Algebraic Algorithm Design and Local Search

Formal, mathematically-based techniques promise to play an expanding role in the development and maintenance of the software on which our technological society depends. Algebraic techniques have been applied successfully to algorithm synthesis by the use of algorithm theories and design tactics, an approach pioneered in the Kestrel Interactive Development System (KIDS). An algorithm theory formally characterizes the essential components of a family of algorithms. A design tactic is a specialized procedure for recognizing in a problem specification the structures identified in an algorithm theory and then synthesizing a program. Design tactics are hard to write, however, and much of the knowledge they use is encoded procedurally in idiosyncratic ways. Algebraic methods promise a way to represent algorithm design knowledge declaratively and uniformly. We describe a general method for performing algorithm design that is more purely algebraic than that of KIDS. This method is then applied to local search. Local search is a large and diverse class of algorithms applicable to a wide range of problems; it is both intrinsically important and representative of algorithm design as a whole. A general theory of local search is formalized to describe the basic properties common to all local search algorithms, and applied to several variants of hill climbing and simulated annealing. The general theory is then specialized to describe some more advanced local search techniques, namely tabu search and the Kernighan-Lin heuristic

Farm Land Ownership as a Source of Retirement Income

Land Economics/Use,

Supersymmetric minisuperspace with non-vanishing fermion number

The Lagrangean of $N=1$ supergravity is dimensionally reduced to one (time-like) dimension assuming spatial homogeneity of any Bianchi type within class A of the classification of Ellis and McCallum. The algebra of the supersymmetry generators, the Lorentz generators, the diffeomorphism generators and the Hamiltonian generator is determined and found to close. In contrast to earlier work, infinitely many physical states with non-vanishing even fermion number are found to exist in these models, indicating that minisuperspace models in supergravity may be just as useful as in pure gravity.Comment: 4 page

Book Reviews

Current Legal Problems 1956 Edited by G. W. Keeton and G. Schwarzenberger London: Stevens & Sons, 1956. Pp. vii, 275. $5.55 reviewer: David F. Maxwell =================================== Some Problems of Proof under the Anglo-American System of Litigation By Edmund Morris Morgan. New York: Columbia University Press, 1956. Pp. xii, 195.$3.50 reviewer: Charles T. McCormick =================================== Effective Drafting of Leases with Check List and Forms By Milton N. Lieberman Newark: Gann Law Books, 1956. Pp. viii, 974 reviewer: Robert N. Cooks =================================== The Law and One Man Among Many By Arthur E. Sutherland Madison: University of Wisconsin Press, 1956. Pp. ix, 101. $2.50 reviewer: Kenneth B. Hughs =================================== Proxy Contests for Corporate Control By Edward Ross Aranow and Herbert A. Einhorn. New York: Columbia University Press,1957. Pp. xxiii, 577.$15.00 reviewer: Jess Halstead =================================== Gibson\u27s Suits in Chancery By Arthur Crownover, Jr. Charlottesville: The Michie Company, 1955-1956. Vol. I, Pp. xxiii, 909; Vol. II,Pp. xv, 949. $45.00. reviewer: Walter P. Armstrong, Jr. =================================== Laissez Faire and the General-Welfare State: A Study of Conflict in American Thought, 1865-1901. By Sidney Fine Ann Arbor: University of Michigan Press, 1956. Pp. x, 468.$7.50. reviewer: Howard Jay Graha

The HST Key Project on the Extragalactic Distance Scale XXV. A Recalibration of Cepheid Distances to Type Ia Supernovae and the Value of the Hubble Constant

