This paper describes continuum models for swarming behavior based on non-local interactions. The interactions are assumed to in uence the velocity of the organisms. The model consists of integro-di erential advection-di usion equations, with convolution terms that describe long range attraction and repulsion. We nd that if density dependence in the repulsion term is of a higher order than in th...

We present a corrected operator splitting COS method for solving nonlinear parabolic equations of convection di usion type The main feature of this method is the ability to correctly resolve nonlinear shock fronts for large time steps as opposed to standard operator splitting OS which fails to do so COS is based on solving a conservation law for modeling convection a heat type equation for mode...

Linear di¬usion is an established model for spatial spread in biological systems, including movement of cell populations. However, for interacting, closely packed cell populations, simple di¬usion is inappropriate, because di¬erent cell populations will not move through one another: rather, a cell will stop moving when it encounters another cell. In this paper, I introduce a nonlinear di¬usion ...

Scale-space representation has been extensively studied in the computer vision community for analyzing image structures at di erent scales. This paper borrows and develops useful mathematical tools from scale-space theory to facilitate the task of image compression. Instead of compressing the original image directly, we propose to compress its scale-space representation obtained by the forward ...

Nonparametric methods are becoming popular recently in estimating continuous-time di¤usion models due to their ‡exibility. This paper provides a new approach to constructing point-wise con…dence intervals for nonparametric drift and di¤usion functions via empirical likelihood (EL) in conjunction with local linear smoothing. It serves as a promising competitor to the conventional asymptotic norm...

This paper provides a review of a new method of addressing problems in di usion Monte Carlo: the Green's function rst-passage method (GFFP). In particular, we address four new strands of thought and their interaction with the GFFP method: the use of angle-averaging methods to reduce vector or tensor Laplace equations to scalar Laplace equations; the use of the simulation-tabulation (ST) method ...

We describe the use of upwind monotonic interpolation methods for the solution of the time-dependent radiative transfer equation in both optically thin and thick media. These methods, originally developed to solve Eulerian advection problems in hydrodynamics, have the ability to propagate sharp features in the ow with very little numerical di usion. We consider the implementation of both explic...

In this paper, a digital halftoning method is proposed based on a recently-proposed multiscale error di usion technique for digital halftoning. It can improve the di usion performance by e ectively removing pattern noise and eliminating boundary and `blackhole' e ects. A dot-overlap compensation scheme is also proposed to eliminate the bias in the gray scale of the printed images. EDICS: IP 3.2...

We employ a nonlinear anisotropic di usion operator like the ones used as a means of ltering and edge enhancement in image processing, in numerical methods for conservation laws. It turns out that algorithms currently used in image processing are very well suited for the design of nonlinear higher-order dissipative terms. In particular, we stabilize the well-known Lax-Wendro formula by means of...