Tree Contractions and Evolutionary Trees

An evolutionary tree is a rooted tree where each internal vertex has at least two children and where the leaves are labeled with distinct symbols representing species. Evolutionary trees are useful for modeling the evolutionary history of species. An agreement subtree of two evolutionary trees is an evolutionary tree which is also a topological subtree of the two given trees. We give an algorithm to determine the largest possible number of leaves in any agreement subtree of two trees T_1 and T_2 with n leaves each. If the maximum degree d of these trees is bounded by a constant, the time complexity is O(n log^2(n)) and is within a log(n) factor of optimal. For general d, this algorithm runs in O(n d^2 log(d) log^2(n)) time or alternatively in O(n d sqrt(d) log^3(n)) time

Multi-Objective Optimal Experimental Designs for ER-fMRI Using MATLAB

Designs for event-related functional magnetic resonance imaging (ER-fMRI) that help to efficiently achieve the statistical goals while taking into account the psychological constraints and customized requirements are in great demand. This is not only because of the popularity of ER-fMRI but also because of the high cost of ER-fMRI experiments; being able to collect highly informative data is crucial. In this paper, we develop a MATLAB program which can accommodate many user-specified experimental conditions to efficiently find ER-fMRI optimal designs.

Another look at charge fractionalization at finite temperature

We study again the phenomenon of charge fractionalization at finite temperature. Our calculations are done in a framework in which the connection between the induced fermion number and the chiral anomaly is manifest. We find that the fractional fermion number induced on a soliton decreases as temperature rises and vanishes at infinite temperature at one-loop level. These results are consistent with previous studies. As an application of our approach, we have also studied the behavior of the induced Chern-Simons term in the (2+1)-dimensional QED at finite temperature.Comment: 9 pages, 2 figure