Brexit outcome unlikely to satisfy anyone

https://www.bu.edu/bostonia/2016/brexit-eu-referendum/Published versio

U-duality in three and four dimensions

Using generalised geometry we study the action of U-duality acting in three and four dimensions on the bosonic fields of eleven dimensional supergravity. We compare the U-duality symmetry with the T-duality symmetry of double field theory and see how the $SL(2)\otimes SL(3)$ and SL(5) U-duality groups reduce to the SO(2,2) and SO(3,3) T-duality symmetry groups of the type IIA theory. As examples we dualise M2-branes, both black and extreme. We find that uncharged black M2-branes become charged under U-duality, generalising the Harrison transformation, while extreme M2-branes will become new extreme M2-branes. The resulting tension and charges are quantised appropriately if we use the discrete U-duality group $E_d(Z)$.Comment: v1: 35 pages; v2: minor corrections in section 4.1.2, many references added; v3: further discussion added on the conformal factor of the generalised metric in section 2 and on the Wick-rotation used to construct examples in section

Quantization on a torus without position operators

We formulate quantum mechanics in the two-dimensional torus without using position operators. We define an algebra with only momentum operators and shift operators and construct irreducible representation of the algebra. We show that it realizes quantum mechanics of a charged particle in a uniform magnetic field. We prove that any irreducible representation of the algebra is unitary equivalent to each other. This work provides a firm foundation for the noncommutative torus theory.Comment: 12 pages, LaTeX2e, the title is changed, minor corrections are made, references are added. To be published in Modern Physics Letters

Group Representations and Analysis

Series of lectures delivered by George W. Mackey in Anderson Hall on April 1, 2, 4, 196

Construction and Software Design for a Microcomputer Controlled pH/Ion Titrator

The construction of an automated titration device is described. The major components include an Apple II+ Microcomputer and 8-bit parallel interface. Fisher Accumet, Model 520 Digital pH/lon Meter, Gilmont Micrometer Buret of 2.5 mL capacity, Sigma stepper motor, power supply and driver to operate the buret, and a constant temperature bath of ± 0.005 °C stability. The limitations of the system are 0.001 pH/0.1 mv for the pH/ion sensing system, and 0.125 μL per step for the buret. The system as described is designed to determine equilibrium constants for metal ion-amino acid complexes. By changing the software a variety of different pH and redox titration experiments may be performed. A computer program used to operate the stepper motor driven syringe buret and record the pH from a digital pH meter is described. The program uses both Apple BASIC and assembly language. This is a closed loop operation in which the data from the pH meter is used to control the amount of reagent delivered by the buret. The results are displayed graphically as the titration proceeds. The variance of the pH readings are calculated using an assembly language subroutine and the calculations are done with zero round-off error

A Causal, Data-Driven Approach to Modeling the Kepler Data

Astronomical observations are affected by several kinds of noise, each with its own causal source; there is photon noise, stochastic source variability, and residuals coming from imperfect calibration of the detector or telescope. The precision of NASA Kepler photometry for exoplanet science---the most precise photometric measurements of stars ever made---appears to be limited by unknown or untracked variations in spacecraft pointing and temperature, and unmodeled stellar variability. Here we present the Causal Pixel Model (CPM) for Kepler data, a data-driven model intended to capture variability but preserve transit signals. The CPM works at the pixel level so that it can capture very fine-grained information about the variation of the spacecraft. The CPM predicts each target pixel value from a large number of pixels of other stars sharing the instrument variabilities while not containing any information on possible transits in the target star. In addition, we use the target star's future and past (auto-regression). By appropriately separating, for each data point, the data into training and test sets, we ensure that information about any transit will be perfectly isolated from the model. The method has four hyper-parameters (the number of predictor stars, the auto-regressive window size, and two L2-regularization amplitudes for model components), which we set by cross-validation. We determine a generic set of hyper-parameters that works well for most of the stars and apply the method to a corresponding set of target stars. We find that we can consistently outperform (for the purposes of exoplanet detection) the Kepler Pre-search Data Conditioning (PDC) method for exoplanet discovery.Comment: Accepted for publication in the PAS