In computational anatomy, organ's shapes are often modeled as deformations of a reference
shape, ie, as elements of a Lie group. To analyze the variability of the human anatomy in this …

Solving nonlinear ordinary differential equations is one of the fundamental and practically
important research challenges in mathematics. However, the problem of their algorithmic …

For a nonlinear ordinary differential equation solved with respect to the highest order
derivative and rational in the other derivatives and in the independent variable, we devise …

This work shows how to associate the Lie algebra hn, of upper triangular matrices, with a
specific combinatorial structure of dimension 2, for n∈ N. The properties of this structure are …

This thesis develops Geometric Statistics to analyze the normal andpathological variability of
organ shapes in Computational Anatomy. Geometricstatistics consider data that belong to …

In this paper, we show an algorithmic procedure to compute abelian subalgebras and ideals
of a given finite-dimensional Leibniz algebra, starting from the non-zero brackets in its law …

A finite dimensional Lie algebra L with magic number c (L) is said to satisfy Rentschler's
property if it admits an abelian Lie subalgebra H of dimension at least c (L)− 1. We study the …

Lie groups appear in many fields from Medical Imaging to Robotics. In Medical Imaging and
particularly in Computational Anatomy, an organ's shape is often modeled as the …

In this paper, we introduce an algorithmic procedure that computes abelian subalgebras and
ideals of a given finite‐dimensional Malcev algebra. All the computations are performed by …

In this paper, the maximal abelian dimension is algorithmically and computationally studied
for the Lie algebra hn, of n× n upper-triangular matrices. More concretely, we define an …