The Measure of a Measurement

While finite non-commutative operator systems lie at the foundation of quantum measurement, they are also tools for understanding geometric iterations as used in the theory of iterated function systems (IFSs) and in wavelet analysis. Key is a certain splitting of the total Hilbert space and its recursive iterations to further iterated subdivisions. This paper explores some implications for associated probability measures (in the classical sense of measure theory), specifically their fractal components. We identify a fractal scale $s$ in a family of Borel probability measures $\mu$ on the unit interval which arises independently in quantum information theory and in wavelet analysis. The scales $s$ we find satisfy $s\in \mathbb{R}_{+}$ and $s\not =1$, some $s 1$. We identify these scales $s$ by considering the asymptotic properties of $\mu(J) /| J| ^{s}$ where $J$ are dyadic subintervals, and $| J| \to0$.Comment: 18 pages, 3 figures, and reference

External Shear in Quadruply Imaged Lens Systems

We use publicly available N-body simulations and semi-analytic models of galaxy formation to estimate the levels of external shear due to structure near the lens in gravitational lens systems. We also describe two selection effects, specific to four-image systems, that enhance the probability of observing systems to have higher external shear. Ignoring additional contributions from "cosmic shear" and assuming that lens galaxies are not significantly flattened, we find that the mean shear at the position of a quadruple lens galaxy is 0.11, the rms shear is roughly 0.15, and there is roughly a 45% likelihood of external shear greater than 0.1. This is much larger than previous estimates and in good agreement with typical measured external shear. The higher shear primarily stems from the tendency of early-type galaxies, which are the majority of lenses, to reside in overdense regions.Comment: 5 pages, 2 figures, ApJ in press, minor revision

High transport currents in mechanically reinforced MgB2 wires

We prepared and characterized monofilamentary MgB2 wires with a mechanically reinforced composite sheath of Ta(Nb)/Cu/steel, which leads to dense filaments and correspondingly high transport currents up to Jc = 10^5 A/cm^2 at 4.2 K, self field. The reproducibility of the measured transport currents was excellent and not depending on the wire diameter. Using different precursors, commercial reacted powder or an unreacted Mg/B powder mixture, a strong influence on the pinning behaviour and the irreversibility field was observed. The critical transport current density showed a nearly linear temperature dependency for all wires being still 52 kA/cm^2 at 20 K and 23 kA/cm^2 at 30 K. Detailed data for Jc(B,T) and Tc(B) were measured.Comment: 21 pages, 13 figures, revised version, to be published in Supercond. Sci. Techno

Infrared Surface Brightness Fluctuations of the Coma Elliptical NGC 4874 and the Value of the Hubble Constant

We have used the Keck I Telescope to measure K-band surface brightness fluctuations (SBFs) of NGC 4874, the dominant elliptical galaxy in the Coma cluster. We use deep HST WFPC2 optical imaging to account for the contamination due to faint globular clusters and improved analysis techniques to derive measurements of the SBF apparent magnitude. Using a new SBF calibration which accounts for the dependence of K-band SBFs on the integrated color of the stellar population, we measure a distance modulus of 34.99+/-0.21 mag (100+/-10 Mpc) for the Coma cluster. The resulting value of the Hubble constant is 71+/-8 km/s/Mpc, not including any systematic error in the HST Cepheid distance scale.Comment: ApJ Letters, in press. Uses emulateapj5.st

Construction of Parseval wavelets from redundant filter systems

We consider wavelets in L^2(R^d) which have generalized multiresolutions. This means that the initial resolution subspace V_0 in L^2(R^d) is not singly generated. As a result, the representation of the integer lattice Z^d restricted to V_0 has a nontrivial multiplicity function. We show how the corresponding analysis and synthesis for these wavelets can be understood in terms of unitary-matrix-valued functions on a torus acting on a certain vector bundle. Specifically, we show how the wavelet functions on R^d can be constructed directly from the generalized wavelet filters.Comment: 34 pages, AMS-LaTeX ("amsproc" document class) v2 changes minor typos in Sections 1 and 4, v3 adds a number of references on GMRA theory and wavelet multiplicity analysis; v4 adds material on pages 2, 3, 5 and 10, and two more reference

Mass-to-Light Ratios of Field Early-Type Galaxies at z~1 from Ultra-Deep Spectroscopy: Evidence for Mass-dependent Evolution

We present an analysis of the Fundamental Plane for a sample of 27 field early-type galaxies in the redshift range 0.6<z<1.15. The galaxies in this sample have high S/N spectra obtained at the VLT and high resolution imaging from the ACS. We find that the mean evolution in M/L of our sample is $Delta ln (M/L_B) = -1.74+/-0.16z$, with a large galaxy-to-galaxy scatter. This value can be too low by 0.3 due to selection effects, resulting in $Delta ln (M/L_B) = -1.43+/-0.16z$. The strong correlation between M/L and rest-frame color indicates that the observed scatter is not due to measurement errors, but due to intrinsic differences between the stellar populations of the galaxies. This pace of evolution is much faster than the evolution of cluster galaxies. However, we find that the measured M/L evolution strongly depends on galaxy mass. For galaxies with masses $M>2 x 10^11 Msol$, we find no significant difference between the evolution of field and cluster galaxies: $Delta ln (M/L_B) = -1.20+/-0.18z for field galaxies and$Delta ln (M/L_B) = -1.12+/-0.06z$ for cluster galaxies. The relation between the measured M/L evolution and mass is partially due to selection effects. However, even when taking selection effects into account, we still find a relation between M/L evolution and mass, which is most likely caused by a lower mean age and a larger intrinsic scatter for low mass galaxies. Results from lensing early-type galaxies, which are mass-selected, show a very similar trend with mass. This, combined with our findings, provides evidence for down-sizing. Previous studies of the rate of evolution of field early-type galaxies found a large range of mutually exclusive values. We show that these differences are largely caused by the differences between fitting methods. (Abridged)Comment: figures 3 and 4 available at http://www.strw.leidenuniv.nl/~vdwel/private/FPpaper

Harmonic analysis of iterated function systems with overlap

In this paper we extend previous work on IFSs without overlap. Our method involves systems of operators generalizing the more familiar Cuntz relations from operator algebra theory, and from subband filter operators in signal processing.Comment: 37 page

Continuous Spectrum of Automorphism Groups and the Infraparticle Problem

This paper presents a general framework for a refined spectral analysis of a group of isometries acting on a Banach space, which extends the spectral theory of Arveson. The concept of continuous Arveson spectrum is introduced and the corresponding spectral subspace is defined. The absolutely continuous and singular-continuous parts of this spectrum are specified. Conditions are given, in terms of the transposed action of the group of isometries, which guarantee that the pure-point and continuous subspaces span the entire Banach space. In the case of a unitarily implemented group of automorphisms, acting on a $C^*$-algebra, relations between the continuous spectrum of the automorphisms and the spectrum of the implementing group of unitaries are found. The group of spacetime translation automorphisms in quantum field theory is analyzed in detail. In particular, it is shown that the structure of its continuous spectrum is relevant to the problem of existence of (infra-)particles in a given theory.Comment: 31 pages, LaTeX. As appeared in Communications in Mathematical Physic