Research Projects

The research projects I am involved with are mostly (but not only) associated with analytical mathematical handling of evolutionary issues. Most of the projects offer both rigorous theoretical analysis and soft implementation and experimental analysis.

1. Supertree Phylogenetics

   The Assembling the Tree of Life (ATOL) program funded by the US NSF fund aims at reconstruction the evolutionary history of several millions of species. This goal cannot be achieved by contempoarry ordinary reconstruction methods. This calls for a supertree method, a method for combining small trees over partial set of species into a big tree over the complete species set. The Cyberinfrastructure for Phylogenetic Research (CIPRES) project is in charge to develop the computational infrastructure for the TAOL program. As part of CIPRES we have developed a novel divide and conquer technique semi-definite programming (SDP) approach. In collaboration with Tandy Warnow from UT Austin, the director of CIPRES and Satish Rao from UC Berkeley.

2. Analytical Detection of Horizontal Transfer.

   Horizontal transfer (HT), the passage of genetic material between genetically distant organisms, is a significant factor in microbial evolution. HT plays a major role in the emergence of novel human diseases, as well as promoting the spread of antibiotic resistance in bacteria species. HT puts in question the validity of a single common tree like evolutionary history suggesting an alternative evolutionary network. Trivial problems on trees turn to be computationally hard on a network setting. Rigorous handling of HT is timely and imperative as reflected from W. Ford Doolittle, among the greatest authorities in HT, from his inaugural article for the National Academy of Sciences: In the near future, even more sophisticated methods should be available, because mathematical research into phylogenetic network reconstruction is presently very active [W. Ford Doolittle and Eric Bapteste,PNAS,2007],. In this article, our previous efforts on ML analys for HT have been acknowledged. In collaboration with various groups from Israel and abroad.
   

3. Convex   Recoloring.

   In collaboration with Shlomo Moran from the Technion, Israel.
   

4. Maximum Likelihood Phylogenetic Reconstruction

   Maximum Likelihood (ML) is currently considered as the most accurate phylogenetics method. However, as the parameter space is tremendously wide, all current practical ML based reconstruction methods use heuristic methods in the search for the optimal solution. These approaches detract the ability to infer inherent structural property about the problem. In a series of works we have found analytical solutions to ML phylogenetic reconstruction for various models of sequence evolution. The novelty of my approach was the representation of the ML problem as a constraint optimization problem and using algebraic geometry tools for obtaining the solution. In collaboration with Benny Chor from Tel Aviv University and Mike Hendy from Massey University, NZ.