1,491 research outputs found
Matrix Interpretations on Polyhedral Domains
We refine matrix interpretations for proving termination and complexity bounds of term rewrite systems we restricting them to domains that satisfy a system of linear inequalities. Admissibility of such a restriction is shown by certificates whose validity can be expressed as a constraint program. This refinement is orthogonal to other features of matrix interpretations (complexity bounds, dependency pairs), but can be used to improve complexity bounds, and we discuss its relation with the usable rules criterion. We present an implementation and experiments
Compactifications of moduli spaces inspired by mirror symmetry
We study moduli spaces of nonlinear sigma-models on Calabi-Yau manifolds,
using the one-loop semiclassical approximation. The data being parameterized
includes a choice of complex structure on the manifold, as well as some ``extra
structure'' described by means of classes in H^2. The expectation that this
moduli space is well-behaved in these ``extra structure'' directions leads us
to formulate a simple and compelling conjecture about the action of the
automorphism group on the K\"ahler cone. If true, it allows one to apply
Looijenga's ``semi-toric'' technique to construct a partial compactification of
the moduli space. We explore the implications which this construction has
concerning the properties of the moduli space of complex structures on a
``mirror partner'' of the original Calabi-Yau manifold. We also discuss how a
similarity which might have been noticed between certain work of Mumford and of
Mori from the 1970's produces (with hindsight) evidence for mirror symmetry
which was available in 1979. [The author is willing to mail hardcopy preprints
upon request.]Comment: 25 pp., LaTeX 2.09 with AmS-Font
Research in interactive scene analysis
Cooperative (man-machine) scene analysis techniques were developed whereby humans can provide a computer with guidance when completely automated processing is infeasible. An interactive approach promises significant near-term payoffs in analyzing various types of high volume satellite imagery, as well as vehicle-based imagery used in robot planetary exploration. This report summarizes the work accomplished over the duration of the project and describes in detail three major accomplishments: (1) the interactive design of texture classifiers; (2) a new approach for integrating the segmentation and interpretation phases of scene analysis; and (3) the application of interactive scene analysis techniques to cartography
Normal singularities with torus actions
We propose a method to compute a desingularization of a normal affine variety
X endowed with a torus action in terms of a combinatorial description of such a
variety due to Altmann and Hausen. This desingularization allows us to study
the structure of the singularities of X. In particular, we give criteria for X
to have only rational, (QQ-)factorial, or (QQ-)Gorenstein singularities. We
also give partial criteria for X to be Cohen-Macaulay or log-terminal. Finally,
we provide a method to construct factorial affine varieties with a torus
action. This leads to a full classification of such varieties in the case where
the action is of complexity one.Comment: 23 page
Recommended from our members
Mechanisms and states of self-stress of planar trusses using graphic statics, part II: Applications and extensions
This paper extends the overview (Mitchell et al. [11]) relating graphic statics and reciprocal diagrams to linear algebra-based matrix structural analysis. Focus is placed on infinitesimal mechanisms, both in-plane (linkage) and out-of-plane (polyhedral Airy stress functions). Each self-stress in the original diagram corresponds to an out-of-plane polyhedral mechanism. Decomposition into sub-polyhedra leads to a basis set of reciprocal figures which may then be linearly combined. This leads to an intuitively-appealing approach to the identification of states of self-stress for use in structural design, and to a natural “structural algebra” for use in structural optimisation. A 90° rotation of the sub-reciprocal generated by any sub-polyhedron leads to the displacement diagram of an in-plane mechanism. Any self-stress in the original thus corresponds to an in-plane mechanism of the reciprocal, summarised by the equation s = M* (where s is the number of states of self-stress in one figure, and M* is the number of in-plane mechanisms, including rigid body rotation, in the other). Since states of self-stress correspond to out-of-plane polyhedral mechanisms, this leads to a form of “conservation of mechanisms” under reciprocity. It is also shown how external forces may be treated via a triple-layer Airy stress function, consisting of a structural layer, a load layer, and a layer formed by coordinate vectors of the structural perimeter
Parabolic equations on uniformly regular Riemannian manifolds and degenerate initial boundary value problems
In this work there is established an optimal existence and regularity theory
for second order linear parabolic differential equations on a large class of
noncompact Riemannian manifolds. Then it is shown that it provides a general
unifying approach to problems with strong degeneracies in the interior or at
the boundary.Comment: To appear in "Recent Developments of Mathematical Fluid Mechanics",
Series: Advances in Mathematical Fluid Mechanics, Birkhaeuser-Verlag,
Editors: G. P. Galdi, J. G. Heywood and R. Rannacher. Some misprints of the
earlier version have been correcte
- …