Measure Recognition Problem

This is an article in mathematics, specifically in set theory. On the example of the Measure Recognition Problem (MRP) the article highlights the phenomenon of the utility of a multidisciplinary mathematical approach to a single mathematical problem, in particular the value of a set-theoretic analysis. MRP asks if for a given Boolean algebra \algB and a property $\Phi$ of measures one can recognize by purely combinatorial means if \algB supports a strictly positive measure with property $\Phi$. The most famous instance of this problem is MRP(countable additivity), and in the first part of the article we survey the known results on this and some other problems. We show how these results naturally lead to asking about two other specific instances of the problem MRP, namely MRP(nonatomic) and MRP(separable). Then we show how our recent work D\v zamonja and Plebanek (2006) gives an easy solution to the former of these problems, and gives some partial information about the latter. The long term goal of this line of research is to obtain a structure theory of Boolean algebras that support a finitely additive strictly positive measure, along the lines of Maharam theorem which gives such a structure theorem for measure algebras

Reachability in Parametric Interval Markov Chains using Constraints

Parametric Interval Markov Chains (pIMCs) are a specification formalism that extend Markov Chains (MCs) and Interval Markov Chains (IMCs) by taking into account imprecision in the transition probability values: transitions in pIMCs are labeled with parametric intervals of probabilities. In this work, we study the difference between pIMCs and other Markov Chain abstractions models and investigate the two usual semantics for IMCs: once-and-for-all and at-every-step. In particular, we prove that both semantics agree on the maximal/minimal reachability probabilities of a given IMC. We then investigate solutions to several parameter synthesis problems in the context of pIMCs -- consistency, qualitative reachability and quantitative reachability -- that rely on constraint encodings. Finally, we propose a prototype implementation of our constraint encodings with promising results

Horn-Coupled, Commercially-Fabricated Aluminum Lumped-Element Kinetic Inductance Detectors for Millimeter Wavelengths

We discuss the design, fabrication, and testing of prototype horn-coupled, lumped-element kinetic inductance detectors (LEKIDs) designed for cosmic microwave background (CMB) studies. The LEKIDs are made from a thin aluminum film deposited on a silicon wafer and patterned using standard photolithographic techniques at STAR Cryoelectronics, a commercial device foundry. We fabricated twenty-element arrays, optimized for a spectral band centered on 150 GHz, to test the sensitivity and yield of the devices as well as the multiplexing scheme. We characterized the detectors in two configurations. First, the detectors were tested in a dark environment with the horn apertures covered, and second, the horn apertures were pointed towards a beam-filling cryogenic blackbody load. These tests show that the multiplexing scheme is robust and scalable, the yield across multiple LEKID arrays is 91%, and the noise-equivalent temperatures (NET) for a 4 K optical load are in the range 26\thinspace\pm6 \thinspace \mu \mbox{K} \sqrt{\mbox{s}}

Master equation approach to DNA-breathing in heteropolymer DNA

After crossing an initial barrier to break the first base-pair (bp) in double-stranded DNA, the disruption of further bps is characterized by free energies between less than one to a few kT. This causes the opening of intermittent single-stranded bubbles. Their unzipping and zipping dynamics can be monitored by single molecule fluorescence or NMR methods. We here establish a dynamic description of this DNA-breathing in a heteropolymer DNA in terms of a master equation that governs the time evolution of the joint probability distribution for the bubble size and position along the sequence. The transfer coefficients are based on the Poland-Scheraga free energy model. We derive the autocorrelation function for the bubble dynamics and the associated relaxation time spectrum. In particular, we show how one can obtain the probability densities of individual bubble lifetimes and of the waiting times between successive bubble events from the master equation. A comparison to results of a stochastic Gillespie simulation shows excellent agreement.Comment: 12 pages, 8 figure

The Role of Patient Activation in Preferences for Shared Decision Making: Results From a National Survey of US Adults

Financial support for this study was provided by a contract with UnitedHealthcare, Optum Institute. The funding agreement ensured our independence in designing the study, interpreting the data, and writing and publishing the report. Samuel G. Smith is supported by a Cancer Research UK Postdoctoral Fellowship (C42785=A17965). Carol J. Simon and Steven R. Rush are employed by the sponsor

The Newtonian Limit for Asymptotically Flat Solutions of the Vlasov-Einstein System

It is shown that there exist families of asymptotically flat solutions of the Einstein equations coupled to the Vlasov equation describing a collisionless gas which have a Newtonian limit. These are sufficiently general to confirm that for this matter model as many families of this type exist as would be expected on the basis of physical intuition. A central role in the proof is played by energy estimates in unweighted Sobolev spaces for a wave equation satisfied by the second fundamental form of a maximal foliation.Comment: 24 pages, plain TE

The Evolution of Distorted Rotating Black Holes III: Initial Data

In this paper we study a new family of black hole initial data sets corresponding to distorted ``Kerr'' black holes with moderate rotation parameters, and distorted Schwarzschild black holes with even- and odd-parity radiation. These data sets build on the earlier rotating black holes of Bowen and York and the distorted Brill wave plus black hole data sets. We describe the construction of this large family of rotating black holes. We present a systematic study of important properties of these data sets, such as the size and shape of their apparent horizons, and the maximum amount of radiation that can leave the system during evolution. These data sets should be a very useful starting point for studying the evolution of highly dynamical black holes and can easily be extended to 3D.Comment: 16 page

A Titanium Nitride Absorber for Controlling Optical Crosstalk in Horn-Coupled Aluminum LEKID Arrays for Millimeter Wavelengths

We discuss the design and measured performance of a titanium nitride (TiN) mesh absorber we are developing for controlling optical crosstalk in horn-coupled lumped-element kinetic inductance detector arrays for millimeter-wavelengths. This absorber was added to the fused silica anti-reflection coating attached to previously-characterized, 20-element prototype arrays of LEKIDs fabricated from thin-film aluminum on silicon substrates. To test the TiN crosstalk absorber, we compared the measured response and noise properties of LEKID arrays with and without the TiN mesh. For this test, the LEKIDs were illuminated with an adjustable, incoherent electronic millimeter-wave source. Our measurements show that the optical crosstalk in the LEKID array with the TiN absorber is reduced by 66\% on average, so the approach is effective and a viable candidate for future kilo-pixel arrays.Comment: 7 pages, 5 figures, accepted for publication in the Journal of Low Temperature Physic

Using LISREL to analyze genetic and environmental covariance structure

Describes a method in which the linear structural relationships (LISREL) computer program is used for the genetic analysis of covariance structure. The method is illustrated with simulated and published twin data, including an analysis of twin data by N. G. Martin et al (1981) on psychomotor performance during alcohol intoxication