10,879 research outputs found
Wave nucleation rate in excitable systems in the low noise limit
Motivated by recent experiments on intracellular calcium dynamics, we study
the general issue of fluctuation-induced nucleation of waves in excitable
media. We utilize a stochastic Fitzhugh-Nagumo model for this study, a
spatially-extended non-potential pair of equations driven by thermal (i.e.
white) noise. The nucleation rate is determined by finding the most probable
escape path via minimization of an action related to the deviation of the
fields from their deterministic trajectories. Our results pave the way both for
studies of more realistic models of calcium dynamics as well as of nucleation
phenomena in other non-equilibrium pattern-forming processes
Evolving Gene Regulatory Networks with Mobile DNA Mechanisms
This paper uses a recently presented abstract, tuneable Boolean regulatory
network model extended to consider aspects of mobile DNA, such as transposons.
The significant role of mobile DNA in the evolution of natural systems is
becoming increasingly clear. This paper shows how dynamically controlling
network node connectivity and function via transposon-inspired mechanisms can
be selected for in computational intelligence tasks to give improved
performance. The designs of dynamical networks intended for implementation
within the slime mould Physarum polycephalum and for the distributed control of
a smart surface are considered.Comment: 7 pages, 8 figures. arXiv admin note: substantial text overlap with
arXiv:1303.722
Beyond Low Rank + Sparse: Multi-scale Low Rank Matrix Decomposition
We present a natural generalization of the recent low rank + sparse matrix
decomposition and consider the decomposition of matrices into components of
multiple scales. Such decomposition is well motivated in practice as data
matrices often exhibit local correlations in multiple scales. Concretely, we
propose a multi-scale low rank modeling that represents a data matrix as a sum
of block-wise low rank matrices with increasing scales of block sizes. We then
consider the inverse problem of decomposing the data matrix into its
multi-scale low rank components and approach the problem via a convex
formulation. Theoretically, we show that under various incoherence conditions,
the convex program recovers the multi-scale low rank components \revised{either
exactly or approximately}. Practically, we provide guidance on selecting the
regularization parameters and incorporate cycle spinning to reduce blocking
artifacts. Experimentally, we show that the multi-scale low rank decomposition
provides a more intuitive decomposition than conventional low rank methods and
demonstrate its effectiveness in four applications, including illumination
normalization for face images, motion separation for surveillance videos,
multi-scale modeling of the dynamic contrast enhanced magnetic resonance
imaging and collaborative filtering exploiting age information
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