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

High-throughput processes and structural characterization of single-nanotube based devices for 3D electronics

We have developed manufacturable approaches to form single, vertically aligned carbon nanotubes, where the tubes are centered precisely, and placed within a few hundred nm of 1-1.5 μm deep trenches. These wafer-scale approaches were enabled by chemically amplified resists and inductively coupled Cryo-etchers to form the 3D nanoscale architectures. The tube growth was performed using dc plasmaenhanced chemical vapor deposition (PECVD), and the materials used for the pre-fabricated 3D architectures were chemically and structurally compatible with the high temperature (700 °C) PECVD synthesis of our tubes, in an ammonia and acetylene ambient. The TEM analysis of our tubes revealed graphitic basal planes inclined to the central or fiber axis, with cone angles up to 30° for the particular growth conditions used. In addition, bending tests performed using a custom nanoindentor, suggest that the tubes are well adhered to the Si substrate. Tube characteristics were also engineered to some extent, by adjusting growth parameters, such as Ni catalyst thickness, pressure and plasma power during growth

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

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

Carbon-based nano-electro-mechanical systems

We provide an overview of our work where carbon-based nanostructures have been applied to twodimensional (2D) planar and three-dimensional (3D) vertically-oriented nano-electro-mechanical (NEM) switches. In the first configuration, laterally oriented single-walled nanotubes (SWNTs) synthesized using thermal chemical vapor deposition (CVD) were implemented for forming bridge-type 2D NEMS switches, where switching voltages were on the order of a few volts. In the second configuration, vertically oriented carbon nanofibers (CNFs) synthesized using plasma-enhanced (PE) CVD have been explored for their potential application in 3D NEMS. We have performed nanomechanical measurements on such vertically oriented tubes using nanoindentation to determine the mechanical properties of the CNFs. Electrostatic switching was demonstrated in the CNFs synthesized on refractory metallic nitride substrates, where a nanoprobe was used as the actuating electrode inside a scanning-electron-microscope. The switching voltages were determined to be in the tens of volts range and van der Waals interactions at these length scales appeared significant, suggesting such structures are promising for nonvolatile memory applications. A finite element model was also developed to determine a theoretical pull-in voltage which was compared to experimental results