This paper deals with the 2-Peripatetic Salesman Problem for the case where costs respect the triangle inequality. The aim is to determine 2 edge disjoint Hamiltonian cycles of minimum total cost on a graph. We first present a straightforward 9/4 approximation algorithm based on the well known Christofides algorithm for the travelling salesman problem. Then we propose a 2(n−1)/n-approximation p...

These notes are based on lectures in algebraic topology taught by Peter May and Henry Chan at the 2016 University of Chicago Math REU. They are loosely chronological, having been reorganized for my benefit and significantly annotated by my personal exposition, plus solutions to in-class/HW exercises, plus content from readings (from May’s Finite Book), books (e.g. May’s Concise Course, Munkres’...

The recent surge of interest in oocyte development has been spurred in large part by the increasing implementation of assisted reproductive technologies (ART) to treat human infertility. What is becoming apparent is that 'egg quality' is a primary factor in the success of ART (Sauer 1998), and yet we know virtually nothing about the molecular signature of a 'high quality' oocyte, i.e., an oocyt...

Earl Brewer discusses his journey into pediatric rheumatology from 1958 to retirement in 1990 in three parts.

avicenna, being influenced by farabi’s specific terms about the dual concepts of existence and quiddity, believed in external occurrence of existence upon quiddity in the contingents and the accidental synthesis of things from them. but bahmanyar, the self-proclaimed commentator on avicenna, expressly states in al-tahsil that the existence of a thing is the objectivity of its external quiddity ...