Recent Results from Daya Bay Reactor Neutrino Experiment

The Daya Bay reactor neutrino experiment announced the discovery of a non-zero value of \sin^22\theta_{13} with significance better than 5 \sigma in 2012. The experiment is continuing to improve the precision of \sin^22\theta_{13} and explore other physics topics. In this talk, I will show the current oscillation and mass-squared difference results which are based on the combined analysis of the measured rates and energy spectra of antineutrino events, an independent measurement of \theta_{13} using IBD events where delayed neutrons are captured on hydrogens, and a search for light sterile neutrinos.Comment: this proceedings is for the Moriond 2015 EW sessio

New Results from the Daya Bay Reactor Neutrino Experiment

This presentation describes a precision result of the neutrino mixing parameter, $\sin^2 2\theta_{13}$, and the first direct measurement of the antineutrino mass-squared difference $\sin^2(\Delta_{ee}) \equiv \cos^2 \theta_{12} \sin^2 \Delta_{31} + \sin^2 \theta_{12} \sin^2 \Delta_{32}$ from the Daya Bay Reactor Neutrino Experiment. The above results are based on the six detector data-taking from 24 December 2011 to 28 July 2012. By using the observed antineutrino rate and the energy spectrum analysis, the results are $\sin^2 2\theta_{13}=0.090^{+0.008}_{-0.009}$ and $| \Delta m^2_{ee}| = 2.59^{+0.19}_{-0.20} \cdot 10^{-3}$eV$^2$ with a $\chi^2$/NDF of 162.7/153. The value of $| \Delta m^2_{ee}|$ is consistent with $| \Delta m^2_{\mu\mu}|$ measured in muon neutrino beam experiments.Comment: to appear in the proceedings of The 10th International Symposium on Cosmology and Particle Astrophysics (CosPA2013

Asymptotic behavior of the nonlinear Schr\"{o}dinger equation on exterior domain

{\bf Abstract} \,\, We consider the following nonlinear Schr\"{o}dinger equation on exterior domain. \begin{equation} \begin{cases} iu_t+\Delta_g u + ia(x)u - |u|^{p-1}u = 0 \qquad (x,t) \in \Omega\times (0,+\infty), \qquad (1)\cr u\big|_\Gamma = 0\qquad t \in (0,+\infty), \cr u(x,0) = u_0(x)\qquad x \in \Omega, \end{cases} \end{equation} where $1<p<\frac{n+2}{n-2}$, $\Omega\subset\mathbb{R}^n$ ($n\ge3$) is an exterior domain and $(\mathbb{R}^n,g)$ is a complete Riemannian manifold. We establish Morawetz estimates for the system (1) without dissipation ($a(x)\equiv 0$ in (1)) and meanwhile prove exponential stability of the system (1) with a dissipation effective on a neighborhood of the infinity. It is worth mentioning that our results are different from the existing studies. First, Morawetz estimates for the system (1) are directly derived from the metric $g$ and are independent on the assumption of an (asymptotically) Euclidean metric. In addition, we not only prove exponential stability of the system (1) with non-uniform energy decay rate, which is dependent on the initial data, but also prove exponential stability of the system (1) with uniform energy decay rate. The main methods are the development of Morawetz multipliers in non (asymptotically) Euclidean spaces and compactness-uniqueness arguments.Comment: 25 page

On the Complexity of One-class SVM for Multiple Instance Learning

In traditional multiple instance learning (MIL), both positive and negative bags are required to learn a prediction function. However, a high human cost is needed to know the label of each bag---positive or negative. Only positive bags contain our focus (positive instances) while negative bags consist of noise or background (negative instances). So we do not expect to spend too much to label the negative bags. Contrary to our expectation, nearly all existing MIL methods require enough negative bags besides positive ones. In this paper we propose an algorithm called "Positive Multiple Instance" (PMI), which learns a classifier given only a set of positive bags. So the annotation of negative bags becomes unnecessary in our method. PMI is constructed based on the assumption that the unknown positive instances in positive bags be similar each other and constitute one compact cluster in feature space and the negative instances locate outside this cluster. The experimental results demonstrate that PMI achieves the performances close to or a little worse than those of the traditional MIL algorithms on benchmark and real data sets. However, the number of training bags in PMI is reduced significantly compared with traditional MIL algorithms

Two Stronger Versions of the Union-closed Sets Conjecture

The union-closed sets conjecture (Frankl's conjecture) says that for any finite union-closed family of finite sets, other than the family consisting only of the empty set, there exists an element that belongs to at least half of the sets in the family. In this paper, we introduce two stronger versions of Frankl's conjecture and give a partial proof. Three related questions are introduced.Comment: 26 pages; a typo on Page 23 was revise

