15,663 research outputs found
Particle Density Estimation with Grid-Projected Adaptive Kernels
The reconstruction of smooth density fields from scattered data points is a
procedure that has multiple applications in a variety of disciplines, including
Lagrangian (particle-based) models of solute transport in fluids. In random
walk particle tracking (RWPT) simulations, particle density is directly linked
to solute concentrations, which is normally the main variable of interest, not
just for visualization and post-processing of the results, but also for the
computation of non-linear processes, such as chemical reactions. Previous works
have shown the superiority of kernel density estimation (KDE) over other
methods such as binning, in terms of its ability to accurately estimate the
"true" particle density relying on a limited amount of information. Here, we
develop a grid-projected KDE methodology to determine particle densities by
applying kernel smoothing on a pilot binning; this may be seen as a "hybrid"
approach between binning and KDE. The kernel bandwidth is optimized locally.
Through simple implementation examples, we elucidate several appealing aspects
of the proposed approach, including its computational efficiency and the
possibility to account for typical boundary conditions, which would otherwise
be cumbersome in conventional KDE
Modelling multi-scale microstructures with combined Boolean random sets: A practical contribution
Boolean random sets are versatile tools to match morphological and topological properties of real structures of materials and particulate systems. Moreover, they can be combined in any number of ways to produce an even wider range of structures that cover a range of scales of microstructures through intersection and union. Based on well-established theory of Boolean random sets, this work provides scientists and engineers with simple and readily applicable results for matching combinations of Boolean random sets to observed microstructures. Once calibrated, such models yield straightforward three-dimensional simulation of materials, a powerful aid for investigating microstructure property relationships. Application of the proposed results to a real case situation yield convincing realisations of the observed microstructure in two and three dimensions
Fast Approximation of EEG Forward Problem and Application to Tissue Conductivity Estimation
Bioelectric source analysis in the human brain from scalp
electroencephalography (EEG) signals is sensitive to the conductivity of the
different head tissues. Conductivity values are subject dependent, so
non-invasive methods for conductivity estimation are necessary to fine tune the
EEG models. To do so, the EEG forward problem solution (so-called lead field
matrix) must be computed for a large number of conductivity configurations.
Computing one lead field requires a matrix inversion which is computationally
intensive for realistic head models. Thus, the required time for computing a
large number of lead fields can become impractical. In this work, we propose to
approximate the lead field matrix for a set of conductivity configurations,
using the exact solution only for a small set of basis points in the
conductivity space. Our approach accelerates the computing time, while
controlling the approximation error. Our method is tested for brain and skull
conductivity estimation , with simulated and measured EEG data, corresponding
to evoked somato-sensory potentials. This test demonstrates that the used
approximation does not introduce any bias and runs significantly faster than if
exact lead field were to be computed.Comment: Copyright (c) 2019 IEEE. Personal use of this material is permitted.
However, permission to use this material for any other purposes must be
obtained from the IEEE by sending a request to [email protected]
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