Some colouring problems for Paley graphs

The Paley graph Pq, where q≡1(mod4) is a prime power, is the graph with vertices the elements of the finite field Fq and an edge between x and y if and only if x-y is a non-zero square in Fq. This paper gives new results on some colouring problems for Paley graphs and related discussion. © 2005 Elsevier B.V. All rights reserved

Experimental open air quantum key distribution with a single photon source

We present a full implementation of a quantum key distribution (QKD) system with a single photon source, operating at night in open air. The single photon source at the heart of the functional and reliable setup relies on the pulsed excitation of a single nitrogen-vacancy color center in diamond nanocrystal. We tested the effect of attenuation on the polarized encoded photons for inferring longer distance performance of our system. For strong attenuation, the use of pure single photon states gives measurable advantage over systems relying on weak attenuated laser pulses. The results are in good agreement with theoretical models developed to assess QKD security

EBEX: A balloon-borne CMB polarization experiment

EBEX is a NASA-funded balloon-borne experiment designed to measure the polarization of the cosmic microwave background (CMB). Observations will be made using 1432 transition edge sensor (TES) bolometric detectors read out with frequency multiplexed SQuIDs. EBEX will observe in three frequency bands centered at 150, 250, and 410 GHz, with 768, 384, and 280 detectors in each band, respectively. This broad frequency coverage is designed to provide valuable information about polarized foreground signals from dust. The polarized sky signals will be modulated with an achromatic half wave plate (AHWP) rotating on a superconducting magnetic bearing (SMB) and analyzed with a fixed wire grid polarizer. EBEX will observe a patch covering ~1% of the sky with 8' resolution, allowing for observation of the angular power spectrum from \ell = 20 to 1000. This will allow EBEX to search for both the primordial B-mode signal predicted by inflation and the anticipated lensing B-mode signal. Calculations to predict EBEX constraints on r using expected noise levels show that, for a likelihood centered around zero and with negligible foregrounds, 99% of the area falls below r = 0.035. This value increases by a factor of 1.6 after a process of foreground subtraction. This estimate does not include systematic uncertainties. An engineering flight was launched in June, 2009, from Ft. Sumner, NM, and the long duration science flight in Antarctica is planned for 2011. These proceedings describe the EBEX instrument and the North American engineering flight.Comment: 12 pages, 9 figures, Conference proceedings for SPIE Millimeter, Submillimeter, and Far-Infrared Detectors and Instrumentation for Astronomy V (2010

The NANOGrav Nine-year Data Set: Excess Noise in Millisecond Pulsar Arrival Times

Gravitational wave (GW) astronomy using a pulsar timing array requires high-quality millisecond pulsars (MSPs), correctable interstellar propagation delays, and high-precision measurements of pulse times of arrival. Here we identify noise in timing residuals that exceeds that predicted for arrival time estimation for MSPs observed by the North American Nanohertz Observatory for Gravitational Waves. We characterize the excess noise using variance and structure function analyses. We find that 26 out of 37 pulsars show inconsistencies with a white-noise-only model based on the short timescale analysis of each pulsar, and we demonstrate that the excess noise has a red power spectrum for 15 pulsars. We also decompose the excess noise into chromatic (radio-frequency-dependent) and achromatic components. Associating the achromatic red-noise component with spin noise and including additional power-spectrum-based estimates from the literature, we estimate a scaling law in terms of spin parameters (frequency and frequency derivative) and data-span length and compare it to the scaling law of Shannon & Cordes. We briefly discuss our results in terms of detection of GWs at nanohertz frequencies

Progressive transmission of pseudo-color images. Appendix 1: Item 4

The transmission of digital images can require considerable channel bandwidth. The cost of obtaining such a channel can be prohibitive, or the channel might simply not be available. In this case, progressive transmission (PT) can be useful. PT presents the user with a coarse initial image approximation, and then proceeds to refine it. In this way, the user tends to receive information about the content of the image sooner than if a sequential transmission method is used. PT finds application in image data base browsing, teleconferencing, medical and other applications. A PT scheme is developed for use with a particular type of image data, the pseudo-color or color mapped image. Such images consist of a table of colors called a colormap, plus a 2-D array of index values which indicate which colormap entry is to be used to display a given pixel. This type of image presents some unique problems for a PT coder, and techniques for overcoming these problems are developed. A computer simulation of the color mapped PT scheme is developed to evaluate its performance. Results of simulation using several test images are presented