Jensen's Inequality for Backward SDEs Driven by GG-Brownian motion

In this note, we consider Jensen's inequality for the nonlinear expectation associated with backward SDEs driven by $G$-Brownian motion ($G$-BSDEs for short). At first, we give a necessary and sufficient condition for $G$-BSDEs under which one-dimensional Jensen inequality holds. Second, we prove that for $n>1$, the $n$-dimensional Jensen inequality holds for any nonlinear expectation if and only if the nonlinear expectation is linear, which is essentially due to Jia (Arch. Math. 94 (2010), 489-499). As a consequence, we give a necessary and sufficient condition for $G$-BSDEs under which the $n$-dimensional Jensen inequality holds.Comment: 11 page

Study of s→dννˉs\to d\nu\bar{\nu} rare hyperon decays within the Standard Model and new physics

FCNC processes offer important tools to test the Standard Model (SM), and to search for possible new physics. In this work, we investigate the $s\to d\nu\bar{\nu}$ rare hyperon decays in SM and beyond. We find that in SM the branching ratios for these rare hyperon decays range from $10^{-14}$ to $10^{-11}$. When all the errors in the form factors are included, we find that the final branching fractions for most decay modes have an uncertainty of about $5\%$ to $10\%$. After taking into account the contribution from new physics, the generalized SUSY extension of SM and the minimal 331 model, the decay widths for these channels can be enhanced by a factor of $2 \sim 7$.Comment: 9 pages, 5 table

Escape Metrics and its Applications

Geodesics escape is widely used to study the scattering of hyperbolic equations. However, there are few progresses except in a simply connected complete Riemannian manifold with nonpositive curvature. We propose a kind of complete Riemannian metrics in $\mathbb{R}^n$, which is called as escape metrics. We expose the relationship between escape metrics and geodesics escape in $\mathbb{R}^n$. Under the escape metric $g$, we prove that each geodesic of $(\mathbb{R}^n,g)$ escapes, that is, $\lim_{t\rightarrow +\infty} |\gamma (t)|=+\infty$ for any $x\in \mathbb{R}^n$ and any unit-speed geodesic $\gamma (t)$ starting at $x$. We also obtain the geodesics escape velocity and give the counterexample that if escape metrics are not satisfied, then there exists an unit-speed geodesic $\gamma (t)$ such that $\overline{\lim}_{t\rightarrow +\infty} |\gamma (t)|<+\infty$. In addition, we establish Morawetz multipliers in Riemannian geometry to derive dispersive estimates for the wave equation on an exterior domain of $\mathbb{R}^n$ with an escape metric. More concretely, for radial solutions, the uniform decay rate of the local energy is independent of the parity of the dimension $n$. For general solutions, we prove the space-time estimation of the energy and uniform decay rate $t^{-1}$ of the local energy. It is worth pointing out that different from the assumption of an Euclidean metric at infinity in the existing studies, escape metrics are more general Riemannian metrics.Comment: 28 page

Special uniform decay rate of local energy for the wave equation with variable coefficients on an exterior domain

We consider the wave equation with variable coefficients on an exterior domain in $\R^n$($n\ge 2$). We are interested in finding a special uniform decay rate of local energy different from the constant coefficient wave equation. More concretely, if the dimensional $n$ is even, whether the uniform decay rate of local energy for the wave equation with variable coefficients can break through the limit of polynomial and reach exponential; if the dimensional $n$ is odd, whether the uniform decay rate of local energy for the wave equation with variable coefficients can hold exponential as the constant coefficient wave equation . \quad \ \ We propose a cone and establish Morawetz's multipliers in a version of the Riemannian geometry to derive uniform decay of local energy for the wave equation with variable coefficients. We find that the cone with polynomial growth is closely related to the uniform decay rate of the local energy. More concretely, for radial solutions, when the cone has polynomial of degree $\frac{n}{2k-1}$ growth, the uniform decay rate of local energy is exponential; when the cone has polynomial of degree $\frac{n}{2k}$ growth, the uniform decay rate of local energy is polynomial at most. In addition, for general solutions, when the cone has polynomial of degree $n$ growth, we prove that the uniform decay rate of local energy is exponential under suitable Riemannian metric. It is worth pointing out that such results are independent of the parity of the dimension $n$, which is the main difference with the constant coefficient wave equation. Finally, for general solutions, when the cone has polynomial of degree $m$ growth, where $m$ is any positive constant, we prove that the uniform decay rate of the local energy is of primary polynomial under suitable Riemannian metric.Comment: 23 pages. arXiv admin note: text overlap with arXiv:1811.1266

MIMO UWB Radar System with Compressive Sensing

A multiple input multiple output ultra-wideband cognitive radar based on compressive sensing is presented in this letter. For traditional UWB radar, high sampling rate analog to digital converter at the receiver is required to meet Shannon theorem, which increases hardware complexity. In order to bypass the bottleneck of ADC or further increase the radar bandwidth using the latest wideband ADC, we propose to exploit CS for signal reconstruction at the receiver of UWB radar for the sparse targets in the surveillance area. Besides, the function of narrowband interference cancellation is integrated into the proposed MIMO UWB radar. The field demonstration proves the feasibility and reliability of the proposed algorithm.Comment: 4 page