8,056 research outputs found
The genotype-phenotype relationship in multicellular pattern-generating models - the neglected role of pattern descriptors
Background: A deep understanding of what causes the phenotypic variation arising from biological patterning
processes, cannot be claimed before we are able to recreate this variation by mathematical models capable of
generating genotype-phenotype maps in a causally cohesive way. However, the concept of pattern in a
multicellular context implies that what matters is not the state of every single cell, but certain emergent qualities
of the total cell aggregate. Thus, in order to set up a genotype-phenotype map in such a spatiotemporal pattern
setting one is actually forced to establish new pattern descriptors and derive their relations to parameters of the
original model. A pattern descriptor is a variable that describes and quantifies a certain qualitative feature of the
pattern, for example the degree to which certain macroscopic structures are present. There is today no general
procedure for how to relate a set of patterns and their characteristic features to the functional relationships,
parameter values and initial values of an original pattern-generating model. Here we present a new, generic
approach for explorative analysis of complex patterning models which focuses on the essential pattern features
and their relations to the model parameters. The approach is illustrated on an existing model for Delta-Notch
lateral inhibition over a two-dimensional lattice.
Results: By combining computer simulations according to a succession of statistical experimental designs,
computer graphics, automatic image analysis, human sensory descriptive analysis and multivariate data modelling,
we derive a pattern descriptor model of those macroscopic, emergent aspects of the patterns that we consider
of interest. The pattern descriptor model relates the values of the new, dedicated pattern descriptors to the
parameter values of the original model, for example by predicting the parameter values leading to particular
patterns, and provides insights that would have been hard to obtain by traditional methods.
Conclusion: The results suggest that our approach may qualify as a general procedure for how to discover and
relate relevant features and characteristics of emergent patterns to the functional relationships, parameter values
and initial values of an underlying pattern-generating mathematical model
Solvable Model of Spiral Wave Chimeras
Spiral waves are ubiquitous in two-dimensional systems of chemical or
biological oscillators coupled locally by diffusion. At the center of such
spirals is a phase singularity, a topological defect where the oscillator
amplitude drops to zero. But if the coupling is nonlocal, a new kind of spiral
can occur, with a circular core consisting of desynchronized oscillators
running at full amplitude. Here we provide the first analytical description of
such a spiral wave chimera, and use perturbation theory to calculate its
rotation speed and the size of its incoherent core.Comment: 4 pages, 4 figures; added reference, figure, further numerical test
Tensile Properties of Five Low-Alloy and Stainless Steels Under High-Heating-Rate and Constant-Temperature Conditions
Tensile properties of five low-alloy and stainless steels under high heating rate and constant temperatur
A German employee network and union renewal: the Siemenskonflikt
The paper shows how redundancies were resisted by Hi-Tech workers in a large German company. It details an employee networkâs emergence to provide support to individuals and to pursue legal cases against the company, and analyzes the networkâs norms and operation. The network operated in complementary ways to the union and works council, to achieve a favourable outcome. The case is used to test theoretical propositions derived from literature on Hi-Tech workers, union renewal and mobilization theory and it is suggested that mobilization theory requires further extension in several directions
Stably non-synchronizable maps of the plane
Pecora and Carroll presented a notion of synchronization where an
(n-1)-dimensional nonautonomous system is constructed from a given
-dimensional dynamical system by imposing the evolution of one coordinate.
