4,266 research outputs found
Gaussian distribution of short sums of trace functions over finite fields
We show that under certain general conditions, short sums of -adic
trace functions over finite fields follow a normal distribution asymptotically
when the origin varies, generalizing results of Erd\H{o}s-Davenport,
Mak-Zaharescu and Lamzouri. In particular, this applies to exponential sums
arising from Fourier transforms such as Kloosterman sums or Birch sums, as we
can deduce from the works of Katz. By approximating the moments of traces of
random matrices in monodromy groups, a quantitative version can be given as in
Lamzouri's article, exhibiting a different phenomenon than the averaging from
the central limit theorem.Comment: 42 page
Filling constraints for spin-orbit coupled insulators in symmorphic and non-symmorphic crystals
We determine conditions on the filling of electrons in a crystalline lattice
to obtain the equivalent of a band insulator -- a gapped insulator with neither
symmetry breaking nor fractionalized excitations. We allow for strong
interactions, which precludes a free particle description. Previous approaches
that extend the Lieb-Schultz-Mattis argument invoked spin conservation in an
essential way, and cannot be applied to the physically interesting case of
spin-orbit coupled systems. Here we introduce two approaches, the first an
entanglement based scheme, while the second studies the system on an
appropriate flat `Bieberbach' manifold to obtain the filling conditions for all
230 space groups. These approaches only assume time reversal rather than spin
rotation invariance. The results depend crucially on whether the crystal
symmetry is symmorphic. Our results clarify when one may infer the existence of
an exotic ground state based on the absence of order, and we point out
applications to experimentally realized materials. Extensions to new situations
involving purely spin models are also mentioned.Comment: 9 pages + 5 page appendices, 4 figures, 2 tables; v4: a typo in
Figure 4 is correcte
Average volume, curvatures, and Euler characteristic of random real algebraic varieties
We determine the expected curvature polynomial of random real projective
varieties given as the zero set of independent random polynomials with Gaussian
distribution, whose distribution is invariant under the action of the
orthogonal group. In particular, the expected Euler characteristic of such
random real projective varieties is found. This considerably extends previously
known results on the number of roots, the volume, and the Euler characteristic
of the solution set of random polynomial equationsComment: 38 pages. Version 2: corrected typos, changed some notation, rewrote
proof of Theorem 5.
Texture classification using discrete Tchebichef moments
In this paper, a method to characterize texture images based on discrete Tchebichef moments is presented. A global signature vector is derived from the moment matrix by taking into account both the magnitudes of the moments and their order. The performance of our method in several texture classification problems was compared with that achieved through other standard approaches. These include Haralick's gray-level co-occurrence matrices, Gabor filters, and local binary patterns. An extensive texture classification study was carried out by selecting images with different contents from the Brodatz, Outex, and VisTex databases. The results show that the proposed method is able to capture the essential information about texture, showing comparable or even higher performance than conventional procedures. Thus, it can be considered as an effective and competitive technique for texture characterization. © 2013 Optical Society of America.J. VÃctor Marcos is a Juan de la Cierva research fellow funded by the Spanish Ministry of Economy and Competitiveness.Peer Reviewe
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