Phase slips and phase synchronization of coupled oscillators

The behaviors of coupled oscillators, each of which has periodic motion with random natural frequency in the absence of coupling, are investigated. Some novel collective phenomena are revealed. At the onset of instability of the phase-locking state, simultaneous phase slips of all oscillators and quantized phase shifts in these phase slips are observed. By incresing the coupling, a bifurcation tree from high-dimensional quasiperiodicity to chaos to quasiperiodicity and periodicity is found. Different orders of phase synchronizations of chaotic oscillators and chaotic clusters play the key role for constructing this tree structure.Comment: 4 pages with 4 eps figures, to appear in Phys. Rev. Let

Observational evidence for self-generation of small-scale magnetic flux ropes from intermittent solar wind turbulence

We present unique {and additional} observational evidence for the self-generation of small-scale coherent magnetic flux rope structures in the solar wind. Such structures with durations between 9 and 361 minutes are identified from Wind in-situ spacecraft measurements through the Grad-Shafranov (GS) reconstruction approach. The event occurrence counts are on the order of 3,500 per year on average and have a clear solar cycle dependence. We build a database of small-scale magnetic flux ropes from twenty-year worth of Wind spacecraft data. We show a power-law distribution of the wall-to-wall time corresponding well to the inertial range turbulence, which agrees with relevant observations and numerical simulation results. We also provide the axial current density distribution from the GS-based observational analysis, which yields a non-Gaussian probability density function consistent with numerical simulation results.Comment: To appear in ApJ

Open Set Adversarial Examples

Adversarial examples in recent works target at closed set recognition systems, in which the training and testing classes are identical. In real-world scenarios, however, the testing classes may have limited, if any, overlap with the training classes, a problem named open set recognition. To our knowledge, the community does not have a specific design of adversarial examples targeting at this practical setting. Arguably, the new setting compromises traditional closed set attack methods in two aspects. First, closed set attack methods are based on classification and target at classification as well, but the open set problem suggests a different task, \emph{i.e.,} retrieval. It is undesirable that the generation mechanism of closed set recognition is different from the aim of open set recognition. Second, given that the query image is usually of an unseen class, predicting its category from the training classes is not reasonable, which leads to an inferior adversarial gradient. In this work, we view open set recognition as a retrieval task and propose a new approach, Opposite-Direction Feature Attack (ODFA), to generate adversarial examples / queries. When using an attacked example as query, we aim that the true matches be ranked as low as possible. In addressing the two limitations of closed set attack methods, ODFA directly works on the features for retrieval. The idea is to push away the feature of the adversarial query in the opposite direction of the original feature. Albeit simple, ODFA leads to a larger drop in Recall@K and mAP than the close-set attack methods on two open set recognition datasets, \emph{i.e.,} Market-1501 and CUB-200-2011. We also demonstrate that the attack performance of ODFA is not evidently superior to the state-of-the-art methods under closed set recognition (Cifar-10), suggesting its specificity for open set problems.Comment: 10 pages, 6 figures, 6 table

A Nonconforming Finite Element Method for Fourth Order Curl Equations in R^3

In this paper we present a nonconforming finite element method for solving fourth order curl equations in three dimensions arising from magnetohydrodynamics models. We show that the method has an optimal error estimate for a model problem involving both curl^2 and curl^4 operators. The element has a very small number of degrees of freedom and it imposes the inter-element continuity along the tangential direction which is appropriate for the approximation of magnetic fields. We also provide explicit formulae of basis functions for this element.Comment: 16 pages, submitte

Cross-Age LFW: A Database for Studying Cross-Age Face Recognition in Unconstrained Environments

Labeled Faces in the Wild (LFW) database has been widely utilized as the benchmark of unconstrained face verification and due to big data driven machine learning methods, the performance on the database approaches nearly 100%. However, we argue that this accuracy may be too optimistic because of some limiting factors. Besides different poses, illuminations, occlusions and expressions, cross-age face is another challenge in face recognition. Different ages of the same person result in large intra-class variations and aging process is unavoidable in real world face verification. However, LFW does not pay much attention on it. Thereby we construct a Cross-Age LFW (CALFW) which deliberately searches and selects 3,000 positive face pairs with age gaps to add aging process intra-class variance. Negative pairs with same gender and race are also selected to reduce the influence of attribute difference between positive/negative pairs and achieve face verification instead of attributes classification. We evaluate several metric learning and deep learning methods on the new database. Compared to the accuracy on LFW, the accuracy drops about 10%-17% on CALFW.Comment: 10 pages, 9 figure

Quasi-continuous random variables and processes under the G-expectation framework

In this paper, we first use PDE techniques and probabilistic methods to identify a kind of quasi-continuous random variables. Then we give a characterization of the $G$-integrable processes and get a kind of quasi-continuous processes by Krylov's estimates. This result is useful for the development of $G$-stochastic analysis theory. Moreover, it also provides a tool for the study of the non-Markovian It\^o processes.Comment: 22 page

On one generalization of modular subgroups

Let $G$ be a finite group. If $M_n < M_{n-1} < \ldots < M_1 < M_{0}=G$ where $M_i$ is a maximal subgroup of $M_{i-1}$ for all $i=1, \ldots ,n$, then $M_n$ ($n > 0$) is an \emph{$n$-maximal subgroup} of $G$. A subgroup $M$ of $G$ is called \emph{modular} if the following conditions are held: (i) $\langle X, M \cap Z \rangle=\langle X, M \rangle \cap Z$ for all $X \leq G, Z \leq G$ such that $X \leq Z$, and (ii) $\langle M, Y \cap Z \rangle=\langle M, Y \rangle \cap Z$ for all $Y \leq G, Z \leq G$ such that $M \leq Z$. In this paper, we study finite groups whose $n$-maximal subgroups are modular.Comment: 13 page

The relation between Hawking radiation via tunnelling and the laws of black hole thermodynamics

In Parikh and Wilczek's original works, the laws of black hole thermodynamics are not referred and it seems that there is no relation between Hawking radiation via tunnelling and the laws of black hole thermodynamics in their works. However, taking examples for the R-N black hole and the Kerr black hole, we find that they are correlated and even consistent if the tunnelling process is a reversible process.Comment: 6 pages, no figur

Theory and experiment of isotropic electromagnetic beam bender made of dielectric materials

In this paper, we utilize the deformation transformation optics (DTO) method to design electromagnetic beam bender, which can change the direction of electromagnetic wave propagation as desire. According to DTO, the transformed material parameters can be expressed by deformation tensor of the spatial transformation. For a beam bender, since the three principal stretches at each point induced by the spatial transformation are independent to each other, there are many possibilities to simplify the transformed material parameters of the bender by adjusting the stretches independently. With the DTO method, we show that the reported reduced parameters of the bender obtained by equivalent dispersion relation can be derived as a special case. An isotropic bender is also proposed according to this method, and it is fabricated by stacking dielectric materials in layered form. Experiments validate the function of the designed isotropic bender for a TE wave; it is also shown that the isotropic bender has a broadband with low loss, compared with the metamaterial bender. The isotropic bender has much easier design and fabrication procedures than the metamaterial bender.Comment: 9 pages, 9 figure

Blowup rate for mass critical rotational nonlinear Schr\"odinger equations

We consider the blowup rate for blowup solutions to $L^2$-critical, focusing NLS with a harmonic potential and a rotation term. Under a suitable spectral condition we prove that there holds the "$\log$-$\log$ law" when the initial data is slightly above the ground state. We also construct minimal mass blowup solutions near the ground state level with distinct blowup rates.Comment: 13 page