Cepheid-based distances to seven Type Ia supernovae (SNe)-host galaxies have been derived using the standard HST Key Project on the Extragalactic Distance Scale pipeline. For the first time, this allows for a transparent comparison of data accumulated as part of three different HST projects, the Key Project, the Sandage et al. Type Ia SNe program, and the Tanvir et al. Leo I Group study. Re-analyzing the Tanvir et al. galaxy and six Sandage et al. galaxies we find a mean (weighted) offset in true distance moduli of 0.12+/-0.07 mag -- i.e., 6% in linear distance -- in the sense of reducing the distance scale, or increasing H0. Adopting the reddening-corrected Hubble relations of Suntzeff et al. (1999), tied to a zero point based upon SNe~1990N, 1981B, 1998bu, 1989B, 1972E and 1960F and the photometric calibration of Hill et al. (1998), leads to a Hubble constant of H0=68+/-2(random)+/-5(systematic) km/s/Mpc. Adopting the Kennicutt et al. (1998) Cepheid period-luminosity-metallicity dependency decreases the inferred H0 by 4%. The H0 result from Type Ia SNe is now in good agreement, to within their respective uncertainties, with that from the Tully-Fisher and surface brightness fluctuation relations.Comment: Accepted for publication in The Astrophysical Journal. 62 pages, LaTeX, 9 Postscript figures. Also available at http://casa.colorado.edu/~bgibson/publications.htm

The HST Key Project on the Extragalactic Distance Scale. XXII. The Discovery of Cepheids in NGC 1326-A

We report on the detection of Cepheids and the first distance measurement to the spiral galaxy NGC 1326-A, a member of the Fornax cluster of galaxies. We have employed data obtained with the Wide Field and Planetary Camera 2 on board the Hubble Space Telescope. Over a 49 day interval, a total of twelve V-band (F555W) and eight I-band (F814W) epochs of observation were obtained. Two photometric reduction packages, ALLFRAME and DoPHOT, have been employed to obtain photometry measures from the three Wide Field CCDs. Variability analysis yields a total of 17 Cepheids in common with both photometry datasets, with periods ranging between 10 and 50 days. Of these 14 Cepheids with high-quality lightcurves are used to fit the V and I period-luminosity relations and derive apparent distance moduli, assuming a Large Magellanic Cloud distance modulus (m-M) (LMC) = 18.50 +- 0.10 mag and color excess E(B-V) = 0.10 mag. Assuming A(V)/E(V-I) = 2.45, the DoPHOT data yield a true distance modulus to NGC 1326-A of (m-M)_0 = 31.36 +- 0.17 (random) +- 0.13 (systematic) mag, corresponding to a distance of 18.7 \pm 1.5 (random) \pm 1.2 (systematic) Mpc. The derived distance to NGC 1326-A is in good agreement with the distance derived previously to NGC 1365, another spiral galaxy member of the Fornax cluster. However the distances to both galaxies are significantly lower than to NGC 1425, a third Cepheid calibrator in the outer parts of the cluster.Comment: 33 pages A gzipped tar file containing 12 figures can be obtained from http://www.ipac.caltech.edu/H0kp/n1326a/n1326a.htm

Early Observations And Analysis Of The Type Ia SN 2014J In M82

We present optical and near infrared (NIR) observations of the nearby Type Ia SN 2014J. Seventeen optical and 23 NIR spectra were obtained from 10 days before (-10d) to 10 days after (+10d) the time of maximum B-band brightness. The relative strengths of absorption features and their patterns of development can be compared at one day intervals throughout most of this period. Carbon is not detected in the optical spectra, but we identify C I lambda 1.0693 in the NIR spectra. Mg II lines with high oscillator strengths have higher initial velocities than other Mg II lines. We show that the velocity differences can be explained by differences in optical depths due to oscillator strengths. The spectra of SN 2014J show that it is a normal SN Ia, but many parameters are near the boundaries between normal and high-velocity subclasses. The velocities for OI, Mg II, Si II, S Ca a, and Fell suggest that SN 2014J has a layered structure with little or no mixing. That result is consistent with the delayed detonation explosion models. We also report photometric observations, obtained from -10d to +29d, in the UBVRIJH and K-s bands. The template fitting package SNooPy is used to interpret the light curves and to derive photometric parameters. Using R-v = 1.46, which is consistent with previous studies, SNooPy finds that A(v) = 1.80 for E(B - V)(host) = 1.23 +/- 0.06 mag. The maximum B-band brightness of -19.19 +/- 0.10 mag was reached on February 1.74 UT +/- 0.13 days and the supernova has a decline parameter, Delta m(15), of 1.12 +/- 0.02 mag.Department of Space, Government of IndiaHungarian OTKA NN-107637NSF AST-1109801, AST-1151462, AST-1211196NSF Astronomy and Astrophysics Postdoctoral Fellowship AST-1302771NASA through a grant from the Space Telescope Science Institute GO-12540NASA NAS5-26555Swedish Research CouncilSwedish National Space BoardDanish Agency for Science and Technology and Innovation realized through a Sapere Aude Level 2 grantAstronom

