Conservation laws of some lattice equations

We derive infinitely many conservation laws for some multi-dimensionally consistent lattice equations from their Lax pairs. These lattice equations are the Nijhoff-Quispel-Capel equation, lattice Boussinesq equation, lattice nonlinear Schr\"{o}dinger equation, modified lattice Boussinesq equation, Hietarinta's Boussinesq-type equations, Schwarzian lattice Boussinesq equation and Toda-modified lattice Boussinesq equation

On a general SU(3) Toda System

We study the following generalized $SU(3)$ Toda System $$ \left\{\begin{array}{ll} -\Delta u=2e^u+\mu e^v & \hbox{ in }\R^2\\ -\Delta v=2e^v+\mu e^u & \hbox{ in }\R^2\\ \int_{\R^2}e^u<+\infty,\ \int_{\R^2}e^v-2$. We prove the existence of radial solutions bifurcating from the radial solution$(\log \frac{64}{(2+\mu) (8+|x|^2)^2}, \log \frac{64}{ (2+\mu) (8+|x|^2)^2})$at the values$\mu=\mu_n=2\frac{2-n-n^2}{2+n+n^2},\ n\in\N $

Deriving conservation laws for ABS lattice equations from Lax pairs

In the paper we derive infinitely many conservation laws for the ABS lattice equations from their Lax pairs. These conservation laws can algebraically be expressed by means of some known polynomials. We also show that H1, H2, H3, Q1, Q2, Q3 and A1 equation in ABS list share a generic discrete Riccati equation.Comment: 16 page

A Proximity-Aware Hierarchical Clustering of Faces

In this paper, we propose an unsupervised face clustering algorithm called "Proximity-Aware Hierarchical Clustering" (PAHC) that exploits the local structure of deep representations. In the proposed method, a similarity measure between deep features is computed by evaluating linear SVM margins. SVMs are trained using nearest neighbors of sample data, and thus do not require any external training data. Clusters are then formed by thresholding the similarity scores. We evaluate the clustering performance using three challenging unconstrained face datasets, including Celebrity in Frontal-Profile (CFP), IARPA JANUS Benchmark A (IJB-A), and JANUS Challenge Set 3 (JANUS CS3) datasets. Experimental results demonstrate that the proposed approach can achieve significant improvements over state-of-the-art methods. Moreover, we also show that the proposed clustering algorithm can be applied to curate a set of large-scale and noisy training dataset while maintaining sufficient amount of images and their variations due to nuisance factors. The face verification performance on JANUS CS3 improves significantly by finetuning a DCNN model with the curated MS-Celeb-1M dataset which contains over three million face images

The Point Spread Function Reconstruction by Using Moffatlets - I

The shear measurement is a crucial task in the current and the future weak lensing survey projects. And the reconstruction of the point spread function(PSF) is one of the essential steps. In this work, we present three different methods, including Gaussianlets, Moffatlets and EMPCA to quantify their efficiency on PSF reconstruction using four sets of simulated LSST star images. Gaussianlets and Moffatlets are two different sets of basis functions whose profiles are based on Gaussian and Moffat functions respectively. Expectation Maximization(EM) PCA is a statistical method performing iterative procedure to find principal components of an ensemble of star images. Our tests show that: 1) Moffatlets always perform better than Gaussianlets. 2) EMPCA is more compact and flexible, but the noise existing in the Principal Components (PCs) will contaminate the size and ellipticity of PSF while Moffatlets keeps them very well.Comment: 19 pages,17 figures,Accepted for publication in RA

Illusion Media: Generating Virtual Objects Using Realizable Metamaterials

We propose a class of optical transformation media, illusion media, which render the enclosed object invisible and generate one or more virtual objects as desired. We apply the proposed media to design a microwave device, which transforms an actual object into two virtual objects. Such an illusion device exhibits unusual electromagnetic behavior as verified by full-wave simulations. Different from the published illusion devices which are composed of left-handed materials with simultaneously negative permittivity and permeability, the proposed illusion media have finite and positive permittivity and permeability. Hence the designed device could be realizable using artificial metamaterials.Comment: 9 pages, 4 figures, published in Appl. Phys. Lett

A class of line-transformed cloaks with easily-realizable constitutive parameters

We propose a class of line-transformed cylindrical cloaks which have easily-realizable constitutive parameters. The scattering properties of such cloaks have been investigated numerically for both transverse-electric (TE) and transverse-magnetic (TM) incidences of plane waves. A line-transformed invisibility cloak with a perfectly electric conducting (PEC) inner boundary is actually a reshaping of a PEC line to which the cloaked object is crushed. The numerical results of near-field distributions and far-field scattering properties have verified the above conclusions. We also investigate the relationship between the constitutive parameters of a line-transformed cloak and the length of the corresponding line. The changing range of constitutive parameters is large when the line is short, while the changing range becomes small when the line is long. The above conclusion provides an efficient way to realize the invisibility cloaks using artificial metamaterials.Comment: 15 pages, 6 figure