A Matrix Method for Quasinormal Modes: Kerr and Kerr-Sen Black Holes

In this letter, a matrix method is employed to study the scalar quasinormal modes of Kerr as well as Kerr-Sen black holes. Discretization is applied to transfer the scalar perturbation equation into a matrix form eigenvalue problem, where the resulting radial and angular equations are derived by the method of separation of variables. The eigenvalues, quasinormal frequencies $\omega$ and angular quantum numbers $\lambda$, are then obtained by numerically solving the resultant homogeneous matrix equation. This work shows that the present approach is an accurate as well as efficient method for investigating quasinormal modes.Comment: The Mathematica programs are attached in the ancillary files on the arXiv serve

Robust Estimation of 3D Human Poses from a Single Image

Human pose estimation is a key step to action recognition. We propose a method of estimating 3D human poses from a single image, which works in conjunction with an existing 2D pose/joint detector. 3D pose estimation is challenging because multiple 3D poses may correspond to the same 2D pose after projection due to the lack of depth information. Moreover, current 2D pose estimators are usually inaccurate which may cause errors in the 3D estimation. We address the challenges in three ways: (i) We represent a 3D pose as a linear combination of a sparse set of bases learned from 3D human skeletons. (ii) We enforce limb length constraints to eliminate anthropomorphically implausible skeletons. (iii) We estimate a 3D pose by minimizing the $L_1$-norm error between the projection of the 3D pose and the corresponding 2D detection. The $L_1$-norm loss term is robust to inaccurate 2D joint estimations. We use the alternating direction method (ADM) to solve the optimization problem efficiently. Our approach outperforms the state-of-the-arts on three benchmark datasets

Intrinsic noise in systems with switching environments

We study individual-based dynamics in finite populations, subject to randomly switching environmental conditions. These are inspired by models in which genes transition between on and off states, regulating underlying protein dynamics. Similarly switches between environmental states are relevant in bacterial populations and in models of epidemic spread. Existing piecewise-deterministic Markov process (PDMP) approaches focus on the deterministic limit of the population dynamics while retaining the randomness of the switching. Here we go beyond this approximation and explicitly include effects of intrinsic stochasticity at the level of the linear-noise approximation. Specifically we derive the stationary distributions of a number of model systems, in good agreement with simulations. This improves existing approaches which are limited to the regimes of fast and slow switching.Comment: 15 pages, 11 figure

Joint Object and Part Segmentation using Deep Learned Potentials

Segmenting semantic objects from images and parsing them into their respective semantic parts are fundamental steps towards detailed object understanding in computer vision. In this paper, we propose a joint solution that tackles semantic object and part segmentation simultaneously, in which higher object-level context is provided to guide part segmentation, and more detailed part-level localization is utilized to refine object segmentation. Specifically, we first introduce the concept of semantic compositional parts (SCP) in which similar semantic parts are grouped and shared among different objects. A two-channel fully convolutional network (FCN) is then trained to provide the SCP and object potentials at each pixel. At the same time, a compact set of segments can also be obtained from the SCP predictions of the network. Given the potentials and the generated segments, in order to explore long-range context, we finally construct an efficient fully connected conditional random field (FCRF) to jointly predict the final object and part labels. Extensive evaluation on three different datasets shows that our approach can mutually enhance the performance of object and part segmentation, and outperforms the current state-of-the-art on both tasks

Recurrent Multimodal Interaction for Referring Image Segmentation

In this paper we are interested in the problem of image segmentation given natural language descriptions, i.e. referring expressions. Existing works tackle this problem by first modeling images and sentences independently and then segment images by combining these two types of representations. We argue that learning word-to-image interaction is more native in the sense of jointly modeling two modalities for the image segmentation task, and we propose convolutional multimodal LSTM to encode the sequential interactions between individual words, visual information, and spatial information. We show that our proposed model outperforms the baseline model on benchmark datasets. In addition, we analyze the intermediate output of the proposed multimodal LSTM approach and empirically explain how this approach enforces a more effective word-to-image interaction.Comment: To appear in ICCV 2017. See http://www.cs.jhu.edu/~cxliu/ for code and supplementary materia

Global Properties of Locally Spatially Homogeneous Cosmological Models with Matter

The existence and nature of singularities in locally spatially homogeneous solutions of the Einstein equations coupled to various phenomenological matter models is investigated. It is shown that, under certain reasonable assumptions on the matter, there are no singularities in an expanding phase of the evolution and that unless the spacetime is empty a contracting phase always ends in a singularity where at least one scalar invariant of the curvature diverges uniformly. The class of matter models treated includes perfect fluids, mixtures of non-interacting perfect fluids and collisionless matter.Comment: 18 pages, MPA-AR-94-