While the promised appearance of fully autonomous vehicles has been pushed back further and further, our highways have silently been transformed by the increasing penetration of hands-off adaptive cruise controllers. We investigate how, given current levels of cruise control availability, we can design driving strategies for these cruise controllers that increase the energy efficiency of the highway by smoothing out spontaneously forming shockwaves. Using multi-agent reinforcement learning, we show that we can design controllers that approximately act like they know the equilibrium speed of the system. These controllers outperform hand-designed control strategies and are robust to variations of the underlying dynamics.

The brewer's yeast cell is entirely non-motile and relies on passive transport to get around. Despite this restriction, during fermentation in a liquid environment complex flows arise driven by the yeast's fermentation activity which result in non-trivial transport and distributions of yeast cells in suspension. I outline multiple elements of modeling this process, which can serve as an example of metabolically-coupled environmental feedback in other cellular organisms. This talk is of relevance to those whose interests lie in cell motility, computational modeling, multiphase fluid flows, or theoretical fluid dynamics.

Place:  Zoom:  https://asu.zoom.us/j/85049043960

The Rayleigh- Taylor (RT) instability occurs along the interface between two fluids, when a layer of lighter fluid is pushing upon a denser one, in the presence of a gravitational field or external potential. In convergent geometry, such as spherical or cylindrical configurations, RT growth is modified by Bell-Plesset (BP) effects. We investigate various linear and nonlinear models for RT and BP growth in convergent geometry, including those that allow for compressibility of the fluids. In particular, we focus on the explicit characterization of BP effects in the underdriven or 'accelerationless' limit where the contribution from RT growth is small. The models are applied to recent cylindrical implosion experiments that directly measure hydrodynamic instability growth in convergent geometries. Extensions of the models are considered, and we apply bifurcation analysis in this setting to study the evolution of our system under parameter variation.

Zoom: https://arizona.zoom.us/j/98593835992     
Password: 021573

Many scientific experiments such as those found in astronomy, geology, microbiology, and X-ray radiography require the use of high-energy instruments to capture images. Due to the imaging system, blur and added noise are inevitably present. Oftentimes the captured images must be deblurred to extract valuable information. In the presence of noise, image deblurring is an ill-posed inverse problem in which regularization is required to obtain useful reconstructions. Choosing the appropriate strength of the regularization, however, is difficult. Moreover, many images contain some mixture of smooth features and edges which requires the use of multi-regularization, i.e., the type of regularization (total variation or Tikhonov) varies across the image. We address these two issues by formulating the image deblurring problem within a hierarchical Bayesian framework, varying both the strength of the regularization, as well as the regularization type across the image. In this way, both the image and the strength of the regularization, which varies across the image, are described by a hierarchical posterior distribution which we can sample by Markov chain Monte Carlo (MCMC), in particular Gibbs samplers that make use of conditional distributions for efficient sampling. We compute the means of the image and parameter samples for simulated test images, and we compare our results with existing non-spatially-varying Bayesian methods to show that our new method both increases the quality and decreases the error of the image reconstruction.  

Zoom:  https://arizona.zoom.us/j/91826900125     
Password:    "Locute"

In this talk I will present a review of recently proposed algorithms for optimal changepoint detection, which are empirically very fast, but we don't have any good theoretical justification as to why this is the case in realistic data settings. Detecting abrupt changes is an important problem in N data gathered over time or space. In this setting, maximum likelihood inference amounts to minimizing a loss function (which encourages data fitting) plus a penalty on the number of changes in the model parameters (which discourages overfitting). Computing the optimal solution to this non-convex problem is possible using classical dynamic programming algorithms, but their O(N^2) complexity is too slow for large data sequences. The functional pruning technique of Rigaill involves storing the optimal cost using functions rather than scalar values. Empirical results from several recent papers show that the functional pruning technique consistently yields optimal algorithms of O(N log N) complexity, which is computationally tractable for very large N. The theoretical results of Rigaill prove that functional pruning is O(N^2) in the worst case and O(N log N) on average (for a special loss function). For future work it would be interesting to further study the average complexity of these algorithms, in order to provide more theoretical justification for these very fast empirical results.

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ID: 87605763752

Advisor:  Matti Morzfeld, Scripps Institute, UC San Diego

Conformal Field Theories, including string theory, are attempts in physics at describing all particle interactions but are also structures that arise naturally in mathematics through the study of representations of finite simple groups and Lie algebras and their connections to number theory and topology.   More recently, both in physics and mathematics, logarithmic theories have garnered much attention.  These theories correspond to allowing for spaces of particle states that include generalized eigenvectors for the quantized energy operator rather than just eigenvectors.   We will give some motivation for the algebraic structures that arise from the geometry of propagating strings, such as vertex operator algebras and their modules, and present some aspects of logarithmic modules for a vertex operator algebra. 

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: Rebecca McGraw; Co-PI: Jennifer Wolfe).  Please contact Jennifer Wolfe (jwolfe628@math.arizona.edu) if you are interested in attending.