Division subspaces and integrable kernels

In this note we prove that the reproducing kernel of a Hilbert space satisfying the division property has integrable form, is locally of trace class, and the Hilbert space itself is a Hilbert space of holomorphic functions.Comment: 11 page

EVALUATING THE IMPACTS OF AGRICULTURAL EXPORTS ON A REGIONAL ECONOMY

Agricultural exports are important to many regional economies, as is the case for agricultural exports wither produced in or shipped through Louisiana. A hybrid (revised and verified) IMPLAN model of the Louisiana economy is used to estimate the direct and indirect impact of agricultural exports. Original model estimates of foreign exports lacked holistic (overall) accuracy. However, other, more general uses of the model were unaffected by this lack of accuracy. While the contributions of agricultural exports to the state economy were substantial, impacts were concentrated in unprocessed products. Increasing the export of processed agricultural products should enhance economic activity.Agricultural exports, Holistic accuracy, IMPLAN, Input-output models, Processed exports, Community/Rural/Urban Development, International Relations/Trade,

A Refined Scaling Law for Spatially Coupled LDPC Codes Over the Binary Erasure Channel

We propose a refined scaling law to predict the finite-length performance in the waterfall region of spatially coupled low-density parity-check codes over the binary erasure channel. In particular, we introduce some improvements to the scaling law proposed by Olmos and Urbanke that result in a better agreement between the predicted and simulated frame error rate. We also show how the scaling law can be extended to predict the bit error rate performance.Comment: Paper accepted to IEEE Information Theory Workshop (ITW) 201

Systematic Analysis of Majorization in Quantum Algorithms

Motivated by the need to uncover some underlying mathematical structure of optimal quantum computation, we carry out a systematic analysis of a wide variety of quantum algorithms from the majorization theory point of view. We conclude that step-by-step majorization is found in the known instances of fast and efficient algorithms, namely in the quantum Fourier transform, in Grover's algorithm, in the hidden affine function problem, in searching by quantum adiabatic evolution and in deterministic quantum walks in continuous time solving a classically hard problem. On the other hand, the optimal quantum algorithm for parity determination, which does not provide any computational speed-up, does not show step-by-step majorization. Lack of both speed-up and step-by-step majorization is also a feature of the adiabatic quantum algorithm solving the 2-SAT ``ring of agrees'' problem. Furthermore, the quantum algorithm for the hidden affine function problem does not make use of any entanglement while it does obey majorization. All the above results give support to a step-by-step Majorization Principle necessary for optimal quantum computation.Comment: 15 pages, 14 figures, final versio