Search

As part of a 3-wk intersession workshop funded by a National Science Foundation Expeditions in Computing award, 15 undergraduate students from the City University of New York1collaborated on a study aimed at characterizing the voltage dynamics and arrhythmogenic behavior of cardiac cells for a broad range of physiologically relevant conditions using an in silico model. The primary goal of the workshop was to cultivate student interest in computational modeling and analysis of complex systems by introducing them through lectures and laboratory activities to current research in cardiac modeling and by engaging them in a hands-on research experience. The success of the workshop lay in the exposure of the students to active researchers and experts in their fields, the use of hands-on activities to communicate important concepts, active engagement of the students in research, and explanations of the significance of results as the students generated them. The workshop content addressed how spiral waves of electrical activity are initiated in the heart and how different parameter values affect the dynamics of these reentrant waves. Spiral waves are clinically associated with tachycardia, when the waves remain stable, and with fibrillation, when the waves exhibit breakup. All in silico experiments were conducted by simulating a mathematical model of cardiac cells on graphics processing units instead of the standard central processing units of desktop computers. This approach decreased the run time for each simulation to almost real time, thereby allowing the students to quickly analyze and characterize the simulated arrhythmias. Results from these simulations, as well as some of the background and methodology taught during the workshop, is presented in this article along with the programming code and the explanations of simulation results in an effort to allow other teachers and students to perform their own demonstrations, simulations, and studies.

We prove that the spaces of unrooted phylogenetic trees are Hamiltonian for two popular search metrics: Subtree Prune and Regraft (SPR) and Tree Bisection and Reconnection (TBR). Further, we make progress on two conjectures of Bryant on searching phylogenetic treespace: treespace under the Nearest Neighbor Interchange (NNI) metric has a 2-walk, and there exist SPR neighborhoods without complete NNI walks.

A nearest-neighbor-interchange (NNI)-walk is a sequence of unrooted phylogenetic trees, $(T_1, T_2, \ldots, T_k)$ where each consecutive pair of trees differs by a single NNI move. We give tight bounds on the length of the shortest NNI-walks that visit all trees in a subtree-prune-and-regraft (SPR) neighborhood of a given tree. For any unrooted, binary tree, $(T)$, on $(n)$ leaves, the shortest walk takes $(\Theta (n^2))$ additional steps more than the number of trees in the SPR neighborhood. This answers Bryant's Second Combinatorial Challenge from the Phylogenetics Challenges List, the Isaac Newton Institute, 2011, and the Penny Ante Problem List, 2009.