Regularities and Exponential Ergodicity in Entropy for SDEs Driven by Distribution Dependent Noise

As two crucial tools characterizing regularity properties of stochastic systems, the log-Harnack inequality and Bismut formula have been intensively studied for distribution dependent (McKean-Vlasov) SDEs. However, due to technical difficulties, existing results mainly focus on the case with distribution free noise. In this paper, we introduce a noise decomposition argument to establish the log-Harnack inequality and Bismut formula for SDEs with distribution dependent noise, in both non-degenerate and degenerate situations. As application, the exponential ergodicity in entropy is investigated.Comment: 23 page

The Υ(1S)\Upsilon(1S) leptonic decay using the principle of maximum conformality

In the paper, we study the $\Upsilon(1S)$ leptonic decay width $\Gamma(\Upsilon(1S)\to \ell^+\ell^-)$ by using the principle of maximum conformality (PMC) scale-setting approach. The PMC adopts the renormalization group equation to set the correct momentum flow of the process, whose value is independent to the choice of the renormalization scale and its prediction thus avoids the conventional renormalization scale ambiguities. Using the known next-to-next-to-next-to-leading order perturbative series together with the PMC single scale-setting approach, we do obtain a renormalization scale independent decay width, $\Gamma_{\Upsilon(1S) \to e^+ e^-} = 1.262^{+0.195}_{-0.175}$ keV, where the error is squared average of those from $\alpha_s(M_{Z})=0.1181\pm0.0011$, $m_b=4.93\pm0.03$ GeV and the choices of factorization scales within $\pm 10\%$ of their central values. To compare with the result under conventional scale-setting approach, this decay width agrees with the experimental value within errors, indicating the importance of a proper scale-setting approach.Comment: 6 pages, 4 figure

Transcribing Content from Structural Images with Spotlight Mechanism

Transcribing content from structural images, e.g., writing notes from music scores, is a challenging task as not only the content objects should be recognized, but the internal structure should also be preserved. Existing image recognition methods mainly work on images with simple content (e.g., text lines with characters), but are not capable to identify ones with more complex content (e.g., structured symbols), which often follow a fine-grained grammar. To this end, in this paper, we propose a hierarchical Spotlight Transcribing Network (STN) framework followed by a two-stage "where-to-what" solution. Specifically, we first decide "where-to-look" through a novel spotlight mechanism to focus on different areas of the original image following its structure. Then, we decide "what-to-write" by developing a GRU based network with the spotlight areas for transcribing the content accordingly. Moreover, we propose two implementations on the basis of STN, i.e., STNM and STNR, where the spotlight movement follows the Markov property and Recurrent modeling, respectively. We also design a reinforcement method to refine the framework by self-improving the spotlight mechanism. We conduct extensive experiments on many structural image datasets, where the results clearly demonstrate the effectiveness of STN framework.Comment: Accepted by KDD2018 Research Track. In proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD'18