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Li Chen

Publications and source records attributed to Li Chen.

At least 613 records · Page 34Linked to original sources
arXiv2018

Computation Over NOMA: Improved Achievable Rate Through Sub-Function Superposition

Massive numbers of nodes will be connected in future wireless networks. This brings great difficulty to collect a large amount of data. Instead of collecting the data individually, computation over multi-access channel (CoMAC) provides an intelligent solution by computing a desired function over the air based on the signal-superposition property of wireless channel. To improve the spectrum efficiency in conventional CoMAC, we propose the use of non-orthogonal multiple access (NOMA) for functions in CoMAC. The desired functions are decomposed into several sub-functions, and multiple sub-functions are selected to be superposed over each resource block (RB). The corresponding achievable rate is derived based on sub-function superposition, which prevents a vanishing computation rate for large numbers of nodes. In order to gain more insights, we further study the limiting case when the number of nodes goes to infinity. An exact expression of the rate is derived which provides a lower bound on the computation rate. Compared with existing CoMAC, the NOMA-based CoMAC (NOMA-CoMAC) not only achieves a higher computation rate, but also provides an improved non-vanishing rate. Furthermore, the diversity order of the computation rate of NOMA-CoMAC is derived, and it shows that the system performance is dominated by the node with the worst channel gain among these sub-functions in each RB.

cs.IT↗
arXiv2018

Understanding the Importance of Single Directions via Representative Substitution

Understanding the internal representations of deep neural networks (DNNs) is crucal to explain their behavior. The interpretation of individual units, which are neurons in MLPs or convolution kernels in convolutional networks, has been paid much attention given their fundamental role. However, recent research (Morcos et al. 2018) presented a counterintuitive phenomenon, which suggests that an individual unit with high class selectivity, called interpretable units, has poor contributions to generalization of DNNs. In this work, we provide a new perspective to understand this counterintuitive phenomenon, which makes sense when we introduce Representative Substitution (RS). Instead of individually selective units with classes, the RS refers to the independence of a unit's representations in the same layer without any annotation. Our experiments demonstrate that interpretable units have high RS which are not critical to network's generalization. The RS provides new insights into the interpretation of DNNs and suggests that we need to focus on the independence and relationship of the representations.

cs.CV↗
arXiv2018

Rigidity of the entire solutions of 2-Hessian equation

In this paper, we prove some rigidity theorems for the entire 2-convex solutions of 2-Hessian equation in Euclidean space. As an application, we obtain a Bernstein type theorem for global special Lagrangian graphs.

math.AP↗
arXiv2018

Rigorous mean-field limit and cross diffusion

The mean-field limit in a weakly interacting stochastic many-particle system for multiple population species in the whole space is proved. The limiting system consists of cross-diffusion equations, modeling the segregation of populations. The mean-field limit is performed in two steps: First, the many-particle system leads in the large population limit to an intermediate nonlocal diffusion system. The local cross-diffusion system is then obtained from the nonlocal system when the interaction potentials approach the Dirac delta distribution. The global existence of the limiting and the intermediate diffusion systems is shown for small initial data, and an error estimate is given.

math.AP↗
arXiv2018

Superconducting spin properties of Majorana nanowires and the associated superconducting anomalous Hall effect

It is difficult to unambiguously confirm the existence of Majorana zero modes (MZMs) due to the absence of smoking-gun signatures in charge transport measurements. Recent studies suggest that the spin degree of freedom of MZMs may provide an alternative detection method. We study the spin properties of the superconducting state in Majorana nanowires and the associated unconventional Josephson effect with realistic experimental parameters taken from [Zhang {\it et al.}, Nature 556, 74 (2018)]. For a superconducting thin film with in-plane polarized spin-triplet pairing, an out-of-plane electric field can generate a supercurrent perpendicular to both the superconducting spin polarization and the electric field, so we name this phenomena as superconducting anomalous Hall effect (ScAHE). In a Majorana nanowire, the regime with finite polarized spin-triplet pairing almost coincides with the chiral regime, which includes the topological regime. We further study the effects of polarized spin-triplet pairing in two types of Josephson junctions. One dramatic finding is that SOC can induce an anomalous supercurrent at zero phase difference only in the U-shape junction, a basic ingredient of scalable topological quantum computation. This can be viewed as a consequence of the ScAHE. Our work reveals that the spin degree of freedom is indeed helpful for detecting MZMs.

cond-mat.mes-hall↗
arXiv2018

Digital Geometry, a Survey

This paper provides an overview of modern digital geometry and topology through mathematical principles, algorithms, and measurements. It also covers recent developments in the applications of digital geometry and topology including image processing, computer vision, and data science. Recent research strongly showed that digital geometry has made considerable contributions to modelings and algorithms in image segmentation, algorithmic analysis, and BigData analytics.

cs.DM↗
arXiv2018

Computation over Wide-Band MAC: Improved Achievable Rate through Sub-Function Allocation

