Approximation Algorithm for Line Segment Coverage for Wireless Sensor Network

The coverage problem in wireless sensor networks deals with the problem of covering a region or parts of it with sensors. In this paper, we address the problem of covering a set of line segments in sensor networks. A line segment ` is said to be covered if it intersects the sensing regions of at least one sensor distributed in that region. We show that the problem of finding the minimum number of sensors needed to cover each member in a given set of line segments in a rectangular area is NP-hard. Next, we propose a constant factor approximation algorithm for the problem of covering a set of axis-parallel line segments. We also show that a PTAS exists for this problem.Comment: 16 pages, 5 figures

Design and construction of a carbon fiber gondola for the SPIDER balloon-borne telescope

We introduce the light-weight carbon fiber and aluminum gondola designed for the SPIDER balloon-borne telescope. SPIDER is designed to measure the polarization of the Cosmic Microwave Background radiation with unprecedented sensitivity and control of systematics in search of the imprint of inflation: a period of exponential expansion in the early Universe. The requirements of this balloon-borne instrument put tight constrains on the mass budget of the payload. The SPIDER gondola is designed to house the experiment and guarantee its operational and structural integrity during its balloon-borne flight, while using less than 10% of the total mass of the payload. We present a construction method for the gondola based on carbon fiber reinforced polymer tubes with aluminum inserts and aluminum multi-tube joints. We describe the validation of the model through Finite Element Analysis and mechanical tests.Comment: 16 pages, 11 figures. Presented at SPIE Ground-based and Airborne Telescopes V, June 23, 2014. To be published in Proceedings of SPIE Volume 914

BICEP2 / Keck Array V: Measurements of B-mode Polarization at Degree Angular Scales and 150 GHz by the Keck Array

The Keck Array is a system of cosmic microwave background (CMB) polarimeters, each similar to the BICEP2 experiment. In this paper we report results from the 2012 and 2013 observing seasons, during which the Keck Array consisted of five receivers all operating in the same (150 GHz) frequency band and observing field as BICEP2. We again find an excess of B-mode power over the lensed-$\Lambda$CDM expectation of $> 5 \sigma$ in the range $30 < \ell < 150$ and confirm that this is not due to systematics using jackknife tests and simulations based on detailed calibration measurements. In map difference and spectral difference tests these new data are shown to be consistent with BICEP2. Finally, we combine the maps from the two experiments to produce final Q and U maps which have a depth of 57 nK deg (3.4 $\mu$K arcmin) over an effective area of 400 deg$^2$ for an equivalent survey weight of 250,000 $\mu$K$^{-2}$. The final BB band powers have noise uncertainty a factor of 2.3 times better than the previous results, and a significance of detection of excess power of $> 6\sigma$.Comment: 13 pages, 9 figure

The Thermal Design, Characterization, and Performance of the SPIDER Long-Duration Balloon Cryostat

We describe the SPIDER flight cryostat, which is designed to cool six millimeter-wavelength telescopes during an Antarctic long-duration balloon flight. The cryostat, one of the largest to have flown on a stratospheric payload, uses liquid helium-4 to deliver cooling power to stages at 4.2 and 1.6 K. Stainless steel capillaries facilitate a high flow impedance connection between the main liquid helium tank and a smaller superfluid tank, allowing the latter to operate at 1.6 K as long as there is liquid in the 4.2 K main tank. Each telescope houses a closed cycle helium-3 adsorption refrigerator that further cools the focal planes down to 300 mK. Liquid helium vapor from the main tank is routed through heat exchangers that cool radiation shields, providing negative thermal feedback. The system performed successfully during a 17 day flight in the 2014-2015 Antarctic summer. The cryostat had a total hold time of 16.8 days, with 15.9 days occurring during flight.Comment: 15 pgs, 17 fig

BICEP2 / Keck Array VIII: Measurement of gravitational lensing from large-scale B-mode polarization

We present measurements of polarization lensing using the 150 GHz maps which include all data taken by the BICEP2 & Keck Array CMB polarization experiments up to and including the 2014 observing season (BK14). Despite their modest angular resolution ($\sim 0.5^\circ$), the excellent sensitivity ($\sim 3\mu$K-arcmin) of these maps makes it possible to directly reconstruct the lensing potential using only information at larger angular scales ($\ell\leq 700$). From the auto-spectrum of the reconstructed potential we measure an amplitude of the spectrum to be $A^{\phi\phi}_{\rm L}=1.15\pm 0.36$ (Planck $\Lambda$CDM prediction corresponds to $A^{\phi\phi}_{\rm L}=1$), and reject the no-lensing hypothesis at 5.8$\sigma$, which is the highest significance achieved to date using an EB lensing estimator. Taking the cross-spectrum of the reconstructed potential with the Planck 2015 lensing map yields $A^{\phi\phi}_{\rm L}=1.13\pm 0.20$. These direct measurements of $A^{\phi\phi}_{\rm L}$ are consistent with the $\Lambda$CDM cosmology, and with that derived from the previously reported BK14 B-mode auto-spectrum ($A^{\rm BB}_{\rm L}=1.20\pm 0.17$). We perform a series of null tests and consistency checks to show that these results are robust against systematics and are insensitive to analysis choices. These results unambiguously demonstrate that the B-modes previously reported by BICEP / Keck at intermediate angular scales ($150\lesssim\ell\lesssim 350$) are dominated by gravitational lensing. The good agreement between the lensing amplitudes obtained from the lensing reconstruction and B-mode spectrum starts to place constraints on any alternative cosmological sources of B-modes at these angular scales.Comment: 12 pages, 8 figure

Antenna-coupled TES bolometers used in BICEP2, Keck array, and SPIDER

We have developed antenna-coupled transition-edge sensor (TES) bolometers for a wide range of cosmic microwave background (CMB) polarimetry experiments, including BICEP2, Keck Array, and the balloon borne SPIDER. These detectors have reached maturity and this paper reports on their design principles, overall performance, and key challenges associated with design and production. Our detector arrays repeatedly produce spectral bands with 20%-30% bandwidth at 95, 150, or 220~GHz. The integrated antenna arrays synthesize symmetric co-aligned beams with controlled side-lobe levels. Cross-polarized response on boresight is typically ~0.5%, consistent with cross-talk in our multiplexed readout system. End-to-end optical efficiencies in our cameras are routinely 35% or higher, with per detector sensitivities of NET~300 uKrts. Thanks to the scalability of this design, we have deployed 2560 detectors as 1280 matched pairs in Keck Array with a combined instantaneous sensitivity of ~9 uKrts, as measured directly from CMB maps in the 2013 season. Similar arrays have recently flown in the SPIDER instrument, and development of this technology is ongoing.Comment: 16 pgs, 20 fig