18,381 research outputs found
Conifold Transitions and Mirror Symmetries
Recent work initiated by Strominger has lead to a consistent physical
interpretation of certain types of transitions between different string vacua.
These transitions, discovered several years ago, involve singular conifold
configurations which connect distinct Calabi-Yau manifolds. In this paper we
discuss a number of aspects of conifold transitions pertinent to both
worldsheet and spacetime mirror symmetry. It is shown that the mirror transform
based on fractional transformations allows an extension of the mirror map to
conifold boundary points of the moduli space of weighted Calabi-Yau manifolds.
The conifold points encountered in the mirror context are not amenable to an
analysis via the original splitting constructions. We describe the first
examples of such nonsplitting conifold transitions, which turn out to connect
the known web of Calabi-Yau spaces to new regions of the collective moduli
space. We then generalize the splitting conifold transition to weighted
manifolds and describe a class of connections between the webs of ordinary and
weighted projective Calabi-Yau spaces. Combining these two constructions we
find evidence for a dual analog of conifold transitions in heterotic N2
compactifications on K3T and in particular describe the first
conifold transition of a Calabi-Yau manifold whose heterotic dual has been
identified by Kachru and Vafa. We furthermore present a special type of
conifold transition which, when applied to certain classes of Calabi-Yau K3
fibrations, preserves the fiber structure.Comment: 23 page
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Themes, iteration and recoverability in action research
This paper develops three concepts important to the practice of action research recoverability, research themes, and iteration by highlighting their applicability beyond single action research studies. The concepts are discussed against a program of action research, undertaken by a multidisciplinary research team, with a research focus on local, sector and national evels. This contrasts with the more usual pattern of action research in single situations. Action research is criticized on the grounds that it lacks generalizability and external validity from one-off studies. Goodness criteria have been derived to address these and other criticisms. The recoverability criterion, less strong than the repeatability of experimentation, is central to these. A second concept, that of research themes, links the recoverability criterion and iteration in action research. Iteration within and between projects and the notion of critical mass, of doing work in more than one setting, address the limitations of single setting studies
A connection between concurrency and language theory
We show that three fixed point structures equipped with (sequential)
composition, a sum operation, and a fixed point operation share the same valid
equations. These are the theories of (context-free) languages, (regular) tree
languages, and simulation equivalence classes of (regular) synchronization
trees (or processes). The results reveal a close relationship between classical
language theory and process algebra
Polynomial-Time Amoeba Neighborhood Membership and Faster Localized Solving
We derive efficient algorithms for coarse approximation of algebraic
hypersurfaces, useful for estimating the distance between an input polynomial
zero set and a given query point. Our methods work best on sparse polynomials
of high degree (in any number of variables) but are nevertheless completely
general. The underlying ideas, which we take the time to describe in an
elementary way, come from tropical geometry. We thus reduce a hard algebraic
problem to high-precision linear optimization, proving new upper and lower
complexity estimates along the way.Comment: 15 pages, 9 figures. Submitted to a conference proceeding
Generic Regular Decompositions for Parametric Polynomial Systems
This paper presents a generalization of our earlier work in [19]. In this
paper, the two concepts, generic regular decomposition (GRD) and
regular-decomposition-unstable (RDU) variety introduced in [19] for generic
zero-dimensional systems, are extended to the case where the parametric systems
are not necessarily zero-dimensional. An algorithm is provided to compute GRDs
and the associated RDU varieties of parametric systems simultaneously on the
basis of the algorithm for generic zero-dimensional systems proposed in [19].
Then the solutions of any parametric system can be represented by the solutions
of finitely many regular systems and the decomposition is stable at any
parameter value in the complement of the associated RDU variety of the
parameter space. The related definitions and the results presented in [19] are
also generalized and a further discussion on RDU varieties is given from an
experimental point of view. The new algorithm has been implemented on the basis
of DISCOVERER with Maple 16 and experimented with a number of benchmarks from
the literature.Comment: It is the latest version. arXiv admin note: text overlap with
arXiv:1208.611
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