Future networks are expected to connect an enormous number of nodes wirelessly using wide-band transmission. This brings great challenges. To avoid collecting a large amount of data from the massive number of nodes, computation over multi-access channel (CoMAC) is proposed to compute a desired function over the air utilizing the signal-superposition property of MAC. Due to frequency selective fading, wide-band CoMAC is more challenging and has never been studied before. In this work, we propose the use of orthogonal frequency division multiplexing (OFDM) in wide-band CoMAC to transmit functions in a similar way to bit sequences through division, allocation and reconstruction of function. An achievable rate without any adaptive resource allocation is derived. To prevent a vanishing computation rate from the increase of the number of nodes, a novel sub-function allocation of sub-carriers is derived. Furthermore, we formulate an optimization problem considering power allocation. A sponge-squeezing algorithm adapted from the classical water-filling algorithm is proposed to solve the optimal power allocation problem. The improved computation rate of the proposed framework and the corresponding allocation has been verified through both theoretical analysis and simulation.

cs.IT↗
arXiv2018

ADAGIO: Interactive Experimentation with Adversarial Attack and Defense for Audio

Adversarial machine learning research has recently demonstrated the feasibility to confuse automatic speech recognition (ASR) models by introducing acoustically imperceptible perturbations to audio samples. To help researchers and practitioners gain better understanding of the impact of such attacks, and to provide them with tools to help them more easily evaluate and craft strong defenses for their models, we present ADAGIO, the first tool designed to allow interactive experimentation with adversarial attacks and defenses on an ASR model in real time, both visually and aurally. ADAGIO incorporates AMR and MP3 audio compression techniques as defenses, which users can interactively apply to attacked audio samples. We show that these techniques, which are based on psychoacoustic principles, effectively eliminate targeted attacks, reducing the attack success rate from 92.5% to 0%. We will demonstrate ADAGIO and invite the audience to try it on the Mozilla Common Voice dataset.

cs.LG↗
arXiv2018

Translating surfaces of the non-parametric mean curvature flow in Lorentz manifold $M^{2}\times\mathbb{R}$

In this paper, for the Lorentz manifold $M^{2}\times\mathbb{R}$, with $M^{2}$ a $2$-dimensional complete surface with nonnegative Gaussian curvature, we investigate its space-like graphs over compact strictly convex domains in $M^{2}$, which are evolving by the non-parametric mean curvature flow with prescribed contact angle boundary condition, and show that solutions converge to ones moving only by translation.

math.DG↗
arXiv2018

Network synchronization with periodic coupling

The synchronization behavior of networked chaotic oscillators with periodic coupling is investigated. It is observed in simulations that the network synchronizability could be significantly influenced by tuning the coupling frequency, even making the network alternated between the synchronous and non-synchronous states. By the method of master stability function, we conduct a detailed analysis on the influence of coupling frequency on network synchronizability, and find that the network synchronizability is maximized at some characteristic frequencies comparable to the intrinsic frequency of the local dynamics. Moremore, it is found that as the amplitude of the coupling increases, the characteristic frequencies are gradually decreased. By the technique of finite-time Lyapunov exponent, we investigate further the mechanism for the maximized synchronizability, and find that at the characteristic frequencies the power spectrum of the finite-time Lyapunov exponent is abruptly changed from the localized to broad distributions. When this feature is absent or not prominent, the network synchronizability is less influenced by the periodic coupling. Our study shows the efficiency of finite-time Lyapunov exponent in exploring the synchronization behavior of temporally coupled oscillators, and sheds lights on the interplay between the system dynamics and structure in the general temporal networks.

nlin.CD↗
arXiv2018

Algebraic Soft Decoding of Reed-Solomon Codes Using Module Minimization

The interpolation based algebraic decoding for Reed-Solomon (RS) codes can correct errors beyond half of the code's minimum Hamming distance. Using soft information, the algebraic soft decoding (ASD) further improves the decoding performance. This paper presents a unified study of two classical ASD algorithms in which the computationally expensive interpolation is solved by the module minimization (MM) technique. An explicit module basis construction for the two ASD algorithms will be introduced. Compared with Koetter's interpolation, the MM interpolation enables the algebraic Chase decoding and the Koetter-Vardy decoding perform less finite field arithmetic operations. Re-encoding transform is applied to further reduce the decoding complexity. Computational cost of the two ASD algorithms as well as their re-encoding transformed variants are analyzed. This research shows re-encoding transform attributes to a lower decoding complexity by reducing the degree of module generators. Furthermore, Monte-Carlo simulation of the two ASD algorithms has been performed to show their decoding and complexity competency.

