Investigation of white-light emission in circular-ribbon flares

Using observations by the Solar Dynamics Observatory from June 2010 to December 2017, we have performed the first statistical investigation of circular-ribbon flares (CFs) and examined the white-light emission in these CFs. We find 90 CFs occurring in 36 active regions (ARs), including 8 X-class, 34 M-class, 48 C- and B-class flares. The occurrence rate of white-light flares (WLFs) is 100\% (8/8) for X-class CFs, $\sim$62\% (21/34) for M-class CFs, and $\sim$8\% (4/48) for C- and B-class CFs. Sometimes we observe several CFs in a single AR, and nearly all of them are WLFs. Compared to normal CFs, CFs with white-light enhancement tend to have a shorter duration, smaller size, stronger electric current and more complicated magnetic field. We find that for X-class WLFs, the white-light enhancement is positively correlated with the flare class, implying that the white-light enhancement is largely determined by the amount of released energy. However, there is no such correlation for M- and C-class WLFs, suggesting that other factors such as the time scale, spatial scale and magnetic field complexity may play important roles in the generation of white-light emission if the released energy is not high enough.Comment: 10 figures, 1 table, accepted by Ap

Canonical measures and Kahler-Ricci flow

We show that the Kahler-Ricci flow on an algebraic manifold of positive Kodaira dimension and semi-ample canonical line bundle converges to a unique canonical metric on its canonical model. It is also shown that there exists a canonical measure of analytic Zariski decomposition on an algebraic manifold of positive Kodaira dimension. Such a canonical measure is unique and invariant under birational transformations under the assumption of the finite generation of canonical rings.Comment: 56 page

Continuous Time Markov Processes on Graphs

We study continuous time Markov processes on graphs. The notion of frequency is introduced, which serves well as a scaling factor between any Markov time of a continuous time Markov process and that of its jump chain. As an application, we study ``multi-person simple random walks'' on a graph G with n vertices. There are n persons distributed randomly at the vertices of G. In each step of this discrete time Markov process, we randomly pick up a person and move it to a random adjacent vertex. We give estimate on the expected number of steps for these $n$ persons to meet all together at a specific vertex, given that they are at different vertices at the begininng. For regular graphs, our estimate is exact.Comment: 18 page

Colored Coalescent Theory

We introduce a colored coalescent process which recovers random colored genealogical trees. Here a colored genealogical tree has its vertices colored black or white. Moving backward along the colored genealogical tree, the color of vertices may change only when two vertice coalesce. The rule that governs the change of color involves a parameter $x$. When $x=1/2$, the colored coalescent process can be derived from a variant of the Wright-Fisher model for a haploid population in population genetics. Explicit computations of the expectation and the cumulative distribution function of the coalescent time are carried out. For example, our calculation shows that when $x=1/2$, for a sample of $n$ colored individuals, the expected time for the colored coalescent process to reach a black MRAC or a white MRAC, respectively, is $3-2/n$. On the other hand, the expected time for the colored coalescent process to reach a MRAC, either black or white, is $2-2/n$, which is the same as that for the standard Kingman coalescent process.Comment: 13 pages, 1 figures. To appear in the Proceedings of the Fifth International Conference on Dynamical Systems and Differential Equations, June 16-19, Pomona, CA, US

Multi-resolution Progressive Computational Ghost Imaging

Ghost imaging needs massive measurements to obtain an image with good visibility and the imaging speed is usually very low. In order to realize real-time high-resolution ghost imaging of a target which is located in a scenario with a large field of view (FOV), we propose a high-speed multi-resolution progressive computational ghost imaging approach. The target area is firstly locked by a low-resolution image with a small number of measurements, then high-resolution imaging of the target can be obtained by only modulating the light fields corresponding to the target area. The experiments verify the feasibility of the approach. The influence of detection signal-to-noise ratio on the quality of multi-resolution progressive computational ghost imaging is also investigated experimentally. This approach may be applied to some practical application scenarios such as ground-to-air or air-to-air imaging with a large FOV

