Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A constructive theory of shape   We formulate a theory of shape valid for objects of arbitrary dimension whose
contours are path connected. We apply this theory to the design and modeling of
viable trajectories of complex dynamical systems. Infinite families of
qualitatively similar shapes are constructed giving as input a finite ordered
set of characteristic points (landmarks) and the value of a continuous
parameter $\kappa \in (0,\infty)$. We prove that all shapes belonging to the
same family are located within the convex hull of the landmarks. The theory is
constructive in the sense that it provides a systematic means to build a
mathematical model for any shape taken from the physical world. We illustrate
this with a variety of examples: (chaotic) time series, plane curves, space
filling curves, knots and strange attractors.

26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex