arXiv subjects

Na Lei

Publications and source records attributed to Na Lei.

At least 55 records · Page 3Linked to original sources

arXiv2018

Metric Based Quadrilateral Mesh Generation

This work proposes a novel metric based algorithm for quadrilateral mesh generating. Each quad-mesh induces a Riemannian metric satisfying special conditions: the metric is a flat metric with cone signualrites conformal to the original metric, the total curvature satisfies the Gauss-Bonnet condition, the holonomy group is a subgroup of the rotation group $\{e^{ikπ/2}\}$, furthermore there is cross field obtained by parallel translation which is aligned with the boundaries, and its streamlines are finite geodesics. Inversely, such kind of metric induces a quad-mesh. Based on discrete Ricci flow and conformal structure deformation, one can obtain a metric satisfying all the conditions and obtain the desired quad-mesh. This method is rigorous, simple and automatic. Our experimental results demonstrate the efficiency and efficacy of the algorithm.

cs.CG↗

arXiv2018

Optical control of magnetism in NiFe/VO2 heterostructures

Optical methods for magnetism manipulation have been considered as a promising strategy for ultralow-power and ultrahigh-speed spin switches, which becomes a hot spot in the field of spintronics. However, a widely applicable and efficient method to combine optical operation with magnetic modulation is still highly desired. Here, the strongly correlated electron material VO2 is introduced to realize phase-transition based optical control of the magnetism in NiFe. The NiFe/VO2 bilayer heterostructure features appreciable modulations in electrical conductivity (55%), coercivity (60%), and magnetic anisotropy (33.5%). Further analyses indicate that interfacial strain coupling plays a crucial role in this modulation. Utilizing this optically controlled magnetism modulation feature, programmable Boolean logic gates (AND, OR, NAND, NOR, XOR, NXOR and NOT) for high-speed and low-power data processing are demonstrated based on this engineered heterostructure. As a demonstration of phase-transition spintronics, this work may pave the way for next-generation electronics in the post-Moore era.

cond-mat.mtrl-sci↗

arXiv2018

Latent Space Optimal Transport for Generative Models

Variational Auto-Encoders enforce their learned intermediate latent-space data distribution to be a simple distribution, such as an isotropic Gaussian. However, this causes the posterior collapse problem and loses manifold structure which can be important for datasets such as facial images. A GAN can transform a simple distribution to a latent-space data distribution and thus preserve the manifold structure, but optimizing a GAN involves solving a Min-Max optimization problem, which is difficult and not well understood so far. Therefore, we propose a GAN-like method to transform a simple distribution to a data distribution in the latent space by solving only a minimization problem. This minimization problem comes from training a discriminator between a simple distribution and a latent-space data distribution. Then, we can explicitly formulate an Optimal Transport (OT) problem that computes the desired mapping between the two distributions. This means that we can transform a distribution without solving the difficult Min-Max optimization problem. Experimental results on an eight-Gaussian dataset show that the proposed OT can handle multi-cluster distributions. Results on the MNIST and the CelebA datasets validate the effectiveness of the proposed method.

cs.LG↗

arXiv2018

Brain Morphometry Analysis with Surface Foliation Theory

Brain morphometry study plays a fundamental role in neuroimaging research. In this work, we propose a novel method for brain surface morphometry analysis based on surface foliation theory. Given brain cortical surfaces with automatically extracted landmark curves, we first construct finite foliations on surfaces. A set of admissible curves and a height parameter for each loop are provided by users. The admissible curves cut the surface into a set of pairs of pants. A pants decomposition graph is then constructed. Strebel differential is obtained by computing a unique harmonic map from surface to pants decomposition graph. The critical trajectories of Strebel differential decompose the surface into topological cylinders. After conformally mapping those topological cylinders to standard cylinders, parameters of standard cylinders (height, circumference) are intrinsic geometric features of the original cortical surfaces and thus can be used for morphometry analysis purpose. In this work, we propose a set of novel surface features rooted in surface foliation theory. To the best of our knowledge, this is the first work to make use of surface foliation theory for brain morphometry analysis. The features we computed are intrinsic and informative. The proposed method is rigorous, geometric, and automatic. Experimental results on classifying brain cortical surfaces between patients with Alzheimer's disease and healthy control subjects demonstrate the efficiency and efficacy of our method.

cs.CG↗

arXiv2018

Robust Edge-Preserved Surface Mesh Polycube Deformation

The problem of polycube construction or deformation is an essential problem in computer graphics. In this paper, we present a robust, simple, efficient and automatic algorithm to deform the meshes of arbitrary shapes into their polycube ones. We derive a clear relationship between a mesh and its corresponding polycube shape. Our algorithm is edge-preserved, and works on surface meshes with or without boundaries. Our algorithm outperforms previous ones in speed, robustness, efficiency. Our method is simple to implement. To demonstrate the robustness and effectiveness of our method, we apply it to hundreds of models of varying complexity and topology. We demonstrat that our method compares favorably to other state-of-the-art polycube deformation methods.

cs.GR↗

arXiv2018

Conformal Mesh Parameterization Using Discrete Calabi Flow

In this paper, we introduce discrete Calabi flow to the graphics research community and present a novel conformal mesh parameterization algorithm. Calabi energy has a succinct and explicit format. Its corresponding flow is conformal and convergent under certain conditions. Our method is based on the Calabi energy and Calabi flow with solid theoretical and mathematical base. We demonstrate our approach on dozens of models and compare it with other related flow based methods, such as the well-known Ricci flow and CETM. Our experiments show that the performance of our algorithm is comparably the same with other methods. The discrete Calabi flow in our method provides another perspective on conformal flow and conformal parameterization.

cs.GR↗

arXiv2018

Geometric Understanding of Deep Learning

Deep learning is the mainstream technique for many machine learning tasks, including image recognition, machine translation, speech recognition, and so on. It has outperformed conventional methods in various fields and achieved great successes. Unfortunately, the understanding on how it works remains unclear. It has the central importance to lay down the theoretic foundation for deep learning. In this work, we give a geometric view to understand deep learning: we show that the fundamental principle attributing to the success is the manifold structure in data, namely natural high dimensional data concentrates close to a low-dimensional manifold, deep learning learns the manifold and the probability distribution on it. We further introduce the concepts of rectified linear complexity for deep neural network measuring its learning capability, rectified linear complexity of an embedding manifold describing the difficulty to be learned. Then we show for any deep neural network with fixed architecture, there exists a manifold that cannot be learned by the network. Finally, we propose to apply optimal mass transportation theory to control the probability distribution in the latent space.

cs.LG↗

arXiv2018

Voltage-Driven High-Speed Skyrmion Motion in a Skyrmion Shift Device

Magnetic skyrmions are promising information carriers for building future high-density and high-speed spintronic devices. However, to achieve a current-driven high-speed skyrmion motion, the required driving current density is usually very large, which could be energy inefficient and even destroy the device due to Joule heating. Here, we propose a voltage-driven skyrmion motion approach in a skyrmion shift device made of magnetic nanowires. The high-speed skyrmion motion is realized by utilizing the voltage shift, and the average skyrmion velocity reaches up to 259 m/s under 0.45 V applied voltage. In comparison with the widely studied vertical current-driven model, the energy dissipation is three orders of magnitude lower in our voltage-driven model, for the same speed motion of skyrmions. Our approach uncovers valuable opportunities for building skyrmion racetrack memories and logic devices with both ultra-low power consumption and ultra-high processing speed, which are appealing features for future spintronic applications.

physics.app-ph↗

arXiv2018

Skyrmions in magnetic tunnel junctions

In this work, we demonstrate that skyrmions can be nucleated in the free layer of a magnetic tunnel junction (MTJ) with Dzyaloshinskii-Moriya interactions (DMI) by a spin-polarized current with the assistance of stray fields from the pinned layer. The size, stability and number of created skyrmions can be tuned by either the DMI strength or the stray field distribution. The interaction between the stray field and the DMI effective field is discussed. A device with multi-level tunneling magnetoresistance is proposed, which could pave the ways for skyrmion-MTJ-based multi-bit storage and artificial neural network computation. Our results may facilitate the efficient nucleation and electrical detection of skyrmions.

