Study Day

Postcard from Mai Doan, during the Linfield College Semester Abroad Program in Aix-en-Provence, Franc

Distancing Strategies, Exclusive Clusters and Other Ironies of my American Peers

Being able to study abroad is a huge privilege. I am very lucky to have been given that privilege twice. I was accepted to Gettysburg College two and a half years ago, and studied abroad in the United States. Now, I am studying abroad again in Copenhagen, Denmark with a program that connects many colleges and universities in the US. It has been a month now and I am having a good time. But my first few weeks in Copenhagen were not the same as my first few weeks in Gettysburg. Strangely enough, it was much more uncomfortable and harder to adjust. [excerpt

I Hope

As I have gotten older, I have learned that no matter how hard I try, I am never going to be able to repay my mother for everything that she did for me. The blood, sweat, and tears she put into nurturing the sick and troublesome, five-year-old me, the rebellious and lazy fifteen-year-old me, and the clumsy, and sometimes lost me now, are insurmountable. I know she had more trouble raising me than she was supposed to. I know her first five years of being a mother did not include taking me to the park, sitting down on a park bench, and having a family picnic in the sun. Most of it was watching me struggle on the white sheet of the hospital bed. That is why I have always felt obligated to be her perfect child, to be a daughter so good that no one would be able to say that she had not done a good job raising me. And it was an obligation that I was very happy to fulfill, because I honestly loved being in the mold that she put me in. [excerpt

Efficient maximum likelihood estimation for L\'{e}vy-driven Ornstein-Uhlenbeck processes

We consider the problem of efficient estimation of the drift parameter of an Ornstein-Uhlenbeck type process driven by a L\'{e}vy process when high-frequency observations are given. The estimator is constructed from the time-continuous likelihood function that leads to an explicit maximum likelihood estimator and requires knowledge of the continuous martingale part. We use a thresholding technique to approximate the continuous part of the process. Under suitable conditions, we prove asymptotic normality and efficiency in the H\'{a}jek-Le Cam sense for the resulting drift estimator. Finally, we investigate the finite sample behavior of the method and compare our approach to least squares estimation.Comment: Published in at http://dx.doi.org/10.3150/13-BEJ510 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Computation of transient viscous flows using indirect radial basis function networks

In this paper, an indirect/integrated radial-basis-function network (IRBFN) method is further developed to solve transient partial differential equations (PDEs) governing fluid flow problems. Spatial derivatives are discretized using one- and two-dimensional IRBFN interpolation schemes, whereas temporal derivatives are approximated using a method of lines and a finite-difference technique. In the case of moving interface problems, the IRBFN method is combined with the level set method to capture the evolution of the interface. The accuracy of the method is investigated by considering several benchmark test problems, including the classical lid-driven cavity flow. Very accurate results are achieved using relatively low numbers of data points

HodgeRank is the limit of Perron Rank

We study the map which takes an elementwise positive matrix to the k-th root of the principal eigenvector of its k-th Hadamard power. We show that as $k$ tends to 0 one recovers the row geometric mean vector and discuss the geometric significance of this convergence. In the context of pairwise comparison ranking, our result states that HodgeRank is the limit of Perron Rank, thereby providing a novel mathematical link between two important pairwise ranking methods