Devaney's chaos revisited

In this note, we give several equivalent definitions of Devaney's chao

Order-Preservation for Multidimensional Stochastic Functional Differential Equations with Jump

Sufficient and necessary conditions are presented for the order-preservation of stochastic functional differential equations on $\R^d$ with non-Lipschitzian coefficients driven by the Brownian motion and Poisson processes. The sufficiency of the conditions extends and improves some known comparison theorems derived recently for one-dimesional equations and multidimensional equations without delay, and the necessity is new even in these special situations.Comment: 18page

Distribution Dependent SDEs with Singular Coefficients

Under integrability conditions on distribution dependent coefficients, existence and uniqueness are proved for McKean-Vlasov type SDEs with non-degenerate noise. When the coefficients are Dini continuous in the space variable, gradient estimates and Harnack type inequalities are derived. These generalize the corresponding results derived for classical SDEs, and are new in the distribution dependent setting.Comment: 28page

Early soft X-ray to UV emission from double neutron star mergers: implications from the long-term radio and X-ray emissions of GW 170817

Recent long-term radio follow-up observations of GW 170817 reveals a simple power-law rising light curve, with a slope of $t^{0.78}$, up to 93 days after the merger. The latest X-ray detection at 109 days is also consistent with such a temporal slope. Such a shallow rise behavior requires a mildly relativistic outflow with a steep velocity gradient profile, so that slower material with larger energy catches up with the decelerating ejecta and re-energizes it. It has been suggested that this mildly relativistic outflow may represent a cocoon of material. We suggest that the velocity gradient profile may form during the stage that the cocoon is breaking out of the merger ejecta, resulted from shock propagation down a density gradient. The cooling of the hot relativistic cocoon material immediately after it breaks out should have produced soft X-ray to UV radiation at tens of seconds to hours after the merger. The soft X-ray emission has a luminosity of $L_{\rm X}\sim 10^{45}{\rm erg s^{-1}}$ over a period of tens of seconds for a merger event like GW 170817. The UV emission shows a rise initially and peaks at about a few hours with a luminosity of $L_{\rm UV}\sim 10^{42} {\rm erg s^{-1}}$. The soft X-ray transients could be detected by future wide-angle X-ray detectors, such as the Chinese mission Einstein Probe. This soft X-ray/UV emission would serve as one of the earliest electromagnetic counterparts of gravitation waves from double neutron star mergers and could provide the earliest localization of the sources.Comment: 5 pages, 2 figures, ApJL in press, discussions on the reverse shock emission in the refreshed shock scenario for the long-term radio and X-ray emissions are adde

Non-Gaussian Parameter in k-Dimensional Euclidean Space

We generalize the non-Gaussian parameter, which is utilized to characterize the distinction of dynamics between realistic and Gaussian Brownian diffusions, in k-dimensional Euclidean space

On the regular-convexity of Ricci shrinker limit spaces

In this paper, we study the structure of the pointed-Gromov-Hausdorff limits of sequences of Ricci shrinkers. We define a regular-singular decomposition following the work of Cheeger-Colding for manifolds with a uniform Ricci curvature lower bound, and prove that the regular part of any Ricci shrinker limit space is convex, inspired by Colding-Naber's original idea of parabolic smoothing of the distance functions.Comment: revised version, to appear in J. Reine Angew. Mat

A numerical simulation of the backward Raman amplifying in plasma

This paper describe a numerical simulation method for the interaction between laser pulses and low density plasmas based on hydrodynamic approximation. We investigate Backward Raman Amplifying (BRA) experiments and their variants. The numerical results are in good agreement with experiments.Comment: 11 pages, 4 figur

Order Preservation for Path-Distribution Dependent SDEs

Sufficient and necessary conditions are presented for the order preservation of path-distribution dependent SDEs. Differently from the corresponding study of distribution independent SDEs, to investigate the necessity of order preservation for the present model we need to construct a family of probability spaces in terms of the ordered pair of initial distributions.Comment: 12 page

Generative Dual Adversarial Network for Generalized Zero-shot Learning

This paper studies the problem of generalized zero-shot learning which requires the model to train on image-label pairs from some seen classes and test on the task of classifying new images from both seen and unseen classes. Most previous models try to learn a fixed one-directional mapping between visual and semantic space, while some recently proposed generative methods try to generate image features for unseen classes so that the zero-shot learning problem becomes a traditional fully-supervised classification problem. In this paper, we propose a novel model that provides a unified framework for three different approaches: visual-> semantic mapping, semantic->visual mapping, and metric learning. Specifically, our proposed model consists of a feature generator that can generate various visual features given class embeddings as input, a regressor that maps each visual feature back to its corresponding class embedding, and a discriminator that learns to evaluate the closeness of an image feature and a class embedding. All three components are trained under the combination of cyclic consistency loss and dual adversarial loss. Experimental results show that our model not only preserves higher accuracy in classifying images from seen classes, but also performs better than existing state-of-the-art models in in classifying images from unseen classes

Inefficient cosmic ray diffusion around Vela X : constraints from H.E.S.S. observations of very high-energy electrons

Vela X is a nearby pulsar wind nebula (PWN) powered by a $\sim 10^4$ year old pulsar. Modeling of the spectral energy distribution of the Vela X PWN has shown that accelerated electrons have largely escaped from the confinement, which is likely due to the disruption of the initially confined PWN by the SNR reverse shock. The escaped electrons propagate to the earth and contribute to the measured local cosmic-ray (CR) electron spectrum. We find that the escaped CR electrons from Vela X would hugely exceed the measured flux by HESS at $\sim 10$ TeV if the standard diffusion coefficient for the interstellar medium is used. We propose that the diffusion may be highly inefficient around Vela X and find that a spatially-dependent diffusion can lead to CR flux consistent with the HESS measurement. Using a two-zone model for the diffusion around Vela X, we find that the diffusion coefficient in the inner region of a few tens of parsecs should be $<10^{28}{\rm cm^2 s^{-1}}$ for $\sim10$ TeV CR electrons, which is about two orders of magnitude lower than the standard value for ISM. Such inefficient diffusion around PWN resembles the case of the Geminga and Monogem PWNe, suggesting that inefficient diffusion may be common in the vicinity of PWNe spanning a wide range of ages.Comment: Accepted by ApJ, more discussions added, conclusions unchanged, 9 pages, 9 figure