cond-mat.mes-hall↗

arXiv2017

A Geometric View of Optimal Transportation and Generative Model

In this work, we show the intrinsic relations between optimal transportation and convex geometry, especially the variational approach to solve Alexandrov problem: constructing a convex polytope with prescribed face normals and volumes. This leads to a geometric interpretation to generative models, and leads to a novel framework for generative models. By using the optimal transportation view of GAN model, we show that the discriminator computes the Kantorovich potential, the generator calculates the transportation map. For a large class of transportation costs, the Kantorovich potential can give the optimal transportation map by a close-form formula. Therefore, it is sufficient to solely optimize the discriminator. This shows the adversarial competition can be avoided, and the computational architecture can be simplified. Preliminary experimental results show the geometric method outperforms WGAN for approximating probability measures with multiple clusters in low dimensional space.

cs.LG↗

arXiv2017

Influence of heavy metal materials on magnetic properties of Pt/Co/heavy metal tri-layered structures

Pt/Co/heavy metal (HM) tri-layered structures with interfacial perpendicular magnetic anisotropy (PMA) are currently under intensive research for several emerging spintronic effects, such as spinorbit torque, domain wall motion, and room temperature skyrmions. HM materials are used as capping layers to generate the structural asymmetry and enhance the interfacial effects. For instance, the Pt/Co/Ta structure attracts a lot of attention as it may exhibit large Dzyaloshinskii-Moriya interaction. However, the dependence of magnetic properties on different capping materials has not been systematically investigated. In this paper, we experimentally show the interfacial PMA and damping constant for Pt/Co/HM tri-layered structures through time-resolved magneto-optical Kerr effect measurements as well as magnetometry measurements, where the capping HM materials are W, Ta, and Pd. We found that the Co/HM interface plays an important role on the magnetic properties. In particular, the magnetic multilayers with a W capping layer features the lowest effective damping value, which may be attributed to the different spin-orbit coupling and interfacial hybridization between Co and HM materials. Our findings allow a deep understanding of the Pt/Co/HM tri-layered structures. Such structures could lead to a better era of data storage and processing devices.

cond-mat.mes-hall↗

arXiv2017

Robot Coverage Path Planning for General Surfaces Using Quadratic Differentials

Robot Coverage Path planning (i.e., provide full coverage of a given domain by one or multiple robots) is a classical problem in the field of robotics and motion planning. The goal is to provide nearly full coverage while also minimize duplicately visited area. In this paper we focus on the scenario of path planning on general surfaces including planar domains with complex topology, complex terrain or general surface in 3D space. The main idea is to adopt a natural, intrinsic and global parametrization of the surface for robot path planning, namely the holomorphic quadratic differentials. Except for a small number of zero points (singularities), each point on the surface is given a uv-coordinates naturally represented by a complex number. We show that natural, efficient robot paths can be obtained by using such coordinate systems. The method is based on intrinsic geometry and thus can be adapted to general surface exploration in 3D.

cs.RO↗

arXiv2016

Large influence of capping layers on tunnel magnetoresistance in magnetic tunnel junctions

It has been reported in experiments that capping layers which enhance the perpendicular magnetic anisotropy (PMA) of magnetic tunnel junctions (MTJs) induce great impact on the tunnel magnetoresistance (TMR). To explore the essential influence caused by capping layers, we carry out ab initio calculations on TMR in the X(001)|CoFe(001)|MgO(001)|CoFe(001)|X(001) MTJ, where X represents the capping layer material which can be tungsten, tantalum or hafnium. We report TMR in different MTJs and demonstrate that tungsten is an ideal candidate for a giant TMR ratio. The transmission spectrum in Brillouin zone is presented. It can be seen that in the parallel condition of MTJ, sharp transmission peaks appear in the minority-spin channel. This phenomenon is attributed to the resonant tunnel transmission effect and we explained it by the layer-resolved density of states (DOS). In order to explore transport properties in MTJs, the density of scattering states (DOSS) was studied from the point of band symmetry. It has been found that CoFe|tungsten interface blocks scattering states transmission in the anti-parallel condition. This work reports TMR and transport properties in MTJs with different capping layers, and proves that tungsten is a proper capping layer material, which would benefit the design and optimization of MTJs.

