1,721,043 research outputs found
Dynamic programming techniques in the approximation of optimal stopping time problems in Hilbert spaces
No full textRecent advances on large-time-steps scheme for Hamilton-Jacobi Equation
No full textInvited conference at the section High order time discretization methodsof the Conference 'Icosahom 2004'. Brown University. Providence, Rhode Island. June 2004.(web page: http://www.dam.brown.edu/icosahom2004/fullschedule.htm
On the relationship between Semi-Lagrangian and Lagrange-Galerkin schemes
No full textFollowing a previous result stating their equivalence under constant advection speed, Semi-Lagrangian and Lagrange-Galerkin schemes are compared in this paper in the situation of variable coefficient advection equations. Once known that Semi-Lagrangian schemes can be proved to be equivalent to area-weighted Lagrange-Galerkin schemes via a suitable definition of the basis functions, we will further prove that area-weighted Lagrange-Galerkin schemes represent a ``small" (more precisely, an )) perturbation of exact Lagrange-Galerkin schemes. This equivalence implies a general result of stability for Semi-Lagrangian schemes
Equivalence of Semi-Lagrangian and Lagrange-Galerkin schemes under constant edvection speed
No full textWe compare in this paper two major implementations of large time-step schemes for advection equations, i.e., Semi-Lagrangian and Lagrange–Galerkin techniques. We show that SL schemes are equivalent to exact LG schemes via a suitable definition of the basis functions. In this paper, this equivalence will be proved assuming some simplifying hypotheses, mainly constant advection speed, uniform space grid, symmetry and translation invariance of the cardinal basis functions for interpolation. As a byproduct of this equivalence, we obtain a simpler proof of stability for SL schemes in the constant-coefficient case
Convergence of semi-Lagrangian approximations to convex Hamilton-Jacobi equations under (very) large Courant numbers
No full textWe consider a class of semi-Lagrangian high-order approximation schemes for convex Hamilton-Jacobi equations. In this framework, we prove that under certain restrictions on the relationship between and , the sequence of approximate solutions is uniformly Lipschitz continuous and hence, by consistency, that it converges to the exact solution. The argument is suitable for most reconstructions of interest, including high-order polynomials and ENO reconstructions
Integrating anisotropic filtering, level set methods and convolutional neural networks for fully automatic segmentation of brain tumors in magnetic resonance imaging
No full textAn accurate, fully automatic detection and segmentation technique for brain tumors in magnetic resonance images (MRI) is introduced. The approach basically combines geometric active contours segmentation with a deep learning-based initialization. As a pre-processing step, an anisotropic filter is used to smooth the image; afterwards, the segmentation process takes place in two phases: the first one is based on the concept of transfer learning, where a pre-trained convolutional neural network coupled with a detector is fine-tuned using a training set of 388 T1-weighted contrast enhanced MRI images that contain a brain tumor (Meningioma); this trained network is able to automatically detect the location of the tumor by generating a bounding box with certain coordinates. The second phase takes place by using the coordinates of the bounding box to initialize the geometric active contour that iteratively evolves towards the tumor's boundaries. While most of the ingredients of this processing chain are more or less well known, the main contribution of this work is in integrating the various techniques in a novel and hopefully clever form, which could take the best of both geometric segmentation algorithms and neural networks, with a relatively light training phase. The performance of such a processing network is evaluated using a separate testing set of 97 MRI images containing the same type of brain tumor. The technique proves to be remarkably effective, with a precision of 97.92%, recall of 96.91%, F-measure of 97.41% and an average Dice similarity coefficient (DSC) for segmented images above 0.95
Stability of some generalized Godunov schemes with linear high-order reconstructions
No full textClassical Semi-Lagrangian schemes have the advantage of allowing large time steps, but fail in general to be conservative. Trying to keep the advantages of both large time steps and conservative structure, Flux-Form Semi-Lagrangian schemes have been proposed for various problems, in a form which represent (at least in a single space dimension) a high-order, large time-step generalization of the Godunov scheme. At the theoretical level, a recent result has shown the equivalence of the two versions of Semi-Lagrangian schemes for constant coefficient advection equations, while, on the other hand, classical Semi-Lagrangian schemes have been proved to be strictly related to area-weighted Lagrange-Galerkin schemes for both constant and variable coefficient equations.
We address in this paper a further issue in this theoretical framework, i.e., the relationship between stability of classical and of Flux-Form Semi-Lagrangian schemes. We show that the stability of the former class implies the stability of the latter, at least in the case of the one-dimensional linear continuity equation
High-order approximations of linear control systems via Runge-Kutta schemes
No full textIt is well known that classical Runge-Kutta approximations for dynamical systems do not converge with high order when the control is not smooth with respect to time. We consider here a generalization of RK schemes far linear systems which preserves its order with measurable controls, and obtain as consequence a result of high-order approximation for the reachable set
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