Spatial Coherence Resonance near Pattern-Forming Instabilities

The analogue of temporal coherence resonance for spatial degrees of freedom is reported. Specifically, we show that spatiotemporal noise is able to optimally extract an intrinsic spatial scale in nonlinear media close to (but before) a pattern-forming instability. This effect is observed in a model of pattern-forming chemical reaction and in the Swift-Hohenberg model of fluid convection. In the latter case, the phenomenon is described analytically via an approximate approach.Comment: 4 pages, 4 figure

Automatic sorting of point pattern sets using Minkowski Functionals

Point pattern sets arise in many different areas of physical, biological, and applied research, representing many random realizations of underlying pattern formation mechanisms. These pattern sets can be heterogeneous with respect to underlying spatial processes, which may not be visually distinguishable. This heterogeneity can be elucidated by looking at statistical measures of the patterns sets and using these measures to divide the pattern set into distinct groups representing like spatial processes. We introduce here a numerical procedure for sorting point pattern sets into spatially homogeneous groups using Functional Principal Component Analysis (FPCA) applied to the approximated Minkowski functionals of each pattern. We demonstrate that this procedure correctly sorts pattern sets into similar groups both when the patterns are drawn from similar processes and when the 2nd-order characteristics of the pattern are identical. We highlight this routine for distinguishing the molecular patterning of fluorescently labeled cell membrane proteins, a subject of much interest in studies investigating complex spatial signaling patterns involved in the human immune response.Comment: 11 pages, 6 figures, submitted to Physical Review E (05 March 2013

Spatial period-multiplying instabilities of hexagonal Faraday waves

A recent Faraday wave experiment with two-frequency forcing reports two types of `superlattice' patterns that display periodic spatial structures having two separate scales. These patterns both arise as secondary states once the primary hexagonal pattern becomes unstable. In one of these patterns (so-called `superlattice-II') the original hexagonal symmetry is broken in a subharmonic instability to form a striped pattern with a spatial scale increased by a factor of 2sqrt{3} from the original scale of the hexagons. In contrast, the time-averaged pattern is periodic on a hexagonal lattice with an intermediate spatial scale (sqrt{3} larger than the original scale) and apparently has 60 degree rotation symmetry. We present a symmetry-based approach to the analysis of this bifurcation. Taking as our starting point only the observed instantaneous symmetry of the superlattice-II pattern presented in and the subharmonic nature of the secondary instability, we show (a) that the superlattice-II pattern can bifurcate stably from standing hexagons; (b) that the pattern has a spatio-temporal symmetry not reported in [1]; and (c) that this spatio-temporal symmetry accounts for the intermediate spatial scale and hexagonal periodicity of the time-averaged pattern, but not for the apparent 60 degree rotation symmetry. The approach is based on general techniques that are readily applied to other secondary instabilities of symmetric patterns, and does not rely on the primary pattern having small amplitude

Converting genetic network oscillations into somite spatial pattern

In most vertebrate species, the body axis is generated by the formation of repeated transient structures called somites. This spatial periodicity in somitogenesis has been related to the temporally sustained oscillations in certain mRNAs and their associated gene products in the cells forming the presomatic mesoderm. The mechanism underlying these oscillations have been identified as due to the delays involved in the synthesis of mRNA and translation into protein molecules [J. Lewis, Current Biol. {\bf 13}, 1398 (2003)]. In addition, in the zebrafish embryo intercellular Notch signalling couples these oscillators and a longitudinal positional information signal in the form of an Fgf8 gradient exists that could be used to transform these coupled temporal oscillations into the observed spatial periodicity of somites. Here we consider a simple model based on this known biology and study its consequences for somitogenesis. Comparison is made with the known properties of somite formation in the zebrafish embryo . We also study the effects of localized Fgf8 perturbations on somite patterning.Comment: 7 pages, 7 figure

Regionalization of landscape pattern indices using multivariate cluster analysis

This project was funded by the Government of Canada through the Mountain Pine Beetle Program, a six-year, $40 million program administered by Natural Resources Canada, Canadian Forest Service. Additional information on the Mountain Pine Beetle Program may be found at: http://mpb.cfs.nrcan.gc.ca.Regionalization, or the grouping of objects in space, is a useful tool for organizing, visualizing, and synthesizing the information contained in multivariate spatial data. Landscape pattern indices can be used to quantify the spatial pattern (composition and configuration) of land cover features. Observable patterns can be linked to underlying processes affecting the generation of landscape patterns (e.g., forest harvesting). The objective of this research is to develop an approach for investigating the spatial distribution of forest pattern across a study area where forest harvesting, other anthropogenic activities, and topography, are all influencing forest pattern. We generate spatial pattern regions (SPR) that describe forest pattern with a regionalization approach. Analysis is performed using a 2006 land cover dataset covering the Prince George and Quesnel Forest Districts, 5.5 million ha of primarily forested land base situated within the interior plateau of British Columbia, Canada. Multivariate cluster analysis (with the CLARA algorithm) is used to group landscape objects containing forest pattern information into SPR. Of the six generated SPR, the second cluster (SPR2) is the most prevalent covering 22% of the study area. On average, landscapes in SPR2 are comprised of 55.5% forest cover, and contain the highest number of patches, and forest/non-forest joins, indicating highly fragmented landscapes. Regionalization of landscape pattern metrics provides a useful approach for examining the spatial distribution of forest pattern. Where forest patterns are associated with positive or negative environmental conditions, SPR can be used to identify similar regions for conservation or management activities.PostprintPeer reviewe