physics.comp-ph↗

arXiv2016

Voltage Controlled Magnetic Skyrmion Motion for Racetrack Memory

Magnetic skyrmion, vortex-like swirling topologically stable spin configurations, is appealing as information carrier for future nanoelectronics, owing to the stability, small size and extremely low driving current density. One of the most promising applications of skyrmion is to build racetrack memory (RM). Compared to domain wall-based RM (DW-RM), skyrmion-based RM (Sky-RM) possesses quite a few benefits in terms of energy, density and speed etc. Until now, the fundamental behaviors, including nucleation/annihilation, motion and detection of skyrmion have been intensively investigated. However, one indispensable function, i.e., pinning/depinning of skyrmion still remains an open question and has to be addressed before applying skyrmion for RM. Furthermore, Current research mainly focuses on physical investigations, whereas the electrical design and evaluation are still lacking. In this work, we aim to promote the development of Sky-RM from fundamental physics to realistic electronics. First, we investigate the pinning/depinning characteristics of skyrmion in a nanotrack with the voltage-controlled magnetic anisotropy (VCMA) effect. Then, we propose a compact model and design framework of Sky-RM for electrical evaluation. This work completes the elementary memory functionality of Sky-RM and fills the technical gap between the physicists and electronic engineers, making a significant step forward for the development of Sky-RM.

cond-mat.mes-hall↗

arXiv2015

A "nearly parametric" solution to Selective Harmonic Elimination PWM

Selective Harmonic Elimination Pulse Width Modulation (SHEPWM) is an important technique to solve PWM problems, which control the output voltage of an inverter via selecting appropriate switching angles. Based on the Rational Univariate Representation (RUR) theory for solving polynomial systems, the paper presents an algorithm to compute a "nearly parametric" solution to a SHEPWM problem. When the number of switching angles N is fixed, a "nearly parametric" solution can be considered as functions of the modulation index m. So we can adapt the amplitude of the output voltage with the same source voltage by changing the modulation index. When m is given as a specific value, complete solutions to the SHEPWM problem can be obtained easily using univariate polynomial solving. Compared with other methods, m is considered as a symbolic parameter for the first time, and this can help avoid totally restarting when m changes. The average time for computing complete solutions associated to 460 modulation indexes based on a "nearly parametric" solution when N=5 is 0.0284s, so the algorithm is practical. Three groups of switching angles associated to N=5, m=0.75 is simulated in MATLAB, and it verifies the algorithm's correctness.

math.NA↗

arXiv2013

The vanishing ideal of a finite set of points with multiplicity structures

Given a finite set of arbitrarily distributed points in affine space with arbitrary multiplicity structures, we present an algorithm to compute the reduced Groebner basis of the vanishing ideal under the lexicographic ordering. Our method discloses the essential geometric connection between the relative position of the points with multiplicity structures and the quotient basis of the vanishing ideal, so we will explicitly know the set of leading terms of elements of I. We split the problem into several smaller ones which can be solved by induction over variables and then use our new algorithm for intersection of ideals to compute the result of the original problem. The new algorithm for intersection of ideals is mainly based on the Extended Euclidean Algorithm.

math.AG↗

arXiv2012

Interfacial charge accumulation effect on magnetic domain wall nucleation and propagation in a Pt/Co/Pt/Al2O3 structure

We report direct observation of charge accumulation effect on magnetization reversal in a Pt/Co(0.5 nm)/Pt(0.5 nm)/Al2O3 structure with perpendicular anisotropy. By imaging magnetic domain with polar Kerr microscopy, we evidence that positive charges accumulating at the Pt/Al2O3 interface result in favoring magnetic domain wall propagation, while negative charges hinder domain wall nucleation and propagation. Our results suggest that magnetic properties in Co layer can be strongly influenced by 5d electron accumulation/depletion in an ultrathin Pt layer.

cond-mat.mtrl-sci↗

arXiv2012

Electric field control of domain wall logic in piezoelec-tric/ferromagnetic nanodevices

Power dissipation is one of the most important factors limiting the future miniaturisation of integrated circuits. The capability of controlling magnetic states with a low voltage through magnetoelectric coupling in magnetostrictive/piezoelectric systems may pave the way toward ultra low-power electronics. Although the former effect has been demon-strated in several multiferroic heterostructures, the incorporation of such complex geometries into practical magnetic memory and logic nanodevices has been lacking. Here, we demonstrate the room temperature control of a domain wall gate with an electric field in a nanowire consisting of a laterally polarized piezoelectric bar inducing a giant strain in a ferromagnetic spin-valve. We propose to use such novel domain wall gate as an elementary brick to generate a complete set of boolean logic functions or stabilize domain walls in high density memory applications.

cond-mat.mtrl-sci↗