The Quantum McKay Correspondence for polyhedral singularities

Let G be a polyhedral group, namely a finite subgroup of SO(3). Nakamura's G-Hilbert scheme provides a preferred Calabi-Yau resolution Y of the polyhedral singularity C^3/G. The classical McKay correspondence describes the classical geometry of Y in terms of the representation theory of G. In this paper we describe the quantum geometry of Y in terms of R, an ADE root system associated to G. Namely, we give an explicit formula for the Gromov-Witten partition function of Y as a product over the positive roots of R. In terms of counts of BPS states (Gopakumar-Vafa invariants), our result can be stated as a correspondence: each positive root of R corresponds to one half of a genus zero BPS state. As an application, we use the crepant resolution conjecture to provide a full prediction for the orbifold Gromov-Witten invariants of [C^3/G].Comment: Introduction rewritten. Issue regarding non-uniqueness of conifold resolution clarified. Version to appear in Inventione

Image encryption and the fractional Fourier transform

A number of method have been recently proposed in the literature for the encryption of 2-D information using optical systems based on the fractional Fourier fransform, FRT. In this paper a brief review of the methods proposed to date is presented. A measure of the strength/robustness of the level of encryption of the various techniques is proposed and a comparison is carried out between the methods. Optical implementations are discussed. Robustness of system with respect to misalignment and blind decryption are also discussed

Generation and measurement of nonstationary random processes technical note no. 3

Generation and measurement of nonstationary stochastic processes related to Monte Carlo studies with analog compute

Inefficiency of classically simulating linear optical quantum computing with Fock-state inputs

Aaronson and Arkhipov recently used computational complexity theory to argue that classical computers very likely cannot efficiently simulate linear, multimode, quantum-optical interferometers with arbitrary Fock-state inputs [Aaronson and Arkhipov, Theory Comput. 9, 143 (2013)]. Here we present an elementary argument that utilizes only techniques from quantum optics. We explicitly construct the Hilbert space for such an interferometer and show that its dimension scales exponentially with all the physical resources. We also show in a simple example just how the Schr\"odinger and Heisenberg pictures of quantum theory, while mathematically equivalent, are not in general computationally equivalent. Finally, we conclude our argument by comparing the symmetry requirements of multiparticle bosonic to fermionic interferometers and, using simple physical reasoning, connect the nonsimulatability of the bosonic device to the complexity of computing the permanent of a large matrix.Comment: 7 pages, 1 figure Published in PRA Phys. Rev. A 89, 022328 (2014

Potential Applications of Active Antenna Technologies for Emerging NASA Space Communications Scenarios

AbstractThe National Aeronautics and Space Administration (NASA) is presently embarking on the implementation of far-reaching changes within the framework of both space and aeronautics communications architectures. For example, near earth relays are looking to transition from the traditional few large geostationary satellites to satellite constellations consisting of thousands of small low earth orbiting satellites while lunar space communications will require the need to relay data from many assets distributed on the lunar surface back to earth. Furthermore, within the aeronautics realm, satellite communications for beyond line of sight (BLOS) links are being investigated in tandem with the proliferation of unmanned aerial systems (UAS) within the urban air mobility (UAM) environment. In all of these scenarios, future communications architectures will demand the need to connect and quickly transition between many nodes for large data volume transport. As such, NASA Glenn Research Center (GRC) has been heavily investigating the development of low cost phased array technologies that can readily address these various scenario conditions. In particular, GRC is presently exploring 5G-based beamformer technologies to leverage commercial timescale and volume production cycles which have heretofore not existed within the frequency allocations utilized for NASA applications. In this paper, an overview of the potential future applications of phased arrays being envisioned by NASA are discussed, along with technology feasibility demonstrations being conducted by GRC implementing low cost, 5G based beamformer technologies

CLONAL CHARACTER OF F1 HYBRID LYMPHOCYTE SUBSET RECOGNITION OF PARENTAL CELLS IN ONE-WAY MIXED LYMPHOCYTE CULTURES

Proliferation of F1 hybrid lymphocytes in mixed lymphocyte cultures is stimulated by mitomycin-blocked parental cells. The demonstration of this phenomenon using F1 hybrids derived from congenic lines of mice establishes that the stimulation is controlled by genes in or closely linked to the major histocompatibility locus chromosome region. In agreement with the finding that tumor-bearing mice have an increased capacity for primary alloantigen recognition, it was observed that the F1 hybrid response to parent was also augmented by tumor bearing. Chromosomal analysis of dividing cells in one-way mixed cultures confirms that F1 cells, and not the blocked parental cells, enter mitosis. Stimulation of F1 cells by a soluble mediator liberated by the parental cells was not observed and mitomycin blocking of parental cells seems to be a completely effective blocking agent ensuring that parental cells can not enter DNA synthesis. The specificity and clonal nature of F1 recognition of parent was demonstrated using a 5-bromodeoxyuridine-suicide procedure. Distinct clones of lymphocytes in F1 spleen cell populations seem to recognize one or the other parent, but not both, in such experiments. These observations and others in tumor systems suggest that most or all heterozygous organisms may possess potentially self-reactive clones of lymphocytes