Reconstructing Evolutionary Graphs: 3D Parsimony

Reconstructing evolutionary graphs: 3D parsimony.

The increasing recognition that symbioses have greatly altered evolution through genome fusions is creating a need for algorithms that can reliably detect and reconstruct fusions. Here, we generalize the bootstrappers gambit algorithm (a quartet method) in order to permit it to analyze both bifurcations and fusions under a single mathematical model, and thereby detect past genomic branchings an...

A Corrected Parsimony Criterion for Reconstructing Phylogenies

In phylogenetic analysis, for non-molecular data, particularly morphology, parsimony optimization is the most commonly employed approach. In the past and present application of the parsimony principle, extra step numbers have been added across different characters without proper justification. This practice, however, has caused the impacts of characters to be inflated or deflated without a vali...

Reconstructing and Correcting 3d Building Models Using Roof Topology Graphs

Reconstructing 3D compact sets

Reconstructing a 3D shape from sample points is a central problem faced in medical applications, reverse engineering, natural sciences, cultural heritage projects, etc. While these applications motivated intense research on 3D surface reconstruction, the problem of reconstructing more general shapes hardly received any attention. This paper develops a reconstruction algorithm changing the 3D re...

Reconstructing Undirected Graphs from Eigenspaces

In this paper, we aim at recovering an undirected weighted graph of N vertices from the knowledge of a perturbed version of the eigenspaces of its adjacency matrix W. Our approach is based on minimizing a cost function given by the Frobenius norm of the commutator AB−BA between symmetric matrices A and B. In the Erdős-Rényi model with no self-loops, we show that identifiability (i.e., the abili...