784 research outputs found
Deformed General Relativity and Torsion
We argue that the natural framework for embedding the ideas of deformed, or
doubly, special relativity (DSR) into a curved spacetime is a generalisation of
Einstein-Cartan theory, considered by Stelle and West. Instead of interpreting
the noncommuting "spacetime coordinates" of the Snyder algebra as endowing
spacetime with a fundamentally noncommutative structure, we are led to consider
a connection with torsion in this framework. This may lead to the usual
ambiguities in minimal coupling. We note that observable violations of charge
conservation induced by torsion should happen on a time scale of 10^3 s, which
seems to rule out these modifications as a serious theory. Our considerations
show, however, that the noncommutativity of translations in the Snyder algebra
need not correspond to noncommutative spacetime in the usual sense.Comment: 20 pages, 1 figure, revtex; expanded sections 3 and 4 for clarity,
moved material to appendix B, corrected a few minor error
Part-to-whole Registration of Histology and MRI using Shape Elements
Image registration between histology and magnetic resonance imaging (MRI) is
a challenging task due to differences in structural content and contrast. Too
thick and wide specimens cannot be processed all at once and must be cut into
smaller pieces. This dramatically increases the complexity of the problem,
since each piece should be individually and manually pre-aligned. To the best
of our knowledge, no automatic method can reliably locate such piece of tissue
within its respective whole in the MRI slice, and align it without any prior
information. We propose here a novel automatic approach to the joint problem of
multimodal registration between histology and MRI, when only a fraction of
tissue is available from histology. The approach relies on the representation
of images using their level lines so as to reach contrast invariance. Shape
elements obtained via the extraction of bitangents are encoded in a
projective-invariant manner, which permits the identification of common pieces
of curves between two images. We evaluated the approach on human brain
histology and compared resulting alignments against manually annotated ground
truths. Considering the complexity of the brain folding patterns, preliminary
results are promising and suggest the use of characteristic and meaningful
shape elements for improved robustness and efficiency.Comment: Paper accepted at ICCV Workshop (Bio-Image Computing
Aspects of Multilinear Harmonic Analysis Related to Transversality
The purpose of this article is to survey certain aspects of multilinear
harmonic analysis related to notions of transversality. Particular emphasis
will be placed on the multilinear restriction theory for the euclidean Fourier
transform, multilinear oscillatory integrals, multilinear geometric
inequalities, multilinear Radon-like transforms, and the interplay between
them.Comment: 28 pages. Article based on a short course given at the 9th
International Conference on Harmonic Analysis and Partial Differential
Equations, El Escorial, 201
The Case of the Missing Gates: Complexity of Jackiw-Teitelboim Gravity
The Jackiw-Teitelboim (JT) model arises from the dimensional reduction of
charged black holes. Motivated by the holographic complexity conjecture, we
calculate the late-time rate of change of action of a Wheeler-DeWitt patch in
the JT theory. Surprisingly, the rate vanishes. This is puzzling because it
contradicts both holographic expectations for the rate of complexification and
also action calculations for charged black holes. We trace the discrepancy to
an improper treatment of boundary terms when naively doing the dimensional
reduction. Once the boundary term is corrected, we find exact agreement with
expectations. We comment on the general lessons that this might hold for
holographic complexity and beyond.Comment: 31 pages, 5 figure
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