44,138 research outputs found
A New General Method to Generate Random Modal Formulae for Testing Decision Procedures
The recent emergence of heavily-optimized modal decision procedures has
highlighted the key role of empirical testing in this domain. Unfortunately,
the introduction of extensive empirical tests for modal logics is recent, and
so far none of the proposed test generators is very satisfactory. To cope with
this fact, we present a new random generation method that provides benefits
over previous methods for generating empirical tests. It fixes and much
generalizes one of the best-known methods, the random CNF_[]m test, allowing
for generating a much wider variety of problems, covering in principle the
whole input space. Our new method produces much more suitable test sets for the
current generation of modal decision procedures. We analyze the features of the
new method by means of an extensive collection of empirical tests
Cosmology with Weak Lensing Surveys
Weak gravitational lensing surveys measure the distortion of the image of
distant sources due to the deflections of light rays by the fluctuations of the
gravitational potential along the line of sight. Since they probe the
non-linear matter power spectrum itself at medium redshift such surveys are
complimentary to both galaxy surveys (which follow stellar light) and cosmic
microwave background observations (which probe the linear regime at high
redshift). Ongoing CMB experiments such as WMAP and the future Planck satellite
mission will measure the standard cosmological parameters with unprecedented
accuracy. The focus of attention will then shift to understanding the nature of
dark matter and vacuum energy: several recent studies suggest that lensing is
the best method for constraining the dark energy equation of state. During the
next 5 year period ongoing and future weak lensing surveys such as the Joint
Dark Energy Mission (JDEM, e.g. SNAP) or the Large-aperture Synoptic Survey
Telescope (LSST) will play a major role in advancing our understanding of the
universe in this direction. In this review article we describe various aspects
of weak lensing surveys and how they can help us in understanding our universe.Comment: 15 pages, review article to appear in 2005 Triennial Issue of Phil.
Trans.
Qualitative Theory for Lensed QSOs
We show that some characteristics of multiply-imaged QSO systems are very
model-independent and can be deduced accurately by simply scrutinizing the
relative positions of images and galaxy-lens center. These include the
time-ordering of the images, the orientation of the lens potential, and the
rough morphology of any ring. Other features can differ considerably between
specific models; H_0 is an example. Surprisingly, properties inherited from a
circularly symmetric lens system are model-dependent, whereas features that
arise from the breaking of circular symmetry are model-independent. We first
develop these results from some abstract geometrical ideas, then illustrate
them for some well-known systems (the quads Q2237+030, H1413+117,
HST14113+5211, PG1115+080, MG0414+0534, B1608+656, B1422+231, and RXJ0911+0551,
and the ten-image system B1933+507), and finally remark on two systems
(B1359+154 and PMN J0134-0931) where the lens properties are more complex. We
also introduce a Java applet which produces simple lens systems, and helps
further illustrate the concepts.Comment: 26 pages, incl. 15 figs; accepted to AJ; java applet available at
http://ankh-morpork.maths.qmw.ac.uk/~saha/astron/lens
Geometry of Universal Magnification Invariants
Recent work in gravitational lensing and catastrophe theory has shown that
the sum of the signed magnifications of images near folds, cusps and also
higher catastrophes is zero. Here, it is discussed how Lefschetz fixed point
theory can be used to interpret this result geometrically. It is shown for the
generic case as well as for elliptic and hyperbolic umbilics in gravitational
lensing.Comment: RevTEX4, 13 pages, submitted to J. Math. Phy
- …