Extending TpT^p automorphisms over \RR^{p+2} and realizing DE attractors

In this paper we consider the realization of DE attractors by self-diffeomorphisms of manifolds. For any expanding self-map $\phi:M\to M$ of a connected, closed $p$-dimensional manifold $M$, one can always realize a $(p,q)$-type attractor derived from $\phi$ by a compactly-supported self-diffeomorphsm of \RR^{p+q}, as long as $q\geq p+1$. Thus lower codimensional realizations are more interesting, related to the knotting problem below the stable range. We show that for any expanding self-map $\phi$ of a standard smooth $p$-dimensional torus $T^p$, there is compactly-supported self-diffeomorphism of \RR^{p+2} realizing an attractor derived from $\phi$. A key ingredient of the construction is to understand automorphisms of $T^p$ which extend over \RR^{p+2} as a self-diffeomorphism via the standard unknotted embedding \imath_p:T^p\hookrightarrow\RR^{p+2}. We show that these automorphisms form a subgroup $E_{\imath_p}$ of \Aut(T^p) of index at most $2^p-1$.Comment: 19 pages, 4 figure

Gene-based Association Analysis for Bivariate Time-to-event Data through Functional Regression with Copula Models

Several gene-based association tests for time-to-event traits have been proposed recently, to detect whether a gene region (containing multiple variants), as a set, is associated with the survival outcome. However, for bivariate survival outcomes, to the best of our knowledge, there is no statistical method that can be directly applied for gene-based association analysis. Motivated by a genetic study to discover gene regions associated with the progression of a bilateral eye disease, Age-related Macular Degeneration (AMD), we implement a novel functional regression method under the copula framework. Specifically, the effects of variants within a gene region are modeled through a functional linear model, which then contributes to the marginal survival functions within the copula. Generalized score test and likelihood ratio test statistics are derived to test for the association between bivariate survival traits and the genetic region. Extensive simulation studies are conducted to evaluate the type-I error control and power performance of the proposed approach, with comparisons to several existing methods for a single survival trait, as well as the marginal Cox functional regression model using the robust sandwich estimator for bivariate survival traits. Finally, we apply our method to a large AMD study, the Age-related Eye Disease Study (AREDS), to identify gene regions that are associated with AMD progression

Phenomenology in Minimal Cascade Seesaw for Neutrino Mass

We make a comprehensive analysis on the phenomenology in the minimal version of cascade seesaw for tiny neutrino mass. The seesaw induces at tree level a neutrino mass operator at dimension nine, by introducing a quadruple scalar $\Phi$ of hypercharge unity and a quintuple fermion $\Sigma$ of hypercharge zero. We work in a framework that handles the complicated Yukawa couplings in a nice way without losing generality. All mixing matrices are essentially expressed in terms of the vacuum expectation value of the quadruple scalar v_\Phi, a free complex parameter, and known neutrino parameters. We show that the low-energy lepton flavor violating transitions of the charged leptons set strong constraints on the free parameters. The constraints have a significant impact on collider physics, and are incorporated in our signal analysis at the LHC. We investigate the signatures of new particles by surveying all potentially important channels. We find that the 4j2\ell^\pm signal is most important for the detection of the scalars and the 2\ell^{\pm}2\ell^{\mp}2j, 3\ell^{\pm}\ell^{\mp}2j and 3\ell^{\pm}2\ell^{\mp}+\cancel{E_T} signals are quite promising for the fermions.Comment: v1: 48 pages, including 18 figures and 10 tables; v2: version to appear in PRD, 50 pages, including 19 figures and 10 tables, changes are: (1) detailed discussion of LFV constraints on parameters together with a new figure (Fig. 3); (2) more refs; (3) typos and grammatical issues fixe

Spin structures and codimension-two homeomorphism extensions

Let \imath: M\to \RR^{p+2} be a smooth embedding from a connected, oriented, closed $p$-dimesional smooth manifold to \RR^{p+2}, then there is a spin structure $\imath^\sharp(\varsigma^{p+2})$ on $M$ canonically induced from the embedding. If an orientation-preserving diffeomorphism $\tau$ of $M$ extends over $\imath$ as an orientation-preserving topological homeomorphism of \RR^{p+2}, then $\tau$ preserves the induced spin structure. Let \esg_\cat(\imath) be the subgroup of the \cat-mapping class group \mcg_\cat(M) consisting of elements whose representatives extend over \RR^{p+2} as orientation-preserving \cat-homeomorphisms, where \cat=\topo, \pl or \diff. The invariance of $\imath^\sharp(\varsigma^{p+2})$ gives nontrivial lower bounds to [\mcg_\cat(M):\esg_\cat(\imath)] in various special cases. We apply this to embedded surfaces in \RR^4 and embedded $p$-dimensional tori in \RR^{p+2}. In particular, in these cases the index lower bounds for \esg_\topo(\imath) are achieved for unknotted embeddings.Comment: 14 pages, 1 figur

Comprehensive Constraints on a Spin-3/2 Singlet Particle as a Dark Matter Candidate

