On The Complexity and Completeness of Static Constraints for Breaking Row and Column Symmetry

We consider a common type of symmetry where we have a matrix of decision variables with interchangeable rows and columns. A simple and efficient method to deal with such row and column symmetry is to post symmetry breaking constraints like DOUBLELEX and SNAKELEX. We provide a number of positive and negative results on posting such symmetry breaking constraints. On the positive side, we prove that we can compute in polynomial time a unique representative of an equivalence class in a matrix model with row and column symmetry if the number of rows (or of columns) is bounded and in a number of other special cases. On the negative side, we show that whilst DOUBLELEX and SNAKELEX are often effective in practice, they can leave a large number of symmetric solutions in the worst case. In addition, we prove that propagating DOUBLELEX completely is NP-hard. Finally we consider how to break row, column and value symmetry, correcting a result in the literature about the safeness of combining different symmetry breaking constraints. We end with the first experimental study on how much symmetry is left by DOUBLELEX and SNAKELEX on some benchmark problems.Comment: To appear in the Proceedings of the 16th International Conference on Principles and Practice of Constraint Programming (CP 2010

A Generalization of the Goldberg-Sachs Theorem and its Consequences

The Goldberg-Sachs theorem is generalized for all four-dimensional manifolds endowed with torsion-free connection compatible with the metric, the treatment includes all signatures as well as complex manifolds. It is shown that when the Weyl tensor is algebraically special severe geometric restrictions are imposed. In particular it is demonstrated that the simple self-dual eigenbivectors of the Weyl tensor generate integrable isotropic planes. Another result obtained here is that if the self-dual part of the Weyl tensor vanishes in a Ricci-flat manifold of (2,2) signature the manifold must be Calabi-Yau or symplectic and admits a solution for the source-free Einstein-Maxwell equations.Comment: 14 pages. This version matches the published on

Zooming into the coexisting regime of ferromagnetism and superconductivity in ErRh4B4 single crystals

High resolution measurements of the dynamic magnetic susceptibility are reported for ferromagnetic re-entrant superconductor, ErRh$_{4}$B$_{4}$. Detailed investigation of the coexisting regime reveals unusual temperature-asymmetric and magnetically anisotropic behavior. The superconducting phase appears via a series of discontinuous steps upon warming from the ferromagnetic normal phase, whereas the ferromagnetic phase develops via a gradual transition. A model based on local field inhomogeneity is proposed to explain the observations

Quantum Dot in 2D Topological Insulator: The Two-channel Kondo Fixed Point

In this work, a quantum dot couples to two helical edge states of a 2D topological insulator through weak tunnelings is studied. We show that if the electron interactions on the edge states are repulsive, with Luttinger liquid parameter $K < 1$, the system flows to a stable two-channel fixed point at low temperatures. This is in contrast to the case of a quantum dot couples to two Luttinger liquid leads. In the latter case, a strong electron-electron repulsion is needed, with $K<1/2$, to reach the two-channel fixed point. This two-channel fixed point is described by a boundary Sine-Gordon Hamiltonian with a $K$ dependent boundary term. The impurity entropy at zero temperature is shown to be $\ln\sqrt{2K}$. The impurity specific heat is $C \propto T^{\frac{2}{K}-2}$ when $2/3 < K < 1$, and $C \propto T$ when $K<2/3$. We also show that the linear conductance across the two helical edges has non-trivial temperature dependence as a result of the renormalization group flow.Comment: 4+\epsilon page

Stability of Quantized Vortices in a Bose-Einstein Condensate Confined in an Optical Lattice

We investigate the existence and especially the linear stability of single and multiple-charge quantized vortex states of nonlinear Schroedinger equations in the presence of a periodic and a parabolic potential in two spatial dimensions. The study is motivated by the examination of pancake-shaped Bose-Einstein condensates in the presence of magnetic and optical confiement. A two-parameter space of the condensate's chemical potential versus the periodic potential's strength is scanned for both single- and double-quantized vortex states located at a local minimum or a local maximum of the lattice. Triply charged vortices are also briefly discussed. Single-charged vortices are found to be stable for cosinusoidal potentials and unstable for sinusoidal ones above a critical strength. Higher charge vortices are more unstable for both types of potentials and their dynamical evolution leads to breakup into single-charged vortices

