Towards Spinning Mellin Amplitudes

We construct the Mellin representation of four point conformal correlation function with external primary operators with arbitrary integer spacetime spins, and obtain a natural proposal for spinning Mellin amplitudes. By restricting to the exchange of symmetric traceless primaries, we generalize the Mellin transform for scalar case to introduce discrete Mellin variables for incorporating spin degrees of freedom. Based on the structures about spinning three and four point Witten diagrams, we also obtain a generalization of the Mack polynomial which can be regarded as a natural kinematical polynomial basis for computing spinning Mellin amplitudes using different choices of interaction vertices.Comment: 32 pages, 2 figures, v2: typos corrected, clarification added, references updated, to appear in NP

Anatomy of Geodesic Witten Diagrams

We revisit the so-called "Geodesic Witten Diagrams" (GWDs) \cite{ScalarGWD}, proposed to be the holographic dual configuration of scalar conformal partial waves, from the perspectives of CFT operator product expansions. To this end, we explicitly consider three point GWDs which are natural building blocks of all possible four point GWDs, discuss their gluing procedure through integration over spectral parameter, and this leads us to a direct identification with the integral representation of CFT conformal partial waves. As a main application of this general construction, we consider the holographic dual of the conformal partial waves for external primary operators with spins. Moreover, we consider the closely related "split representation" for the bulk to bulk spinning propagator, to demonstrate how ordinary scalar Witten diagram with arbitrary spin exchange, can be systematically decomposed into scalar GWDs. We also discuss how to generalize to spinning cases.Comment: 40 pages, 4 figures, v2: typos corrected, references added, Appendix E and a Mellin space discussion added, v3: typos correcte

Multistage interconnection networks : improved routing algorithms and fault tolerance

Multistage interconnection networks for use by multiprocessor systems are optimal in terms of the number of switching element, but the routing algorithms used to set up these networks are suboptimal in terms of time. The network set-up time and reliability are the major factors to affect the performance of multistage interconnection networks. This work improves routing on Benes and Clos networks as well as the fault tolerant capability. The permutation representation is examined as well as the Clos and Benes networks. A modified edge coloring algorithm is applied to the regular bipartite multigraph which represents a Clos network. The looping and parallel looping algorithms are examined and a modified Tree-Connected Computer is adopted to execute a bidirectional parallel looping algorithm for Benes networks. A new fault tolerant Clos network is presented

The constant impedance tapered lossless transmission line

Considerable work has been done on the theory and development of the distributed RC network which is a special case of the general distributed network type of transmission line. Sir William Thompson analyzed telegraph cables, assuming the RC line as a model. Oliver Heaviside made numerous contributions to transmission line theory. The solution of a two-wire transmission line with constant parameters R and C is obtainable by direct solution of the telegraphist\u27s equations which are developed from the equivalent circuit of an incremental length of the network. The sinusoidal steady-state solutions of certain tapered RC lines have been exhibited. The exact and numerical analyses of RC lines have also been exhibited. The general line has per unit length parameters of resistance R, inductance L, capacitance c, and leakage conductance G. If R and G are negligible, a distributed lossless network results. In this thesis, lossless tapered lines that have identical taper functions for L and C are considered. The uniform LC line is just a special case of this tapered transmission line --Introduction, page 1

Zero on-axis backscattering of an anisotropically coated shell of revolution

This report was sponsored by Sandia National Laboratories

T Oligo-Primed Polymerase Chain Reaction (TOP-PCR): A Robust Method for the Amplification of Minute DNA Fragments in Body Fluids.

Body fluid DNA sequencing is a powerful noninvasive approach for the diagnosis of genetic defects, infectious agents and diseases. The success relies on the quantity and quality of the DNA samples. However, numerous clinical samples are either at low quantity or of poor quality due to various reasons. To overcome these problems, we have developed T oligo-primed polymerase chain reaction (TOP-PCR) for full-length nonselective amplification of minute quantity of DNA fragments. TOP-PCR adopts homogeneous "half adaptor" (HA), generated by annealing P oligo (carrying a phosphate group at the 5' end) and T oligo (carrying a T-tail at the 3' end), for efficient ligation to target DNA and subsequent PCR amplification primed by the T oligo alone. Using DNA samples from body fluids, we demonstrate that TOP-PCR recovers minute DNA fragments and maintains the DNA size profile, while enhancing the major molecular populations. Our results also showed that TOP-PCR is a superior method for detecting apoptosis and outperforms the method adopted by Illumina for DNA amplification

A Web-based Multimedia Annotation System for Language Learning

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