Integrability as a consequence of discrete holomorphicity: the Z_N model

It has recently been established that imposing the condition of discrete holomorphicity on a lattice parafermionic observable leads to the critical Boltzmann weights in a number of lattice models. Remarkably, the solutions of these linear equations also solve the Yang-Baxter equations. We extend this analysis for the Z_N model by explicitly considering the condition of discrete holomorphicity on two and three adjacent rhombi. For two rhombi this leads to a quadratic equation in the Boltzmann weights and for three rhombi a cubic equation. The two-rhombus equation implies the inversion relations. The star-triangle relation follows from the three-rhombus equation. We also show that these weights are self-dual as a consequence of discrete holomorphicity.Comment: 11 pages, 7 figures, some clarifications and a reference adde

A numerical adaptation of SAW identities from the honeycomb to other 2D lattices

Recently, Duminil-Copin and Smirnov proved a long-standing conjecture by Nienhuis that the connective constant of self-avoiding walks on the honeycomb lattice is $\sqrt{2+\sqrt{2}}.$ A key identity used in that proof depends on the existence of a parafermionic observable for self-avoiding walks on the honeycomb lattice. Despite the absence of a corresponding observable for SAW on the square and triangular lattices, we show that in the limit of large lattices, some of the consequences observed on the honeycomb lattice persist on other lattices. This permits the accurate estimation, though not an exact evaluation, of certain critical amplitudes, as well as critical points, for these lattices. For the honeycomb lattice an exact amplitude for loops is proved.Comment: 21 pages, 7 figures. Changes in v2: Improved numerical analysis, giving greater precision. Explanation of why we observe what we do. Extra reference

Self-avoiding walks and connective constants

The connective constant $\mu(G)$ of a quasi-transitive graph $G$ is the asymptotic growth rate of the number of self-avoiding walks (SAWs) on $G$ from a given starting vertex. We survey several aspects of the relationship between the connective constant and the underlying graph $G$. $\bullet$ We present upper and lower bounds for $\mu$ in terms of the vertex-degree and girth of a transitive graph. $\bullet$ We discuss the question of whether $\mu\ge\phi$ for transitive cubic graphs (where $\phi$ denotes the golden mean), and we introduce the Fisher transformation for SAWs (that is, the replacement of vertices by triangles). $\bullet$ We present strict inequalities for the connective constants $\mu(G)$ of transitive graphs $G$, as $G$ varies. $\bullet$ As a consequence of the last, the connective constant of a Cayley graph of a finitely generated group decreases strictly when a new relator is added, and increases strictly when a non-trivial group element is declared to be a further generator. $\bullet$ We describe so-called graph height functions within an account of "bridges" for quasi-transitive graphs, and indicate that the bridge constant equals the connective constant when the graph has a unimodular graph height function. $\bullet$ A partial answer is given to the question of the locality of connective constants, based around the existence of unimodular graph height functions. $\bullet$ Examples are presented of Cayley graphs of finitely presented groups that possess graph height functions (that are, in addition, harmonic and unimodular), and that do not. $\bullet$ The review closes with a brief account of the "speed" of SAW.Comment: Accepted version. arXiv admin note: substantial text overlap with arXiv:1304.721

Galactic Globular Cluster Metallicity Scale from the Ca II Triplet. I. Catalog

We have obtained 2640 CCD spectra with resolution ~4 Angstrom in the region 7250-9000 Angstroms for 976 stars lying near the red giant branches in color-magnitude diagrams of 52 Galactic globular clusters. Radial velocities of ~16 km/second accuracy per star determined from the spectra are combined with other criteria to assess quantitative membership probabilities. Measurements of the equivalent widths of the infrared calcium triplet lines yield a relative metal-abundance ranking with a precision that compares favorably to other techniques. Regressions between our system and those of others are derived. Our reduction procedures are discussed in detail, and the resultant catalog of derived velocities and equivalent widths is presented. The metal abundances derived from these data will be the subject of a future paper.Comment: To appear in August 1997 PASP. Also available at http://www.hia.nrc.ca/eprints.htm

