Single-cell 3D genome reconstruction in the haploid setting using rigidity theory

S Dewar, G Grasegger, K Kubjas… - arxiv preprint arxiv …, 2024 - arxiv.org
This article considers the problem of 3-dimensional genome reconstruction for single-cell
data, and the uniqueness of such reconstructions in the setting of haploid organisms. We …

Inferring whole-genome 3D chromatin structures from diploid Hi-C data

G Cauer - 2023 - search.proquest.com
The three-dimensional organization of the genome plays an important part in regulating
numerous basic cellular functions, including gene regulation, differentiation, the cell cycle …

On the uniqueness of collections of pennies and marbles

S Dewar, G Grasegger, K Kubjas… - arxiv preprint arxiv …, 2023 - arxiv.org
In this note we study the uniqueness problem for collections of pennies and marbles. More
generally, consider a collection of unit $ d $-spheres that may touch but not overlap. Given …

Configurations in the Euclidean space related to the 3D genome reconstruction problem from partially phased data

A Korchmaros - arxiv preprint arxiv:2403.00407, 2024 - arxiv.org
A motivation for studying the following problems comes from applications to Biology; see\cite
{cifuentes20233d}. In the $3 $-dimensional Euclidean space ${\bf {E}}^ 3$, fix six pairwise …

System of equations and configurations in the Euclidean space

A Korchmaros - Aequationes mathematicae, 2024 - Springer
In the 3-dimensional Euclidean space E 3, fix six pairwise distinct points A=(a 1, a 2, a 3),
B=(b 1, b 2, b 3), C=(c 1, c 2, c 3), D=(d 1, d 2, d 3), E=(e 1, e 2, e 3), F=(f 1, f 2, f 3) together …

[PDF][PDF] 3D genome reconstruction and numerical algebraic geometry

K Kubjas - 2023 - mycourses.aalto.fi
▶ If all pairs are unambiguous, ie, U=[n], then constructing the original points translates to a
classical problem in Euclidean distance geometry.▶ First we convert contacts to distances …