We consider the proposal that dark matter (DM) is composed of a spin-3/2 particle that is a singlet of the standard model (SM). Its leading effective interactions with ordinary matter involve a pair of their fields and a pair of SM fermions, in the form of products of chiral currents. We make a comprehensive analysis on possible phenomenological effects of the interactions in various experiments and observations. These include collider searches for monojet plus missing transverse energy events, direct detections of DM scattering off nuclei, possible impacts on the gamma rays and antiproton-to-proton flux ratio in cosmic rays, and the observed relic density. The current data already set strong constraints on the effective interactions in a complementary manner. The constraint from collider searches is most effective at a relatively low mass of DM, and the antiproton-to-proton flux ratio offers the best bound for a heavy DM, while the spin-independent direct detection is the best in between. For DM mass of order 10 GeV to 1 TeV, the effective interaction scale is constrained to be typically above a few tens TeV.Comment: 24 pages, 10 figure

Externally seeded backward lasing radiation from femtosecond laser filament in nitrogen gas

Recently, S. Mitryukovskiy et al. presented experimental evidence showing that backward stimulated radiation at 337 nm can be obtained from plasma filaments in nitrogen gas pumped by circularly polarized 800 nm femtosecond pulses (Opt. Express, 22, 12750 (2014)). Here, we report that this backward stimulated radiation is enhanced by a factor of ~ 16 in the presence of a seed pulse. This enhanced stimulated radiation can be either linearly or circularly polarized, dictated by the seeding pulse, which is distinct from the non-polarized nature of the ASE without seeding pulse. We also measured the spatial profile and estimated the energy of the radiation. This seeding effect confirms unambiguously the existence of population inversion between the C3{\Pi}u and B3{\Pi}g state of nitrogen molecules inside plasma filament and provides a possible solution to control the properties of this backward stimulated radiation.Comment: 6 pages, 5 figure

Femtosecond two-photon-excited backward lasing of atomic hydrogen in flame

We report on an observation of bi-directional 656 nm lasing action of atomic hydrogen in premixed CH4/air flame induced by resonant femtosecond 205 nm two-photon excitation. In particular, the backward-propagating lasing pulse is systematically characterized in the spectral, spatial and temporal domains for the sake of single-ended diagnostic. Its picosecond-scale duration enables spatially resolved concentration measurements of hydrogen atoms in millimeter range, which is successfully demonstrated using two narrow welding flames.Comment: 13 pages, 5 figures, submitted to Optic

Fine-grained Video Categorization with Redundancy Reduction Attention

For fine-grained categorization tasks, videos could serve as a better source than static images as videos have a higher chance of containing discriminative patterns. Nevertheless, a video sequence could also contain a lot of redundant and irrelevant frames. How to locate critical information of interest is a challenging task. In this paper, we propose a new network structure, known as Redundancy Reduction Attention (RRA), which learns to focus on multiple discriminative patterns by sup- pressing redundant feature channels. Specifically, it firstly summarizes the video by weight-summing all feature vectors in the feature maps of selected frames with a spatio-temporal soft attention, and then predicts which channels to suppress or to enhance according to this summary with a learned non-linear transform. Suppression is achieved by modulating the feature maps and threshing out weak activations. The updated feature maps are then used in the next iteration. Finally, the video is classified based on multiple summaries. The proposed method achieves out- standing performances in multiple video classification datasets. Further- more, we have collected two large-scale video datasets, YouTube-Birds and YouTube-Cars, for future researches on fine-grained video categorization. The datasets are available at http://www.cs.umd.edu/~chenzhu/fgvc.Comment: Correcting a typo in ECCV versio

Can the observed enhancement in the mass spectrum of p \bar p in J/\psi \to \gamma p \bar p be interpreted by a possible p \bar p bound state

Provided the enhancement in the $p \bar{p}$ spectrum in radiative decay $J/\psi \to \gamma p \bar{p}$ observed by the BES collaboration is due to an existence of a $p \bar{p}$ molecular state, we calculate its binding energy and lifetime in the linear $\sigma$ model. We consider a possibility that the enhancement is due to a $p \bar p$ resonance which is in either S-wave or P-wave structure and compare our results with the data.Comment: 15 pages, 3 figure

Study on the structure of the four-quark states in terms of the Born-Oppenheimer approximation

In this work, we use the Born-Oppenheimer approximation where the potential between atoms can be approximated as a function of distance between the two nuclei to study the four-quark bound states. By the approximation, Heitler and London calculated the spectrum of hydrogen molecule which includes two protons (heavy) and two electrons (light). Generally, the observed exotic mesons $Z_b(10610)$, $Z_b(10650)$, $Z_c(3900)$ and $Z_c(4020)$($Z_c(4025)$) may be molecular states made of two physical mesons and/or in diquark-anti-diquark structures. In analog to the Heitler-London method for calculating the mass of hydrogen molecule, we investigate whether there exist energy minima for these two structures. By contrary to the hydrogen molecule case where only the spin-triplet possesses an energy minimum, there exist minima for both of them. It implies that both molecule and tetraquark states can be stable objects. But since they have the same quantum numbers, the two states may mix to result in the physical states. A consequence would be that partner exotic states co-existing with $Z_b(10610)$, $Z_b(10650)$, $Z_c(3900)$ and $Z_c(4020)$($Z_c(4025)$) are predicted and should be experimentally observed.Comment: 13 pages, 10 figure