Schubert Polynomials for the affine Grassmannian of the symplectic group

We study the Schubert calculus of the affine Grassmannian Gr of the symplectic group. The integral homology and cohomology rings of Gr are identified with dual Hopf algebras of symmetric functions, defined in terms of Schur's P and Q-functions. An explicit combinatorial description is obtained for the Schubert basis of the cohomology of Gr, and this is extended to a definition of the affine type C Stanley symmetric functions. A homology Pieri rule is also given for the product of a special Schubert class with an arbitrary one.Comment: 45 page

Implementing Unitarity in Perturbation Theory

Unitarity cannot be perserved order by order in ordinary perturbation theory because the constraint UU^\dagger=\1 is nonlinear. However, the corresponding constraint for $K=\ln U$, being $K=-K^\dagger$, is linear so it can be maintained in every order in a perturbative expansion of $K$. The perturbative expansion of $K$ may be considered as a non-abelian generalization of the linked-cluster expansion in probability theory and in statistical mechanics, and possesses similar advantages resulting from separating the short-range correlations from long-range effects. This point is illustrated in two QCD examples, in which delicate cancellations encountered in summing Feynman diagrams of are avoided when they are calculated via the perturbative expansion of $K$. Applications to other problems are briefly discussed.Comment: to appear in Phys. Rev.

Dynamin-related protein 1 is required for normal mitochondrial bioenergetic and synaptic function in CA1 hippocampal neurons.

Disrupting particular mitochondrial fission and fusion proteins leads to the death of specific neuronal populations; however, the normal functions of mitochondrial fission in neurons are poorly understood, especially in vivo, which limits the understanding of mitochondrial changes in disease. Altered activity of the central mitochondrial fission protein dynamin-related protein 1 (Drp1) may contribute to the pathophysiology of several neurologic diseases. To study Drp1 in a neuronal population affected by Alzheimer's disease (AD), stroke, and seizure disorders, we postnatally deleted Drp1 from CA1 and other forebrain neurons in mice (CamKII-Cre, Drp1lox/lox (Drp1cKO)). Although most CA1 neurons survived for more than 1 year, their synaptic transmission was impaired, and Drp1cKO mice had impaired memory. In Drp1cKO cell bodies, we observed marked mitochondrial swelling but no change in the number of mitochondria in individual synaptic terminals. Using ATP FRET sensors, we found that cultured neurons lacking Drp1 (Drp1KO) could not maintain normal levels of mitochondrial-derived ATP when energy consumption was increased by neural activity. These deficits occurred specifically at the nerve terminal, but not the cell body, and were sufficient to impair synaptic vesicle cycling. Although Drp1KO increased the distance between axonal mitochondria, mitochondrial-derived ATP still decreased similarly in Drp1KO boutons with and without mitochondria. This indicates that mitochondrial-derived ATP is rapidly dispersed in Drp1KO axons, and that the deficits in axonal bioenergetics and function are not caused by regional energy gradients. Instead, loss of Drp1 compromises the intrinsic bioenergetic function of axonal mitochondria, thus revealing a mechanism by which disrupting mitochondrial dynamics can cause dysfunction of axons

XUV Frequency Combs via Femtosecond Enhancement Cavities

We review the current state of tabletop extreme ultraviolet (XUV) sources based on high harmonic generation (HHG) in femtosecond enhancement cavities (fsEC). Recent developments have enabled generation of high photon flux (1014 photons/sec) in the XUV, at high repetition rates (>50 MHz) and spanning the spectral region from 40 nm - 120 nm. This level of performance has enabled precision spectroscopy with XUV frequency combs and promises further applications in XUV spectroscopic and photoemission studies. We discuss the theory of operation and experimental details of the fsEC and XUV generation based on HHG, including current technical challenges to increasing the photon flux and maximum photon energy produced by this type of system. Current and future applications for these sources are also discussed.Comment: invited review article, 38 page

Self-aligned nanoscale SQUID on a tip

A nanometer-sized superconducting quantum interference device (nanoSQUID) is fabricated on the apex of a sharp quartz tip and integrated into a scanning SQUID microscope. A simple self-aligned fabrication method results in nanoSQUIDs with diameters down to 100 nm with no lithographic processing. An aluminum nanoSQUID with an effective area of 0.034 $\mu$m$^2$ displays flux sensitivity of 1.8$\cdot 10^{-6}$ $\Phi_0/\mathrm{Hz}^{1/2} and operates in fields as high as 0.6 T. With projected spin sensitivity of 65$\mu_B/\mathrm{Hz}^{1/2}$ and high bandwidth, the SQUID on a tip is a highly promising probe for nanoscale magnetic imaging and spectroscopy.Comment: 14 manuscript pages, 5 figure

