The Analysis, Dynamics and Applications seminar will have an organizational meeting this Tuesday, August 27, at 12:30pm in Math 402. If you would like to speak this semester or nominate someone to speak this semester, please attend this meeting or write to either of the organizers - myself and Minh Kha.  If you do not already subscribe to seminar announcements, please send an email to: appliedmath@math.arizona.edu

This talk will give an overview of a few Bayesian methods implemented for Astrophysics data analysis. These examples include algorithms for the analysis of the Cosmic Microwave background (CMB) data from Planck satellite and analysis of Exoplanet high contrast imaging data such as Gemini Planet Imager, GPI, data.  A discussion of Bayesian object detection algorithms in both CMB and Exoplanet data will be provided.

Advisor:  Timothy Secomb, Physiology, University of Arizona

Co-Advisor:  Ardith El-Kareh Fox, Physiology, University of Arizona

Come sign up to give Brown Bag talk! Priority goes to students in the department and the rest of the positions will be filled by outside guest speakers. Brown bag talks are a great opportunity to present your research and gain public feedback! This Friday we will create a sign up sheet, discuss Brown Bag and SIAM Student Chapter organization, and elect a new student Grad Representative! We briefly discuss what the organizations are about, what open positions are available, and their respective duties. These positions are great opportunities to gain organizational experience.

This is a series of NSF Noyce Seminars for the AZ Noyce Mathematics Teaching (MaTh) Scholars Project in Secondary Mathematics Education. (PI: Cynthia Anhalt; Co-PI: Marta Civil; Co-PI: Jennifer Eli; Co-PI: Rebecca McGraw).

The question of how difficult or easy it is to control a certain network of interconnected dynamical agents is fundamental to understanding engineered or naturally occurring networks, such as vehicular formations or  power grids amongst many others. I will argue that standard notions of stability and controllability as binary properties (e.g. a system is either stable or not), convergence rates, or even reachability analysis may fail to predict the behavior of large networks. These apparent difficulties motivate a notion of network controllability based on hard limits on performance in optimal and robust control problems with structural constraints. While such problems are known to be generally intractable, I will show certain examples from vehicular platoons and power grids where informative and simple answers are possible in the asymptotic limit of large system size. This analysis gives asymptotic bounds on network performance in the presence of uncertainty, and shows its dependence on both the complexity of individual node dynamics,  as well as network connectivity. Some interesting fragilities of certain networks emerge in the large system size limit.  Connections between these results and the statistical mechanics of disordered media will be highlighted.

Bio:

Bassam Bamieh is Professor of Mechanical Engineering at the University of California at Santa Barbara. His research interests are in the fundamentals of Control and Dynamical Systems such Robust, Optimal and Distributed Control, as well as the applications of systems and feedback techniques in several physical and engineering systems including shear flow transition and turbulence, and the use of feedback in thermoacoustic energy conversion devices. He is a past recipient of the National Science Foundation CAREER award, the AACC Hugo Schuck Best Paper Award,  and the IEEE Control Systems Society G. S. Axelby Outstanding Paper Award (twice). He is a Fellow of the International Federation of Automatic Control (IFAC) , and a Fellow of the IEEE.

Gas chromatography (GC) is a technique used in analytical chemistry for separation and analysis  of compounds that can be vaporized without decomposition. In particular, separation of different components of a mixture or the relative amounts of such components may be achieved. When applied to biodiesel fuels, GC allows us to identify the fatty acid methyl esters (FAMEs) present in the sample, whose presence depends on the underlying feedstock type.  Typically, a set of replicate chromatograms is measured for each sample, and several biofuel classes are compared together. Each chromatogram quantifies molecular abundance at each of several retention times, which in turn correspond to particular carbon chains. Variation in peak height relative to retention time serves to differentiate biofuel classes. However, inherent in GC is measurement error in the form of variation in peak location (known as drift), which must be removed prior to chemometric analysis. This is usually accomplished by aligning each chromatogram to that of a reference sample.  Another important factor to consider in GC is the type of column used, which is essentially a tube coated on the inside with a polymer. A carrier gas (mobile phase) provides a mechanism for the sample to interact with the column (stationary phase) and the data to be measured. This causes each compound to elute at a different retention time and thus different FAMEs may be identified. Longer columns yield better separation of FAMEs at the cost of longer data acquisition time.  In the first part of this talk, I will discuss a method of optimizing chromatogram alignment using the Hotelling trace criterion (HTC). The HTC can be thought of as the multivariate and multi-class extension of the square of the two-sample t-statistic. Large values for the HTC correspond to better separation of groups of principal component scores for each class.  In the second part of this talk, I will discuss an approach to quantifying equivalence between  longer and shorter columns using the Mahalanobis distance. The Mahalanobis distance measures the distance between the multivariate means of two probability distributions while accounting for variation and the correlation between random variables. I will show that a shorter, faster column can produce statistically equivalent data, relative to a longer, slower column.  Finally, I will briefly discuss current/future work on identification of an optimal reference sample for chromatogram alignment.

This is a series of NSF Noyce Seminars for the AZ Noyce Mathematics Teaching (MaTh) Scholars Project in Secondary Mathematics Education. (PI: Cynthia Anhalt; Co-PI: Marta Civil; Co-PI: Jennifer Eli; Co-PI: Rebecca McGraw).