We investigated the radio wavefront of cosmic-ray air showers with LOPES measurements and CoREAS simulations: the wavefront is of approximately hyperbolic shape and its steepness is sensitive to the shower maximum. For this study we used 316 events w
ith an energy above 0.1 EeV and zenith angles below $45^circ$ measured by the LOPES experiment. LOPES was a digital radio interferometer consisting of up to 30 antennas on an area of approximately 200 m x 200 m at an altitude of 110 m above sea level. Triggered by KASCADE-Grande, LOPES measured the radio emission between 43 and 74 MHz, and our analysis might strictly hold only for such conditions. Moreover, we used CoREAS simulations made for each event, which show much clearer results than the measurements suffering from high background. A detailed description of our result is available in our recent paper published in JCAP09(2014)025. The present proceeding contains a summary and focuses on some additional aspects, e.g., the asymmetry of the wavefront: According to the CoREAS simulations the wavefront is slightly asymmetric, but on a much weaker level than the lateral distribution of the radio amplitude.
LOPES was a digital antenna array detecting the radio emission of cosmic-ray air showers. The calibration of the absolute amplitude scale of the measurements was done using an external, commercial reference source, which emits a frequency comb with d
efined amplitudes. Recently, we obtained improved reference values by the manufacturer of the reference source, which significantly changed the absolute calibration of LOPES. We reanalyzed previously published LOPES measurements, studying the impact of the changed calibration. The main effect is an overall decrease of the LOPES amplitude scale by a factor of $2.6 pm 0.2$, affecting all previously published values for measurements of the electric-field strength. This results in a major change in the conclusion of the paper Comparing LOPES measurements of air-shower radio emission with REAS 3.11 and CoREAS simulations published in Astroparticle Physics 50-52 (2013) 76-91: With the revised calibration, LOPES measurements now are compatible with CoREAS simulations, but in tension with REAS 3.11 simulations. Since CoREAS is the latest version of the simulation code incorporating the current state of knowledge on the radio emission of air showers, this new result indicates that the absolute amplitude prediction of current simulations now is in agreement with experimental data.
The Murnaghan-Nakayama rule expresses the product of a Schur function with a Newton power sum in the basis of Schur functions. We establish a version of the Murnaghan-Nakayama rule for Schubert polynomials and a version for the quantum cohomology rin
g of the Grassmannian. These rules compute all intersections of Schubert cycles with tautological classes coming from the Chern character.
The current work introduces the notion of pdominant sets and studies their recursion-theoretic properties. Here a set A is called pdominant iff there is a partial A-recursive function {psi} such that for every partial recursive function {phi} and alm
ost every x in the domain of {phi} there is a y in the domain of {psi} with y<= x and {psi}(y) > {phi}(x). While there is a full {pi}01-class of nonrecursive sets where no set is pdominant, there is no {pi}01-class containing only pdominant sets. No weakly 2-generic set is pdominant while there are pdominant 1-generic sets below K. The halves of Chaitins {Omega} are pdominant. No set which is low for Martin-Lof random is pdominant. There is a low r.e. set which is pdominant and a high r.e. set which is not pdominant.
Characterizing macromolecular kinetics from molecular dynamics (MD) simulations requires a distance metric that can distinguish slowly-interconverting states. Here we build upon diffusion map theory and define a kinetic distance for irreducible Marko
v processes that quantifies how slowly molecular conformations interconvert. The kinetic distance can be computed given a model that approximates the eigenvalues and eigenvectors (reaction coordinates) of the MD Markov operator. Here we employ the time-lagged independent component analysis (TICA). The TICA components can be scaled to provide a kinetic map in which the Euclidean distance corresponds to the kinetic distance. As a result, the question of how many TICA dimensions should be kept in a dimensionality reduction approach becomes obsolete, and one parameter less needs to be specified in the kinetic model construction. We demonstrate the approach using TICA and Markov state model (MSM) analyses for illustrative models, protein conformation dynamics in bovine pancreatic trypsin inhibitor and protein-inhibitor association in trypsin and benzamidine.
Billey and Braden defined a geometric pattern map on flag manifolds which extends the generalized pattern map of Billey and Postnikov on Weyl groups. The interaction of this torus equivariant map with the Bruhat order and its action on line bundles l
ead to formulas for its pullback on the equivariant cohomology ring and on equivariant K-theory. These formulas are in terms of the Borel presentation, the basis of Schubert classes, and localization at torus fixed points.
We give a Descartes-like bound on the number of positive solutions to a system of fewnomials that holds when its exponent vectors are not in convex position and a sign condition is satisfied. This was discovered while developing algorithms and softwa
re for computing the Gale transform of a fewnomial system, which is our main goal. This software is a component of a package we are developing for Khovanskii-Rolle continuation, which is a numerical algorithm to compute the real solutions to a system of fewnomials.
Formulating a Schubert problem as the solutions to a system of equations in either Plucker space or in the local coordinates of a Schubert cell usually involves more equations than variables. Using reduction to the diagonal, we previously gave a prim
al-dual formulation for Schubert problems that involved the same number of variables as equations (a square formulation). Here, we give a different square formulation by lifting incidence conditions which typically involves fewer equations and variables. Our motivation is certification of numerical computation using Smales alpha-theory.
A new method to determine the spin tune is described and tested. In an ideal planar magnetic ring, the spin tune - defined as the number of spin precessions per turn - is given by $ u_s = gamma G$ (gamma is the Lorentz factor, $G$ the magnetic anomal
y). For 970 MeV/c deuterons coherently precessing with a frequency of ~120 kHz in the Cooler Synchrotron COSY, the spin tune is deduced from the up-down asymmetry of deuteron carbon scattering. In a time interval of 2.6 s, the spin tune was determined with a precision of the order $10^{-8}$, and to $1 cdot 10^{-10}$ for a continuous 100 s accelerator cycle. This renders the presented method a new precision tool for accelerator physics: controlling the spin motion of particles to high precision is mandatory, in particular, for the measurement of electric dipole moments of charged particles in a storage ring.
In this article we give necessary and sufficient conditions that a complex number must satisfy to be a continuous eigenvalue of a minimal Cantor system. Similarly, for minimal Cantor systems of finite rank, we provide necessary and sufficient conditi
ons for having a measure theoretical eigenvalue. These conditions are established from the combinatorial information of the Bratteli-Vershik representations of such systems. As an application, from any minimal Cantor system, we construct a strong orbit equivalent system without irrational eigenvalues which shares all measure theoretical eigenvalues with the original system. In a second application a minimal Cantor system is constructed satisfying the so-called maximal continuous eigenvalue group property.