On b-colorings and b-continuity of graphs

A b-coloring of G is a proper vertex coloring such that there is a vertex in each color class, which is adjacent to at least one vertex in every other color class. Such a vertex is called a color-dominating vertex. The b-chromatic number of G is the largest k such that there is a b-coloring of G by k colors. Moreover, if for every integer k, between chromatic number and b-chromatic number, there exists a b-coloring of G by k colors, then G is b-continuous. Determining the b-chromatic number of a graph G and the decision whether the given graph G is b-continuous or not is NP-hard. Therefore, it is interesting to find new results on b-colorings and b-continuity for special graphs. In this thesis, for several graph classes some exact values as well as bounds of the b-chromatic number were ascertained. Among all we considered graphs whose independence number, clique number, or minimum degree is close to its order as well as bipartite graphs. The investigation of bipartite graphs was based on considering of the so-called bicomplement which is used to determine the b-chromatic number of special bipartite graphs, in particular those whose bicomplement has a simple structure. Then we studied some graphs whose b-chromatic number is close to its t-degree. At last, the b-continuity of some graphs is studied, for example, for graphs whose b-chromatic number was already established in this thesis. In particular, we could prove that Halin graphs are b-continuous.:Contents 1 Introduction 2 Preliminaries 2.1 Basic terminology 2.2 Colorings of graphs 2.2.1 Vertex colorings 2.2.2 a-colorings 3 b-colorings 3.1 General bounds on the b-chromatic number 3.2 Exact values of the b-chromatic number for special graphs 3.2.1 Graphs with maximum degree at most 2 3.2.2 Graphs with independence number close to its order 3.2.3 Graphs with minimum degree close to its order 3.2.4 Graphs G with independence number plus clique number at most number of vertices 3.2.5 Further known results for special graphs 3.3 Bipartite graphs 3.3.1 General bounds on the b-chromatic number for bipartite graphs 3.3.2 The bicomplement 3.3.3 Bicomplements with simple structure 3.4 Graphs with b-chromatic number close to its t-degree 3.4.1 Regular graphs 3.4.2 Trees and Cacti 3.4.3 Halin graphs 4 b-continuity 4.1 b-spectrum of special graphs 4.2 b-continuous graph classes 4.2.1 Known b-continuous graph classes 4.2.2 Halin graphs 4.3 Further graph properties concerning b-colorings 4.3.1 b-monotonicity 4.3.2 b-perfectness 5 Conclusion Bibliograph

The Near Infrared and Multiwavelength Afterglow of GRB 000301c

We present near-infrared observations of the counterpart of GRB 000301c. The K' filter (2.1 micron) light curve shows a well-sampled break in the decay slope at t=3.5 days post-burst. The early time slope is very shallow (~ -0.1), while the late time slope is steep (-2.2). Comparison with the optical (R band) light curve shows marginally significant differences, especially in the early time decay slope (which is steeper in the optical) and the break time (which occurs later in the optical). This is contrary to the general expectation that light curve breaks should either be achromatic (e.g., for breaks due to collimation effects) or should occur later at longer wavelengths (for most other breaks). The observed color variations might be intrinsic to the afterglow, or might indicate systematic errors of > 0.08 magnitude in all fluxes. Even if the break is achromatic, we argue that its sharpness poses difficulties for explanations that depend on collimated ejecta. The R light curve shows further signs of fairly rapid variability (a bump, steep drop, and plateau) that are not apparent in the K' light curve. In addition, by combining the IR-optical-UV data with millimeter and radio fluxes, we are able to constrain the locations of the self-absorption break and cooling break and to infer the location of the spectral peak at t=3 days: f_nu = 3.4 mJy at nu=1e12 Hz. Using the multiwavelength spectral energy distribution, we are able to constrain the blast wave energy, which was E > 3e53 erg if the explosion was isotropic. This implies a maximum gamma ray production efficiency of ~ 0.15 for GRB 000301C.Comment: Accepted to The Astrophysical Journal. 24 pages, 4 figures, 3 tables; uses AASTeX 5 macros. This version includes a new figure (R-K' color vs. time), a better sampled R band light curve, and more extensive discussion of the optical data and error analysi

An extensive English language bibliography on graph theory and its applications, supplement 1

Graph theory and its applications - bibliography, supplement

T\mathbb{T}-Operator Limits on Optical Communication: Metaoptics, Computation, and Input-Output Transformations

We present an optimization framework based on Lagrange duality and the scattering $\mathbb{T}$ operator of electromagnetism to construct limits on the possible features that may be imparted to a collection of output fields from a collection of input fields, i.e., constraints on achievable optical transformations and the characteristics of structured materials as communication channels. Implications of these bounds on the performance of representative optical devices having multi-wavelength or multiport functionalities are examined in the context of electromagnetic shielding, focusing, near-field resolution, and linear computing