexistent. It is found that clockwise and counterclockwise spin helix is distinctly separated in the conductance and shot noise spectrum. Their variation pattern is a combined result of helimagnetism and electric polarization.

cond-mat.mes-hall↗

arXiv2015

Shot noise of the conductance through a superconducting barrier in graphene

We investigated the conductance and shot noise properties of quasiparticle-transport through a superconducting barrier in graphene. Based on the Blonder, Tinkham, and Klapwijk (BTK) formulation, the theory to investigate the transport properties in the superconductive graphene is developed. In comparison, we considered the two cases that are the transport in the presence and absence of the specular Andreev reflection. It is shown that the conductance and shot noise exhibit essentially different features in the two cases. It is found that the shot noise is suppressed as a result of more tunneling channels contributing to the transport when the superconducting gate is applied. The dependence of the shot noise behavior on the potential strength and the width of the superconducting barrier differs in the two cases. In the presence of the specular Andreev reflection, the shot noise spectrum is more sensitive to the potential strength and the width of the superconducting barrier. In both of the two cases, total transmission occurs at a certain parameter setting, which contributes greatly to the conductance and suppresses the shot noise at the same time.

cond-mat.mes-hall↗

arXiv2015

Fano Resonance in the Nonadiabatically Pumped Shot Noise of a Time-Dependent Quantum Well in 2DEG and Graphene

Interference between different quantum paths can generate Fano resonance. One of the examples is transport through a quasibound state driven by time-dependent scattering potential. Previously it is found that Fano resonance occurs as a result of energy matching in one-dimensional systems. In this work, we demonstrate that when transverse motion is present, Fano resonance occurs precisely at the wavevector matching situation. Using the Floquet scattering theory, we considered the transport properties of a nonadiabatic time-dependent well both in the 2DEG and monolayer graphene structure. Dispersion of the quasibound state of a static quantum well is obtained with transverse motion present. We found that Fano resonance occurs when the wavevector in the transport direction of one of the Floquet sidebands is exactly identical to that of the quasibound state in the well at equilibrium and follows the dispersion pattern of the latter. To observe the Fano resonance phenomenon in the transmission spectrum, we also considered the pumped shot noise properties when time and spatial symmetry secures vanishing current in the considered configuration. Prominent Fano resonance is found in the differential pumped shot noise to the reservoir Fermi energy.

cond-mat.mes-hall↗

arXiv2014

Fano resonance in the nonadiabatic pumped shot noise of a time-dependent potential well

We use the Floquet scattering theory to study the correlation properties of the nonadiabatic pumped dc current and heat flow through a time-dependent potential well. Oscillator induced quasibound states of electrons can transit to the Floquet states leading to resonant tunneling effect. Virtual electron scattering processes can produce pumped heat flow, pumped shot noise and pumped heat flow noise, with presence of time and spatial reversal symmetry. When one of the Floquet levels matches the quasibound level there strikes a "Fano" resonance.

cond-mat.mes-hall↗

arXiv2014

Absence of a transport signature of spin-orbit coupling in graphene with indium adatoms

Enhancement of the spin-orbit coupling in graphene may lead to various topological phenomena and also find applications in spintronics. Adatom absorption has been proposed as an effective way to achieve the goal. In particular, great hope has been held for indium in strengthening the spin-orbit coupling and realizing the quantum spin Hall effect. To search for evidence of the spin-orbit coupling in graphene absorbed with indium adatoms, we carry out extensive transport measurements, i.e., weak localization magnetoresistance, quantum Hall effect and non-local spin Hall effect. No signature of the spin-orbit coupling is found. Possible explanations are discussed.

cond-mat.mes-hall↗

arXiv2014

Diffraction induced Spin Pumping in Normal-Metal/Multiferroic-Helimagnet/Ferromagnet Heterostructures

Generally the adiabatic quantum pumping phenomenon can be interpreted by the surface integral of the Berry curvature inside the cyclic loop. Spin angular momentum flow without charge current can be pumped out by magnetization precession in ferromagnet-based structures. When an electron is scattered by a helimagnet, spin-dependent diffraction occurs due to the spatial modulation of the spiral. In this work, we consider the charge and spin flow driven by magnetization precession in normal-metal/multiferroic-helimagnet/ferromagnet heterostructures. The pumping behavior is governed by the diffracted states. Gauge dependence in the pumped current was encountered, which does not occur in the static transport properties or pumping behaviors in other systems.

cond-mat.mes-hall↗

arXiv2014

Anharmonic Effect of Adiabatic Quantum Pumping

Based on the scattering matrix approach, we systematically investigate the anharmonic effect of the pumped current in double-barrier structures with adiabatic time-modulation of two sinusoidal AC driven potential heights. The pumped current as a function of the phase difference between the two driven potentials looks like to be sinusoidal, but actually it contains sine functions of double and more phase difference. It is found that this kind of anharmonic effect of the pumped current is determined combinedly by the Be rry curvature and parameter variation loop trajectory. Therefore small ratio of the driving amplitude and the static amplitude is not necessary for harmonic pattern in the pumped current to dominate for smooth Berry curvature on the surface within the parameter variation loop.

cond-mat.mes-hall↗

arXiv2014

Resonant tunneling through double-barrier structures on graphene

Quantum resonant tunneling behaviors of double-barrier structures on graphene are investigated under the tight-binding approximation. The Klein tunneling and resonant tunneling are demonstrated for the quasiparticles with energy close to the Dirac points. The Klein tunneling vanishes by increasing the height of the potential barriers to more than 300 meV. The Dirac transport properties continuously change to the Schrodinger ones. It is found that the peaks of resonant tunneling approximate to the eigen-levels of graphene nanoribbons under appropriate boundary conditions. A comparison between the zigzag- and armchair-edge barriers is given.

cond-mat.mes-hall↗