Twisted topological structures related to M-branes II: Twisted Wu and Wu^c structures

Studying the topological aspects of M-branes in M-theory leads to various structures related to Wu classes. First we interpret Wu classes themselves as twisted classes and then define twisted notions of Wu structures. These generalize many known structures, including Pin^- structures, twisted Spin structures in the sense of Distler-Freed-Moore, Wu-twisted differential cocycles appearing in the work of Belov-Moore, as well as ones introduced by the author, such as twisted Membrane and twisted String^c structures. In addition, we introduce Wu^c structures, which generalize Pin^c structures, as well as their twisted versions. We show how these structures generalize and encode the usual structures defined via Stiefel-Whitney classes.Comment: 20 page

Upscaling single unit monomer insertion to synthesize discrete oligomers

As one of the emerging techniques for preparing discrete oligomers, the photo-RAFT single unit monomer insertion (SUMI) process has shown its uniqueness and superiority in the control of both monomer sequence and stereochemistry. However, current precision polymer synthesis techniques are still burdened by the scalability challenges, such as low reaction yields, small product quantities, and long production times. Herein, we successfully established a practical protocol to address scalability problems in the photo-RAFT SUMI processes. A series of discrete oligomers containing up to five monomer units were synthesized in batch and flow reactors by sequential and alternating SUMI of two monomers into a trithiocarbonate RAFT agent under mild reaction conditions and purified by automated flash chromatography. This protocol offers the process with large quantity (grams scale), excellent isolated yields (82%–95% for each step and 59% for five iterations), and short production time (several days for a pentamer). © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019, 57, 1947–1955

Time-averaged MSD of Brownian motion

We study the statistical properties of the time-averaged mean-square displacements (TAMSD). This is a standard non-local quadratic functional for inferring the diffusion coefficient from an individual random trajectory of a diffusing tracer in single-particle tracking experiments. For Brownian motion, we derive an exact formula for the Laplace transform of the probability density of the TAMSD by mapping the original problem onto chains of coupled harmonic oscillators. From this formula, we deduce the first four cumulant moments of the TAMSD, the asymptotic behavior of the probability density and its accurate approximation by a generalized Gamma distribution

Unitary Representations of Unitary Groups

In this paper we review and streamline some results of Kirillov, Olshanski and Pickrell on unitary representations of the unitary group \U(\cH) of a real, complex or quaternionic separable Hilbert space and the subgroup \U_\infty(\cH), consisting of those unitary operators $g$ for which g - \1 is compact. The Kirillov--Olshanski theorem on the continuous unitary representations of the identity component \U_\infty(\cH)_0 asserts that they are direct sums of irreducible ones which can be realized in finite tensor products of a suitable complex Hilbert space. This is proved and generalized to inseparable spaces. These results are carried over to the full unitary group by Pickrell's Theorem, asserting that the separable unitary representations of \U(\cH), for a separable Hilbert space \cH, are uniquely determined by their restriction to \U_\infty(\cH)_0. For the $10$ classical infinite rank symmetric pairs $(G,K)$ of non-unitary type, such as (\GL(\cH),\U(\cH)), we also show that all separable unitary representations are trivial.Comment: 42 page

The Distance of the Gamma-ray Binary 1FGL J1018.6-5856

The recently discovered gamma-ray binary 1FGL J1018.6-5856 has a proposed optical/near-infrared (OIR) counterpart 2MASS 10185560-5856459. We present Stromgren photometry of this star to investigate its photometric variability and measure the reddening and distance to the system. We find that the gamma-ray binary has E(B-V) = 1.34 +/- 0.04 and d = 5.4^+4.6_-2.1 kpc. While E(B-V) is consistent with X-ray observations of the neutral hydrogen column density, the distance is somewhat closer than some previous authors have suggested.Comment: Accepted to PAS

New Results in Sasaki-Einstein Geometry

This article is a summary of some of the author's work on Sasaki-Einstein geometry. A rather general conjecture in string theory known as the AdS/CFT correspondence relates Sasaki-Einstein geometry, in low dimensions, to superconformal field theory; properties of the latter are therefore reflected in the former, and vice versa. Despite this physical motivation, many recent results are of independent geometrical interest, and are described here in purely mathematical terms: explicit constructions of infinite families of both quasi-regular and irregular Sasaki-Einstein metrics; toric Sasakian geometry; an extremal problem that determines the Reeb vector field for, and hence also the volume of, a Sasaki-Einstein manifold; and finally, obstructions to the existence of Sasaki-Einstein metrics. Some of these results also provide new insights into Kahler geometry, and in particular new obstructions to the existence of Kahler-Einstein metrics on Fano orbifolds.Comment: 31 pages, no figures. Invited contribution to the proceedings of the conference "Riemannian Topology: Geometric Structures on Manifolds"; minor typos corrected, reference added; published version; Riemannian Topology and Geometric Structures on Manifolds (Progress in Mathematics), Birkhauser (Nov 2008

The Comparative Toxicogenomics Database (CTD).

The Mount Desert Island Biological Laboratory in Salsbury Cove, Maine, USA, is developing the Comparative Toxicogenomics Database (CTD), a community-supported genomic resource devoted to genes and proteins of human toxicologic significance. CTD will be the first publicly available database to a) provide annotated associations among genes, proteins, references, and toxic agents, with a focus on annotating data from aquatic and mammalian organisms; b) include nucleotide and protein sequences from diverse species; c) offer a range of analysis tools for customized comparative studies; and d) provide information to investigators on available molecular reagents. This combination of features will facilitate cross-species comparisons of toxicologically significant genes and proteins. These comparisons will promote understanding of molecular evolution, the significance of conserved sequences, the genetic basis of variable sensitivity to environmental agents, and the complex interactions between the environment and human health. CTD is currently under development, and the planned scope and functions of the database are described herein. The intent of this report is to invite community participation in the development of CTD to ensure that it will be a valuable resource for environmental health, molecular biology, and toxicology research

Collisional relaxation of Feshbach molecules and three-body recombination in 87Rb Bose-Einstein condensates

We predict the resonance enhanced magnetic field dependence of atom-dimer relaxation and three-body recombination rates in a $^{87}$Rb Bose-Einstein condensate (BEC) close to 1007 G. Our exact treatments of three-particle scattering explicitly include the dependence of the interactions on the atomic Zeeman levels. The Feshbach resonance distorts the entire diatomic energy spectrum causing interferences in both loss phenomena. Our two independent experiments confirm the predicted recombination loss over a range of rate constants that spans four orders of magnitude.Comment: 4 pages, 3 eps figures (updated references

Quasi Harmonic Lattice Dynamics and Molecular Dynamics calculations for the Lennard-Jones solids

We present Molecular Dynamics (MD), Quasi Harmonic Lattice Dynamics (QHLD) and Energy Minimization (EM) calculations for the crystal structure of Ne, Ar, Kr and Xe as a function of pressure and temperature. New Lennard-Jones (LJ) parameters are obtained for Ne, Kr and Xe to reproduce the experimental pressure dependence of the density. We employ a simple method which combines results of QHLD and MD calculations to achieve densities in good agreement with experiment from 0 K to melting. Melting is discussed in connection with intrinsic instability of the solid as given by the QHLD approximation. (See http://www.fci.unibo.it/~valle for related papers)Comment: 7 pages, 5 figures, REVte