The parafermionic observable in SLE

The parafermionic observable has recently been used by number of authors to study discrete models, believed to be conformally invariant and to prove convergence results for these processes to SLE. We provide a definition for a one parameter family of continuum versions of the paraferminonic observable for SLE, which takes the form of a normalized limit of expressions identical to the discrete definition. We then show the limit defining the observable exists, compute the value of the observable up to a finite multiplicative constant, and prove this constant is non-zero for a wide range of kappa. Finally, we show our observable for SLE becomes a holomorphic function for a particular choice of the parameter, which helps illuminate a fundamental property of the discrete observable.Comment: 29 pages, 7 figure

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

Sistem Informasi Strategis Mendayagunakan Sistem Informasi untuk Mencapai Keunggulan Kompetitif

While most companies are content to develop and implement computer-based information systems to improve their operational and managerial effectiveness, a few also rely on innovative systems to give them an edge over the competition. An information system that is specifically designed with the aim to create a competitive advantage for its firm is called a strategic information system.To build a strategic information system, one should have a good understanding as to what factors contribute towards competitive advantage. It is here that the analyses by Michael E. Porter on this subject are particularly invaluable. Furthermore, one should also realize what the modern computer excels at fast processing time, fast data retrieval, fast communications, and reliability.There are also risks inherent to strategic information systems. These include the large capital outlay involved, as well as the reality that any competitive advantage thus achieved is not sustainable for long

Initial Hubble Diagram Results from the Nearby Supernova Factory

The use of Type Ia supernovae as distance indicators led to the discovery of the accelerating expansion of the universe a decade ago. Now that large second generation surveys have significantly increased the size and quality of the high-redshift sample, the cosmological constraints are limited by the currently available sample of ~50 cosmologically useful nearby supernovae. The Nearby Supernova Factory addresses this problem by discovering nearby supernovae and observing their spectrophotometric time development. Our data sample includes over 2400 spectra from spectral timeseries of 185 supernovae. This talk presents results from a portion of this sample including a Hubble diagram (relative distance vs. redshift) and a description of some analyses using this rich dataset.Comment: Short version of proceedings for ICHEP08, Philadelphia PA, July 2008; see v1 for full-length versio

Probing a regular orbit with spectral dynamics

We have extended the spectral dynamics formalism introduced by Binney & Spergel, and have implemented a semi-analytic method to represent regular orbits in any potential, making full use of their regularity. We use the spectral analysis code of Carpintero & Aguilar to determine the nature of an orbit (irregular, regular, resonant, periodic) from a short-time numerical integration. If the orbit is regular, we approximate it by a truncated Fourier time series of a few tens of terms per coordinate. Switching to a description in action-angle variables, this corresponds to a reconstruction of the underlying invariant torus. We then relate the uniform distribution of a regular orbit on its torus to the non-uniform distribution in the space of observables by a simple Jacobian transformation between the two sets of coordinates. This allows us to compute, in a cell-independent way, all the physical quantities needed in the study of the orbit, including the density and in the line-of-sight velocity distribution, with much increased accuracy. The resulting flexibility in the determination of the orbital properties, and the drastic reduction of storage space for the orbit library, provide a significant improvement in the practical application of Schwarzschild's orbit superposition method for constructing galaxy models. We test and apply our method to two-dimensional orbits in elongated discs, and to the meridional motion in axisymmetric potentials, and show that for a given accuracy, the spectral dynamics formalism requires an order of magnitude fewer computations than the more traditional approaches.Comment: 13 pages, 18 eps figures, submitted to MNRA

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

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

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