Operator-Schmidt decomposition of the quantum Fourier transform on C^N1 tensor C^N2

Operator-Schmidt decompositions of the quantum Fourier transform on C^N1 tensor C^N2 are computed for all N1, N2 > 1. The decomposition is shown to be completely degenerate when N1 is a factor of N2 and when N1>N2. The first known special case, N1=N2=2^n, was computed by Nielsen in his study of the communication cost of computing the quantum Fourier transform of a collection of qubits equally distributed between two parties. [M. A. Nielsen, PhD Thesis, University of New Mexico (1998), Chapter 6, arXiv:quant-ph/0011036.] More generally, the special case N1=2^n1<2^n2=N2 was computed by Nielsen et. al. in their study of strength measures of quantum operations. [M.A. Nielsen et. al, (accepted for publication in Phys Rev A); arXiv:quant-ph/0208077.] Given the Schmidt decompositions presented here, it follows that in all cases the communication cost of exact computation of the quantum Fourier transform is maximal.Comment: 9 pages, LaTeX 2e; No changes in results. References and acknowledgments added. Changes in presentation added to satisfy referees: expanded introduction, inclusion of ommitted algebraic steps in the appendix, addition of clarifying footnote

40 Years of FOIA, 20 Years of Delay: Oldest Pending Freedom of Information Requests Date Back to the 1980s

Presents findings from the Knight Open Government Survey, which surveys government offices and agencies on the status of their public information requests, and finds that extensive backlogs persist

Properties of etimated characteristic roots

Estimated characteristic roots in stationary autoregressions are shown to give rather noisy information about their population equivalents. This is remarkable given the central role of the characteristic roots in the theory of autoregressive processes. In the asymptotic analysis the problems appear when multiple roots are present as this imply a non-differentiability so the d-method does not apply, convergence rates are slow, and the asymptotic distribution is non-normal. In finite samples this has a considerable influence on the finite sample distribution unless the roots are far apart. With increasing order of the autoregressions it becomes increasingly difficult to place the roots far apart giving a very noisy signal from the characteristic roots.Autoregression; Characteristic root.

Cramer-Rao Lower Bound and Information Geometry

This article focuses on an important piece of work of the world renowned Indian statistician, Calyampudi Radhakrishna Rao. In 1945, C. R. Rao (25 years old then) published a pathbreaking paper, which had a profound impact on subsequent statistical research.Comment: To appear in Connected at Infinity II: On the work of Indian mathematicians (R. Bhatia and C.S. Rajan, Eds.), special volume of Texts and Readings In Mathematics (TRIM), Hindustan Book Agency, 201

The Owlet Moths of Ohio, Order Lepidoptera Family Noctuidae, by Roy W. Rings, Eric Metzler, Fred J. Arnold, and David H. Harris. 1992. Published by College of Biological Sciences, The Ohio State University, in Cooperation with Ohio Department of Natural Resources, Division of Wildlife and the Ohio Lepidopterists, Columbus, Ohio 43210. VI + 219 pp., 9 text figures, 8 color plates, 8 black and white plates. Soft cover, 8.5 x 11 in.(21.6 x 27.9 cm), ISSN 0078-3994, $20.00 U.S.

(excerpt) The authors are to be commended for producing an extremely useful and thoroughly complete compilation of this fascinating but frequently ignored group of Lepidoptera. Itis, without a doubt, the finest state systematic check- list that this reviewer has previously read and one that will probably not be exceeded in the near future. This monograph, a systematic checklist of the owlet moths (Noctuidae) of Ohio, is the second monograph to present the lepidopterological results of a cooperative effort among the Ohio Biological Survey, the Ohio Lepidopterists, and the Ohio Department of Natural His- tory. It follows a very comprehensive survey of the state\u27s butterfly fauna, Butterflies and Skippers of Ohio , by David C. Iftner, John A. Shuey, and John V. Calhoun

Properties of Estimated Characteristic Roots

Estimated characteristic roots in stationary autoregressions are shown to give rather noisy information about their population equivalents. This is remarkable given the central role of the characteristic roots in the theory of autoregressive processes. In the asymptotic analysis the problems appear when multiple roots are present as this imply a non-differentiability so the δ-method does not apply, convergence rates are slow, and the asymptotic distribution is non-normal. In finite samples this has a considerable influence on the finite sample distribution unless the roots are far apart. With increasing order of the autoregressions it becomes increasingly difficult to place the roots far apart giving a very noisy signal from the characteristic roots.autoregression; characteristic root