40,510 research outputs found
A numerical comparison between degenerate parabolic and quasilinear hyperbolic models of cell movements under chemotaxis
We consider two models which were both designed to describe the movement of
eukaryotic cells responding to chemical signals. Besides a common standard
parabolic equation for the diffusion of a chemoattractant, like chemokines or
growth factors, the two models differ for the equations describing the movement
of cells. The first model is based on a quasilinear hyperbolic system with
damping, the other one on a degenerate parabolic equation. The two models have
the same stationary solutions, which may contain some regions with vacuum. We
first explain in details how to discretize the quasilinear hyperbolic system
through an upwinding technique, which uses an adapted reconstruction, which is
able to deal with the transitions to vacuum. Then we concentrate on the
analysis of asymptotic preserving properties of the scheme towards a
discretization of the parabolic equation, obtained in the large time and large
damping limit, in order to present a numerical comparison between the
asymptotic behavior of these two models. Finally we perform an accurate
numerical comparison of the two models in the time asymptotic regime, which
shows that the respective solutions have a quite different behavior for large
times.Comment: One sentence modified at the end of Section 4, p. 1
A Semi-Lagrangian Scheme with Radial Basis Approximation for Surface Reconstruction
We propose a Semi-Lagrangian scheme coupled with Radial Basis Function
interpolation for approximating a curvature-related level set model, which has
been proposed by Zhao et al. in \cite{ZOMK} to reconstruct unknown surfaces
from sparse, possibly noisy data sets. The main advantages of the proposed
scheme are the possibility to solve the level set method on unstructured grids,
as well as to concentrate the reconstruction points in the neighbourhood of the
data set, with a consequent reduction of the computational effort. Moreover,
the scheme is explicit. Numerical tests show the accuracy and robustness of our
approach to reconstruct curves and surfaces from relatively sparse data sets.Comment: 14 pages, 26 figure
Single- and Multiple-Shell Uniform Sampling Schemes for Diffusion MRI Using Spherical Codes
In diffusion MRI (dMRI), a good sampling scheme is important for efficient
acquisition and robust reconstruction. Diffusion weighted signal is normally
acquired on single or multiple shells in q-space. Signal samples are typically
distributed uniformly on different shells to make them invariant to the
orientation of structures within tissue, or the laboratory coordinate frame.
The Electrostatic Energy Minimization (EEM) method, originally proposed for
single shell sampling scheme in dMRI, was recently generalized to multi-shell
schemes, called Generalized EEM (GEEM). GEEM has been successfully used in the
Human Connectome Project (HCP). However, EEM does not directly address the goal
of optimal sampling, i.e., achieving large angular separation between sampling
points. In this paper, we propose a more natural formulation, called Spherical
Code (SC), to directly maximize the minimal angle between different samples in
single or multiple shells. We consider not only continuous problems to design
single or multiple shell sampling schemes, but also discrete problems to
uniformly extract sub-sampled schemes from an existing single or multiple shell
scheme, and to order samples in an existing scheme. We propose five algorithms
to solve the above problems, including an incremental SC (ISC), a sophisticated
greedy algorithm called Iterative Maximum Overlap Construction (IMOC), an 1-Opt
greedy method, a Mixed Integer Linear Programming (MILP) method, and a
Constrained Non-Linear Optimization (CNLO) method. To our knowledge, this is
the first work to use the SC formulation for single or multiple shell sampling
schemes in dMRI. Experimental results indicate that SC methods obtain larger
angular separation and better rotational invariance than the state-of-the-art
EEM and GEEM. The related codes and a tutorial have been released in DMRITool.Comment: Accepted by IEEE transactions on Medical Imaging. Codes have been
released in dmritool
https://diffusionmritool.github.io/tutorial_qspacesampling.htm
Pathway-Based Genomics Prediction using Generalized Elastic Net.
We present a novel regularization scheme called The Generalized Elastic Net (GELnet) that incorporates gene pathway information into feature selection. The proposed formulation is applicable to a wide variety of problems in which the interpretation of predictive features using known molecular interactions is desired. The method naturally steers solutions toward sets of mechanistically interlinked genes. Using experiments on synthetic data, we demonstrate that pathway-guided results maintain, and often improve, the accuracy of predictors even in cases where the full gene network is unknown. We apply the method to predict the drug response of breast cancer cell lines. GELnet is able to reveal genetic determinants of sensitivity and resistance for several compounds. In particular, for an EGFR/HER2 inhibitor, it finds a possible trans-differentiation resistance mechanism missed by the corresponding pathway agnostic approach
(k,q)-Compressed Sensing for dMRI with Joint Spatial-Angular Sparsity Prior
Advanced diffusion magnetic resonance imaging (dMRI) techniques, like
diffusion spectrum imaging (DSI) and high angular resolution diffusion imaging
(HARDI), remain underutilized compared to diffusion tensor imaging because the
scan times needed to produce accurate estimations of fiber orientation are
significantly longer. To accelerate DSI and HARDI, recent methods from
compressed sensing (CS) exploit a sparse underlying representation of the data
in the spatial and angular domains to undersample in the respective k- and
q-spaces. State-of-the-art frameworks, however, impose sparsity in the spatial
and angular domains separately and involve the sum of the corresponding sparse
regularizers. In contrast, we propose a unified (k,q)-CS formulation which
imposes sparsity jointly in the spatial-angular domain to further increase
sparsity of dMRI signals and reduce the required subsampling rate. To
efficiently solve this large-scale global reconstruction problem, we introduce
a novel adaptation of the FISTA algorithm that exploits dictionary
separability. We show on phantom and real HARDI data that our approach achieves
significantly more accurate signal reconstructions than the state of the art
while sampling only 2-4% of the (k,q)-space, allowing for the potential of new
levels of dMRI acceleration.Comment: To be published in the 2017 Computational Diffusion MRI Workshop of
MICCA
Convergent and conservative schemes for nonclassical solutions based on kinetic relations
We propose a new numerical approach to compute nonclassical solutions to
hyperbolic conservation laws. The class of finite difference schemes presented
here is fully conservative and keep nonclassical shock waves as sharp
interfaces, contrary to standard finite difference schemes. The main challenge
is to achieve, at the discretization level, a consistency property with respect
to a prescribed kinetic relation. The latter is required for the selection of
physically meaningful nonclassical shocks. Our method is based on a
reconstruction technique performed in each computational cell that may contain
a nonclassical shock. To validate this approach, we establish several
consistency and stability properties, and we perform careful numerical
experiments. The convergence of the algorithm toward the physically meaningful
solutions selected by a kinetic relation is demonstrated numerically for
several test cases, including concave-convex as well as convex-concave
flux-functions.Comment: 31 page
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