Quantum Modeling

We present a modification of Simon's algorithm that in some cases is able to fit experimentally obtained data to appropriately chosen trial functions with high probability. Modulo constants pertaining to the reliability and probability of success of the algorithm, the algorithm runs using only O(polylog(|Y|)) queries to the quantum database and O(polylog(|X|,|Y|)) elementary quantum gates where |X| is the size of the experimental data set and |Y| is the size of the parameter space.We discuss heuristics for good performance, analyze the performance of the algorithm in the case of linear regression, both one-dimensional and multidimensional, and outline the algorithm's limitations.Comment: 16 pages, 5 figures, in Proceedings, SPIE Conference on Quantum Computation and Quantum Information, pp. 116-127, April 21-22, 200

Efficient Geometric Probabilities of Multi-Transiting Exoplanetary Systems from CORBITS

NASA's Kepler Space Telescope has successfully discovered thousands of exoplanet candidates using the transit method, including hundreds of stars with multiple transiting planets. In order to estimate the frequency of these valuable systems, it is essential to account for the unique geometric probabilities of detecting multiple transiting extrasolar planets around the same parent star. In order to improve on previous studies that used numerical methods, we have constructed an efficient, semi-analytical algorithm called CORBITS which, given a collection of conjectured exoplanets orbiting a star, computes the probability that any particular group of exoplanets can be observed to transit. The algorithm applies theorems of elementary differential geometry to compute the areas bounded by circular curves on the surface of a sphere (see Ragozzine & Holman 2010). The implemented algorithm is more accurate and orders of magnitude faster than previous algorithms, based on comparisons with Monte Carlo simulations. We use CORBITS to show that the present solar system would only show a maximum of 3 transiting planets, but that this varies over time due to dynamical evolution. We also used CORBITS to geometrically debias the period ratio and mutual Hill sphere distributions of Kepler's multi-transiting planet candidates, which results in shifting these distributions towards slightly larger values. In an Appendix, we present additional semi-analytical methods for determining the frequency of exoplanet mutual events, i.e., the geometric probability that two planets will transit each other (Planet-Planet Occultation, relevant to transiting circumbinary planets) and the probability that this transit occurs simultaneously as they transit their star. The CORBITS algorithms and several worked examples are publicly available at https://github.com/jbrakensiek/CORBITSComment: 15 pages, 7 figures, accepted by the Astrophysical Journa

Dynamic response and control of a jet-transport aircraft encountering a single-axis vortex

The dynamic responses of a jet-transport aircraft to two types of single-axis wind vortex encounters are studied. Aircraft attitude, flight path angle, and aerodynamic angle excursions are analyzed and dominating dynamic forcing effects are identified for each encounter. A simple departure-preventing LQR controller is designed to demonstrate the benefits of using automatic control to reduce the wind vortex hazard. A Proportional-Integral-Filter controller structure successfully regulates the critical parameters, roll angle, phi, and sideslip angle, beta, for the two different vortex encounters considered in this study

A global study of enhanced stretching and diffusion in chaotic tangles

A global, finite-time study is made of stretching and diffusion in a class of chaotic tangles associated with fluids described by periodically forced two-dimensional dynamical systems. Invariant lobe structures formed by intersecting global stable and unstable manifolds of persisting invariant hyperbolic sets provide the geometrical framework for studying stretching of interfaces and diffusion of passive scalars across these interfaces. In particular, the present study focuses on the material curve that initially lies on the unstable manifold segment of the boundary of the entraining turnstile lobe.A knowledge of the stretch profile of a corresponding curve that evolves according to the unperturbed flow, coupled with an appreciation of a symbolic dynamics that applies to the entire original material curve in the perturbed flow, provides the framework for understanding the mechanism for, and topology of, enhanced stretching in chaotic tangles. Secondary intersection points (SIP's) of the stable and unstable manifolds are particularly relevant to the topology, and the perturbed stretch profile is understood in terms of the unperturbed stretch profile approximately repeating itself on smaller and smaller scales. For sufficiently thin diffusion zones, diffusion of passive scalars across interfaces can be treated as a one-dimensional process, and diffusion rates across interfaces are directly related to the stretch history of the interface.An understanding of interface stretching thus directly translates to an understanding of diffusion across interfaces. However, a notable exception to the thin diffusion zone approximation occurs when an interface folds on top of itself so that neighboring diffusion zones overlap. An analysis which takes into account the overlap of nearest neighbor diffusion zones is presented, which is sufficient to capture new phenomena relevant to efficiency of mixing. The analysis adds to the concentration profile a saturation term that depends on the distance between neighboring segments of the interface. Efficiency of diffusion thus depends not only on efficiency of stretching along the interface, but on how this stretching is distributed relative to the distance between neighboring segments of the interface

Determination of the Topology of a Directed Network

We consider strongly-connected directed networks of identical synchronous, finite-state processors with in- and out-degree uniformly bounded by a network constant. Via a straightforward extension of Ostrovsky and Wilkerson's Backwards Communication Algorithm in [OW], we exhibit a protocol which solves the Global Topology Determination Problem, the problem of having the root processor map the global topology of a network of unknown size and topology, with running time O(ND) where N represents the number of processors and D represents the diameter of the network. A simple counting argument suffices to show that the Global Topology Determination Problem has time-complexity Omega(N logN) which makes the protocol presented asymptotically time-optimal for many large networks.Comment: 9 pages, no figures, accepted to appear in IPDPS 2002 (unable to attend), (journal version to appear in Information Processing Letters

Copyrights in Computer-Generated Works: Whom, if Anyone, Do We Reward?

Computer-generated works raise grave authorship concerns under U.S. copyright law, with arguments in favor of allocating copyrights to the computer user, programmer, the computer itself, or some combination therein. The author discusses the issues and paradoxes inherent in these choices, and assesses the nature of mathematical graphical processes in light of the idea/expression dichotomy