173,851 research outputs found
String theory and the Kauffman polynomial
We propose a new, precise integrality conjecture for the colored Kauffman
polynomial of knots and links inspired by large N dualities and the structure
of topological string theory on orientifolds. According to this conjecture, the
natural knot invariant in an unoriented theory involves both the colored
Kauffman polynomial and the colored HOMFLY polynomial for composite
representations, i.e. it involves the full HOMFLY skein of the annulus. The
conjecture sheds new light on the relationship between the Kauffman and the
HOMFLY polynomials, and it implies for example Rudolph's theorem. We provide
various non-trivial tests of the conjecture and we sketch the string theory
arguments that lead to it.Comment: 36 pages, many figures; references and examples added, typos
corrected, final version to appear in CM
Density of classical points in eigenvarieties
In this short note, we study the geometry of the eigenvariety parametrizing p-adic automorphic forms for GL(1) over a number field, as constructed by Buzzard. We show that if K is not totally real and contains no CM subfield, points in this space arising from classical automorphic forms (i.e. algebraic Grossencharacters of K) are not Zariski-dense in the eigenvariety (as a rigid space); but the eigenvariety posesses a natural formal scheme model, and the set of classical points is Zariski-dense in the formal scheme.
We also sketch the theory for GL(2) over an imaginary quadratic field, following Calegari and Mazur, emphasizing the strong formal similarity with the case of GL(1) over a general number field
The anomaly line bundle of the self-dual field theory
In this work, we determine explicitly the anomaly line bundle of the abelian
self-dual field theory over the space of metrics modulo diffeomorphisms,
including its torsion part. Inspired by the work of Belov and Moore, we propose
a non-covariant action principle for a pair of Euclidean self-dual fields on a
generic oriented Riemannian manifold. The corresponding path integral allows to
study the global properties of the partition function over the space of metrics
modulo diffeomorphisms. We show that the anomaly bundle for a pair of self-dual
fields differs from the determinant bundle of the Dirac operator coupled to
chiral spinors by a flat bundle that is not trivial if the underlying manifold
has middle-degree cohomology, and whose holonomies are determined explicitly.
We briefly sketch the relevance of this result for the computation of the
global gravitational anomaly of the self-dual field theory, that will appear in
another paper.Comment: 41 pages. v2: A few typos corrected. Version accepted for publication
in CM
Cover
Front cover illustration: Chamberlin, Solomon. A Sketch of the Experience of Solomon Chamberlin, To Which is Added a Remarkable Revelation, or Trance of His Father-In-Law Philip Haskins: How His Soul Actually Left His Body and Was Guided by a Holy Angel to Eternal Day. Lyons, N.Y., 1829. 12 p. 18.4 cm
Flow-Aware Elephant Flow Detection for Software-Defined Networks
Software-defined networking (SDN) separates the network control plane from the packet forwarding plane, which provides comprehensive network-state visibility for better network management and resilience. Traffic classification, particularly for elephant flow detection, can lead to improved flow control and resource provisioning in SDN networks. Existing elephant flow detection techniques use pre-set thresholds that cannot scale with the changes in the traffic concept and distribution. This paper proposes a flow-aware elephant flow detection applied to SDN. The proposed technique employs two classifiers, each respectively on SDN switches and controller, to achieve accurate elephant flow detection efficiently. Moreover, this technique allows sharing the elephant flow classification tasks between the controller and switches. Hence, most mice flows can be filtered in the switches, thus avoiding the need to send large numbers of classification requests and signaling messages to the controller. Experimental findings reveal that the proposed technique outperforms contemporary methods in terms of the running time, accuracy, F-measure, and recall
Learning Active Basis Models by EM-Type Algorithms
EM algorithm is a convenient tool for maximum likelihood model fitting when
the data are incomplete or when there are latent variables or hidden states. In
this review article we explain that EM algorithm is a natural computational
scheme for learning image templates of object categories where the learning is
not fully supervised. We represent an image template by an active basis model,
which is a linear composition of a selected set of localized, elongated and
oriented wavelet elements that are allowed to slightly perturb their locations
and orientations to account for the deformations of object shapes. The model
can be easily learned when the objects in the training images are of the same
pose, and appear at the same location and scale. This is often called
supervised learning. In the situation where the objects may appear at different
unknown locations, orientations and scales in the training images, we have to
incorporate the unknown locations, orientations and scales as latent variables
into the image generation process, and learn the template by EM-type
algorithms. The E-step imputes the unknown locations, orientations and scales
based on the currently learned template. This step can be considered
self-supervision, which involves using the current template to recognize the
objects in the training images. The M-step then relearns the template based on
the imputed locations, orientations and scales, and this is essentially the
same as supervised learning. So the EM learning process iterates between
recognition and supervised learning. We illustrate this scheme by several
experiments.Comment: Published in at http://dx.doi.org/10.1214/09-STS281 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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