Gauge Independent Effective Potential and the Higgs Mass Bound

We introduce the Vilkovisky-DeWitt formalism for deriving the lower bound of the Higgs boson mass. We illustrate the formalism with a simplified version of the Standard Electroweak Model, where all charged boson fields as well as the bottom-quark field are disregarded. The effective potential obtained in this approach is gauge independent. We derive from the effective potential the mass bound of the Higgs boson. The result is compared to its counterpart obtained from the ordinary effective potential.Comment: 15 pages, Revtex; version to appear in Phys. Rev.

Tropical Geometry of Phylogenetic Tree Space: A Statistical Perspective

Phylogenetic trees are the fundamental mathematical representation of evolutionary processes in biology. As data objects, they are characterized by the challenges associated with "big data," as well as the complication that their discrete geometric structure results in a non-Euclidean phylogenetic tree space, which poses computational and statistical limitations. We propose and study a novel framework to study sets of phylogenetic trees based on tropical geometry. In particular, we focus on characterizing our framework for statistical analyses of evolutionary biological processes represented by phylogenetic trees. Our setting exhibits analytic, geometric, and topological properties that are desirable for theoretical studies in probability and statistics, as well as increased computational efficiency over the current state-of-the-art. We demonstrate our approach on seasonal influenza data.Comment: 28 pages, 5 figures, 1 tabl

Combining Local Appearance and Holistic View: Dual-Source Deep Neural Networks for Human Pose Estimation

We propose a new learning-based method for estimating 2D human pose from a single image, using Dual-Source Deep Convolutional Neural Networks (DS-CNN). Recently, many methods have been developed to estimate human pose by using pose priors that are estimated from physiologically inspired graphical models or learned from a holistic perspective. In this paper, we propose to integrate both the local (body) part appearance and the holistic view of each local part for more accurate human pose estimation. Specifically, the proposed DS-CNN takes a set of image patches (category-independent object proposals for training and multi-scale sliding windows for testing) as the input and then learns the appearance of each local part by considering their holistic views in the full body. Using DS-CNN, we achieve both joint detection, which determines whether an image patch contains a body joint, and joint localization, which finds the exact location of the joint in the image patch. Finally, we develop an algorithm to combine these joint detection/localization results from all the image patches for estimating the human pose. The experimental results show the effectiveness of the proposed method by comparing to the state-of-the-art human-pose estimation methods based on pose priors that are estimated from physiologically inspired graphical models or learned from a holistic perspective.Comment: CVPR 201

Galaxy formation with cold gas accretion and evolving stellar initial mass function

The evolution of the galaxy stellar mass function is especially useful to test the current model of galaxy formation. Observational data have revealed a few inconsistencies with predictions from the $\Lambda {\rm CDM}$ model. For example, most massive galaxies have already been observed at very high redshifts, and they have experienced only mild evolution since then. In conflict with this, semi-analytical models of galaxy formation predict an insufficient number of massive galaxies at high redshift and a rapid evolution between redshift 1 and 0 . In addition, there is a strong correlation between star formation rate and stellar mass for star-forming galaxies, which can be roughly reproduced with the model, but with a normalization that is too low at high redshift. Furthermore, the stellar mass density obtained from the integral of the cosmic star formation history is higher than the measured one by a factor of 2. In this paper, we study these issues using a semi-analytical model that includes: 1) cold gas accretion in massive halos at high redshift; 2) tidal stripping of stellar mass from satellite galaxies; and 3) an evolving stellar initial mass function (bottom-light) with a higher gas recycle fraction. Our results show that the combined effects from 1) and 2) can predict sufficiently massive galaxies at high redshifts and reproduce their mild evolution at low redshift, While the combined effects of 1) and 3) can reproduce the correlation between star formation rate and stellar mass for star-forming galaxies across wide range of redshifts. A bottom-light/top-heavy stellar IMF could partly resolve the conflict between the stellar mass density and cosmic star formation history.Comment: 9 pages, 7 figures. Accepted for publication in Ap

Resolving Scale Ambiguity Via XSlit Aspect Ratio Analysis

In perspective cameras, images of a frontal-parallel 3D object preserve its aspect ratio invariant to its depth. Such an invariance is useful in photography but is unique to perspective projection. In this paper, we show that alternative non-perspective cameras such as the crossed-slit or XSlit cameras exhibit a different depth-dependent aspect ratio (DDAR) property that can be used to 3D recovery. We first conduct a comprehensive analysis to characterize DDAR, infer object depth from its AR, and model recoverable depth range, sensitivity, and error. We show that repeated shape patterns in real Manhattan World scenes can be used for 3D reconstruction using a single XSlit image. We also extend our analysis to model slopes of lines. Specifically, parallel 3D lines exhibit depth-dependent slopes (DDS) on their images which can also be used to infer their depths. We validate our analyses using real XSlit cameras, XSlit panoramas, and catadioptric mirrors. Experiments show that DDAR and DDS provide important depth cues and enable effective single-image scene reconstruction