4,604 research outputs found
Level sets of functions and symmetry sets of smooth surface sections
We prove that the level sets of a real C^s function of two variables near a
non-degenerate critical point are of class C^[s/2] and apply this to the study
of planar sections of surfaces close to the singular section by the tangent
plane at hyperbolic points or elliptic points, and in particular at umbilic
points.
We also analyse the cases coming from degenerate critical points,
corresponding to elliptic cusps of Gauss on a surface, where the
differentiability is now reduced to C^[s/4].
However in all our applications to symmetry sets of families of plane curves,
we assume the C^infty smoothness.Comment: 15 pages, Latex, 6 grouped figures. The final version will appear in
Mathematics of Surfaces. Lecture Notes in Computer Science (2005
Geometry of isophote curves
In this paper, we consider the intensity surface of a 2D image, we study the
evolution of the symmetry sets (and medial axes) of 1-parameter families of
iso-intensity curves. This extends the investigation done on 1-parameter
families of smooth plane curves (Bruce and Giblin, Giblin and Kimia, etc.) to
the general case when the family of curves includes a singular member, as will
happen if the curves are obtained by taking plane sections of a smooth surface,
at the moment when the plane becomes tangent to the surface.
Looking at those surface sections as isophote curves, of the pixel values of
an image embedded in the real plane, this allows us to propose to combine
object representation using a skeleton or symmetry set representation and the
appearance modelling by representing image information as a collection of
medial representations for the level-sets of an image.Comment: 15 pages, 7 figure
Continuum percolation theory of epimorphic regeneration
A biophysical model of epimorphic regeneration based on a continuum
percolation process of fully penetrable disks in two dimensions is proposed.
All cells within a randomly chosen disk of the regenerating organism are
assumed to receive a signal in the form of a circular wave as a result of the
action/reconfiguration of neoblasts and neoblast-derived mesenchymal cells in
the blastema. These signals trigger the growth of the organism, whose cells
read, on a faster time scale, the electric polarization state responsible for
their differentiation and the resulting morphology. In the long time limit, the
process leads to a morphological attractor that depends on experimentally
accessible control parameters governing the blockage of cellular gap junctions
and, therefore, the connectivity of the multicellular ensemble. When this
connectivity is weakened, positional information is degraded leading to more
symmetrical structures. This general theory is applied to the specifics of
planaria regeneration. Computations and asymptotic analyses made with the model
show that it correctly describes a significant subset of the most prominent
experimental observations, notably anterior-posterior polarization (and its
loss) or the formation of four-headed planaria.Comment: This author wish to retract the paper arXiv:1705.06720 because it
began as part of a collaboration that later fell apart and it was published
without the consent from the collaborators. Furthermore, the collaborators
have managed to provide a better solution to this proble
Learning place cells, grid cells and invariances with excitatory and inhibitory plasticity
Neurons in the hippocampus and adjacent brain areas show a large diversity in their tuning to location and head direction, and the underlying circuit mechanisms are not yet resolved. In particular, it is unclear why certain cell types are selective to one spatial variable, but invariant to another. For example, place cells are typically invariant to head direction. We propose that all observed spatial tuning patterns – in both their selectivity and their invariance – arise from the same mechanism: Excitatory and inhibitory synaptic plasticity driven by the spatial tuning statistics of synaptic inputs. Using simulations and a mathematical analysis, we show that combined excitatory and inhibitory plasticity can lead to localized, grid-like or invariant activity. Combinations of different input statistics along different spatial dimensions reproduce all major spatial tuning patterns observed in rodents. Our proposed model is robust to changes in parameters, develops patterns on behavioral timescales and makes distinctive experimental predictions.BMBF, 01GQ1201, Lernen und Gedächtnis in balancierten Systeme
Mechanical identification of layer-specific properties of mouse carotid arteries using 3D-DIC and a hyperelastic anisotropic constitutive model
The role of mechanics is known to be of primary order in many arterial
diseases; however, determining mechanical properties of arteries remains a
challenge. This paper discusses the identifiability of the passive mechanical
properties of a mouse carotid artery, taking into account the orientation of
collagen fibres in the medial and adventitial layers. On the basis of 3D
digital image correlation measurements of the surface strain during an
inflation/extension test, an inverse identification method is set up. It
involves a 3D finite element mechanical model of the mechanical test and an
optimisation algorithm. A two-layer constitutive model derived from the
Holzapfel model is used, with five and then seven parameters. The
five-parameter model is successfully identified providing layer-specific fibre
angles. The seven-parameter model is over parameterised, yet it is shown that
additional data from a simple tension test make the identification of refined
layer-specific data reliable.Comment: PB-CMBBE-15.pd
Computing a Compact Spline Representation of the Medial Axis Transform of a 2D Shape
We present a full pipeline for computing the medial axis transform of an
arbitrary 2D shape. The instability of the medial axis transform is overcome by
a pruning algorithm guided by a user-defined Hausdorff distance threshold. The
stable medial axis transform is then approximated by spline curves in 3D to
produce a smooth and compact representation. These spline curves are computed
by minimizing the approximation error between the input shape and the shape
represented by the medial axis transform. Our results on various 2D shapes
suggest that our method is practical and effective, and yields faithful and
compact representations of medial axis transforms of 2D shapes.Comment: GMP14 (Geometric Modeling and Processing
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