Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extending the mathematical palette for developmental pattern formation:
  Piebaldism   Piebaldism usually manifests as white areas of fur, hair or skin due to the
absence of pigment-producing cells in those regions. The distribution of the
white and colored zones does not follow the classical Turing patterns. Here we
present a modeling framework for pattern formation that enables to easily
modify the relationship between three factors with different feedback
mechanisms. These factors consist of two diffusing factors and a
cell-autonomous immobile transcription factor. Globally the model allowed to
distinguishing four different situations. Two situations result in the
production of classical Turing patterns; regularly spaced spots and labyrinth
patterns. Moreover, an initial slope in the activation of the transcription
factor produces straight lines. The third situation does not lead to patterns,
but results in different homogeneous color tones. Finally, the fourth one sheds
new light on the possible mechanisms leading to the formation of piebald
patterns exemplified by the random patterns on the fur of some cow strains and
Dalmatian dogs. We demonstrate that these piebald patterns are of transient
nature, develop from random initial conditions and rely on a system's
bi-stability. The main novelty lies in our finding that the presence of a
cell-autonomous factor not only expands the range of reaction diffusion
parameters in which a pattern may arise, but also extends the pattern-forming
abilities of the reaction-diffusion equations.

36
The categories of this paper are: cmp-lg
17
The categories of this paper are: q-fin
34
The categories of this paper are: chem-ph
2
The categories of this paper are: math
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
6
The categories of this paper are: astro-ph
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
20
The categories of this paper are: acc-phys