Finite random coverings of one-complexes and the Euler characteristic

This article presents an algebraic topology perspective on the problem of finding a complete coverage probability of a one dimensional domain $X$ by a random covering, and develops techniques applicable to the problem beyond the one dimensional case. In particular we obtain a general formula for the chance that a collection of finitely many compact connected random sets placed on $X$ has a union equal to $X$. The result is derived under certain topological assumptions on the shape of the covering sets (the covering ought to be {\em good}, which holds if the diameter of the covering elements does not exceed a certain size), but no a priori requirements on their distribution. An upper bound for the coverage probability is also obtained as a consequence of the concentration inequality. The techniques rely on a formulation of the coverage criteria in terms of the Euler characteristic of the nerve complex associated to the random covering.Comment: 25 pages,2 figures; final published versio

Overview and status of EXCLAIM, the experiment for cryogenic large-aperture intensity mapping

The EXperiment for Cryogenic Large-Aperture Intensity Mapping (EXCLAIM) is a balloon-borne far-infrared telescope that will survey star formation history over cosmological time scales to improve our understanding of why the star formation rate declined at redshift z < 2, despite continued clustering of dark matter. Specifically,EXCLAIM will map the emission of redshifted carbon monoxide and singly-ionized carbon lines in windows over a redshift range 0 < z < 3.5, following an innovative approach known as intensity mapping. Intensity mapping measures the statistics of brightness fluctuations of cumulative line emissions instead of detecting individual galaxies, thus enabling a blind, complete census of the emitting gas. To detect this emission unambiguously, EXCLAIM will cross-correlate with a spectroscopic galaxy catalog. The EXCLAIM mission uses a cryogenic design to cool the telescope optics to approximately 1.7 K. The telescope features a 90-cm primary mirror to probe spatial scales on the sky from the linear regime up to shot noise-dominated scales. The telescope optical elements couple to six {\mu}-Spec spectrometer modules, operating over a 420-540 GHz frequency band with a spectral resolution of 512 and featuring microwave kinetic inductance detectors. A Radio Frequency System-on-Chip (RFSoC) reads out the detectors in the baseline design. The cryogenic telescope and the sensitive detectors allow EXCLAIM to reach high sensitivity in spectral windows of low emission in the upper atmosphere. Here, an overview of the mission design and development status since the start of the EXCLAIM project in early 2019 is presented.Comment: SPIE Astronomical Telescopes + Instrumentation. arXiv admin note: substantial text overlap with arXiv:1912.0711

Astro2020 APC White Paper: The MegaMapper: a z &gt; 2 spectroscopic instrument for the study of Inflation and Dark Energy

MegaMapper is a proposed ground-based experiment to measure Inflation parameters and Dark Energy from galaxy redshifts at

The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Large-scale structure catalogues for cosmological analysis

We present large-scale structure catalogues from the completed extended Baryon Oscillation Spectroscopic Survey (eBOSS). Derived from Sloan Digital Sky Survey (SDSS) IV Data Release 16 (DR16), these catalogues provide the data samples, corrected for observational systematics, and random positions sampling the survey selection function. Combined, they allow large-scale clustering measurements suitable for testing cosmological models. We describe the methods used to create these catalogues for the eBOSS DR16 Luminous Red Galaxy (LRG) and Quasar samples. The quasar catalogue contains 343 708 redshifts with 0.8 1000 km s−1). For quasars, these rates are 95 and 2 per cent (with Δz > 3000 km s−1). We apply corrections for trends between the number densities of our samples and the properties of the imaging and spectroscopic data. For example, the quasar catalogue obtains a χ2/DoF = 776/10 for a null test against imaging depth before corrections and a χ2/DoF= 6/8 after. The catalogues, combined with careful consideration of the details of their construction found here-in, allow companion papers to present cosmological results with negligible impact from observational systematic uncertainties

Experiment for cryogenic large-aperture intensity mapping: instrument design

The experiment for cryogenic large-aperture intensity mapping (EXCLAIM) is a balloon-borne telescope designed to survey star formation in windows from the present to z  =  3.5. During this time, the rate of star formation dropped dramatically, while dark matter continued to cluster. EXCLAIM maps the redshifted emission of singly ionized carbon lines and carbon monoxide using intensity mapping, which permits a blind and complete survey of emitting gas through statistics of cumulative brightness fluctuations. EXCLAIM achieves high sensitivity using a cryogenic telescope coupled to six integrated spectrometers employing kinetic inductance detectors covering 420 to 540 GHz with spectral resolving power R  =  512 and angular resolution ≈4  arc min. The spectral resolving power and cryogenic telescope allow the survey to access dark windows in the spectrum of emission from the upper atmosphere. EXCLAIM will survey 305  deg2 in the Sloan Digital Sky Survey Stripe 82 field from a conventional balloon flight in 2023. EXCLAIM will also map several galactic fields to study carbon monoxide and neutral carbon emission as tracers of molecular gas. We summarize the design phase of the mission

Polymorphism in a T-cell receptor variable gene is associated with susceptibility to a juvenile rheumatoid arthritis subset

This report demonstrates a T-cell receptor (Tcr) restriction fragment length polymorphism, defined by a Tcrb-V6.1 gene probe and Bgl II restriction enzyme, to be absolutely correlated with allelic variation in the coding sequence of a Tcrb-V6.1 gene. A pair of non-conservative amino acid substitutions distinguish the Tcrb-V6.1 allelic variants. An association of this Tcrb-V6.1 gene allelic variant with one form of juvenile rheumatoid arthritis (JRA) was established in a cohort of 126 patients. The association was observed in patients possessing the HLA-DQA1*0101 gene. Among HLA-DQA*0101 individuals, 19 of 26 patients (73.1%) carried one particular Tcrb-V6.1 gene allele as opposed to 11 of 33 controls (33%; p<0.005). Haplotypes carrying this HLA gene have previously been shown to confer increased risk for progression of arthritis in JRA. This demonstration of a disease-associated Tcrb-V gene allelic variant has not, to our knowledge, been previously reported and supports the contribution of polymorphism in the Tcr variable region genomic repertoire to human autoimmune disease.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46750/1/251_2004_Article_BF00166831.pd