Projects: Stefan Forcey, students and collaborators.
Kron reduction and Kalmanson networks.
Resistance : electric circuits :: mutation : genetic history.
Examples and questions:
Finding the Kron reduction,
aka the Dirichlet-to-Neumann map,
aka the Response matrix
...and the reduced Resistance matrix
Papers: Kalmanson metrics and networks
- Kron Reduction
- Resistance Distance
- Response Matrix
- Totally non-negative Grassmannian
Balanced Minimal Evolution Polytopes for Phylogenetic Networks
Galois connections for phylogenetic networks and their polytopes
Level-1 Phylogenetic Networks and their Balanced Minimum Evolution Polytopes. (with C. Durell)
preprint ] [submitted to journal] [arxiv]
Split Network Polytopes and Network Spaces. (with S. Devadoss, C. Durell)
DMTCS Proceedings, FPSAC 31, 2019. [
preprint ] [ extended abstract] [arxiv]
Galois connections and duality between phylogenetic network spaces and polytopes
[Draft] paper with Drew Scalzo
FPSAC 2019, University of Ljubljana, Slovenia Split network polytopes and network spaces [
Encyclopedia entry: BME polytope
Encyclopedia entry: STSP polytope
The Neighbor-Net Algorithm, Dan Levy, Lior Pachter, Section 2: The Mathematics.
A space of Phylogenetic Networks, Satyan Devadoss and Samantha Petti.
Hamilton Mathematics Institute: Geometry and combinatorics of associativity, Dublin 2017
Clades and tubes: facets of graph associahedra and phylogenetic polytopes. Slides: [], [], []
Short intro: notes and project ideas.
Cassandra Durell's thesis
Game theory for environmental protection.
Paper: When does compromise prevent more pollution?
(with C. Clemons, J. Cossey, M. Ferrara, T. Norfolk, G. Obeng, D. Ricciardi, G. Young)
Notices of the A.M.S, 59(9), pp 1223-1234, 2012.
[ journal ]
Use excel to find games for the examples in the above paper.
D. Crawford's thesis: Minimizing Pollution Through Semi-Antagonistic Equilibrium Points.
A. Fernandes's thesis: A Carbon Credits Game, under advisor Jerzy Filar.
New work with Joe Johnson and Francesco Renna: A sequential game with monitoring.
Use excel to find games for the case of optional monitoring, after the fact.
Use wolfram alpha to solve for the four percentages in mixed equilibria.
Application to food safety:
G. Obeng's thesis.
Ideas about polyhexes, benzene, and the composihedron.