1,536 research outputs found
Positional Information – a concept underpinning our understanding of developmental biology
© 2019 Wiley Periodicals, Inc.Peer reviewedPostprin
Thurston's pullback map on the augmented Teichm\"uller space and applications
Let be a postcritically finite branched self-cover of a 2-dimensional
topological sphere. Such a map induces an analytic self-map of a
finite-dimensional Teichm\"uller space. We prove that this map extends
continuously to the augmented Teichm\"uller space and give an explicit
construction for this extension. This allows us to characterize the dynamics of
Thurston's pullback map near invariant strata of the boundary of the augmented
Teichm\"uller space. The resulting classification of invariant boundary strata
is used to prove a conjecture by Pilgrim and to infer further properties of
Thurston's pullback map. Our approach also yields new proofs of Thurston's
theorem and Pilgrim's Canonical Obstruction theorem.Comment: revised version, 28 page
Finding the center reliably: robust patterns of developmental gene expression
We investigate a mechanism for the robust identification of the center of a
developing biological system. We assume the existence of two morphogen
gradients, an activator emanating from the anterior, and a co-repressor from
the posterior. The co-repressor inhibits the action of the activator in
switching on target genes. We apply this system to Drosophila embryos, where we
predict the existence of a hitherto undetected posterior co-repressor. Using
mathematical modelling, we show that a symmetric activator-co-repressor model
can quantitatively explain the precise mid-embryo expression boundary of the
hunchback gene, and the scaling of this pattern with embryo size.Comment: 4 pages, 3 figure
Quantitative analysis of cell types during growth and morphogenesis in Hydra
Tissue maceration was used to determine the absolute number and the distribution of cell types in Hydra. It was shown that the total number of cells per animal as well as the distribution of cells vary depending on temperature, feeding conditions, and state of growth. During head and foot regeneration and during budding the first detectable change in the cell distribution is an increase in the number of nerve cells at the site of morphogenesis. These results and the finding that nerve cells are most concentrated in the head region, diminishing in density down the body column, are discussed in relation to tissue polarity
Geometric Aspects of the Moduli Space of Riemann Surfaces
This is a survey of our recent results on the geometry of moduli spaces and
Teichmuller spaces of Riemann surfaces appeared in math.DG/0403068 and
math.DG/0409220. We introduce new metrics on the moduli and the Teichmuller
spaces of Riemann surfaces with very good properties, study their curvatures
and boundary behaviors in great detail. Based on the careful analysis of these
new metrics, we have a good understanding of the Kahler-Einstein metric from
which we prove that the logarithmic cotangent bundle of the moduli space is
stable. Another corolary is a proof of the equivalences of all of the known
classical complete metrics to the new metrics, in particular Yau's conjectures
in the early 80s on the equivalences of the Kahler-Einstein metric to the
Teichmuller and the Bergman metric.Comment: Survey article of our recent results on the subject. Typoes
corrrecte
Predicting Fluid Intelligence of Children using T1-weighted MR Images and a StackNet
In this work, we utilize T1-weighted MR images and StackNet to predict fluid
intelligence in adolescents. Our framework includes feature extraction, feature
normalization, feature denoising, feature selection, training a StackNet, and
predicting fluid intelligence. The extracted feature is the distribution of
different brain tissues in different brain parcellation regions. The proposed
StackNet consists of three layers and 11 models. Each layer uses the
predictions from all previous layers including the input layer. The proposed
StackNet is tested on a public benchmark Adolescent Brain Cognitive Development
Neurocognitive Prediction Challenge 2019 and achieves a mean squared error of
82.42 on the combined training and validation set with 10-fold
cross-validation. In addition, the proposed StackNet also achieves a mean
squared error of 94.25 on the testing data. The source code is available on
GitHub.Comment: 8 pages, 2 figures, 3 tables, Accepted by MICCAI ABCD-NP Challenge
2019; Added ND
Spatial and spatio-temporal patterns in a cell-haptotaxis model
We investigate a cell-haptotaxis model for the generation of spatial and spatio-temporal patterns in one dimension. We analyse the steady state problem for specific boundary conditions and show the existence of spatially hetero-geneous steady states. A linear analysis shows that stability is lost through a Hopf bifurcation. We carry out a nonlinear multi-time scale perturbation procedure to study the evolution of the resulting spatio-temporal patterns. We also analyse the model in a parameter domain wherein it exhibits a singular dispersion relation
Sum of Lyapunov exponents of the Hodge bundle with respect to the Teichmuller geodesic flow
We compute the sum of the positive Lyapunov exponents of the Hodge bundle
with respect to the Teichmuller geodesic flow. The computation is based on the
analytic Riemann-Roch Theorem and uses a comparison of determinants of flat and
hyperbolic Laplacians when the underlying Riemann surface degenerates.Comment: Minor corrections. To appear in Publications mathematiques de l'IHE
Self-repair ability of evolved self-assembling systems in cellular automata
Self-repairing systems are those that are able to reconfigure themselves following disruptions to bring them back into a defined normal state. In this paper we explore the self-repair ability of some cellular automata-like systems, which differ from classical cellular automata by the introduction of a local diffusion process inspired by chemical signalling processes in biological development. The update rules in these systems are evolved using genetic programming to self-assemble towards a target pattern. In particular, we demonstrate that once the update rules have been evolved for self-assembly, many of those update rules also provide a self-repair ability without any additional evolutionary process aimed specifically at self-repair
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