Sept 12, Yi (Grace) Wang, Duke UniversityTitle. Data Analysis with Low-dimensional Structures
Abstract. Analyzing data collected from many areas is a challenge facing scientists and engineers. The property of being high-dimensional makes these data sets hard to tackle. Fortunately, one can work with some low-dimensional structures, because in many cases, data concentrates around a low-dimensional subspace or does so in a local neighborhood. After an introduction of the area, I will present in detail a regression problem and use that as an example to show how to capture the low-dimensional structure of data and make decisions based on the learned structure. In the regression problem, more specifically, a set of data points x and the corresponding responses y is given, one wants to find a mapping f such that f(x) approximates y well and this mapping f can be applied to unobserved instances. An algorithm with piecewise linear mappings built on a tree structure is proposed. The proposed method can be applied when both x and y are high-dimensional and can handle it well in particular when the closeness in x is not consistent with that in y. By comparing the proposed method to its competitors in experiments, it is shown to be advantageous.
- Dr. Nikolai Chernov was invited to become a Fellow of the AMS for the 2015 class. Of course, he can not accept this invitation anymore but it is our understanding that he will still be listed among the Fellows of the AMS.
- Graduate student Rachel Ejem won the 2014-2015 Kauffman award for excellence in first year graduate studies.
- Jordan Walton received the 2014-2015 O'Neil Scholarship.
- Garrett Higginbotham is the recipient of the 2014-2015 Warner Scholarship.
- Lara Putnam and Elizabeth Liddle were awarded 2014-2015 Travis Wood Memorial Scholarships.
- Alexandra Fry, Tori Gandy, Jarrod Hicks, and Calla McCulley received College of Arts and Sciences Scholarships.
- Andrew Arnold, Fatoumata Sanogo, William Tidwell, and Samuel Wunderly received Department of Mathematics Scholarships.
- Our Colleague Dr. Nikolai (Kolya) Chernov passed away on Thursday, August 7, 2014. Dr. Hongkum Zhang, a former student of Kolya, has set up a memorial page. Kolya's mathematical contributions are reviewed in this encomium.
- The Greater Birmingham Mathematics Partnership, under the direction of Dr. John Mayer, was awarded funding for a third year by the Alabama Department of Education.
- Dr. Roman Shterenberg won support for his project Spectral Properties of Almost Periodic Operators from the Simons Foundation.
- Dr. Paul Jung won an NSA grant for his project Fractional Stable Fields.
- On July 11 Terrence Muthoka successfully defended his Ph.D. thesis American Options and Semilinear Parabolic Partial Differential Equations in Weighted Sobolev Spaces. His studies were directed by Dr. M. Nkashama.
- The article Singularities and non-hyperbolic manifolds do not coincide by Dr. Nandor Simanyi was selected for inclusion in the 2013 Highlights Collection by the journal Nonlinearity.
- The article Solving Multilinear Systems via Tensor Inversion by Dr. Carmeliza Navasca et al. is among the 20 most read articles for the SIAM Journal on Matrix Analysis and Applications.
- The Southeastern Section of the Mathematical Association of America awarded their Distinguished Service Award for 2014 to Dr. John Mayer for his many contributions to the MAA, to mathematics, and to mathematics education at all levels. The honor is well deserved.
- Fast-track student Jarrod Hicks scored among the top 15% of participants on the 2013 William Lowell Putnam Mathematical Competition, considered to be one of the most prestigious mathematics examination in the world. Congratulations! UAB's Putnam team is coached by Profs. Jung and Simanyi. The competition is held once a year in December.
- Mitch Wyatt, John Samples, and Gaurav Verma were chosen as the department's Outstanding PhD Student, Outstanding Master's Student, and Outstanding Undergraduate Student, respectively. Congratulations to all.
- On April 8 an Interdisciplinary Innovation Forum on Mathematical Biology will take place in the UAB National Alumni Society House from 1pm to 3pm.
- Fast-track student Alexandra Fry has been selected to participate at the highly competitive 2014 Program for Women and Mathematics on Random Matrix Theory held at the Institute of Advanced Study in Princeton, NJ.
- Graduate student Nichole Pompey won first place at the Emerging Researchers National Conference in Washington, DC, for her presentation on "A Randomized Algorithm for Tensor Decomposition".
- Ph.D. student Kyle Besing won a first place at the 2014 Graduate Student Research Days.
- On February 27 Ajay Mahato successfully defended his Ph.D. thesis The Inverse Volatility Problem for American Options. His studies were directed by Dr. I. Knowles.
- Dr. John Mayer was appointed co-director of the UABTeach initiative which was recently awarded a $1.45 million dollar grant from the National Math and Science Initiative (NMSI). The UABTeach initiative will revolutionize the preparation of Science, Technology, Engineering and Mathematics (STEM) teachers at UAB and will dramatically impact the science education of Alabama's future K-12 students. For further information see the announcements here and here and, of course, the UABTeach site.
- Profs. Starr, Stolz, and Jung won an NSF grant supporting the CBMS Conference: Quantum Spin Systems which will take place in June 2014.