26,625 research outputs found
How Does a Fundamental String Stretch its Horizon?
It has recently been shown that if we take into account a class of higher
derivative corrections to the effective action of heterotic string theory, the
entropy of the black hole solution representing elementary string states
correctly reproduces the statistical entropy computed from the degeneracy of
elementary string states. So far the form of the solution has been analyzed at
distance scales large and small compared to the string scale. We analyze the
solution that interpolates between these two limits and point out a subtlety in
constructing such a solution due to the presence of higher derivative terms in
the effective action. We also study the T-duality transformation rules to
relate the moduli fields of the effective field theory to the physical
compactification radius in the presence of higher derivative corrections and
use these results to find the physical radius of compactification near the
horizon of the black hole. The radius approaches a finite value even though the
corresponding modulus field vanishes. Finally we discuss the non-leading
contribution to the black hole entropy due to space-time quantum corrections to
the effective action and the ambiguity involved in comparing this result to the
statistical entropy.Comment: LaTeX file, 38 pages; v2: minor changes and added reference
Particle Learning and Smoothing
Particle learning (PL) provides state filtering, sequential parameter
learning and smoothing in a general class of state space models. Our approach
extends existing particle methods by incorporating the estimation of static
parameters via a fully-adapted filter that utilizes conditional sufficient
statistics for parameters and/or states as particles. State smoothing in the
presence of parameter uncertainty is also solved as a by-product of PL. In a
number of examples, we show that PL outperforms existing particle filtering
alternatives and proves to be a competitor to MCMC.Comment: Published in at http://dx.doi.org/10.1214/10-STS325 the Statistical
Science (http://www.imstat.org/sts/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Particle Learning for General Mixtures
This paper develops particle learning (PL) methods for the estimation of general mixture models. The approach is distinguished from alternative particle filtering methods in two major ways. First, each iteration begins by resampling particles according to posterior predictive probability, leading to a more efficient set for propagation. Second, each particle tracks only the "essential state vector" thus leading to reduced dimensional inference. In addition, we describe how the approach will apply to more general mixture models of current interest in the literature; it is hoped that this will inspire a greater number of researchers to adopt sequential Monte Carlo methods for fitting their sophisticated mixture based models. Finally, we show that PL leads to straight forward tools for marginal likelihood calculation and posterior cluster allocation.Business Administratio
A Numerical Procedure for 2D Fluid Flow Simulation in Unstructured Meshes
The present work addresses the numerical simulation of fluid flow for 2D problems. The physical principles and numerical models implemented in the software package EasyCFD are presented in a synthetic and clear way. The 2D form of the Navier-Stokes equations is considered, using the eddy-viscosity concept to take into account turbulence effects upon the mean flow field. The k-ε and the k-ω Shear Stress Transport (SST) turbulence models allow for the calculation of the turbulent viscosity. The numerical model is based on a control volume approach, using the SIMPLEC algorithm on an unstructured quadrilateral mesh. The mesh arrangement is a non-staggered type. The coordinate transformation, integration discretization and solution method for the governing equations are fully described. As an example of application, the airflow around a NACA 0012 airfoil is calculated and the results for the aerodynamic coefficients are compared with available experimental data
On the canonical map of surfaces with q>=6
We carry out an analysis of the canonical system of a minimal complex surface
of general type with irregularity q>0. Using this analysis we are able to
sharpen in the case q>0 the well known Castelnuovo inequality K^2>=3p_g+q-7.
Then we turn to the study of surfaces with p_g=2q-3 and no fibration onto a
curve of genus >1. We prove that for q>=6 the canonical map is birational.
Combining this result with the analysis of the canonical system, we also prove
the inequality: K^2>=7\chi+2. This improves an earlier result of the first and
second author [M.Mendes Lopes and R.Pardini, On surfaces with p_g=2q-3, Adv. in
Geom. 10 (3) (2010), 549-555].Comment: Dedicated to Fabrizio Catanese on the occasion of his 60th birthday.
To appear in the special issue of Science of China Ser.A: Mathematics
dedicated to him. V2:some typos have been correcte
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