cs.IT↗
arXiv2018

Pattern dynamics of interacting contagions

The spread of infectious diseases, rumors, fashions, innovations are complex contagion processes, embedded both in networked and spatial contexts. Here we investigate the pattern dynamics of a complex contagion, where two agents, say $A$ and $B$, interact with each other and diffuse simultaneously in the geographic space. The contagion process for each follows the classical susceptible-infected-susceptible kinetics, and their interaction introduces a potential change in the secondary infection propensity compared to the baseline reproduction ratio $R_0$. We show that nontrivial spatial infection patterns arise, when the susceptible move faster than the infected and the interaction between the two agents is neither too competitive nor too cooperative. Interestingly, the system exhibits pattern hysteresis phenomena that quite different parameter regions allowing for patterns exist in the direction of increasing $R_0$ and in the direction of eradication by its reduction. The latter shows a remarkable enhancement in the contagion prevalence, meaning that the infection eradication now becomes extremely difficult compared to the single-agent scenario and to the coinfection without space. Linearization analysis supports our observations, and we identified the required elements and dynamical mechanism behind the emergence of a pattern. These findings call for further investigation for their close relevance, both in biological and social contagions.

physics.soc-ph↗
arXiv2018

An Approximate Solver for Multi-medium Riemann Problem with Mie-Grüneisen Equations of State

We propose an approximate solver for multi-medium Riemann problems with materials described by a family of general Mie-Grüneisen equations of state, which are widely used in practical applications. The solver provides the interface pressure and normal velocity by an iterative method. The well-posedness and convergence of the solver is verified with mild assumptions on the equations of state. To validate the solver, it is employed in computing the numerical flux on phase interfaces of a numerical scheme on Eulerian grids that was developed recently for compressible multi-medium flows. Numerical examples are presented for Riemann problems, air blast and underwater explosion applications.

math.NA↗
arXiv2018

Integrated Linear Reconstruction for Finite Volume Scheme on Arbitrary Unstructured Grids

In [L. Chen and R. Li, Journal of Scientific Computing, Vol. 68, pp. 1172--1197, (2016)], an integrated linear reconstruction was proposed for finite volume methods on unstructured grids. However, the geometric hypothesis of the mesh to enforce a local maximum principle is too restrictive to be satisfied by, for example, locally refined meshes or distorted meshes generated by arbitrary Lagrangian-Eulerian methods in practical applications. In this paper, we propose an improved integrated linear reconstruction approach to get rid of the geometric hypothesis. The resulting optimization problem is a convex quadratic programming problem, and hence can be solved efficiently by classical active-set methods. The features of the improved integrated linear reconstruction include that i). the local maximum principle is fulfilled on arbitrary unstructured grids, ii). the reconstruction is parameter-free, and iii). the finite volume scheme is positivity-preserving when the reconstruction is generalized to the Euler equations. A variety of numerical experiments are presented to demonstrate the performance of this method.

math.NA↗
arXiv2018

TCP Decoupling for Next Generation Communication System

In traditional networks, interfaces of network nodes are duplex. But, emerging communication technologies such as visible light communication, millimeter-wave communications, can only provide a unidirectional interface when cost is limited. It's urgent to find effective solutions to utilize such new unidirectional communication skills. Decoupling implies separating one single resource to two independent resources. This idea can be applied at physical layer, link layer, network layer, even transport layer. TCP decoupling is an end to end solution provided at transport layer. With decoupled TCP, two distinct unidirectional path can be created to meet the requirements of reliable information transfer. However, it is not an easy task to decouple a bidirectional logical path at transport layer. In this paper, we dwell on the idea of TCP decoupling. Advantages of decoupling at transport layer are analyzed also. In addition, an experiment is carried out to figure out how to implement a decouple TCP. Our results show decoupling at transport layer is possible and the modified protocol is available.

cs.NI↗
arXiv2018

Entangled Pauli Principles: the DNA of Quantum Hall Fluids

A formalism is developed for the rigorous study of solvable fractional quantum Hall parent Hamiltonians with Landau level mixing. The idea of organization through "generalized Pauli principles" is expanded to allow for root level entanglement, giving rise to "entangled Pauli principles". Through the latter, aspects of the effective field theory description become ingrained in exact microscopic solutions for a great wealth of phases for which no similar single Landau level description is known. We discuss in detail braiding statistic, edge theory, and rigorous zero mode counting for the Jain-221 state as derived from a microscopic Hamiltonian. The relevant root-level entanglement is found to feature an AKLT-type MPS structure associated with an emergent SU(2) symmetry.

cond-mat.str-el↗
arXiv2018

Spin exchange-induced spin-orbit coupling in a superuid mixture

We investigate the ground-state properties of a dual-species spin-1/2 Bose-Einstein condensate. One of the species is subjected to a pair of Raman laser beams that induces spin-orbit (SO) coupling, whereas the other species is not coupled to the Raman laser. In certain limits, analytical results can be obtained. It is clearly shown that, through the inter-species spin-exchange interaction, the second species also exhibits SO coupling. This mixture system displays a very rich phase diagram, with many of the phases not present in an SO coupled single-species condensate. Our work provides a new way of creating SO coupling in atomic quantum gases, and opens up a new avenue of research in SO coupled superfluid mixtures. From a practical point of view, the spin exchange-induced SO coupling may overcome the heating issue for certain atomic species when subjected to the Raman beams.

cond-mat.quant-gas↗