QBDT, a new boosting decision tree method with systematic uncertainties into training for High Energy Physics

A new boosting decision tree (BDT) method, QBDT, is proposed for the classification problem in the field of high energy physics (HEP). In many HEP researches, great efforts are made to increase the signal significance with the presence of huge background and various systematical uncertainties. Why not develop a BDT method targeting the significance directly? Indeed, the significance plays a central role in this new method. It is used to split a node in building a tree and to be also the weight contributing to the BDT score. As the systematical uncertainties can be easily included in the significance calculation, this method is able to learn about reducing the effect of the systematical uncertainties via training. Taking the search of the rare radiative Higgs decay in proton-proton collisions $pp \to h + X \to \gamma\tau^+\tau^-+X$ as example, QBDT and the popular Gradient BDT (GradBDT) method are compared. QBDT is found to reduce the correlation between the signal strength and systematical uncertainty sources and thus to give a better significance. The contribution to the signal strength uncertainty from the systematical uncertainty sources using the new method is 50-85~\% of that using the GradBDT method.Comment: 29 pages, accepted for publication in NIMA, algorithm available at https://github.com/xialigang/QBD

Standing sausage modes in coronal loops with plasma flow

Magnetohydrodynamic waves are important for diagnosing the physical parameters of coronal plasmas. Field-aligned flows appear frequently in coronal loops.We examine the effects of transverse density and plasma flow structuring on standing sausage modes trapped in coronal loops, and examine their observational implications. We model coronal loops as straight cold cylinders with plasma flow embedded in a static corona. An eigen-value problem governing propagating sausage waves is formulated, its solutions used to construct standing modes. Two transverse profiles are distinguished, one being the generalized Epstein distribution (profile E) and the other (N) proposed recently in Nakariakov et al.(2012). A parameter study is performed on the dependence of the maximum period $P_\mathrm{max}$ and cutoff length-to-radius ratio $(L/a)_{\mathrm{cutoff}}$ in the trapped regime on the density parameters ($\rho_0/\rho_\infty$ and profile steepness $p$) and flow parameters (magnitude $U_0$ and profile steepness $u$). For either profile, introducing a flow reduces $P_\mathrm{max}$ relative to the static case. $P_\mathrm{max}$ depends sensitively on $p$ for profile N but is insensitive to $p$ for profile E. By far the most important effect a flow introduces is to reduce the capability for loops to trap standing sausage modes: $(L/a)_{\mathrm{cutoff}}$ may be substantially reduced in the case with flow relative to the static one. If the density distribution can be described by profile N, then measuring the sausage mode period can help deduce the density profile steepness. However, this practice is not feasible if profile E better describes the density distribution. Furthermore, even field-aligned flows with magnitudes substantially smaller than the ambient Alfv\'en speed can make coronal loops considerably less likely to support trapped standing sausage modes.Comment: 11 pages, 9 figures, to appear in Astronomy & Astrophysic

Hypothesis Testing of Matrix Graph Model with Application to Brain Connectivity Analysis

Brain connectivity analysis is now at the foreground of neuroscience research. A connectivity network is characterized by a graph, where nodes represent neural elements such as neurons and brain regions, and links represent statistical dependences that are often encoded in terms of partial correlations. Such a graph is inferred from matrix-valued neuroimaging data such as electroencephalography and functional magnetic resonance imaging. There have been a good number of successful proposals for sparse precision matrix estimation under normal or matrix normal distribution; however, this family of solutions do not offer a statistical significance quantification for the estimated links. In this article, we adopt a matrix normal distribution framework and formulate the brain connectivity analysis as a precision matrix hypothesis testing problem. Based on the separable spatial-temporal dependence structure, we develop oracle and data-driven procedures to test the global hypothesis that all spatial locations are conditionally independent, which are shown to be particularly powerful against the sparse alternatives. In addition, simultaneous tests for identifying conditional dependent spatial locations with false discovery rate control are proposed in both oracle and data-driven settings. Theoretical results show that the data-driven procedures perform asymptotically as well as the oracle procedures and enjoy certain optimality properties. The empirical finite-sample performance of the proposed tests is studied via simulations, and the new tests are applied on a real electroencephalography data analysis