9,703 research outputs found
Estimation of vector fields in unconstrained and inequality constrained variational problems for segmentation and registration
Vector fields arise in many problems of computer vision, particularly in non-rigid registration. In this paper, we develop coupled partial differential equations (PDEs) to estimate vector fields that define the deformation between
objects, and the contour or surface that defines the segmentation of the objects as well.We also explore the utility of inequality constraints applied to variational problems in vision such as estimation of deformation fields in non-rigid registration and tracking. To solve inequality constrained vector
field estimation problems, we apply tools from the Kuhn-Tucker theorem in optimization theory. Our technique differs from recently popular joint segmentation and registration algorithms, particularly in its coupled set of PDEs derived from the same set of energy terms for registration and
segmentation. We present both the theory and results that demonstrate our approach
Localizing Volatilities
We propose two main applications of Gy\"{o}ngy (1986)'s construction of
inhomogeneous Markovian stochastic differential equations that mimick the
one-dimensional marginals of continuous It\^{o} processes. Firstly, we prove
Dupire (1994) and Derman and Kani (1994)'s result. We then present Bessel-based
stochastic volatility models in which this relation is used to compute
analytical formulas for the local volatility. Secondly, we use these mimicking
techniques to extend the well-known local volatility results to a stochastic
interest rates framework
Estimating the rate constant of cyclic GMP hydrolysis by activated phosphodiesterase in photoreceptors
The early steps of light response occur in the outer segment of rod and cone
photoreceptor. They involve the hydrolysis of cGMP, a soluble cyclic
nucleotide, that gates ionic channels located in the outer segment membrane. We
shall study here the rate by which cGMP is hydrolyzed by activated
phosphodiesterase (PDE). This process has been characterized experimentally by
two different rate constants and : accounts
for the effect of all spontaneously active PDE in the outer segment, and
characterizes cGMP hydrolysis induced by a single light-activated
PDE. So far, no attempt has been made to derive the experimental values of
and from a theoretical model, which is the goal of this
work. Using a model of diffusion in the confined rod geometry, we derive
analytical expressions for and by calculating the flux
of cGMP molecules to an activated PDE site. We obtain the dependency of these
rate constants as a function of the outer segment geometry, the PDE activation
and deactivation rates and the aqueous cGMP diffusion constant. Our formulas
show good agreement with experimental measurements. Finally, we use our
derivation to model the time course of the cGMP concentration in a
transversally well stirred outer segment.Comment: 20 pages, revtex4, 5 figure
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