97 research outputs found

    Anonymous quantum communication

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    We present the first protocol for the anonymous transmission of a quantum state that is information-theoretically secure against an active adversary, without any assumption on the number of corrupt participants. The anonymity of the sender and receiver is perfectly preserved, and the privacy of the quantum state is protected except with exponentially small probability. Even though a single corrupt participant can cause the protocol to abort, the quantum state can only be destroyed with exponentially small probability: if the protocol succeeds, the state is transferred to the receiver and otherwise it remains in the hands of the sender (provided the receiver is honest).Comment: 11 pages, to appear in Proceedings of ASIACRYPT, 200

    Distribution of satellite galaxies in high redshift groups

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    We use galaxy groups at redshifts between 0.4 and 1.0 selected from the Great Observatories Origins Deep Survey (GOODS) to study the color-morphological properties of satellite galaxies, and investigate possible alignment between the distribution of the satellites and the orientation of their central galaxy. We confirm the bimodal color and morphological type distribution for satellite galaxies at this redshift range: the red and blue classes corresponds to the early and late morphological types respectively, and the early-type satellites are on average brighter than the late-type ones. Furthermore, there is a {\it morphological conformity} between the central and satellite galaxies: the fraction of early-type satellites in groups with an early-type central is higher than those with a late-type central galaxy. This effect is stronger at smaller separations from the central galaxy. We find a marginally significant signal of alignment between the major axis of the early-type central galaxy and its satellite system, while for the late-type centrals no significant alignment signal is found. We discuss the alignment signal in the context of shape evolution of groups.Comment: 7 pages, 7 figures, accepted by Ap

    Derandomized Squaring of Graphs

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    We introduce a “derandomized ” analogue of graph squaring. This op-eration increases the connectivity of the graph (as measured by the second eigenvalue) almost as well as squaring the graph does, yet only increases the degree of the graph by a constant factor, instead of squaring the degree. One application of this product is an alternative proof of Reingold’s re-cent breakthrough result that S-T Connectivity in Undirected Graphs can be solved in deterministic logspace.

    Braid Group Action and Quantum Affine Algebras

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    We lift the lattice of translations in the extended affine Weyl group to a braid group action on the quantum affine algebra. This action fixes the Heisenberg subalgebra pointwise. Loop like generators are found for the algebra which satisfy the relations of Drinfel'd's new realization. Coproduct formulas are given and a PBW type basis is constructed.Comment: 15 page

    Likelihood Geometry

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    We study the critical points of monomial functions over an algebraic subset of the probability simplex. The number of critical points on the Zariski closure is a topological invariant of that embedded projective variety, known as its maximum likelihood degree. We present an introduction to this theory and its statistical motivations. Many favorite objects from combinatorial algebraic geometry are featured: toric varieties, A-discriminants, hyperplane arrangements, Grassmannians, and determinantal varieties. Several new results are included, especially on the likelihood correspondence and its bidegree. These notes were written for the second author's lectures at the CIME-CIRM summer course on Combinatorial Algebraic Geometry at Levico Terme in June 2013.Comment: 45 pages; minor changes and addition

    Complete intersections: Moduli, Torelli, and good reduction

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    We study the arithmetic of complete intersections in projective space over number fields. Our main results include arithmetic Torelli theorems and versions of the Shafarevich conjecture, as proved for curves and abelian varieties by Faltings. For example, we prove an analogue of the Shafarevich conjecture for cubic and quartic threefolds and intersections of two quadrics.Comment: 37 pages. Typo's fixed. Expanded Section 2.

    On Albanese torsors and the elementary obstruction

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    We show that the elementary obstruction to the existence of 0-cycles of degree 1 on an arbitrary variety X (over an arbitrary field) can be expressed in terms of the Albanese 1-motives associated with dense open subsets of X. Arithmetic applications are given

    Sur la p-dimension des corps

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    Let A be an excellent integral henselian local noetherian ring, k its residue field of characteristic p>0 and K its fraction field. Using an algebraization technique introduced by the first named author, and the one-dimension case already proved by Kazuya KATO, we prove the following formula: cd_p(K) = dim(A) + p-rank(k), if k is separably closed and K of characteristic zero. A similar statement is valid without those assumptions on k and K

    Cohomological Hasse principle and motivic cohomology for arithmetic schemes

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    In 1985 Kazuya Kato formulated a fascinating framework of conjectures which generalizes the Hasse principle for the Brauer group of a global field to the so-called cohomological Hasse principle for an arithmetic scheme. In this paper we prove the prime-to-characteristic part of the cohomological Hasse principle. We also explain its implications on finiteness of motivic cohomology and special values of zeta functions.Comment: 47 pages, final versio

    On the pp-supports of a holonomic D\mathcal{D}-module

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    For a smooth variety YY over a perfect field of positive characteristic, the sheaf DYD_Y of crystalline differential operators on YY (also called the sheaf of PDPD-differential operators) is known to be an Azumaya algebra over TY,T^*_{Y'}, the cotangent space of the Frobenius twist YY' of Y.Y. Thus to a sheaf of modules MM over DYD_Y one can assign a closed subvariety of TY,T^*_{Y'}, called the pp-support, namely the support of MM seen as a sheaf on TY.T^*_{Y'}. We study here the family of pp-supports assigned to the reductions modulo primes pp of a holonomic D\mathcal{D}-module. We prove that the Azumaya algebra of differential operators splits on the regular locus of the pp-support and that the pp-support is a Lagrangian subvariety of the cotangent space, for pp large enough. The latter was conjectured by Kontsevich. Our approach also provides a new proof of the involutivity of the singular support of a holonomic D\mathcal{D}-module, by reduction modulo p.p.Comment: The article has been rewritten with much improved exposition as well as some additional results, e.g. Corollary 6.3.1. This is the final version, accepted for publication in Inventiones Mathematica
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