The HST Key Project on the Extragalactic Distance Scale. XXVIII. Combining the Constraints on the Hubble Constant

Since the launch of the Hubble Space Telescope nine years ago, Cepheid distances to 25 galaxies have been determined for the purpose of calibrating secondary distance indicators. A variety of these can now be calibrated, and the accompanying papers by Sakai, Kelson, Ferrarese, and Gibson employ the full set of 25 galaxies to consider the Tully-Fisher relation, the fundamental plane of elliptical galaxies, Type Ia supernovae, and surface brightness fluctuations. When calibrated with Cepheid distances, each of these methods yields a measurement of the Hubble constant and a corresponding measurement uncertainty. We combine these measurements in this paper, together with a model of the velocity field, to yield the best available estimate of the value of H_0 within the range of these secondary distance indicators and its uncertainty. The result is H_0 = 71 +/- 6 km/sec/Mpc. The largest contributor to the uncertainty of this 67% confidence level result is the distance of the Large Magellanic Cloud, which has been assumed to be 50 +/- 3 kpc

Triad representation of the Chern-Simons state in quantum gravity

We investigate a triad representation of the Chern-Simons state of quantum gravity with a non-vanishing cosmological constant. It is shown that the Chern-Simons state, which is a well-known exact wavefunctional within the Ashtekar theory, can be transformed to the real triad representation by means of a suitably generalized Fourier transformation, yielding a complex integral representation for the corresponding state in the triad variables. It is found that topologically inequivalent choices for the complex integration contour give rise to linearly independent wavefunctionals in the triad representation, which all arise from the one Chern-Simons state in the Ashtekar variables. For a suitable choice of the normalization factor, these states turn out to be gauge-invariant under arbitrary, even topologically non-trivial gauge-transformations. Explicit analytical expressions for the wavefunctionals in the triad representation can be obtained in several interesting asymptotic parameter regimes, and the associated semiclassical 4-geometries are discussed. In restriction to Bianchi-type homogeneous 3-metrics, we compare our results with earlier discussions of homogeneous cosmological models. Moreover, we define an inner product on the Hilbert space of quantum gravity, and choose a natural gauge-condition fixing the time-gauge. With respect to this particular inner product, the Chern-Simons state of quantum gravity turns out to be a non-normalizable wavefunctional.Comment: Latex, 30 pages, 1 figure, to appear in Phys. Rev.

The HST Key Project on the Extragalactic Distance Scale XVII. The Cepheid Distance to NGC 4725

The distance to NGC 4725 has been derived from Cepheid variables, as part of the Hubble Space Telescope Key Project on the Extragalactic Distance Scale. Thirteen F555W (V) and four F814W (I) epochs of cosmic-ray-split Wide Field and Planetary Camera 2 observations were obtained. Twenty Cepheids were discovered, with periods ranging from 12 to 49 days. Adopting a Large Magellanic Cloud distance modulus and extinction of 18.50+/-0.10 mag and E(V-I)=0.13 mag, respectively, a true reddening-corrected distance modulus (based on an analysis employing the ALLFRAME software package) of 30.50 +/- 0.16 (random) +/- 0.17 (systematic) mag was determined for NGC 4725. The corresponding of distance of 12.6 +/- 1.0 (random) +/- 1.0 (systematic) Mpc is in excellent agreement with that found with an independent analysis based upon the DoPHOT photometry package. With a foreground reddening of only E(V-I)=0.02, the inferred intrinsic reddening of this field in NGC 4725, E(V-I)=0.19, makes it one of the most highly-reddened, encountered by the HST Key Project, to date.Comment: To be published in The Astrophysical Journal, Vol. 512 (1999). 34 pages, LaTeX, 9 jpg figure