3,627 research outputs found
Towards non-reductive geometric invariant theory
We study linear actions of algebraic groups on smooth projective varieties X.
A guiding goal for us is to understand the cohomology of "quotients" under such
actions, by generalizing (from reductive to non-reductive group actions)
existing methods involving Mumford's geometric invariant theory (GIT). We
concentrate on actions of unipotent groups H, and define sets of stable points
X^s and semistable points X^{ss}, often explicitly computable via the methods
of reductive GIT, which reduce to the standard definitions due to Mumford in
the case of reductive actions. We compare these with definitions in the
literature. Results include (1) a geometric criterion determining whether or
not a ring of invariants is finitely generated, (2) the existence of a
geometric quotient of X^s, and (3) the existence of a canonical "enveloping
quotient" variety of X^{ss}, denoted X//H, which (4) has a projective
completion given by a reductive GIT quotient and (5) is itself projective and
isomorphic to Proj(k[X]^H) when k[X]^H is finitely generated.Comment: 37 pages, 1 figure (parabola2.eps), in honor of Bob MacPherson's 60th
birthda
Cohomology of Line Bundles: A Computational Algorithm
We present an algorithm for computing line bundle valued cohomology classes
over toric varieties. This is the basic starting point for computing massless
modes in both heterotic and Type IIB/F-theory compactifications, where the
manifolds of interest are complete intersections of hypersurfaces in toric
varieties supporting additional vector bundles.Comment: 11 pages, 1 figure, 2 tables; v2: typos and references corrected; v3:
proof-related statements updated, cohomCalg implementation available at
http://wwwth.mppmu.mpg.de/members/blumenha/cohomcalg
Finding and using exact solutions of the Einstein equations
The evolution of the methods used to find solutions of Einstein's field
equations during the last 100 years is described. Early papers used assumptions
on the coordinate forms of the metrics. Since the 1950s more invariant methods
have been deployed in most new papers. The uses to which the solutions found
have been put are discussed, and it is shown that they have played an important
role in the development of many aspects, both mathematical and physical, of
general relativity.Comment: 15 pages, LaTeX2e, aipproc.cls, invited lecture to appear in the
Proceedings of ERE05 (the Spanish Relativity Meeting), Oviedo, September
2005, to be published by the American Institute of Physics. v2: Remarks on
black hole entropy corrected. Other minor change
Verified Correctness and Security of mbedTLS HMAC-DRBG
We have formalized the functional specification of HMAC-DRBG (NIST 800-90A),
and we have proved its cryptographic security--that its output is
pseudorandom--using a hybrid game-based proof. We have also proved that the
mbedTLS implementation (C program) correctly implements this functional
specification. That proof composes with an existing C compiler correctness
proof to guarantee, end-to-end, that the machine language program gives strong
pseudorandomness. All proofs (hybrid games, C program verification, compiler,
and their composition) are machine-checked in the Coq proof assistant. Our
proofs are modular: the hybrid game proof holds on any implementation of
HMAC-DRBG that satisfies our functional specification. Therefore, our
functional specification can serve as a high-assurance reference.Comment: Appearing in CCS '1
Joint asymptotics for semi-nonparametric regression models with partially linear structure
We consider a joint asymptotic framework for studying semi-nonparametric
regression models where (finite-dimensional) Euclidean parameters and
(infinite-dimensional) functional parameters are both of interest. The class of
models in consideration share a partially linear structure and are estimated in
two general contexts: (i) quasi-likelihood and (ii) true likelihood. We first
show that the Euclidean estimator and (pointwise) functional estimator, which
are re-scaled at different rates, jointly converge to a zero-mean Gaussian
vector. This weak convergence result reveals a surprising joint asymptotics
phenomenon: these two estimators are asymptotically independent. A major goal
of this paper is to gain first-hand insights into the above phenomenon.
Moreover, a likelihood ratio testing is proposed for a set of joint local
hypotheses, where a new version of the Wilks phenomenon [Ann. Math. Stat. 9
(1938) 60-62; Ann. Statist. 1 (2001) 153-193] is unveiled. A novel technical
tool, called a joint Bahadur representation, is developed for studying these
joint asymptotics results.Comment: Published at http://dx.doi.org/10.1214/15-AOS1313 in the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Inference on Counterfactual Distributions
Counterfactual distributions are important ingredients for policy analysis
and decomposition analysis in empirical economics. In this article we develop
modeling and inference tools for counterfactual distributions based on
regression methods. The counterfactual scenarios that we consider consist of
ceteris paribus changes in either the distribution of covariates related to the
outcome of interest or the conditional distribution of the outcome given
covariates. For either of these scenarios we derive joint functional central
limit theorems and bootstrap validity results for regression-based estimators
of the status quo and counterfactual outcome distributions. These results allow
us to construct simultaneous confidence sets for function-valued effects of the
counterfactual changes, including the effects on the entire distribution and
quantile functions of the outcome as well as on related functionals. These
confidence sets can be used to test functional hypotheses such as no-effect,
positive effect, or stochastic dominance. Our theory applies to general
counterfactual changes and covers the main regression methods including
classical, quantile, duration, and distribution regressions. We illustrate the
results with an empirical application to wage decompositions using data for the
United States.
As a part of developing the main results, we introduce distribution
regression as a comprehensive and flexible tool for modeling and estimating the
\textit{entire} conditional distribution. We show that distribution regression
encompasses the Cox duration regression and represents a useful alternative to
quantile regression. We establish functional central limit theorems and
bootstrap validity results for the empirical distribution regression process
and various related functionals.Comment: 55 pages, 1 table, 3 figures, supplementary appendix with additional
results available from the authors' web site
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