22,384 research outputs found
On Degrees of Freedom of Projection Estimators with Applications to Multivariate Nonparametric Regression
In this paper, we consider the nonparametric regression problem with
multivariate predictors. We provide a characterization of the degrees of
freedom and divergence for estimators of the unknown regression function, which
are obtained as outputs of linearly constrained quadratic optimization
procedures, namely, minimizers of the least squares criterion with linear
constraints and/or quadratic penalties. As special cases of our results, we
derive explicit expressions for the degrees of freedom in many nonparametric
regression problems, e.g., bounded isotonic regression, multivariate
(penalized) convex regression, and additive total variation regularization. Our
theory also yields, as special cases, known results on the degrees of freedom
of many well-studied estimators in the statistics literature, such as ridge
regression, Lasso and generalized Lasso. Our results can be readily used to
choose the tuning parameter(s) involved in the estimation procedure by
minimizing the Stein's unbiased risk estimate. As a by-product of our analysis
we derive an interesting connection between bounded isotonic regression and
isotonic regression on a general partially ordered set, which is of independent
interest.Comment: 72 pages, 7 figures, Journal of the American Statistical Association
(Theory and Methods), 201
On the effective action of a space-like brane
Starting from the non-BPS D-brane action we derive an effective action
in space dimensions by studying the fluctuations of various bosonic
fields around the time-like tachyonic kink solution (obtained by Wick rotation
of the space-like tachyonic kink solution) of the non-BPS brane. In real time
this describes the dynamics of a space-like or Euclidean brane in
-dimensions containing a Dirac-Born-Infeld part and a Wess-Zumino part.
The WZ part is purely imaginary and so the action is complex if it represents
the source of the time-dependent background of type II string theory i.e. the
S-brane. On the other hand, the WZ part as well as the action is real if it
represents the source in type II string theory i.e. the E-brane. The DBI
part is the same as obtained before using different method. This is then
further illustrated by considering brane probe in space-like brane background.Comment: 14 pages, LaTeX, no figures, minor corrections and acknowledgement
added, version to appear in Phys. Lett.
LOX manifold tee analysis
A 4000 Hz vibration phenomena was observed during the test firings of several space shuttle main engines (SSME). Experimental studies of this phenomena suggest that the problem might be associated with vortex shedding from the vanes within the LOX tee manifold. The objective of this study was to determine the unsteady, 3-D flow associated with these vanes by computational methods to identify and better understand the 4000 Hz vibration phenomena. A flow solver, FDNS, for the turbulent conservation equations was validated for predicting high frequency vortex dynamics and used to predict 2-D and 3-D flows within the LOX tee. 4000 Hz excitation oscillations were predicted for some flows and the entire 3-D flow structure was predicted for LOX tee flow. The complexity of the flow was revealed by this analysis, and computational methods for predicting these high frequency oscillations in future engine systems were established
Computation of turbulent boundary layer flows with an algebraic stress turbulence model
An algebraic stress turbulence model is presented, characterized by the following: (1) the eddy viscosity expression is derived from the Reynolds stress turbulence model; (2) the turbulent kinetic energy dissipation rate equation is improved by including a production range time scale; and (3) the diffusion coefficients for turbulence equations are adjusted so that the kinetic energy profile extends further into the free stream region found in most experimental data. The turbulent flow equations were solved using a finite element method. Examples include: fully developed channel flow, fully developed pipe flow, flat plate boundary layer flow, plane jet exhausting into a moving stream, circular jet exhausting into a moving stream, and wall jet flow. Computational results compare favorably with experimental data for most of the examples considered. Significantly improved results were obtained for the plane jet flow, the circular jet flow, and the wall jet flow; whereas the remainder are comparable to those obtained by finite difference methods using the standard kappa-epsilon turbulence model. The latter seems to be promising with further improvement of the expression for the eddy viscosity coefficient
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