1,834,560 research outputs found
On large-sample estimation and testing via quadratic inference functions for correlated data
Hansen (1982) proposed a class of "generalized method of moments" (GMMs) for
estimating a vector of regression parameters from a set of score functions.
Hansen established that, under certain regularity conditions, the estimator
based on the GMMs is consistent, asymptotically normal and asymptotically
efficient. In the generalized estimating equation framework, extending the
principle of the GMMs to implicitly estimate the underlying correlation
structure leads to a "quadratic inference function" (QIF) for the analysis of
correlated data. The main objectives of this research are to (1) formulate an
appropriate estimated covariance matrix for the set of extended score functions
defining the inference functions; (2) develop a unified large-sample
theoretical framework for the QIF; (3) derive a generalization of the QIF test
statistic for a general linear hypothesis problem involving correlated data
while establishing the asymptotic distribution of the test statistic under the
null and local alternative hypotheses; (4) propose an iteratively reweighted
generalized least squares algorithm for inference in the QIF framework; and (5)
investigate the effect of basis matrices, defining the set of extended score
functions, on the size and power of the QIF test through Monte Carlo simulated
experiments.Comment: 32 pages, 2 figure
An action principle for Vasiliev's four-dimensional higher-spin gravity
We provide Vasiliev's fully nonlinear equations of motion for bosonic gauge
fields in four spacetime dimensions with an action principle. We first extend
Vasiliev's original system with differential forms in degrees higher than one.
We then derive the resulting duality-extended equations of motion from a
variational principle based on a generalized Hamiltonian sigma-model action.
The generalized Hamiltonian contains two types of interaction freedoms: One set
of functions that appears in the Q-structure of the generalized curvatures of
the odd forms in the duality-extended system; and another set depending on the
Lagrange multipliers, encoding a generalized Poisson structure, i.e. a set of
polyvector fields of ranks two or higher in target space. We find that at least
one of the two sets of interaction-freedom functions must be linear in order to
ensure gauge invariance. We discuss consistent truncations to the minimal Type
A and B models (with only even spins), spectral flows on-shell and provide
boundary conditions on fields and gauge parameters that are compatible with the
variational principle and that make the duality-extended system equivalent, on
shell, to Vasiliev's original system.Comment: 37 pages. References added, corrected typo
A new method for the representation and evolution of three dimensional discontinuity surfaces in XFEM/GFEM
The ability of the extended and generalized finite element methods of modeling discontinuities independent of mesh alignment requires a suitable representation for the discontinuity surfaces. In the present paper a method for constructing level set functions based on vector data and geometric operations in three dimensions is presented. In contrast to classical level set methods, the proposed approach does not require the integration of differential evolution equations, resulting in a particularly simple structure and easy implementatio
Microstructural enrichment functions based on stochastic Wang tilings
This paper presents an approach to constructing microstructural enrichment
functions to local fields in non-periodic heterogeneous materials with
applications in Partition of Unity and Hybrid Finite Element schemes. It is
based on a concept of aperiodic tilings by the Wang tiles, designed to produce
microstructures morphologically similar to original media and enrichment
functions that satisfy the underlying governing equations. An appealing feature
of this approach is that the enrichment functions are defined only on a small
set of square tiles and extended to larger domains by an inexpensive stochastic
tiling algorithm in a non-periodic manner. Feasibility of the proposed
methodology is demonstrated on constructions of stress enrichment functions for
two-dimensional mono-disperse particulate media.Comment: 27 pages, 12 figures; v2: completely re-written after the first
revie
Nambu Quantum Mechanics: A Nonlinear Generalization of Geometric Quantum Mechanics
We propose a generalization of the standard geometric formulation of quantum
mechanics, based on the classical Nambu dynamics of free Euler tops. This
extended quantum mechanics has in lieu of the standard exponential time
evolution, a nonlinear temporal evolution given by Jacobi elliptic functions.
In the limit where latter's moduli parameters are set to zero, the usual
geometric formulation of quantum mechanics, based on the Kahler structure of a
complex projective Hilbert space, is recovered. We point out various novel
features of this extended quantum mechanics, including its geometric aspects.
Our approach sheds a new light on the problem of quantization of Nambu
dynamics. Finally, we argue that the structure of this nonlinear quantum
mechanics is natural from the point of view of string theory.Comment: 15 pages, LaTeX, typos correcte
EXTENDED PARTIAL ORDERS: A UNIFYING STRUCTURE FOR ABSTRACT CHOICE THEORY
The concept of a strict extended partial order (SEPO) has turned out to be very useful in explaining (resp. rationalizing) non-binary choice functions. The present paper provides a general account of the concept of extended binary relations, i.e., relations between subsets and elements of a given universal set of alternatives. In particular, we define the concept of a weak extended partial order (WEPO) and show how it can be used in order to represent rankings of opportunity sets that display a ""preference for opportunities."" We also clarify the relationship between SEPOs and WEPOs, which involves a non-trivial condition, called ""strict properness."" Several characterizations of strict (and weak) properness are provided based on which we argue for properness as an appropriate condition demarcating ""choice based"" preference.
A Constraint-based Model for Multi-objective Repair Planning
This work presents a constraint based model for the
planning and scheduling of disconnection and connection
tasks when repairing faulty components in a system.
Since multi-mode operations are considered, the
problem involves the ordering and the selection of the
tasks and modes from a set of alternatives, using the
shared resources efficiently. Additionally, delays due to
change of configurations and transportation are considered.
The goal is the minimization of two objective functions:
makespan and cost. The set of all feasible plans
are represented by an extended And/Or graph, that embodies
all of the constraints of the problem, allowing non
reversible and parallel plans. A simple branch-and-bound
algorithm has been used for testing the model with different
combinations of the functions to minimize using the
weighted-sum approach.Ministerio de Educación y Ciencia DIP2006-15476-C02-0
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