A NOTE ON PARITY CONSTRAINED ORIENTATIONS

This note extends a result of Frank, Jordan, and Szigeti [3] on parity constrained orientations with connectivity requirements. Given a hypergraph H, a non-negative intersecting supermodular set function p, and a preferred in-degree parity for every node, a formula is given on the minimum number of nodes with wrong in-degree parity in an orientation of H covering p

Non-parametric Reconstruction of Cluster Mass Distribution from Strong Lensing: Modelling Abell 370

We describe a new non-parametric technique for reconstructing the mass distribution in galaxy clusters with strong lensing, i.e., from multiple images of background galaxies. The observed positions and redshifts of the images are considered as rigid constraints and through the lens (ray-trace) equation they provide us with linear constraint equations. These constraints confine the mass distribution to some allowed region, which is then found by linear programming. Within this allowed region we study in detail the mass distribution with minimum mass-to-light variation; also some others, such as the smoothest mass distribution. The method is applied to the extensively studied cluster Abell 370, which hosts a giant luminous arc and several other multiply imaged background galaxies. Our mass maps are constrained by the observed positions and redshifts (spectroscopic or model-inferred by previous authors) of the giant arc and multiple image systems. The reconstructed maps obtained for \a370 reveal a detailed mass distribution, with substructure quite different from the light distribution. The method predicts the bimodal nature of the cluster and that the projected mass distribution is indeed elongated along the axis defined by the two dominant cD galaxies. But the peaks in the mass distribution appear to be offset from the centres of the cDs. We also present an estimate for the total mass of the central region of the cluster. This is in good agreement with previous mass determinations. The total mass of the central region is M=(2.0-2.7) 10^14 Msun/h50, depending on the solution chosen.Comment: 14 pages(19 postscript figures), minor corrections, MNRAS in pres

Systematic errors in cosmic microwave background polarization measurements

We investigate the impact of instrumental systematic errors on the potential of cosmic microwave background polarization experiments targeting primordial B-modes. To do so, we introduce spin-weighted Muller matrix-valued fields describing the linear response of the imperfect optical system and receiver, and give a careful discussion of the behaviour of the induced systematic effects under rotation of the instrument. We give the correspondence between the matrix components and known optical and receiver imperfections, and compare the likely performance of pseudo-correlation receivers and those that modulate the polarization with a half-wave plate. The latter is shown to have the significant advantage of not coupling the total intensity into polarization for perfect optics, but potential effects like optical distortions that may be introduced by the quasi-optical wave plate warrant further investigation. A fast method for tolerancing time-invariant systematic effects is presented, which propagates errors through to power spectra and cosmological parameters. The method extends previous studies to an arbitrary scan strategy, and eliminates the need for time-consuming Monte-Carlo simulations in the early phases of instrument and survey design. We illustrate the method with both simple parametrized forms for the systematics and with beams based on physical-optics simulations. Example results are given in the context of next-generation experiments targeting tensor-to-scalar ratios r ~ 0.01.Comment: 19 pages, 7 figures; Minor changes to match version accepted by MNRA

Ising Anyons in Frustration-Free Majorana-Dimer Models

Dimer models have long been a fruitful playground for understanding topological physics. Here we introduce a new class - termed Majorana-dimer models - wherein bosonic dimers are decorated with pairs of Majorana modes. We find that the simplest examples of such systems realize an intriguing, intrinsically fermionic phase of matter that can be viewed as the product of a chiral Ising theory, which hosts deconfined non-Abelian quasiparticles, and a topological $p_x - ip_y$ superconductor. While the bulk anyons are described by a single copy of the Ising theory, the edge remains fully gapped. Consequently, this phase can arise in exactly solvable, frustration-free models. We describe two parent Hamiltonians: one generalizes the well-known dimer model on the triangular lattice, while the other is most naturally understood as a model of decorated fluctuating loops on a honeycomb lattice. Using modular transformations, we show that the ground-state manifold of the latter model unambiguously exhibits all properties of the $\text{Ising} \times (p_x-ip_y)$ theory. We also discuss generalizations with more than one Majorana mode per site, which realize phases related to Kitaev's 16-fold way in a similar fashion