Image halftoning converts a high-resolution image to a low-resolution image, e.g. an 8-bit grayscale image to a binary image, for printing and display. Conventional error di usion halftoning produces worms and other objectionable artifacts. Tone Dependent error di usion (Li and Allebach) helps reduce these artifacts by controlling di usion of quantization errors based on the input graylevel val...

|The error di usion algorithm for digital halftoning is equivalent in form to a noise-shaping feedback coder, a class of delta-sigma modulator. The white noise assumption of the quantizer error is known to be false; in fact, the quantizer error is seen to be highly correlated with the input image. To account for this correlation, we use a gain model for the quantizer. This model accurately pred...

Di usion magnetic resonance imaging (dMRI) is the reference in vivo modality to study the connectivity of the brain white matter. Images obtained through dMRI are indeed related to the probability density function (pdf) of displacement of water molecules subject to restricted di usion in the brain white matter. The knowledge of this di usion pdf is therefore of primary importance. Several metho...

This paper investigates the statistical relationship of the GARCH model and its di usion limit. Regarding the two types of models as two statistical experiments formed by discrete observations from the models, we study their asymptotic equivalence in terms of Le Cam's de ciency distance. To our surprise, we are able to show that the GARCH model and its di usion limit are asymptotically equivale...

Water pollution by industrial and agricultural waste is an increasingly major public health issue. It is therefore important for water engineers and managers to be able to predict accurately the local behaviour of water-borne pollutants. This paper describes the novel and ecient coupling of dynamically adaptive hierarchical grids with standard solvers of the advection±di€usion equation. Adapti...

Grayscale error di usion introduces nonlinear distortion (directional artifacts and false textures), linear distortion (sharpening), and additive noise. In color error di usion what color to render is a major concern in addition to nding optimal dot patterns. This article presents a survey of key methods for artifact reduction in grayscale and color error di usion. The linear gain model by Kite...

This appendix shows simulation results using URDME and MesoRD for a simple di↵usion problem. This problem illustrates the advantage of unstructured meshes: the ability to resolve processes on curved surfaces without causing a unnecessarily fine discretization. We also evaluate the accuracy of the software on a non-trivial reaction-di↵usion system by simulating the example of Min oscillations pr...

A three-dimensional model for release and di usion of glutamate in the synaptic cleft was developed and solved analytically. The model consists of a source function describing transmitter release from the vesicle and a di usion function describing the spread of transmitter in the cleft. Concentration pro les of transmitter at the postsynaptic side were calculated for di erent transmitter concen...

The linear and nonlinear scale spaces are generalized in the complex domain, by combining the di usion equation with the simpli ed Schr odinger equation. A fundamental solution for the linear case is developed. Preliminary analysis of the complex di usion shows that the generalized di usion has properties of both forward and inverse di usion. An important observation, supported theoretically a...

We investigate the relative importance of di®usion and jumps in a new jump di®usion model for asset returns. In contrast to the standard modelling of jumps for asset returns, the jump component of our process can display ̄nite or in ̄nite activity, and ̄nite or in ̄nite variation. Empirical investigations of time series indicate that index dynamics are essentially devoid of a di®usion component, ...