Fall 2019 New Professors Lecture

Distributed Feature Screening for Massive Data via ADMM

By Chen Xu, Assistant Professor, Department of Mathematics and Statistics

Abstract: Feature screening is a powerful tool for modeling high dimensional data. It aims at reducing the dimensionality by removing most irrelevant features before an elaborative analysis. When a dataset is massive in both sample size N and dimensionality p, classic screening methods become inefficient or even infeasible due to the high computational burden.  We propose a distributed screening method for the large-N-large-p setup. The new method is built upon an ‘alternating direction method of multipliers’ (ADMM) updating procedure of L_0-constrained consensus regression, where data are processed in m manageable segments by multiple local computers. In the procedure, the local computers improve screening results iteratively by communicating with each other via a global computer. The joint effects between features are also accounted naturally in the screening process. It thus provides a computationally viable and reliable route for screening features with big data. Under mild conditions, we show that the proposed updating procedure is convergent and leads to an accurate screening even when m=o(N).  Moreover, with a proper starting value, the procedure enjoys the sure screening property within finite number of iterations. The promising performance of the method is supported by extensive numerical studies.

Biography: Dr. Xu’s research is in sparse modeling and statistical learning. His interests include feature selection, regularization methods, high-dimensional regression, kernel methods, and statistical computing. Recently, he focuses on developing efficient processing methods for big data, where traditional methods are less helpful due to the high computational burden. His works emphasize on both theoretical and computational aspects, which have a wide application scope in various disciplines such as genetics, biology, health science, geology, finance, and internet studies. Dr. Xu is currently serving as Associate Editor for The Canadian Journal of Statistics.

Boundary mode lubrication of articular cartilage with a biomimetic diblock copolymer

By Delphine Gourdon, Associate Professor, Department of Physics

Abstract: We report the design of a diblock copolymer with architecture and function inspired by the lubricating glycoprotein lubricin. This diblock copolymer, synthesized by sequential reversible addition– fragmentation chain-transfer polymerization, consists of a cationic cartilage-binding domain and a brush-lubricating domain. It reduces the coefficient of friction of articular cartilage under boundary mode conditions (0.088 ± 0.039) to a level equivalent to that provided by lubricin (0.093 ± 0.011). Like lubricin, the tribological properties of this polymer are dependent on molecular architecture. When the same monomer composition was evaluated either as an AB diblock copolymer or as a random copolymer, the diblock effectively lubricated cartilage under boundary mode conditions whereas the random copolymer did not. Additionally, the individual polymer blocks did not lubricate independently, and lubrication could be competitively inhibited with an excess of binding domain. This diblock copolymer is an example of a synthetic polymer with lubrication properties equal to lubricin under boundary mode conditions, suggesting its potential utility as a therapy for joint pathologies like osteoarthritis.

Biography: Dr. Delphine Gourdon joined the Department of Physics at University of Ottawa as an associate professor in 2017. She is the Head of the Mechanobiology and Tribology Laboratory, which belongs to the Biophysics cluster of the Physics department.

Delphine received her BSc in Applied Physics from University of Bordeaux (France) in 1995, and her PhD in Physics from the Swiss Federal Institute of Technology Lausanne (EPFL, Switzerland) in 1999 for work done in nanomechanics and nanotribology. She was then a Swiss NSF postdoctoral fellow in Prof. Jacob Israelachvili's laboratory at UC Santa Barbara (California) where she addressed a variety of research issues in the fields of surface and polymer science with an emphasis on biomaterials, in particular on bioadhesion and biolubrication by nano-films of adhesive proteins and polysaccharides. Delphine next complemented her expertise in bioengineering by joining the Laboratory for Biologically Oriented Materials of Prof. Viola Vogel at the Swiss Federal Institute of Technology Zurich (ETHZ, Switzerland) as a senior scientist, working on cell adhesion and extracellular matrix proteins, in particular the mechanotransducer protein: fibronectin. She then moved in 2010 to the Department of Materials Science and Engineering with an affiliation to the Department of Cornell University (New York) as an assistant professor before joining uOttawa in 2017.

Operator algebras: noncommutative spaces

By Aaron Tikuisis, Associate Professor, Department of Mathematics and Statistics

Abstract: A space is a set of points with a qualitative notion of distance between the points; it is an abstraction of many things including a geometrical body, the state space of a (classical) physical system, or a set of data points. I will explain how a space can be encoded by the continuous functions over it, and how this encoding leads to the idea of a noncommutative space.

Noncommutative spaces provide a backbone to quantum physics, and also naturally encode a space enriched with a notion of symmetry on the space. As I will explain, an Operator Algebra is the precise mathematical formulation of a noncommutative space.

Biography:Aaron Tikuisis obtained his Ph.D. from the University of Toronto in 2011. Before coming to the University of Ottawa, he was a Reader at the University of Aberdeen, and before that, he held a postdoctoral position at the University of Münster.

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