They noticed that the resulting dynamics may be contracting even if the
original dynamics are not. It is easy to construct flows or maps such that no
coordinate has synchronizing properties, but this cannot be done in an open set
of linear maps or flows in , . In this paper we give examples of
real analytic homeomorphisms of such that the non-synchronizability is
stable in the sense that in a full neighborhood of the given map, no
homeomorphism is synchronizable
A comparison of predicted and observed ocean tidal loading in Alaska
We investigate the elastic and anelastic response of the crust and upper mantle across Alaska to mass loading by ocean tides. GPS-inferred surface displacements recorded by the Plate Boundary Observatory network are compared with predictions of deformation associated with the redistribution of ocean water due to the tides. We process more than 5 yr of GPS data from 131 stations using a kinematic precise point positioning algorithm and estimate tidal contributions using harmonic analysis. We also forward calculate load-induced surface displacements by convolving ocean-tide models with load Greenâs functions derived from spherically symmetric Earth models. We make the comparisons for dominant tidal harmonics in three frequency bands: semidiurnal (Mâ), diurnal (Oâ) and fortnightly (M_f). Vector differences between predicted and observed ocean tidal loading (OTL) displacements are predominantly sub-mm in magnitude in all three frequency bands and spatial components across the network, with larger residuals of up to several mm in some coastal areas. Accounting for the effects of anelastic dispersion in the upper mantle using estimates of Q from standard Earth models reduces the residuals for the Mâ harmonic by an average of 0.1â0.2 mm across the network and by more than 1 mm at some individual stations. For the relatively small M_f tide, the effects of anelastic dispersion (<0.03 mm) are undetectable within current measurement error. Incorporating a local ocean-tide model for the northeastern Pacific Ocean reduces the Mâ vertical residuals by an average of 0.2 mm, with improvements of up to 5 mm at some coastal stations. Estimated RMS observational uncertainties in the vertical component for the Mâ and Oâ tides are approximately ±0.08 mm at the two-sigma level (±0.03 mm in the horizontal components), and ±0.21 mm for the M_f harmonic (±0.07 mm in the horizontal components). For the Mâ harmonic, discrepancies between predicted and observed OTL displacements exceed observational uncertainties by about one order of magnitude. None of the ocean tide and Earth model combinations is found to reduce the Mâ residuals below the observational uncertainty, and no single forward model provides a best fit to the observed displacements across all tidal harmonics and spatial components. For the Oâ harmonic, discrepancies between predicted and observed displacements are generally several-fold larger than the observational uncertainties. For the M_f harmonic, the discrepancies are roughly within a factor of two of the observational uncertainties. We find that discrepancies between predicted and observed OTL displacements can be significantly reduced by removing a network-uniform tidal-harmonic displacement, and that the remaining discrepancies exhibit some regional-scale spatial coherency, particularly for the Mâ harmonic. We suggest that the remaining discrepancies for the Mâ, Oâ and M_f tides cannot be fully explained by measurement error and instead convey information about deficiencies in ocean-tide models and deviations from spherically symmetric Earth structure
A quantitative evaluation of metallic conduction in conjugated polymers
As the periodicity in crystalline materials creates the optimal condition for
electronic delocalization, one might expect that in partially crystalline
conjugated polymers delocalization is impeded by intergrain transport. However,
for the best conducting polymers this presumption fails. Delocalization is
obstructed by interchain rather than intergrain charge transfer and we propose
a model of weakly coupled disordered chains to describe the physics near the
metal-insulator transition. Our quantitative calculations match the outcome of
recent broad-band optical experiments and provide a consistent explanation of
metallic conduction in polymers.Comment: 4 pages incl. 3 figure
Entropic particle transport: higher order corrections to the Fick-Jacobs diffusion equation
Transport of point-size Brownian particles under the influence of a constant
and uniform force field through a three-dimensional channel with smoothly
varying periodic cross-section is investigated. Here, we employ an asymptotic
analysis in the ratio between the difference of the widest and the most narrow
constriction divided through the period length of the channel geometry. We
demonstrate that the leading order term is equivalent to the Fick-Jacobs
approximation. By use of the higher order corrections to the probability
density we derive an expression for the spatially dependent diffusion
coefficient D(x) which substitutes the constant diffusion coefficient present
in the common Fick-Jacobs equation. In addition, we show that in the diffusion
dominated regime the average transport velocity is obtained as the product of
the zeroth-order Fick-Jacobs result and the expectation value of the spatially
dependent diffusion coefficient . The analytic findings are corroborated
with the precise numerical results of a finite element calculation of the
Smoluchowski diffusive particle dynamics occurring in a reflection symmetric
sinusoidal-shaped channel.Comment: 9 pages, 3 figure
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