Thinking beyond the hybrid:“actually-existing” cities “after neoliberalism” in Boyle <i>et al.</i>

In their article, ‘The spatialities of actually existing neoliberalism in Glasgow, 1977 to present’, Mark Boyle, Christopher McWilliams and Gareth Rice (2008) usefully problematise our current understanding of neoliberal urbanism. Our response is aimed at developing a sympathetic but critical approach to Boyle et al's understanding of neoliberal urbanism as illustrated by the Glasgow example. In particular, the counterposing by Boyle et al of a 'hybrid, mutant' model to a 'pure' model of neoliberalism for us misrepresents existing models of neoliberalism as a perfectly finished object rather than a roughly mottled process. That they do not identify any ‘pure’ model leads them to create a straw construct against which they can claim a more sophisticated, refined approach to the messiness of neoliberal urbanism. In contrast, we view neoliberalism as a contested and unstable response to accumulation crises at various scales of analysis

Quantum state transfer and entanglement distribution among distant nodes in a quantum network

We propose a scheme to utilize photons for ideal quantum transmission between atoms located at spatially-separated nodes of a quantum network. The transmission protocol employs special laser pulses which excite an atom inside an optical cavity at the sending node so that its state is mapped into a time-symmetric photon wavepacket that will enter a cavity at the receiving node and be absorbed by an atom there with unit probability. Implementation of our scheme would enable reliable transfer or sharing of entanglement among spatially distant atoms.Comment: 4 pages, 3 postscript figure

Galaxy Zoo Supernovae

This paper presents the first results from a new citizen science project: Galaxy Zoo Supernovae. This proof of concept project uses members of the public to identify supernova candidates from the latest generation of wide-field imaging transient surveys. We describe the Galaxy Zoo Supernovae operations and scoring model, and demonstrate the effectiveness of this novel method using imaging data and transients from the Palomar Transient Factory (PTF). We examine the results collected over the period April-July 2010, during which nearly 14,000 supernova candidates from PTF were classified by more than 2,500 individuals within a few hours of data collection. We compare the transients selected by the citizen scientists to those identified by experienced PTF scanners, and find the agreement to be remarkable - Galaxy Zoo Supernovae performs comparably to the PTF scanners, and identified as transients 93% of the ~130 spectroscopically confirmed SNe that PTF located during the trial period (with no false positive identifications). Further analysis shows that only a small fraction of the lowest signal-to-noise SN detections (r > 19.5) are given low scores: Galaxy Zoo Supernovae correctly identifies all SNe with > 8{\sigma} detections in the PTF imaging data. The Galaxy Zoo Supernovae project has direct applicability to future transient searches such as the Large Synoptic Survey Telescope, by both rapidly identifying candidate transient events, and via the training and improvement of existing machine classifier algorithms.Comment: 13 pages, 10 figures, accepted MNRA

On the reliability of polarization estimation using Rotation Measure Synthesis

We benchmark the reliability of the Rotation Measure (RM) synthesis algorithm using the 1005 Centaurus A field sources of Feain et al. (2009). The RM synthesis solutions are compared with estimates of the polarization parameters using traditional methods. This analysis provides verification of the reliability of RM synthesis estimates. We show that estimates of the polarization parameters can be made at lower S/N if the range of RMs is bounded, but reliable estimates of individual sources with unusual RMs require unconstrainted solutions and higher S/N. We derive from first principles the statistical properties of the polarization amplitude associated with RM synthesis in the presence of noise. The amplitude distribution depends explicitly on the amplitude of the underlying (intrinsic) polarization signal. Hence it is necessary to model the underlying polarization signal distribution in order to estimate the reliability and errors in polarization parameter estimates. We introduce a Bayesian method to derive the distribution of intrinsic amplitudes based on the distribution of measured amplitudes. The theoretically-derived distribution is compared with the empirical data to provide quantitative estimates of the probability that an RM synthesis solution is correct as a function of S/N. We provide quantitative estimates of the probability that any given RM synthesis solution is correct as a function of measured polarized amplitude and the intrinsic polarization amplitude compared to the noise.Comment: accepted for publication in the Astrophysical Journa