Recent Results from Telescope Array

The Telescope Array (TA) is an experiment to observe Ultra-High Energy Cosmic Rays (UHECRs). TA's recent results, the energy spectrum and anisotropy based on the 6-year surface array data, and the primary composition obtained from the shower maximum Xmax are reported. The spectrum demonstrates a clear dip and cutoff. The shape of the spectrum is well described by the energy loss of extra-galactic protons interacting with the cosmic microwave background (CMB). Above the cutoff, a medium-scale (20 degrees radius) flux enhancement was observed near the Ursa-Major. A chance probability of creating this hotspot from the isotropic flux is 4.0 sigma. The measured Xmax is consistent with the primary being proton or light nuclei for energies 10^18.2 eV - 10^19.2 eV.Comment: 8 pages, 15 figures, ISVHECRI2014, CERN, August 18th-22nd, 201

Instanton and Monopole in External Chromomagnetic Fields

We study properties of instanton and monopole in an external chromomagnetic field. Generally, the 't Hooft ansatz is no longer a solution of the Yang-Mills field equation in the presence of external fields. Therefore, we investigate a stabilized instanton solution with minimal total Yang-Mills action in a nontrivial topological sector. With this aim, we consider numerical minimization of the action with respect to the global color orientation, the anisotropic scale transformation and the local gauge-like transformation starting from a simple superposed gauge field of the 't Hooft ansatz and the external color field. Here, the external color field is, for simplicity, chosen to be a constant Abelian magnetic field along a certain direction. Then, the 4-dimensional rotational symmetry O(4) of the instanton solution is reduced to two 2-dimensional rotational symmetries $O(2)\times O(2)$ due to the effect of a homogeneous external field. In the space \mib{R}^{3} at fixed $t$, we find a quadrupole deformation of this instanton solution. In the presence of a magnetic field $\vec{H}$, a prolate deformation occurs along the direction of $\vec{H}$. Contrastingly, in the presence of an electric field $\vec{E}$ an oblate deformation occurs along the direction of $\vec{E}$. We further discuss the local correlation between the instanton and the monopole in the external field in the maximally Abelian gauge. The external field affects the appearance of the monopole trajectory around the instanton. In fact, a monopole and anti-monopole pair appears around the instanton center, and this monopole loop seems to partially screen the external field.Comment: 15 pages,8 figure

Confinement Properties in the Multi-Instanton System

We investigate the confinement properties in the multi-instanton system, where the size distribution is assumed to be $\rho^{-5}$ for the large instanton size $\rho$. We find that the instanton vacuum gives the area law behavior of the Wilson loop, which indicates existence of the linear confining potential. In the multi-instanton system, the string tension increases monotonously with the instanton density, and takes the standard value $\sigma \simeq 1 GeV/fm$ for the density $(N/V)^{{1/4}} = 200 MeV$. Thus, instantons directly relate to color confinement properties.Comment: Talk presented by M. Fukushima at ``Lattice '97'', the International Symposium on Lattice Field Theory, 22 - 26 July 1997, in Edinburgh, Scotland, 3 pages, Plain Late

Perimeter of sublevel sets in infinite dimensional spaces

We compare the perimeter measure with the Airault-Malliavin surface measure and we prove that all open convex subsets of abstract Wiener spaces have finite perimeter. By an explicit counter-example, we show that in general this is not true for compact convex domains

Invariant, super and quasi-martingale functions of a Markov process

We identify the linear space spanned by the real-valued excessive functions of a Markov process with the set of those functions which are quasimartingales when we compose them with the process. Applications to semi-Dirichlet forms are given. We provide a unifying result which clarifies the relations between harmonic, co-harmonic, invariant, co-invariant, martingale and co-martingale functions, showing that in the conservative case they are all the same. Finally, using the co-excessive functions, we present a two-step approach to the existence of invariant probability measures

Views of the Chiral Magnetic Effect

My personal views of the Chiral Magnetic Effect are presented, which starts with a story about how we came up with the electric-current formula and continues to unsettled subtleties in the formula. There are desirable features in the formula of the Chiral Magnetic Effect but some considerations would lead us to even more questions than elucidations. The interpretation of the produced current is indeed very non-trivial and it involves a lot of confusions that have not been resolved.Comment: 19 pages, no figure; typos corrected, references significantly updated, to appear in Lect. Notes Phys. "Strongly interacting matter in magnetic fields" (Springer), edited by D. Kharzeev, K. Landsteiner, A. Schmitt, H.-U. Ye

Are Muslims the New Catholics? Europe’s Headscarf Laws in Comparative Historical Perspective

In this paper a biologically-inspired model for partly occluded patterns is proposed. The model is based on the hypothesis that in human visual system occluding patterns play a key role in recognition as well as in reconstructing internal representation for a pattern’s occluding parts. The proposed model is realized with a bidirectional hierarchical neural network. In this network top-down cues, generated by direct connections from the lower to higher levels of hierarchy, interact with the bottom-up information, generated from the un-occluded parts, to recognize occluded patterns. Moreover, positional cues of the occluded as well as occluding patterns, that are computed separately but in the same network, modulate the top-down and bottom-up processing to reconstruct the occluded patterns. Simulation results support the presented hypothesis as well as effectiveness of the model in providing a solution to recognition of occluded patterns. The behavior of the model is in accordance to the known human behavior on the occluded patterns

Polyakov loop and the color-flavor locked phase of Quantum Chromodynamics

We consider the Polyakov Nambu Jona Lasinio model with three massless quarks at high density and moderate temperature in the superconductive color flavor locking phase. We compute the critical temperature $T_c$ as a function of the baryonic chemical potential for the phase transition from the superconductive state to the normal phase. We find that $T_c$ is higher by a factor 1.5 -2 in comparison to the model containing no Polyakov loop. We also compute the specific heat $C_v$ near the second order phase transition and we show that the inclusion of the Polyakov loop does not change the value of the critical exponent.Comment: 7 pages, 2 figures, RevTeX4 styl