66,198 research outputs found
Fluctuation Induced Instabilities in Front Propagation up a Co-Moving Reaction Gradient in Two Dimensions
We study 2D fronts propagating up a co-moving reaction rate gradient in
finite number reaction-diffusion systems. We show that in a 2D rectangular
channel, planar solutions to the deterministic mean-field equation are stable
with respect to deviations from planarity. We argue that planar fronts in the
corresponding stochastic system, on the other hand, are unstable if the channel
width exceeds a critical value. Furthermore, the velocity of the stochastic
fronts is shown to depend on the channel width in a simple and interesting way,
in contrast to fronts in the deterministic MFE. Thus, fluctuations alter the
behavior of these fronts in an essential way. These affects are shown to be
partially captured by introducing a density cutoff in the reaction rate. Some
of the predictions of the cutoff mean-field approach are shown to be in
quantitative accord with the stochastic results
How Many Dissimilarity/Kernel Self Organizing Map Variants Do We Need?
In numerous applicative contexts, data are too rich and too complex to be
represented by numerical vectors. A general approach to extend machine learning
and data mining techniques to such data is to really on a dissimilarity or on a
kernel that measures how different or similar two objects are. This approach
has been used to define several variants of the Self Organizing Map (SOM). This
paper reviews those variants in using a common set of notations in order to
outline differences and similarities between them. It discusses the advantages
and drawbacks of the variants, as well as the actual relevance of the
dissimilarity/kernel SOM for practical applications
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