The Nearby Supernova Factory

The Nearby Supernova Factory (SNfactory) is an ambitious project to find and study in detail approximately 300 nearby Type Ia supernovae (SNe~Ia) at redshifts 0.03<z<0.08. This program will provide an exceptional data set of well-studied SNe in the nearby smooth Hubble flow that can be used as calibration for the current and future programs designed to use SNe to measure the cosmological parameters. The first key ingredient for this program is a reliable supply of Hubble-flow SNe systematically discovered in unprecedented numbers using the same techniques as those used in distant SNe searches. In 2002, 35 SNe were found using our test-bed pipeline for automated SN search and discovery. The pipeline uses images from the asteroid search conducted by the Near Earth Asteroid Tracking group at JPL. Improvements in our subtraction techniques and analysis have allowed us to increase our effective SN discovery rate to ~12 SNe/month in 2003.Comment: 7 pages, 3 figures to be published in New Astronomy Review

Algebraic properties of CFT coset construction and Schramm-Loewner evolution

Schramm-Loewner evolution appears as the scaling limit of interfaces in lattice models at critical point. Critical behavior of these models can be described by minimal models of conformal field theory. Certain CFT correlation functions are martingales with respect to SLE. We generalize Schramm-Loewner evolution with additional Brownian motion on Lie group $G$ to the case of factor space $G/A$. We then study connection between SLE description of critical behavior with coset models of conformal field theory. In order to be consistent such construction should give minimal models for certain choice of groups.Comment: 10 pages, 2 figures, talk given at the conference "Quantum Theory and Symmetries (QTS-7)

Historic Light Curve and Long-term Optical Variation of BL Lacertae 2200+420

In this paper, historical optical(UBVRI) data and newly observed data from the Yunnan Observatory of China(about100 years) are presented for BL Lacertae. Maximum variations in UBVRI: 5.12, 5.31, 4.73, 2.59, and 2.54 and color indices of U-B = -0.11 +/- 0.20, B-V= 1.0 +/- 0.11, V-R= 0.73 +/- 0.19, V-I= 1.42 +/- 0.25, R-I= 0.82 +/- 0.11, and B-I= 2.44 +/- 0.29 have been obtained from the literature; The Jurkevich method is used to investigate the existence of periods in the B band light curve, and a long-term period of 14 years is found. The 0.6 and 0.88 year periods reported by Webb et al.(1988) are confirmed. In addition, a close relation between B-I and B is found, suggesting that the spectra flattens when the source brightens.Comment: 21 pages, 6 figures, 2 table, aasms4.sty, to be published in ApJ, Vol. 507, 199

Reducing Zero-point Systematics in Dark Energy Supernova Experiments

We study the effect of filter zero-point uncertainties on future supernova dark energy missions. Fitting for calibration parameters using simultaneous analysis of all Type Ia supernova standard candles achieves a significant improvement over more traditional fit methods. This conclusion is robust under diverse experimental configurations (number of observed supernovae, maximum survey redshift, inclusion of additional systematics). This approach to supernova fitting considerably eases otherwise stringent mission calibration requirements. As an example we simulate a space-based mission based on the proposed JDEM satellite; however the method and conclusions are general and valid for any future supernova dark energy mission, ground or space-based.Comment: 30 pages,8 figures, 5 table, one reference added, submitted to Astroparticle Physic

Automated reliability assessment for spectroscopic redshift measurements

We present a new approach to automate the spectroscopic redshift reliability assessment based on machine learning (ML) and characteristics of the redshift probability density function (PDF). We propose to rephrase the spectroscopic redshift estimation into a Bayesian framework, in order to incorporate all sources of information and uncertainties related to the redshift estimation process, and produce a redshift posterior PDF that will be the starting-point for ML algorithms to provide an automated assessment of a redshift reliability. As a use case, public data from the VIMOS VLT Deep Survey is exploited to present and test this new methodology. We first tried to reproduce the existing reliability flags using supervised classification to describe different types of redshift PDFs, but due to the subjective definition of these flags, soon opted for a new homogeneous partitioning of the data into distinct clusters via unsupervised classification. After assessing the accuracy of the new clusters via resubstitution and test predictions, unlabelled data from preliminary mock simulations for the Euclid space mission are projected into this mapping to predict their redshift reliability labels.Comment: Submitted on 02 June 2017 (v1). Revised on 08 September 2017 (v2). Latest version 28 September 2017 (this version v3