A note on K\"ahler-Ricci soliton

In this note we provide a proof of the following: Any compact KRS with positive bisectional curvature is biholomorphic to the complex projective space. As a corollary, we obtain an alternative proof of the Frankel conjecture by using the K\"ahler-Ricci flow.Comment: A lemma added; an error correcte

On characterization of Poisson integrals of Schr\"odinger operators with Morrey traces

Let $L$ be a Schr\"odinger operator of the form $L=-\Delta+V$ acting on $L^2(\mathbb R^n)$ where the nonnegative potential $V$ belongs to the reverse H\"older class $B_q$ for some $q\geq n.$ In this article we will show that a function $f\in L^{2, \lambda}({\mathbb{R}^n}), 0<\lambda<n$ is the trace of the solution of ${\mathbb L}u=-u_{tt}+L u=0, u(x,0)= f(x),$ where $u$ satisfies a Carleson type condition \begin{eqnarray*} \sup_{x_B, r_B} r_B^{-\lambda}\int_0^{r_B}\int_{B(x_B, r_B)} t|\nabla u(x,t)|^2 {dx dt} \leq C <\infty. \end{eqnarray*} Its proof heavily relies on investigate the intrinsic relationship between the classical Morrey spaces and the new Campanato spaces $\mathscr{L}_L^{2,\lambda}({\mathbb{R}^n})$ associated to the operator $L$, i.e. $$\mathscr{L}_L^{2,\lambda}(\mathbb{R}^n)= {L}^{2,\lambda}(\mathbb{R}^n).$$ Conversely, this Carleson type condition characterizes all the ${\mathbb L}$-harmonic functions whose traces belong to the space $L^{2, \lambda}({\mathbb{R}^n})$ for all $0<\lambda<n$. This extends the previous results of [FJN, DYZ, JXY].Comment: 16page

Collapsing behavior of Ricci-flat Kahler metrics and long time solutions of the Kahler-Ricci flow

We prove a uniform diameter bound for long time solutions of the normalized Kahler-Ricci flow on an $n$-dimensional projective manifold $X$ with semi-ample canonical bundle under the assumption that the Ricci curvature is uniformly bounded for all time in a fixed domain containing a fibre of $X$ over its canonical model $X_{can}$. This assumption on the Ricci curvature always holds when the Kodaira dimension of $X$ is $n$, $n-1$ or when the general fibre of $X$ over its canonical model is a complex torus. In particular, the normalized Kahler-Ricci flow converges in Gromov-Hausdorff topolopy to its canonical model when $X$ has Kodaira dimension $1$ with $K_X$ being semi-ample and the general fibre of $X$ over its canonical model being a complex torus. We also prove the Gromov-Hausdorff limit of collapsing Ricci-flat Kahler metrics on a holomorphically fibred Calabi-Yau manifold is unique and is homeomorphic to the metric completion of the corresponding twisted Kahler-Einstein metric on the regular part of its base

Broadcasting Correlated Vector Gaussians

The problem of sending two correlated vector Gaussian sources over a bandwidth-matched two-user scalar Gaussian broadcast channel is studied in this work, where each receiver wishes to reconstruct its target source under a covariance distortion constraint. We derive a lower bound on the optimal tradeoff between the transmit power and the achievable reconstruction distortion pair. Our derivation is based on a new bounding technique which involves the introduction of appropriate remote sources. Furthermore, it is shown that this lower bound is achievable by a class of hybrid schemes for the special case where the weak receiver wishes to reconstruct a scalar source under the mean squared error distortion constraint.Comment: 13 page

Burau representation and random walk on string links

Using a probabilistic interpretation of the Burau representation of the braid group offered by Vaughan Jones, we generalize the Burau representation to a representation of the semigroup of string links. This representation is determined by a linear system, and is dominated by finite type string link invariants. For positive string links, the representation matrix can be interpreted as the transition matrix of a Markov process. For positive non-separable links, we show that all states are persistent. (This is an extensively revised version of the first author's original paper titled "Burau representation and random walk on knots".)Comment: AMSTEX, 12 pages with 4 figure