219 research outputs found
On multipartite invariant states II. Orthogonal symmetry
We construct a new class of multipartite states possessing orthogonal
symmetry. This new class defines a convex hull of multipartite states which are
invariant under the action of local unitary operations introduced in our
previous paper "On multipartite invariant states I. Unitary symmetry". We study
basic properties of multipartite symmetric states: separability criteria and
multi-PPT conditions.Comment: 6 pages; slight corrections + new reference
Two extensions of Thurston's spectral theorem for surface diffeomorphisms
Thurston obtained a classification of individual surface homeomorphisms via
the dynamics of the corresponding mapping class elements on Teichm\"uller
space. In this paper we present certain extended versions of this, first, to
random products of homeomorphisms and second, to holomorphic self-maps of
Teichm\"uller spaces.Comment: 11 page
Higher Spin Klein Surfaces
We find all m-spin structures on Klein surfaces of genus larger than one. An m-spin structure on a Riemann surface P is a complex line bundle on P whose m-th tensor power is the cotangent bundle of P. A Klein surface can be described by a pair (P,tau), where P is a Riemann surface and tau is an anti-holomorphic involution on P. An m-spin structure on a Klein surface (P,tau) is an m-spin structure on the Riemann surface P which is preserved under the action of the anti-holomorphic involution tau. We determine the conditions for the existence and give a complete description of all real m-spin structures on a Klein surface. In particular we compute the number of m-spin structures on a Klein surface (P,tau) in terms of its natural topological invariants
Homogeneous -shifts
The classification of homogeneous scalar weighted shifts is known. Recently,
Kor\'{a}nyi obtained a large class of inequivalent irreducible homogeneous
bi-lateral -by- block shifts. In this paper, we construct two distinct
classes of examples not in the list of Kor\'{a}nyi. It is then shown that these
new examples of irreducible homogeneous bi-lateral -by- block shifts,
together with the ones found earlier by Kor\'{a}nyi, account for every
unitarily inequivalent irreducible homogeneous bi-lateral -by- block
shift.Comment: 26 page
Model categories in deformation theory
The aim is the formalization of Deformation Theory in an abstract model category, in order to study several geometric deformation problems from a unified point of view. The main geometric application is the description of the DG-Lie algebra controlling infinitesimal deformations of a separated scheme over a field of characteristic 0
Moduli Spaces of Higher Spin Klein Surfaces
We study the connected components of the space of higher spin bundles on hyperbolic Klein surfaces. A Klein surface is a generalisation of a Riemann surface to the case of non-orientable surfaces or surfaces with boundary. The category of Klein surfaces is isomorphic to the category of real algebraic curves. An m-spin bundle on a Klein surface is a complex line bundle whose m-th tensor power is the cotangent bundle. The spaces of higher spin bundles on Klein surfaces are important because of their applications in singularity theory and real algebraic geometry, in particular for the study of real forms of Gorenstein quasi-homogeneous surface singularities. In this paper we describe all connected components of the space of higher spin bundles on hyperbolic Klein surfaces in terms of their topological invariants and prove that any connected component is homeomorphic to a quotient of an Euclidean space by a discrete group
Communication Complexity of Set-Disjointness for All Probabilities
We study set-disjointness in a generalized model of randomized two-party communication where the probability of acceptance must be at least alpha(n) on yes-inputs and at most beta(n) on no-inputs, for some functions alpha(n)>beta(n). Our main result is a complete characterization of the private-coin communication complexity of set-disjointness for all functions alpha and beta, and a near-complete characterization for public-coin protocols. In particular, we obtain a simple proof of a theorem of Braverman and Moitra (STOC 2013), who studied the case where alpha=1/2+epsilon(n) and beta=1/2-epsilon(n). The following contributions play a crucial role in our characterization and are interesting in their own right.
(1) We introduce two communication analogues of the classical complexity class that captures small bounded-error computations: we define a "restricted" class SBP (which lies between MA and AM) and an "unrestricted" class USBP. The distinction between them is analogous to the distinction between the well-known communication classes PP and UPP.
(2) We show that the SBP communication complexity is precisely captured by the classical corruption lower bound method. This sharpens a theorem of Klauck (CCC 2003).
(3) We use information complexity arguments to prove a linear lower bound on the USBP complexity of set-disjointness
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