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The zero set of a solution of a parabolic equation.
On etudie l'ensemble nul d'une solution u(t,x) de l'equation u t =a(x,t)u xx +b(x,t)u x +C(x,t)u, sous des hypotheses tres generales sur les coefficients a, b, et c
Nonlinear analytic semiflows
In this paper a local existence and regularity theory is given for nonlinear parabolic initial value problems ( x ′( t ) = f ( x ( t ))), and quasilinear initial value problems ( x ′( t )= A ( x ( t
Parabolic equations for curves on surfaces Part I. Curves with $p$-integrable curvature
This is the first of a two-part paper in which we develop a theory of parabolic equations for curves on surfaces which can be applied to the so-called curve shortening of flow-by-mean-curvature
Membrane Tension Maintains Cell Polarity by Confining Signals to the Leading Edge during Neutrophil Migration
TLDR
It is suggested that tension, rather than diffusible molecules generated or sequestered at the leading edge, is the dominant source of long-range inhibition that constrains the spread of the existing front and prevents the formation of secondary fronts.
Conformal Surface Parameterization for Texture Mapping
TLDR
This work gives an explicit method for mapping any simply connected surface onto the sphere in a manner which preserves angles and provides a new way to automatically assign texture coordinates to complex undulating surfaces.
Optimal Mass Transport for Registration and Warping
TLDR
This paper presents a method for computing elastic registration and warping maps based on the Monge–Kantorovich theory of optimal mass transport, and shows how this approach leads to practical algorithms, and demonstrates the method with a number of examples, including those from the medical field.
Minimizing Flows for the Monge-Kantorovich Problem
TLDR
This work derives a novel gradient descent flow for the computation of the optimal transport map (when it exists) in the Monge-Kantorovich framework, and studies certain properties of the flow, including weak solutions as well as short- and long-term existence.
An example of neckpinching for Ricci flow on $S^{n+1}$
We give an example of a class of metrics on Sn+1 that evolve under the Ricci Flow into a “neckpinch.” We show that the solution has a Type I singularity, and that the length of the neck, i.e. the
On the spontaneous emergence of cell polarity
TLDR
This work identifies an intrinsic stochastic mechanism through which positive feedback alone is sufficient to account for the spontaneous establishment of a single site of polarity, and finds that the polarization frequency has an inverse dependence on the number of signalling molecules: the frequency of polarization decreases as theNumber of molecules becomes large.
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