The groupoidal analogue Theta~ to Joyal's category Theta is a test category

We introduce the groupoidal analogue \tilde\Theta to Joyal's cell category \Theta and we prove that \tilde\Theta is a strict test category in the sense of Grothendieck. This implies that presheaves on \tilde\Theta model homotopy types in a canonical way. We also prove that the canonical functor from \Theta to \tilde\Theta is aspherical, again in the sense of Grothendieck. This allows us to compare weak equivalences of presheaves on \tilde\Theta to weak equivalences of presheaves on \Theta. Our proofs apply to other categories analogous to \Theta.Comment: 41 pages, v2: references added, Remark 7.3 added, v3: metadata update

Site-selective quantum correlations revealed by magnetic anisotropy in the tetramer system SeCuO3

We present the investigation of a monoclinic compound SeCuO3 using x-ray powder diffraction, magnetization, torque and electron-spin-resonance (ESR). Structurally based analysis suggests that SeCuO3 can be considered as a 3D network of tetramers. The values of intra-tetramer exchange interactions are extracted from the temperature dependence of the susceptibility and amount to ~200 K. The inter-tetramer coupling leads to the development of long-range antiferromagnetic order at TN = 8 K. An unusual temperature dependence of the effective g-tensors is observed, accompanied with a rotation of macroscopic magnetic axes. We explain this unique observation as due to site-selective quantum correlations

Isolated Prompt Photon Production in Hadronic Final States of e+e−e^+e^- Annihilation

We provide complete analytic expressions for the isolated prompt photon production cross section in $e^+e^-$ annihilation reactions through one-loop order in quantum chromodynamics (QCD) perturbation theory. Functional dependences on the isolation cone size $\delta$ and isolation energy parameter $\epsilon$ are derived. The energy dependence as well as the full angular dependence of the cross section on $\theta_\gamma$ are displayed, where $\theta_\gamma$ specifies the direction of the photon with respect to the $e^+e^-$ collision axis. We point out that conventional perturbative QCD factorization breaks down for isolated photon production in $e^+e^-$ annihilation reactions in a specific region of phase space. We discuss the implications of this breakdown for the extraction of fragmentation functions from $e^+e^-$ annihilation data and for computations of prompt photon production in hadron-hadron reactions.Comment: 54 pages RevTeX plus 19 postscript figures submitted together in one compressed fil

Production of a Prompt Photon in Association with Charm at Next-to-Leading Order in QCD

A second order, $O(\alpha ^2_s)$, calculation in perturbative quantum chromodynamics of the two particle inclusive cross section is presented for the reaction $p +\bar{p}\rightarrow \gamma + c + X$ for large values of the transverse momentum of the prompt photon and charm quark. The combination of analytic and Monte Carlo integration methods used here to perform phase-space integrations facilitates imposition of photon isolation restrictions and other selections of relevance in experiments. Differential distributions are provided for various observables. Positive correlations in rapidity are predicted.Comment: 27 pages in RevTex plus 14 figures in one compressed PS fil

Analytic Calculation of Prompt Photon plus Associated Heavy Flavor at Next-to-Leading Order in QCD

Contributions through second order, $O(\alpha ^2_s)$, in perturbative quantum chromodynamics are calculated analytically for inclusive associated production of a prompt photon and a charm quark at large values of transverse momentum in high energy hadron-hadron collisions. Seven partonic subprocesses contribute at order $\alpha^2_s$. We find important corrections to the lowest order, $O(\alpha_s)$, subprocess $c g \rightarrow \gamma c$. We demonstrate to what extent data from $p +\bar{p}\rightarrow \gamma + c + X$ may serve to measure the charm quark density in the nucleon.Comment: 34 pages RevTex plus 9 figures submitted as uuencoded ps files; figures replaced and text revised to include one additional referenc

