Designing an Analytic Deliberative Process for Environmental Health Policy Making in the U.S. Nuclear Weapons Complex

Using a National Research Council Report as a centerpiece, Drs. Tuler and Webler evaluate the effectiveness of a conceptual approach to risk policy-making

Algebraic Aspects of Conditional Independence and Graphical Models

This chapter of the forthcoming Handbook of Graphical Models contains an overview of basic theorems and techniques from algebraic geometry and how they can be applied to the study of conditional independence and graphical models. It also introduces binomial ideals and some ideas from real algebraic geometry. When random variables are discrete or Gaussian, tools from computational algebraic geometry can be used to understand implications between conditional independence statements. This is accomplished by computing primary decompositions of conditional independence ideals. As examples the chapter presents in detail the graphical model of a four cycle and the intersection axiom, a certain implication of conditional independence statements. Another important problem in the area is to determine all constraints on a graphical model, for example, equations determined by trek separation. The full set of equality constraints can be determined by computing the model's vanishing ideal. The chapter illustrates these techniques and ideas with examples from the literature and provides references for further reading.Comment: 20 pages, 1 figur

A qq-Queens Problem. II. The Square Board

We apply to the $n\times n$ chessboard the counting theory from Part I for nonattacking placements of chess pieces with unbounded straight-line moves, such as the queen. Part I showed that the number of ways to place $q$ identical nonattacking pieces is given by a quasipolynomial function of $n$ of degree $2q$, whose coefficients are (essentially) polynomials in $q$ that depend cyclically on $n$. Here we study the periods of the quasipolynomial and its coefficients, which are bounded by functions, not well understood, of the piece's move directions, and we develop exact formulas for the very highest coefficients. The coefficients of the three highest powers of $n$ do not vary with $n$. On the other hand, we present simple pieces for which the fourth coefficient varies periodically. We develop detailed properties of counting quasipolynomials that will be applied in sequels to partial queens, whose moves are subsets of those of the queen, and the nightrider, whose moves are extended knight's moves. We conclude with the first, though strange, formula for the classical $n$-Queens Problem and with several conjectures and open problems.Comment: 23 pp., 1 figure, submitted. This = second half of 1303.1879v1 with great improvements. V2 has a new proposition, better definitions, and corrected conjectures. V3 has results et al. renumbered to correspond with published version, and expands dictionary's cryptic abbreviation

Fast spectral source integration in black hole perturbation calculations

This paper presents a new technique for achieving spectral accuracy and fast computational performance in a class of black hole perturbation and gravitational self-force calculations involving extreme mass ratios and generic orbits. Called \emph{spectral source integration} (SSI), this method should see widespread future use in problems that entail (i) point-particle description of the small compact object, (ii) frequency domain decomposition, and (iii) use of the background eccentric geodesic motion. Frequency domain approaches are widely used in both perturbation theory flux-balance calculations and in local gravitational self-force calculations. Recent self-force calculations in Lorenz gauge, using the frequency domain and method of extended homogeneous solutions, have been able to accurately reach eccentricities as high as $e \simeq 0.7$. We show here SSI successfully applied to Lorenz gauge. In a double precision Lorenz gauge code, SSI enhances the accuracy of results and makes a factor of three improvement in the overall speed. The primary initial application of SSI--for us its \emph{raison d'\^{e}tre}--is in an arbitrary precision \emph{Mathematica} code that computes perturbations of eccentric orbits in the Regge-Wheeler gauge to extraordinarily high accuracy (e.g., 200 decimal places). These high accuracy eccentric orbit calculations would not be possible without the exponential convergence of SSI. We believe the method will extend to work for inspirals on Kerr, and will be the subject of a later publication. SSI borrows concepts from discrete-time signal processing and is used to calculate the mode normalization coefficients in perturbation theory via sums over modest numbers of points around an orbit. A variant of the idea is used to obtain spectral accuracy in solution of the geodesic orbital motion.Comment: 15 pages, 7 figure

