Linearized Weyl-Weyl Correlator in a de Sitter Breaking Gauge

We use a de Sitter breaking graviton propagator to compute the tree order correlator between noncoincident Weyl tensors on a locally de Sitter background. An explicit, and very simple result is obtained, for any spacetime dimension D, in terms of a de Sitter invariant length function and the tensor basis constructed from the metric and derivatives of this length function. Our answer does not agree with the one derived previously by Kouris, but that result must be incorrect because it not transverse and lacks some of the algebraic symmetries of the Weyl tensor. Taking the coincidence limit of our result (with dimensional regularization) and contracting the indices gives the expectation value of the square of the Weyl tensor at lowest order. We propose the next order computation of this as a true test of de Sitter invariance in quantum gravity.Comment: 31 pages, 2 tables, no figures, uses LaTex2

A high-speed digital signal processor for atmospheric radar, part 7.3A

The Model SP-320 device is a monolithic realization of a complex general purpose signal processor, incorporating such features as a 32-bit ALU, a 16-bit x 16-bit combinatorial multiplier, and a 16-bit barrel shifter. The SP-320 is designed to operate as a slave processor to a host general purpose computer in applications such as coherent integration of a radar return signal in multiple ranges, or dedicated FFT processing. Presently available is an I/O module conforming to the Intel Multichannel interface standard; other I/O modules will be designed to meet specific user requirements. The main processor board includes input and output FIFO (First In First Out) memories, both with depths of 4096 W, to permit asynchronous operation between the source of data and the host computer. This design permits burst data rates in excess of 5 MW/s

A circuit topology approach to categorizing changes in biomolecular structure

The biological world is composed of folded linear molecules of bewildering topological complexity and diversity. The topology of folded biomolecules such as proteins and ribonucleic acids is often subject to change during biological processes. Despite intense research, we lack a solid mathematical framework that summarizes these operations in a principled manner. Circuit topology, which formalizes the arrangements of intramolecular contacts, serves as a general mathematical framework to analyze the topological characteristics of folded linear molecules. In this work, we translate familiar molecular operations in biology, such as duplication, permutation, and elimination of contacts, into the language of circuit topology. We show that for such operations there are corresponding matrix representations as well as basic rules that serve as a foundation for understanding these operations within the context of a coherent algebraic framework. We present several biological examples and provide a simple computational framework for creating and analyzing the circuit diagrams of proteins and nucleic acids. We expect our study and future developments in this direction to facilitate a deeper understanding of natural molecular processes and to provide guidance to engineers for generating complex polymeric materials

Improving the Single Scalar Consistency Relation

We propose a test of single-scalar inflation based on using the well-measured scalar power spectrum to reconstruct the tensor power spectrum, up to a single integration constant. Our test is a sort of integrated version of the single-scalar consistency relation. This sort of test can be used effectively, even when the tensor power spectrum is measured too poorly to resolve the tensor spectral index. We give an example using simulated data based on a hypothetical detection with tensor-to-scalar ratio $r = 0.01$. Our test can also be employed for correlating scalar and tensor features in the far future when the data is good.Comment: 16 pages, 1 figure, uses LaTeX2e version 2 extensively revised for publicatio