Fourier, Gauss, Fraunhofer, Porod and the Shape from Moments Problem

We show how the Fourier transform of a shape in any number of dimensions can be simplified using Gauss's law and evaluated explicitly for polygons in two dimensions, polyhedra three dimensions, etc. We also show how this combination of Fourier and Gauss can be related to numerous classical problems in physics and mathematics. Examples include Fraunhofer diffraction patterns, Porods law, Hopfs Umlaufsatz, the isoperimetric inequality and Didos problem. We also use this approach to provide an alternative derivation of Davis's extension of the Motzkin-Schoenberg formula to polygons in the complex plane.Comment: 21 pages, no figure

Spin-stripe phase in a frustrated zigzag spin-1/2 chain

Motifs of periodic modulations are encountered in a variety of natural systems, where at least two rival states are present. In strongly correlated electron systems such behaviour has typically been associated with competition between short- and long-range interactions, e.g., between exchange and dipole-dipole interactions in the case of ferromagnetic thin films. Here we show that spin-stripe textures may develop also in antiferromagnets, where long-range dipole-dipole magnetic interactions are absent. A comprehensive analysis of magnetic susceptibility, high-field magnetization, specific heat, and neutron diffraction measurements unveils $\beta$-TeVO$_4$ as a nearly perfect realization of a frustrated (zigzag) ferromagnetic spin-1/2 chain. Strikingly, a narrow spin stripe phase develops at elevated magnetic fields due to weak frustrated short-range interchain exchange interactions possibly assisted by the symmetry allowed electric polarization. This concept provides an alternative route for the stripe formation in strongly correlated electron systems and may help understanding other widespread, yet still elusive, stripe-related phenomena.Comment: accapted in Nature Communication

New limits on "odderon" amplitudes from analyticity constraints

In studies of high energy $pp$ and $\bar pp$ scattering, the odd (under crossing) forward scattering amplitude accounts for the difference between the $pp$ and $\bar pp$ cross sections. Typically, it is taken as $f_-=-\frac{p}{4\pi}Ds^{\alpha-1}e^{i\pi(1-\alpha)/2}$ ($\alpha\sim 0.5$), which has $\Delta\sigma, \Delta\rho\to0$ as $s\to\infty$, where $\rho$ is the ratio of the real to the imaginary portion of the forward scattering amplitude. However, the odd-signatured amplitude can have in principle a strikingly different behavior, ranging from having $\Delta\sigma\to$non-zero constant to having $\Delta\sigma \to \ln s/s_0$ as $s\to\infty$, the maximal behavior allowed by analyticity and the Froissart bound. We reanalyze high energy $pp$ and $\bar pp$ scattering data, using new analyticity constraints, in order to put new and precise limits on the magnitude of ``odderon'' amplitudes.Comment: 13 pages LaTex, 6 figure

Timed Multiparty Session Types

We propose a typing theory, based on multiparty session types, for modular verification of real-time choreographic interactions. To model real-time implementations, we introduce a simple calculus with delays and a decidable static proof system. The proof system ensures type safety and time-error freedom, namely processes respect the prescribed timing and causalities between interactions. A decidable condition on timed global types guarantees time-progress for validated processes with delays, and gives a sound and complete characterisation of a new class of CTAs with general topologies that enjoys progress and liveness

Manufacture of Gowdy spacetimes with spikes

In numerical studies of Gowdy spacetimes evidence has been found for the development of localized features (spikes) involving large gradients near the singularity. The rigorous mathematical results available up to now did not cover this kind of situation. In this work we show the existence of large classes of Gowdy spacetimes exhibiting features of the kind discovered numerically. These spacetimes are constructed by applying certain transformations to previously known spacetimes without spikes. It is possible to control the behaviour of the Kretschmann scalar near the singularity in detail. This curvature invariant is found to blow up in a way which is non-uniform near the spike in some cases. When this happens it demonstrates that the spike is a geometrically invariant feature and not an artefact of the choice of variables used to parametrize the metric. We also identify another class of spikes which are artefacts. The spikes produced by our method are compared with the results of numerical and heuristic analyses of the same situation.Comment: 25 page