38,185 research outputs found
The complexity of classification problems for models of arithmetic
We observe that the classification problem for countable models of arithmetic
is Borel complete. On the other hand, the classification problems for finitely
generated models of arithmetic and for recursively saturated models of
arithmetic are Borel; we investigate the precise complexity of each of these.
Finally, we show that the classification problem for pairs of recursively
saturated models and for automorphisms of a fixed recursively saturated model
are Borel complete.Comment: 15 page
Exact Bayesian curve fitting and signal segmentation.
We consider regression models where the underlying functional relationship between the response and the explanatory variable is modeled as independent linear regressions on disjoint segments. We present an algorithm for perfect simulation from the posterior distribution of such a model, even allowing for an unknown number of segments and an unknown model order for the linear regressions within each segment. The algorithm is simple, can scale well to large data sets, and avoids the problem of diagnosing convergence that is present with Monte Carlo Markov Chain (MCMC) approaches to this problem. We demonstrate our algorithm on standard denoising problems, on a piecewise constant AR model, and on a speech segmentation problem
On Gauge Theory and Topological String in Nekrasov-Shatashvili Limit
We study the Nekrasov-Shatashvili limit of the N=2 supersymmetric gauge
theory and topological string theory on certain local toric Calabi-Yau
manifolds. In this limit one of the two deformation parameters \epsilon_{1,2}
of the Omega background is set to zero and we study the perturbative expansion
of the topological amplitudes around the remaining parameter. We derive
differential equations from Seiberg-Witten curves and mirror geometries, which
determine the higher genus topological amplitudes up to a constant. We show
that the higher genus formulae previously obtained from holomorphic anomaly
equations and boundary conditions satisfy these differential equations. We also
provide a derivation of the holomorphic anomaly equations in the
Nekrasov-Shatashvili limit from these differential equations.Comment: 41 pages, no figure. v2: references adde
Towards an explicit expression of the Seiberg-Witten map at all orders
The Seiberg-Witten map links noncommutative gauge theories to ordinary gauge
theories, and allows to express the noncommutative variables in terms of the
commutative ones. Its explicit form can be found order by order in the
noncommutative parameter theta and the gauge potential A by the requirement
that gauge orbits are mapped on gauge orbits. This of course leaves
ambiguities, corresponding to gauge transformations, and there is an infinity
of solutions. Is there one better, clearer than the others ? In the abelian
case, we were able to find a solution, linked by a gauge transformation to
already known formulas, which has the property of admitting a recursive
formulation, uncovering some pattern in the map. In the special case of a pure
gauge, both abelian and non-abelian, these expressions can be summed up, and
the transformation is expressed using the parametrisation in terms of the gauge
group.Comment: 17 pages. Latex, 1 figure. v2: minor changes, published versio
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