A topological realization of the congruence subgroup Kernel A

A number of years ago, Kumar Murty pointed out to me that the computation of the fundamental group of a Hilbert modular surface ([7],IV,${\S}$6), and the computation of the congruence subgroup kernel of SL(2) ([6]) were surprisingly similar. We puzzled over this, in particular over the role of elementary matrices in both computations. We formulated a very general result on the fundamental group of a Satake compactification of a locally symmetric space. This lead to our joint paper [1] with Lizhen Ji and Les Saper on these fundamental groups. Although the results in it were intriguingly similar to the corresponding calculations of the congruence subgroup kernel of the underlying algebraic group in [5], we were not able to demonstrate a direct connection (cf. [1], ${\S}$7). The purpose of this note is to explain such a connection. A covering space is constructed from inverse limits of reductive Borel-Serre compactifications. The congruence subgroup kernel then appears as the group of deck transformations of this covering. The key to this is the computation of the fundamental group in [1]

Continuous monitoring can improve indistinguishability of a single-photon source

A new engineering technique using continuous quantum measurement in conjunction with feed-forward is proposed to improve indistinguishability of a single-photon source. The technique involves continuous monitoring of the state of the emitter, processing the noisy output signal with a simple linear estimation algorithm, and feed forward to control a variable delay at the output. In the weak coupling regime, the information gained by monitoring the state of the emitter is used to reduce the time uncertainty inherent in photon emission from the source, which improves the indistinguishability of the emitted photons.Comment: 4 pages, 4 figure

SARAS: a precision system for measurement of the Cosmic Radio Background and signatures from the Epoch of Reionization

SARAS is a correlation spectrometer purpose designed for precision measurements of the cosmic radio background and faint features in the sky spectrum at long wavelengths that arise from redshifted 21-cm from gas in the reionization epoch. SARAS operates in the octave band 87.5-175 MHz. We present herein the system design arguing for a complex correlation spectrometer concept. The SARAS design concept provides a differential measurement between the antenna temperature and that of an internal reference termination, with measurements in switched system states allowing for cancellation of additive contaminants from a large part of the signal flow path including the digital spectrometer. A switched noise injection scheme provides absolute spectral calibration. Additionally, we argue for an electrically small frequency-independent antenna over an absorber ground. Various critical design features that aid in avoidance of systematics and in providing calibration products for the parametrization of other unavoidable systematics are described and the rationale discussed. The signal flow and processing is analyzed and the response to noise temperatures of the antenna, reference termination and amplifiers is computed. Multi-path propagation arising from internal reflections are considered in the analysis, which includes a harmonic series of internal reflections. We opine that the SARAS design concept is advantageous for precision measurement of the absolute cosmic radio background spectrum; therefore, the design features and analysis methods presented here are expected to serve as a basis for implementations tailored to measurements of a multiplicity of features in the background sky at long wavelengths, which may arise from events in the dark ages and subsequent reionization era.Comment: 49 pages, 17 figure

Phase behavior of two-component lipid membranes: theory and experiments

The structure of the ripple phase of phospholipid membranes remains poorly understood in spite of a large number of theoretical studies, with many experimentally established structural features of this phase unaccounted for. In this article we present a phenomenological theory of phase transitions in single- and two-component achiral lipid membranes in terms of two coupled order parameters -- a scalar order parameter describing {\it lipid chain melting}, and a vector order parameter describing the {\it tilt of the hydrocarbon chains} below the chain-melting transition. This model reproduces all the salient structural features of the ripple phase, providing a unified description of the phase diagram and microstructure. In addition, it predicts a variant of this phase which does not seem to have been experimentally observed. Using this model we have calculated generic phase diagrams of two-component membranes. We have also determined the phase diagram of a two-component lipid membrane from x-ray diffraction studies on aligned multilayers. This phase diagram is found to be in good agreement with that calculated from the model.Comment: 10 pages, 10 figure

Theory of the asymmetric ripple phase in achiral lipid membranes

We present a phenomenological theory of phase transitions in achiral lipid membranes in terms of two coupled order parameters -- a scalar order parameter describing lipid chain melting, and a vector order parameter describing the tilt of the hydrocarbon chains below the chain-melting transition. Existing theoretical models fail to account for all the observed features of the phase diagram, in particular the detailed microstructure of the asymmetric ripple phase lying between the fluid and the tilted gel phase. In contrast, our two-component theory reproduces all the salient structural features of the ripple phase, providing a unified description of the phase diagram and microstructure

A measurement of the cosmic microwave background temperature 1280 MHz

The absolute temperature of the Cosmic Microwave Background (CMB) has been measured at a frequency of 1280 MHz. The observation was made with a modified version of the L-band receiver used in the Giant Metre wavelength Radio Telescope (GMRT): the feed horn was replaced by a corrugated plate and the receiver was placed on the ground, directed at zenith and shielded from ground radiation by an aluminium screen with corrugated edges. Novel techniques have been adopted for • Reducing and cancelling unwanted contributions to the system temperature of the receiver and • Calibrating the contributions from the feed assembly and receiver.The thermodynamic temperature of the CMB is estimated to be 3.45 ± 0.78 K

Bayesian sensitivity analysis of incomplete data: bridging pattern‐mixture and selection models

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/109600/1/sim6302.pd

Structure of phospholipid-cholesterol membranes: an X-ray diffraction study

We have studied the phase behavior of mixtures of cholesterol with dipalmitoyl phosphatidylcholine (DPPC), dimyristoyl phosphatidylcholine (DMPC), and dilauroyl phosphatidylethanolamine (DLPE), using X-ray diffraction techniques. Phosphatidylcholine (PC)-cholesterol mixtures are found to exhibit a modulated phase for cholesterol concentrations around 15 mol % at temperatures below the chain melting transition. Lowering the relative humidity from 98% to 75% increases the temperature range over which it exists. An electron density map of this phase in DPPC-cholesterol mixtures, calculated from the X-ray diffraction data, shows bilayers with a periodic height modulation, as in the ripple phase observed in many PCs in between the main- and pretransitions. However, these two phases differ in many aspects, such as the dependence of the modulation wavelength on the cholesterol content and thermodynamic stability at reduced humidities. This modulated phase is found to be absent in DLPE-cholesterol mixtures. At higher cholesterol contents the gel phase does not occur in any of these three systems, and the fluid lamellar phase is observed down to the lowest temperature studied (5°C)