Generalizing Lieb's Concavity Theorem via Operator Interpolation

We introduce the notion of $k$-trace and use interpolation of operators to prove the joint concavity of the function $(A,B)\mapsto\text{Tr}_k\big[(B^\frac{qs}{2}K^*A^{ps}KB^\frac{qs}{2})^{\frac{1}{s}}\big]^\frac{1}{k}$, which generalizes Lieb's concavity theorem from trace to a class of homogeneous functions $\text{Tr}_k[\cdot]^\frac{1}{k}$. Here $\text{Tr}_k[A]$ denotes the $k_{\text{th}}$ elementary symmetric polynomial of the eigenvalues of $A$. This result gives an alternative proof for the concavity of $A\mapsto\text{Tr}_k\big[\exp(H+\log A)\big]^\frac{1}{k}$ that was obtained and used in a recent work to derive expectation estimates and tail bounds on partial spectral sums of random matrices

A generalized Lieb's theorem and its applications to spectrum estimates for a sum of random matrices

In this paper we prove the concavity of the $k$-trace functions, $A\mapsto (\text{Tr}_k[\exp(H+\ln A)])^{1/k}$, on the convex cone of all positive definite matrices. $\text{Tr}_k[A]$ denotes the $k_{\mathrm{th}}$ elementary symmetric polynomial of the eigenvalues of $A$. As an application, we use the concavity of these $k$-trace functions to derive tail bounds and expectation estimates on the sum of the $k$ largest (or smallest) eigenvalues of a sum of random matrices.Comment: 22 page

Constraining the (Low-Energy) Type-I Seesaw

The type-I seesaw Lagrangian yields a non-generic set of active-sterile oscillation parameters - the neutrino mass eigenvalues and the physical elements of the full mixing matrix are entwined. For this reason one is able to, in principle, test the model by performing enough measurements which are sensitive to neutrino masses and lepton mixing. We point out that for light enough right-handed neutrino masses - less than 10 eV - next-generation short-baseline neutrino oscillation experiments may be able to unambiguously rule out (or "rule in") the low energy seesaw as the Lagrangian that describes neutrino masses. These types of searches are already under consideration in order to address the many anomalies from accelerator neutrino experiments (LSND, MiniBooNe), reactor neutrino experiments (the "reactor anomaly") and others. In order to test the low-energy seesaw, it is crucial to explore different oscillation channels, including nu_e and nu_mu disappearance and nu_mu to nu_tau appearance.Comment: 15 pages, five figure

R2-D2: ColoR-inspired Convolutional NeuRal Network (CNN)-based AndroiD Malware Detections

The influence of Deep Learning on image identification and natural language processing has attracted enormous attention globally. The convolution neural network that can learn without prior extraction of features fits well in response to the rapid iteration of Android malware. The traditional solution for detecting Android malware requires continuous learning through pre-extracted features to maintain high performance of identifying the malware. In order to reduce the manpower of feature engineering prior to the condition of not to extract pre-selected features, we have developed a coloR-inspired convolutional neuRal networks (CNN)-based AndroiD malware Detection (R2-D2) system. The system can convert the bytecode of classes.dex from Android archive file to rgb color code and store it as a color image with fixed size. The color image is input to the convolutional neural network for automatic feature extraction and training. The data was collected from Jan. 2017 to Aug 2017. During the period of time, we have collected approximately 2 million of benign and malicious Android apps for our experiments with the help from our research partner Leopard Mobile Inc. Our experiment results demonstrate that the proposed system has accurate security analysis on contracts. Furthermore, we keep our research results and experiment materials on http://R2D2.TWMAN.ORG.Comment: Verison 2018/11/15, IEEE BigData 2018, Seattle, WA, USA, Dec 10-13, 2018. (Accepted