Polyhedral Combinatorics of UPGMA Cones

Distance-based methods such as UPGMA (Unweighted Pair Group Method with Arithmetic Mean) continue to play a significant role in phylogenetic research. We use polyhedral combinatorics to analyze the natural subdivision of the positive orthant induced by classifying the input vectors according to tree topologies returned by the algorithm. The partition lattice informs the study of UPGMA trees. We give a closed form for the extreme rays of UPGMA cones on n taxa, and compute the normalized volumes of the UPGMA cones for small n. Keywords: phylogenetic trees, polyhedral combinatorics, partition lattic

Innovation as Evolution

Cellular phone is one of the most developing technological artifacts today. The evolution occurs through random innovation. Our effort is trying to view the evolution of this artifact from memetic’s point of view. By constructing a phylomemetic tree based on cellular phone memes to infer or estimate the evolutionary history and relationship among cellular phone. We adopt several methods, which are commonly used in constructing phylogenetic tree, they are UPGMA algorithm and Parsimony Maximum algorithm to construct cellphone phylomemetic tree. Therefore we compare with the innovation tree, which is based on serial number and their appearance time. From phylomemetic tree, we then analyze the process of a cellular phone innovation through looking out on the cellular phone type lies in the same cluster. The comparison of the simulation tree result shows a generally different branching pattern, giving a presumption that innovation in cellular phone is not really relating with their serial number, but occurs merely because of random mutation of allomeme design and competes with its technological development

An Algorithm For Building Language Superfamilies Using Swadesh Lists

The main contributions of this thesis are the following: i. Developing an algorithm to generate language families and superfamilies given for each input language a Swadesh list represented using the international phonetic alphabet (IPA) notation. ii. The algorithm is novel in using the Levenshtein distance metric on the IPA representation and in the way it measures overall distance between pairs of Swadesh lists. iii. Building a Swadesh list for the author\u27s native Kinyarwanda language because a Swadesh list could not be found even after an extensive search for it. Adviser: Peter Reves

When do improved covariance matrix estimators enhance portfolio optimization? An empirical comparative study of nine estimators

The use of improved covariance matrix estimators as an alternative to the sample estimator is considered an important approach for enhancing portfolio optimization. Here we empirically compare the performance of 9 improved covariance estimation procedures by using daily returns of 90 highly capitalized US stocks for the period 1997-2007. We find that the usefulness of covariance matrix estimators strongly depends on the ratio between estimation period T and number of stocks N, on the presence or absence of short selling, and on the performance metric considered. When short selling is allowed, several estimation methods achieve a realized risk that is significantly smaller than the one obtained with the sample covariance method. This is particularly true when T/N is close to one. Moreover many estimators reduce the fraction of negative portfolio weights, while little improvement is achieved in the degree of diversification. On the contrary when short selling is not allowed and T>N, the considered methods are unable to outperform the sample covariance in terms of realized risk but can give much more diversified portfolios than the one obtained with the sample covariance. When T<N the use of the sample covariance matrix and of the pseudoinverse gives portfolios with very poor performance.Comment: 30 page