Test of Universality in the Ising Spin Glass Using High Temperature Graph Expansion

We calculate high-temperature graph expansions for the Ising spin glass model with 4 symmetric random distribution functions for its nearest neighbor interaction constants J_{ij}. Series for the Edwards-Anderson susceptibility \chi_EA are obtained to order 13 in the expansion variable (J/(k_B T))^2 for the general d-dimensional hyper-cubic lattice, where the parameter J determines the width of the distributions. We explain in detail how the expansions are calculated. The analysis, using the Dlog-Pad\'e approximation and the techniques known as M1 and M2, leads to estimates for the critical threshold (J/(k_B T_c))^2 and for the critical exponent \gamma in dimensions 4, 5, 7 and 8 for all the distribution functions. In each dimension the values for \gamma agree, within their uncertainty margins, with a common value for the different distributions, thus confirming universality.Comment: 13 figure

Tensor decomposition and homotopy continuation

A computationally challenging classical elimination theory problem is to compute polynomials which vanish on the set of tensors of a given rank. By moving away from computing polynomials via elimination theory to computing pseudowitness sets via numerical elimination theory, we develop computational methods for computing ranks and border ranks of tensors along with decompositions. More generally, we present our approach using joins of any collection of irreducible and nondegenerate projective varieties $X_1,\ldots,X_k\subset\mathbb{P}^N$ defined over $\mathbb{C}$. After computing ranks over $\mathbb{C}$, we also explore computing real ranks. Various examples are included to demonstrate this numerical algebraic geometric approach.Comment: We have added two examples: A Coppersmith-Winograd tensor, Matrix multiplication with zeros. (26 pages, 1 figure

Polarized Diffuse Emission at 2.3 GHz in a High Galactic Latitude Area

Polarized diffuse emission observations at 2.3 GHz in a high Galactic latitude area are presented. The 2\degr X 2\degr field, centred in (\alpha=5^h,\delta=-49\degr), is located in the region observed by the BOOMERanG experiment. Our observations has been carried out with the Parkes Radio telescope and represent the highest frequency detection done to date in low emission areas. Because of a weaker Faraday rotation action, the high frequency allows an estimate of the Galactic synchrotron contamination of the Cosmic Microwave Background Polarization (CMBP) that is more reliable than that done at 1.4 GHz. We find that the angular power spectra of the E- and B-modes have slopes of \beta_E = -1.46 +/- 0.14 and \beta_B = -1.87 +/- 0.22, indicating a flattening with respect to 1.4 GHz. Extrapolated up to 32 GHz, the E-mode spectrum is about 3 orders of magnitude lower than that of the CMBP, allowing a clean detection even at this frequency. The best improvement concerns the B-mode, for which our single-dish observations provide the first estimate of the contamination on angular scales close to the CMBP peak (about 2 degrees). We find that the CMBP B-mode should be stronger than synchrotron contamination at 90 GHz for models with T/S > 0.01. This low level could move down to 60-70 GHz the optimal window for CMBP measures.Comment: 5 pages, 6 figures, accepted for publication in MNRAS Letter

Program schemes with deep pushdown storage.

Inspired by recent work of Meduna on deep pushdown automata, we consider the computational power of a class of basic program schemes, TeX, based around assignments, while-loops and non- deterministic guessing but with access to a deep pushdown stack which, apart from having the usual push and pop instructions, also has deep-push instructions which allow elements to be pushed to stack locations deep within the stack. We syntactically define sub-classes of TeX by restricting the occurrences of pops, pushes and deep-pushes and capture the complexity classes NP and PSPACE. Furthermore, we show that all problems accepted by program schemes of TeX are in EXPTIME

Early-type galaxies in the SDSS. II. Correlations between observables

A magnitude limited sample of nearly 9000 early-type galaxies, in the redshift range 0.01 < z < 0.3, was selected from the Sloan Digital Sky Survey using morphological and spectral criteria. The sample was used to study how early-type galaxy observables, including luminosity L, effective radius R_o, surface brightness I_o, color, and velocity dispersion sigma, are correlated with one another. Measurement biases are understood with mock catalogs which reproduce all of the observed scaling relations and their dependences on fitting technique. At any given redshift, the intrinsic distribution of luminosities, sizes and velocity dispersions in our sample are all approximately Gaussian. A maximum likelihood analysis shows that sigma ~ L^{0.25\pm 0.012}, R_o ~ L^{0.63\pm 0.025}, and R_o ~ I^{-0.75\pm 0.02} in the r* band. In addition, the mass-to-light ratio within the effective radius scales as M_o/L ~ L^{0.14\pm 0.02} or M_o/L ~ M_o^{0.22\pm 0.05}, and galaxies with larger effective masses have smaller effective densities: Delta_o ~ M_o^{-0.52\pm 0.03}. These relations are approximately the same in the g*, i* and z* bands. Relative to the population at the median redshift in the sample, galaxies at lower and higher redshifts have evolved only little, with more evolution in the bluer bands. The luminosity function is consistent with weak passive luminosity evolution and a formation time of about 9 Gyrs ago.Comment: 29 pages, 11 figures. Accepted by AJ (scheduled for April 2003). This paper is part II of a revised version of astro-ph/011034

Critical exponents in Ising spin glasses

We determine accurate values of ordering temperatures and critical exponents for Ising Spin Glass transitions in dimension 4, using a combination of finite size scaling and non-equilibrium scaling techniques. We find that the exponents $\eta$ and $z$ vary with the form of the interaction distribution, indicating non-universality at Ising spin glass transitions. These results confirm conclusions drawn from numerical data for dimension 3.Comment: 6 pages, RevTeX (or Latex, etc), 10 figures, Submitted to PR

PC1643+4631A,B: The Lyman-Alpha Forest at the Edge of Coherence

This is the first measurement and detection of coherence in the intergalactic medium (IGM) at substantially high redshift (z~3.8) and on large physical scales (~2.5 h^-1 Mpc). We perform the measurement by presenting new observations from Keck LRIS of the high redshift quasar pair PC 1643+4631A, B and their Ly-alpha absorber coincidences. This experiment extends multiple sightline quasar absorber studies to higher redshift, higher opacity, larger transverse separation, and into a regime where coherence across the IGM becomes weak and difficult to detect. We fit 222 discrete Ly-alpha absorbers to sightline A and 211 to sightline B. Relative to a Monte Carlo pairing test (using symmetric, nearest neighbor matching) the data exhibit a 4sigma excess of pairs at low velocity splitting (<150 km/s), thus detecting coherence on transverse scales of ~2.5 h^-1 Mpc. We use spectra extracted from an SPH simulation to analyze symmetric pair matching, transmission distributions as a function of redshift and compute zero-lag cross-correlations to compare with the quasar pair data. The simulations agree with the data with the same strength (~4sigma) at similarly low velocity splitting above random chance pairings. In cross-correlation tests, the simulations agree when the mean flux (as a function of redshift) is assumed to follow the prescription given by Kirkman et al. (2005). While the detection of flux correlation (measured through coincident absorbers and cross-correlation amplitude) is only marginally significant, the agreement between data and simulations is encouraging for future work in which even better quality data will provide the best insight into the overarching structure of the IGM and its understanding as shown by SPH simulations.Comment: 15 pages, 11 figures; accepted for publication in Astronomical Journa