4 papers
The maximum quartet distance between phylogenetic trees
Lior Pachter
The quartet distance counts the four-leaf subsets on which two binary phylogenetic trees display different topologies. We prove that its maximum over trees on leaves is $(2/3+o…
Optimal pebbling of the hypercube
Lior Pachter
We prove that the optimal pebbling number of the -dimensional hypercube is \[ o(Q_n)\,=\,Î\!\left(\left(\frac43\right)^n\right). \]
Optimizing alluvial plots
Joseph Rich, Conrad Oakes, Lior Pachter
Alluvial plots can be effective for visualization of multivariate data, but rely on ordering of alluvia that can be non-trivial to arrange. We formulate two optimization problems t…
The virial theorem and the Price equation
Catherine Felce, Steinunn Liorsdóttir, Lior Pachter
We observe that the time averaged continuous Price equation is identical to the positive momentum virial theorem, and we discuss the applications and implications of this connectio…