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Permutation Tableaux and the Dashed Permutation Pattern 32–1
Permutation tableaux dashed permutation patten
2014/6/3
We give a solution to a problem posed by Corteel and Nadeau concerning permutation tableaux of length n and the number of occurrences of the dashed pattern 32–1 in permutations on [n]. We introduce th...
MD-Predicted Phase diagrams for Pattern Formation due to Ion Irradiation
MD-Predicted Phase diagrams Pattern Formation Ion Irradiation
2011/3/3
Energetic particle irradiation of solids can cause surface ultra-smoothening 1, selforganized
nanoscale pattern formation 2, or degradation of the structural integrity of nuclear reactor components 3...
Pattern closure of groups of tree automorphisms
closed self-similar groups finitely constrained groups
2011/1/19
It is shown that a group defined by forbidding all patterns of size s + 1 that do not appear in a given self-simialr group of tree automorphisms is the topological closure of a self-similar, countable...
Fluid-induced pattern-formation in 3D photonic crystals with spatially varying surface functionalization
3D photonic spatially varying surface functionalization
2010/12/28
We introduce a 3D porous photonic crystal whose inner surfaces are chemically functionalized in arbitrary spatial patterns with micro-scale resolution. We use this platform to demonstrate pattern-form...
Time and category information in pattern-based codes
category information pattern-based codes
2011/1/4
Sensory stimuli are usually composed of different features (the what) appearing at irregular times (the when). Neural responses often use spike patterns to represent sensory information. The what is h...
Using homological duality in consecutive pattern avoidance
pattern avoidance exponential generating function linear differential equations
2010/12/14
Using the approach suggested in [2] we present below a sufficient condition guaranteeing
that two collections of patterns of permutations have the same exponential generating functions for the number...
A Spectral Approach to Consecutive Pattern-Avoiding Permutations
Spectral Approach Consecutive Pattern-Avoiding Permutations
2010/12/3
We consider the problem of enumerating permutations in the symmetric group on n elements
which avoid a given set of consecutive pattern S, and in particular computing asymptotics as n
tends to infin...
State-of-the-art review of cellular automata, cellular automata for partial differential equations, differential equations for cellular automata and pattern formation in biology and engineering.
Switch and template pattern formation in a discrete reaction diffusion system inspired by the Drosophila eye
Switch template pattern formation discrete reaction diffusion Drosophila eye
2010/4/1
We examine a spatially discrete reaction diffusion model based on the interactions that create a periodic pattern in the Drosophila eye imaginal disc. This model is capable of generating a regular hex...