958 research outputs found
zoo: S3 Infrastructure for Regular and Irregular Time Series
zoo is an R package providing an S3 class with methods for indexed totally
ordered observations, such as discrete irregular time series. Its key design
goals are independence of a particular index/time/date class and consistency
with base R and the "ts" class for regular time series. This paper describes
how these are achieved within zoo and provides several illustrations of the
available methods for "zoo" objects which include plotting, merging and
binding, several mathematical operations, extracting and replacing data and
index, coercion and NA handling. A subclass "zooreg" embeds regular time series
into the "zoo" framework and thus bridges the gap between regular and irregular
time series classes in R.Comment: 24 pages, 5 figure
Representability of Hilbert schemes and Hilbert stacks of points
We show that the Hilbert functor of points on an arbitrary separated
algebraic stack is an algebraic space. We also show the algebraicity of the
Hilbert stack of points on an algebraic stack and the algebraicity of the Weil
restriction of an algebraic stack along a finite flat morphism. For the latter
two results, no separation assumptions are necessary.Comment: 15 pages; major revision, final versio
Formal groups arising from formal punctured ribbons
We investigate Picard functor of a formal punctured ribbon. We prove that
under some conditions this functor is representable by a formal group scheme.
Formal punctured ribbons were introduced in arXiv:0708.0985.Comment: 42 pages, minor change
On the cohomology of stable map spaces
We describe an approach to calculating the cohomology rings of stable map
spaces. The method we use is due to Akildiz-Carrell and employs a C^*-action
and a vector field which is equivariant with respect to this C^*-action. We
give an explicit description of the big Bialynicky-Birula cell of the
C^*-action on Mbar_00(P^n,d) as a vector bundle on Mbar_0d. This is used to
calculate explicitly the cohomology ring of Mbar_00(P^n,d) in the cases d=2 and
d=3. Of particular interest is the case as n approaches infinity.Comment: 63 page
A proof of the Grothendieck-Serre conjecture on principal bundles over regular local rings containing infinite fields
Let R be a regular local ring, containing an infinite field. Let G be a
reductive group scheme over R. We prove that a principal G-bundle over R is
trivial, if it is trivial over the fraction field of R.Comment: Section "Formal loops and affine Grassmannians" is removed as this is
now covered in arXiv:1308.3078. Exposition is improved and slightly
restructured. Some minor correction
Torsion functors with monomial support
The dependence of torsion functors on their supporting ideals is
investigated, especially in the case of monomial ideals of certain subrings of
polynomial algebras over not necessarily Noetherian rings. As an application it
is shown how flatness of quasicoherent sheaves on toric schemes is related to
graded local cohomology.Comment: updated reference
New Bell inequalities for the singlet state: Going beyond the Grothendieck bound
Contemporary versions of Bell's argument against local hidden variable (LHV)
theories are based on the Clauser Horne Shimony and Holt (CHSH) inequality, and
various attempts to generalize it. The amount of violation of these
inequalities cannot exceed the bound set by the Grothendieck constants.
However, if we go back to the original derivation by Bell, and use the perfect
anti-correlation embodied in the singlet spin state, we can go beyond these
bounds. In this paper we derive two-particle Bell inequalities for traceless
two-outcome observables, whose violation in the singlet spin state go beyond
the Grothendieck constants both for the two and three dimensional cases.
Moreover, creating a higher dimensional analog of perfect correlations, and
applying a recent result of Alon and his associates (Invent. Math. 163 499
(2006)) we prove that there are two-particle Bell inequalities for traceless
two-outcome observables whose violation increases to infinity as the dimension
and number of measurements grow. Technically these result are possible because
perfect correlations (or anti-correlations) allow us to transport the indices
of the inequality from the edges of a bipartite graph to those of the complete
graph. Finally, it is shown how to apply these results to mixed Werner states,
provided that the noise does not exceed 20%.Comment: 18 pages, two figures, some corrections and additional references,
published versio
Cartier and Weil Divisors on Varieties with Quotient Singularities
The main goal of this paper is to show that the notions of Weil and Cartier
-divisors coincide for -manifolds and give a procedure to
express a rational Weil divisor as a rational Cartier divisor. The theory is
illustrated on weighted projective spaces and weighted blow-ups.Comment: 16 page
Grothendieck's constant and local models for noisy entangled quantum states
We relate the nonlocal properties of noisy entangled states to Grothendieck's
constant, a mathematical constant appearing in Banach space theory. For
two-qubit Werner states \rho^W_p=p \proj{\psi^-}+(1-p){\one}/{4}, we show
that there is a local model for projective measurements if and only if , where is Grothendieck's constant of order 3. Known bounds
on prove the existence of this model at least for ,
quite close to the current region of Bell violation, . We
generalize this result to arbitrary quantum states.Comment: 6 pages, 1 figur
Complete moduli of cubic threefolds and their intermediate Jacobians
The intermediate Jacobian map, which associates to a smooth cubic threefold
its intermediate Jacobian, does not extend to the GIT compactification of the
space of cubic threefolds, not even as a map to the Satake compactification of
the moduli space of principally polarized abelian fivefolds. A much better
"wonderful" compactification of the space of cubic threefolds was constructed
by the first and fourth authors --- it has a modular interpretation, and
divisorial normal crossing boundary. We prove that the intermediate Jacobian
map extends to a morphism from the wonderful compactification to the second
Voronoi toroidal compactification of the moduli of principally polarized
abelian fivefolds --- the first and fourth author previously showed that it
extends to the Satake compactification. Since the second Voronoi
compactification has a modular interpretation, our extended intermediate
Jacobian map encodes all of the geometric information about the degenerations
of intermediate Jacobians, and allows for the study of the geometry of cubic
threefolds via degeneration techniques. As one application we give a complete
classification of all degenerations of intermediate Jacobians of cubic
threefolds of torus rank 1 and 2.Comment: 56 pages; v2: multiple updates and clarification in response to
detailed referee's comment
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