Eigenvalue Estimation of Differential Operators

We demonstrate how linear differential operators could be emulated by a quantum processor, should one ever be built, using the Abrams-Lloyd algorithm. Given a linear differential operator of order 2S, acting on functions psi(x_1,x_2,...,x_D) with D arguments, the computational cost required to estimate a low order eigenvalue to accuracy Theta(1/N^2) is Theta((2(S+1)(1+1/nu)+D)log N) qubits and O(N^{2(S+1)(1+1/nu)} (D log N)^c) gate operations, where N is the number of points to which each argument is discretized, nu and c are implementation dependent constants of O(1). Optimal classical methods require Theta(N^D) bits and Omega(N^D) gate operations to perform the same eigenvalue estimation. The Abrams-Lloyd algorithm thereby leads to exponential reduction in memory and polynomial reduction in gate operations, provided the domain has sufficiently large dimension D > 2(S+1)(1+1/nu). In the case of Schrodinger's equation, ground state energy estimation of two or more particles can in principle be performed with fewer quantum mechanical gates than classical gates.Comment: significant content revisions: more algorithm details and brief analysis of convergenc

The radial velocity curve of HD153919 (4U1700-37) revisited

We have re-analysed all available high-resolution ultraviolet IUE spectra of the high-mass X-ray binary HD153919/4U1700-37. The radial velocity semi-amplitude of 20.6 +/- 1.0 km/s and orbital eccentricity of 0.22 +/- 0.04 agree very well with the values obtained earlier from optical spectra. They disagree with earlier conclusions for the same data reduced by Heap & Corcoran (1992) and by Stickland & Lloyd (1993).Comment: 6 pages, latex, figure included, Astronomy & Astrophysics, in pres

The Epidemiology of Stargardt Disease in the United Kingdom

The authors thank the British Ophthalmological Surveillance Unit (BOSU) for the support received, as well as Mr Barnaby Foot, research coordinator for BOSU, for his help and advice on this project. The authors thank the following ophthalmologists who assisted with data collection for this study: N. Acharya, S. Anwar, V. Bansal, P.N. Bishop, D. Byles, J.S. Chawla, A. Churchill, M. Clarke, B. Dhillon, M. Ekstein, S. George, J. Gillian, J.T. Gillow, D. Gilmour, R. Gray, P.T.S. Gregory, R. Gupta, S.P. Kelly, I.C. Lloyd, A. Lotery, M. McKibbin, R. MacLaren, G. Menon, A.T. Moore, A. Mulvihill, Y. Osoba, R. Pilling, H. Porooshani, A. Raghu Ram, T. Rimmer, I. Russell-Eggitt, M. Sarhan, R. Savides, S. Shafquat, A. Smith, A. Tekriwal, P. Tesha, P. Watts.Peer reviewedPublisher PD

Report of the Higher Education Study Commission [to the Governor and the General Assembly of Virginia]

This 1965 Report of the Higher Education Commission, appointed by Governor Albertis S. Harrison, Jr., was created to review higher education in Virginia to be used as a basis for long-range planning by the Commonwealth of Virginia. The Commission was led by Senator Lloyd C. Bird and supported by the staff of the State Council for Higher Education. Divided into eleven sections, this 200-page report details information including geographical location of students, library services, and different instructional services.https://scholarscompass.vcu.edu/vcu_books/1005/thumbnail.jp