171 research outputs found
Estimating a Polya frequency function_2
We consider the non-parametric maximum likelihood estimation in the class of
Polya frequency functions of order two, viz. the densities with a concave
logarithm. This is a subclass of unimodal densities and fairly rich in general.
The NPMLE is shown to be the solution to a convex programming problem in the
Euclidean space and an algorithm is devised similar to the iterative convex
minorant algorithm by Jongbleod (1999). The estimator achieves Hellinger
consistency when the true density is a PFF_2 itself.Comment: Published at http://dx.doi.org/10.1214/074921707000000184 in the IMS
Lecture Notes Monograph Series
(http://www.imstat.org/publications/lecnotes.htm) by the Institute of
Mathematical Statistics (http://www.imstat.org
Diagrammatic perturbation theory for Stochastic nonlinear oscillators
We consider the stochastically driven one dimensional nonlinear oscillator
where f(t) is a
Gaussian noise which, for the bulk of the work, is delta correlated (white
noise). We construct the linear response function in frequency space in a
systematic Feynman diagram-based perturbation theory. As in other areas of
physics, this expansion is characterized by the number of loops in the diagram.
This allows us to show that the damping coefficient acquires a correction at
which is the two loop order. More importantly, it leads to the
numerically small but conceptually interesting finding that the response is a
function of the frequency at which a stochastic system is probed. The method is
easily generalizable to different kinds of nonlinearity and replacing the
nonlinear term in the above equation by , we can discuss the issue of
noise driven escape from a potential well. If we add a periodic forcing to the
cubic nonlinearity situation, then we find that the response function can have
a contribution jointly proportional to the strength of the noise and the
amplitude of the periodic drive. To treat the stochastic Kapitza problem in
perturbation theory we find that it is necessary to have a coloured noise.Comment: Page 23 ,5 figure
Theoretical quantification of shape distortion in fuzzy hough transform
We present a generalization of classical Hough transform in fuzzy set theoretic framework (called fuzzy Hough transform or FHT) in order to handle the impreciseness/ill-definedness in shape description. In addition to identifying the shapes, the methodology can quantify the amount of distortion present in each shape by suitably characterizing the parametric space. We extended FHT to take care of gray level images (gray FHT) in order to handle the gray level variation along with shape distortion. The gray FHT gives rise to a scheme for image segmentation based on the a priori knowledge about the shapes
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