Quantum Hopfield neural network

Quantum computing allows for the potential of significant advancements in both the speed and the capacity of widely used machine learning techniques. Here we employ quantum algorithms for the Hopfield network, which can be used for pattern recognition, reconstruction, and optimization as a realization of a content-addressable memory system. We show that an exponentially large network can be stored in a polynomial number of quantum bits by encoding the network into the amplitudes of quantum states. By introducing a classical technique for operating the Hopfield network, we can leverage quantum algorithms to obtain a quantum computational complexity that is logarithmic in the dimension of the data. We also present an application of our method as a genetic sequence recognizer.Comment: 13 pages, 3 figures, final versio

Structural Studies of Nep1/Emg1 RNA Methyltransferase and Atypical Rio3 Kinase

Nucleolar Essential Protein 1 (Nep1) is required for small subunit (SSU) ribosomal RNA (rRNA) maturation and is mutated in Bowen-Conradi Syndrome. Although yeast (Saccharomyces cerevisiae) Nep1 interacts with a consensus sequence found in three regions of the SSU rRNA, the molecular details of the interaction are unknown. Nep1 is a SPOUT RNA methyltransferase, and can catalyze methylation at the N1 position of pseudouridine. Nep1 is also involved in assembly of Rps19, an SSU ribosomal protein, into the SSU. Mutations in Nep1 that result in decreased methyl donor binding do not result in lethality, suggesting that enzymatic activity may not be required for function, and RNA binding may play a more important role. To study these interactions, the crystal structures of the ScNep1 dimer and its complexes with RNA were determined. The results demonstrate that Nep1 recognizes its RNA site via base-specific interactions and stabilizes a stem-loop in the bound RNA. Furthermore, the observed RNA structure contradicts the structures of the Nep1-binding sites within mature rRNA, suggesting that the Nep1 changes rRNA structure upon binding. Finally, a uridine base is bound in the active site of Nep1, positioned for a methyltransfer at the C5 position, supporting Nep1's role as an N1-specific pseudouridine methyltransferase. In addition to the work completed with the Nep1 project, structural characterization of Rio3 Kinase is reported, as well as collaborative work in the structure determination of Ubiquitin and Ubiquitin complexes and Iodotyrosine Deiodinase

Monitoring Changes in Hemodynamics Following Optogenetic Stimulation

The brain is composed of billions of neurons, all of which connected through a vast network. After years of study and applications of different technologies and techniques, there are still more questions than answers when it comes to the fundamental functions of the brain. This project aims to provide a new tool which can be used to gain a better understanding of the fundamental mechanisms that govern neurological processes inside the brain. In order for neural networks to operate, blood has to be supplied through neighboring blood vessels. As such, the increase or decrease in the blood supply has been used as an indicator of neural activity. The neural activity and blood supply relationship is known as neural vasculature coupling. Monitoring the hemodynamics is used as an indicator of neurological activity, but the causal relationship is an area of current research. Gaining a better understanding of the coupling of neural activity and the surrounding vasculature provides a more accurate methodology to evaluate regional neural activity. The new optical technology applied in this project provides a set of tools to both stimulate and monitor this coupling relationship. Optogenetics provides the capability of stimulating neural activity using specific wavelengths of light. Essentially this tool allows for the direct stimulation of networks of neurons by simply shining one color of light onto the brain. Optical Coherence Tomography (OCT), another new optical technology applied in this project, can record volumetric images of blood vessels and flow using only infrared light. The combination of the two optical technologies is then capable of stimulating neural activity and monitoring the hemodynamic response inside the brain using only light. As a result of this project we have successfully demonstrated the capability of both stimulating and imaging the brain using new optical technologies. The optical stimulation of neural activity has evoked a direct hemodynamic effect as anticipated through neural-vasculature coupling. Changes in blood velocity, flow and dilatation were all recorded using the high resolution and high speed capabilities of the OCT system