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Computing the Geodesic Interpolating Spline
Get PDFWe examine non-rigid image registration by knotpoint
matching. We consider registering two images, each with a set of
knotpoints marked, where one of the images is to be registered to the
other by a nonlinear warp so that the knotpoints on the template image
are exactly aligned with the corresponding knotpoints on the reference
image.
We explore two approaches to computing the Geodesic Interpolating
Spline registration. First, we describe a method which exploits the
structure of the objective function and constraints to permit
efficient optimisation and second, we outline an approach using the
framework of classical mechanics
Tomographic reconstruction of stress from photoelastic measurements using elastic regularization.
Get PDFIn this paper we consider the problem of recovering the stress tensor field of a three dimensional object from
measurements of the polarization state of transmitted light. In contrast to the ray transform approach suggested
by Sharafutdinov, which uses the inversion of planar Radon transforms to recover a single component of the
deviatoric stress normal to a plane, we study the simultaneous reconstruction of all components of the deviatoric
stress in each voxel using a matrix approximation to the truncated transverse ray transform. This approach allows us to employ partial differential operators related to linear elasticity in a regularizing penalty term resulting in a well posed problem. We note that the hydrostatic stress is determined by the deviatoric stress (up to
an additive constant) from the equilibrium equation, and that our numerical results confirm that the full stress tensor can be recovered using elastic regularization
Numerical Modelling of Eulerian Two-Phase Gas-Solid Flow
Get PDFThis paper investigates the numerical solution of the equations governing two-phase flow of a solid granular material dispersed in a gas. We consider two different models in both of which the dispersed and continuous phases are treated as continua. An Eulerian description of the flow is adopted. Four different formulations of the two models are derived and a high resolution scheme is presented to obtain numerical solutions of the equations in each of the formulations. We investigate whether the chosen numerical scheme is suitable for the equations governing the models and use the numerical results to obtain quantitative and qualitative insight into the predictions of each of the models. Three test cases, new to the literature, are considered, and the numerical results compared
A Schur-Newton Method for the Matrix p'th Root and its Inverse
Get PDFNewton's method for the inverse matrix th root, , has
the attraction that it involves only matrix multiplication. We
show that if the starting matrix is for then
the iteration converges quadratically to if the
eigenvalues of lie in a wedge-shaped convex set containing the
disc . We derive an optimal choice of
for the case where has real, positive eigenvalues. An
application is described to roots of transition matrices from
Markov models, in which for certain problems the convergence
condition is satisfied with . Although the basic Newton
iteration is numerically unstable, a coupled version is stable and
a simple modification of it provides a new coupled iteration for
the matrix th root. For general matrices we develop a hybrid
algorithm that computes a Schur decomposition, takes square roots
of the upper (quasi)triangular factor, and applies the coupled
Newton iteration to a matrix for which fast convergence is
guaranteed. The new algorithm can be used to compute either
or , and for large that are not highly
composite it is more efficient than the method of Smith based
entirely on the Schur decomposition
Multitype randomised Reed-Frost epidemics and epidemics upon random graphs
No full textWe consider a multitype epidemic model which is a natural exten-
sion of the randomised Reed-Frost epidemic model. The main result
is the derivation of an asympotic Gaussian limit theorem for the ¯nal
size of the epidemic. The method of proof is simpler, and more direct,
than is used for similar results elsewhere in the epidemics literature.
In particular, the results are specialised to epidemics upon extensions
of the Bernoulli random graph
On Levy Processes Conditioned to Stay Positive
Get PDFWe construct the law of Levy processes conditioned to stay positive under general
hypotheses. We obtain a Williams type path decomposition at the minimum of these processes.
This result is then applied to prove the weak convergence of the law of Levy processes conditioned to stay positive as their initial state tends to 0. We describe an absolute continuity
relationship between the limit law and the measure of the excursions away from 0 of the underlying Levy process reflected at its minimum. Then, when the Levy process creeps upwards,
we study the lower tail at 0 of the law of the height this excursion
Curve Crossing for the Reflected Process
Get PDFLet R_n = max0<=j<=n S_j − S_n be a random walk S_n reflected in its
maximum. We give necessary and sufficient conditions for finiteness of passage times of Rn above horizontal or certain curved (power law) boundaries. Necessary and sufficient conditions are also given for the
finiteness of the expected passage time of R_n above linear and square root boundaries
Properties of Option Prices in a Jump Diffusion Model
Get PDFWe study convexity and monotonicity properties of option
prices in a jump-diffusion model using the fact that these prices satisfy
certain parabolic integro-differential equations. Conditions are provided
under which preservation of convexity holds, i.e. under which the value,
calculated under a chosen martingale measure, of an option with a convex
contract function is convex as a function of the underlying stock
price. The preservation of convexity is then used to derive monotonicity
properties of the option value with respect to the different parameters of
the model, such as the volatility, the jump size and the jump intensity
A continuum of inductive methods arising from a generalized principle of instantial relevance
No full textWe consider a natural generalization of the
Principle of Instantial Relevance and give a complete characterization of the probabilistic belief functions satisfying this principle as a family of discrete probability functions parameterized by a single real number in [0,1)