Any opinions expressed in this memoir are those of the author(s) and do not necessarily reflect the views of the National Academy of Sciences. University of Rome on a Sheldon Traveling Fellowship from Harvard. He began his teaching career in 1912 as assistant professor of mathematics at the newly established Rice Institute , now Rice University, in Houston, Texas. He became professor there in 1...

We want to describe a procedure for enlarging real vector spaces to complex vector spaces in a natural way. For instance, the natural complex analogues of Rn, Mn(R), and R[X] are Cn, Mn(C) and C[X]. Why do we want to complexify real vector spaces? One reason is related to solving equations. If we want to prove theorems about real solutions to a system of real linear equations or a system of rea...

Throughout his prolific publishing career Conrad Gessner composed abundant paratexts which offer valuable insight into his methods of working. Gessner wrote many dedications, only a minority of which were addressed to major patrons of his day. Instead he used them to thank dozens of physicians and scholars for sending him information, images, and manuscripts for his ongoing projects. Gessner ac...

From Definition 1.1, checking a polynomial is separable requires building a splitting field to check the roots are distinct. But we will see in Section 2 a criterion for deciding when a polynomial is separable (that is, has no multiple roots) without having to work in a splitting field. In Section 3 we will define what it means for a field extension to be separable and then prove the primitive ...

We present Conrad, the first comparative gene predictor based on semi-Markov conditional random fields (SMCRFs). Unlike the best standalone gene predictors, which are based on generalized hidden Markov models (GHMMs) and trained by maximum likelihood, Conrad is discriminatively trained to maximize annotation accuracy. In addition, unlike the best annotation pipelines, which rely on heuristic an...