Measurement-Adaptive Cellular Random Access Protocols

This work considers a single-cell random access channel (RACH) in cellular wireless networks. Communications over RACH take place when users try to connect to a base station during a handover or when establishing a new connection. Within the framework of Self-Organizing Networks (SONs), the system should self- adapt to dynamically changing environments (channel fading, mobility, etc.) without human intervention. For the performance improvement of the RACH procedure, we aim here at maximizing throughput or alternatively minimizing the user dropping rate. In the context of SON, we propose protocols which exploit information from measurements and user reports in order to estimate current values of the system unknowns and broadcast global action-related values to all users. The protocols suggest an optimal pair of user actions (transmission power and back-off probability) found by minimizing the drift of a certain function. Numerical results illustrate considerable benefits of the dropping rate, at a very low or even zero cost in power expenditure and delay, as well as the fast adaptability of the protocols to environment changes. Although the proposed protocol is designed to minimize primarily the amount of discarded users per cell, our framework allows for other variations (power or delay minimization) as well.Comment: 31 pages, 13 figures, 3 tables. Springer Wireless Networks 201

Transition from an electron solid to the sequence of fractional quantum Hall states at very low Landau level filling factor

At low Landau level filling of a two-dimensional electron system, typically associated with the formation of an electron crystal, we observe local minima in Rxx at filling factors nu=2/11, 3/17, 3/19, 2/13, 1/7, 2/15, 2/17, and 1/9. Each of these developing fractional quantum Hall (FQHE) states appears only above a filling factor-specific temperature. This can be interpreted as the melting of an electron crystal and subsequent FQHE liquid formation. The observed sequence of FQHE states follow the series of composite fermion states emanating from nu=1/6 and nu=1/8

Freezing of the quantum Hall liquid at ν=\nu = 1/7 and 1/9

We compare the free energy computed from the ground state energy and low-lying excitations of the 2-D Wigner solid and the fractional quantum Hall liquid, at magnetic filling factors $\nu = 1/7$ and 1/9. We find that the Wigner solid melts into the fractional quantum Hall liquid at roughly the same temperature as that of some recent luminescence experiments, while it remains a solid at the lower temperatures characteristic of the transport experiments. We propose this melting as a consistent interpretation of both sets of experiments.Comment: uses RevTeX 2.0 or 3.

An examination of the effects of self-regulatory focus on the perception of the media richness: the case of email

Communication is a key element in organizations’ business success. The media richness theory and the channel expansion theory are two of the most influential theories regarding the selection and use of communication media in organizations; however, literature has focused little on the effects of self-regulation by managers and employees in these theories. To analyze these topics, this study develops an empirical investigation by gathering data from 600 managers and employees using a questionnaire. The results suggest that the perception of media richness is positively affected when the individual shows a promotion focus or strategy.Peer ReviewedPostprint (author’s final draft

K2 Variable Catalogue: Variable Stars and Eclipsing Binaries in K2 Campaigns 1 and 0

We have created a catalogue of variable stars found from a search of the publicly available K2 mission data from Campaigns 1 and 0. This catalogue provides the identifiers of 8395 variable stars, including 199 candidate eclipsing binaries with periods up to 60d and 3871 periodic or quasi-periodic objects, with periods up to 20d for Campaign 1 and 15d for Campaign 0. Lightcurves are extracted and detrended from the available data. These are searched using a combination of algorithmic and human classification, leading to a classifier for each object as an eclipsing binary, sinusoidal periodic, quasi periodic, or aperiodic variable. The source of the variability is not identified, but could arise in the non-eclipsing binary cases from pulsation or stellar activity. Each object is cross-matched against variable star related guest observer proposals to the K2 mission, which specifies the variable type in some cases. The detrended lightcurves are also compared to lightcurves currently publicly available. The resulting catalogue is made available online via the MAST archive at https://archive.stsci.edu/prepds/k2varcat/, and gives the ID, type, period, semi-amplitude and range of the variation seen. We also make available the detrended lightcurves for each object.Comment: Accepted by A&A. 6 pages, 6 figures. Catalogue and lightcurves are available online via MAST at https://archive.stsci.edu/prepds/k2varcat