9 papers
A Conditional Rank-Count Theory for the Combinatorial Discretizable Distance Geometry Problem
Michael Souza, Wagner da Rocha, Carlile Lavor
The Combinatorial Discretizable Distance Geometry Problem combines a finite binary lateration process with additional distance constraints. When predecessor sets are not consecutiv…
A Rank-Count Theory for the Combinatorial Discretizable Distance Geometry Problem
Michael Souza, Wagner da Rocha, Carlile Lavor
The Distance Geometry Problem (DGP) asks for a geometric realization of a weighted graph with \(n\) vertices in \(\mathbb{R}^K\) such that Euclidean distances between vertices matc…
A Continuous Nonlinear Optimization Perspective on the Spin Glass Problem
Phil Duxbury, Carlile Lavor, Luiz Leduino de Salles-Neto
We present a continuous nonlinear optimization model for the Spin Glass Problem (SGP), building on a classical result by Rosenberg (1972), which shows that for a class of multiline…
On the Complexity of the Ordered Covering Problem in Distance Geometry
Michael Souza, Júlio Araújo, John Kesley Costa +1
The Ordered Covering Problem (OCP) arises in the context of the Discretizable Molecular Distance Geometry Problem (DMDGP), where the ordering of pruning edges significantly impacts…
Conformal Coordinates for Molecular Geometry: from 3D to 5D
Jesus Camargo, Carlile Lavor, Michael Souza
This paper introduces the conformal model (an extension of the homogeneous coordinate system) for molecular geometry, where 3D space is represented within R^5 with an inner product…
A hybrid combinatorial-continuous strategy for solving molecular distance geometry problems
Leonardo D. Secchin, Wagner da Rocha, Mariana da Rosa +2
The Molecular Distance Geometry Problem (MDGP) is essential in structural biology, as it seeks to determine three-dimensional protein structures from partial interatomic distances.…