234,429 research outputs found
Exact Post Model Selection Inference for Marginal Screening
We develop a framework for post model selection inference, via marginal
screening, in linear regression. At the core of this framework is a result that
characterizes the exact distribution of linear functions of the response ,
conditional on the model being selected (``condition on selection" framework).
This allows us to construct valid confidence intervals and hypothesis tests for
regression coefficients that account for the selection procedure. In contrast
to recent work in high-dimensional statistics, our results are exact
(non-asymptotic) and require no eigenvalue-like assumptions on the design
matrix . Furthermore, the computational cost of marginal regression,
constructing confidence intervals and hypothesis testing is negligible compared
to the cost of linear regression, thus making our methods particularly suitable
for extremely large datasets. Although we focus on marginal screening to
illustrate the applicability of the condition on selection framework, this
framework is much more broadly applicable. We show how to apply the proposed
framework to several other selection procedures including orthogonal matching
pursuit, non-negative least squares, and marginal screening+Lasso
A paradigmatic flow for small-scale magnetohydrodynamics: properties of the ideal case and the collision of current sheets
We propose two sets of initial conditions for magnetohydrodynamics (MHD) in
which both the velocity and the magnetic fields have spatial symmetries that
are preserved by the dynamical equations as the system evolves. When
implemented numerically they allow for substantial savings in CPU time and
memory storage requirements for a given resolved scale separation. Basic
properties of these Taylor-Green flows generalized to MHD are given, and the
ideal non-dissipative case is studied up to the equivalent of 2048^3 grid
points for one of these flows. The temporal evolution of the logarithmic
decrements, delta, of the energy spectrum remains exponential at the highest
spatial resolution considered, for which an acceleration is observed briefly
before the grid resolution is reached. Up to the end of the exponential decay
of delta, the behavior is consistent with a regular flow with no appearance of
a singularity. The subsequent short acceleration in the formation of small
magnetic scales can be associated with a near collision of two current sheets
driven together by magnetic pressure. It leads to strong gradients with a fast
rotation of the direction of the magnetic field, a feature also observed in the
solar wind.Comment: 8 pages, 4 figure
A theoretical basis for the analysis of redundant software subject to coincident errors
Fundamental to the development of redundant software techniques fault-tolerant software, is an understanding of the impact of multiple-joint occurrences of coincident errors. A theoretical basis for the study of redundant software is developed which provides a probabilistic framework for empirically evaluating the effectiveness of the general (N-Version) strategy when component versions are subject to coincident errors, and permits an analytical study of the effects of these errors. The basic assumptions of the model are: (1) independently designed software components are chosen in a random sample; and (2) in the user environment, the system is required to execute on a stationary input series. The intensity of coincident errors, has a central role in the model. This function describes the propensity to introduce design faults in such a way that software components fail together when executing in the user environment. The model is used to give conditions under which an N-Version system is a better strategy for reducing system failure probability than relying on a single version of software. A condition which limits the effectiveness of a fault-tolerant strategy is studied, and it is posted whether system failure probability varies monotonically with increasing N or whether an optimal choice of N exists
Modal expansions and non-perturbative quantum field theory in Minkowski space
We introduce a spectral approach to non-perturbative field theory within the
periodic field formalism. As an example we calculate the real and imaginary
parts of the propagator in 1+1 dimensional phi^4 theory, identifying both
one-particle and multi-particle contributions. We discuss the computational
limits of existing diagonalization algorithms and suggest new quasi-sparse
eigenvector methods to handle very large Fock spaces and higher dimensional
field theories.Comment: new material added, 12 pages, 6 figure
Lattice calculations for A=3,4,6,12 nuclei using chiral effective field theory
We present lattice calculations for the ground state energies of tritium,
helium-3, helium-4, lithium-6, and carbon-12 nuclei. Our results were
previously summarized in a letter publication. This paper provides full details
of the calculations. We include isospin-breaking, Coulomb effects, and
interactions up to next-to-next-to-leading order in chiral effective field
theory.Comment: 38 pages, 11 figures, final publication versio
Langley Atmospheric Information Retrieval System (LAIRS): System description and user's guide
This document presents the user's guide, system description, and mathematical specifications for the Langley Atmospheric Information Retrieval System (LAIRS). It also includes a description of an optimal procedure for operational use of LAIRS. The primary objective of the LAIRS Program is to make it possible to obtain accurate estimates of atmospheric pressure, density, temperature, and winds along Shuttle reentry trajectories for use in postflight data reduction
- …