Calendar

Apr
25
Tue
Colloquium: Eric Kostelich (ASU) @ Keller 402
Apr 25 @ 3:30 pm – 4:30 pm

Title: Short-term Forecasting of Weather and Cancer: Finding
Initial Conditions and Parameters for Dynamical Models from Noisy Data

Speaker: Eric Kostelich, School of Mathematical & Statistical Sciences,
Arizona State University

Abstract: Computer models are essential to modern weather prediction.
They implement numerical methods to approximate the solutions of the
so-called primitive equations of atmospheric flow, but like any
differential equations, initial conditions must be supplied. However,
it is not possible to measure the state of the atmosphere at every model
grid point. Data assimilation refers to a class of methods to infer the
initial conditions from a sparse set of initial conditions and a set
of numerical forecasts. I will provide an overview of the problem
and describe a particular data assimilation method that is highly
accurate and efficient for numerical weather prediction and related
models. In addition, I will survey some potential applications
(and inherent difficulties) of data assimilation in mathematical
biology, especially differential equation models of prostate cancer
and glioma (brain tumors).

Bio: Eric Kostelich is President’s Professor of Mathematics at
Arizona State University. He received his Ph.D. degree in applied
mathematics from the University of Maryland at College Park and completed
postdoctoral work in physics at the University of Texas, Austin.
His research interests are in nonlinear dynamical systems, mathematical
biology, and high-performance computing, including data assimilation
for geophysical flows. Professor Kostelich was one of the principal
investigators in the Mathematics and Climate Research Network,
supported by the National Science Foundation. He has directed
undergraduate research program in computational mathematics at ASU
since 2008. He is a member of the Society for Industrial and Applied
Mathematics, the American Mathematical Society, and the American
Meteorological Society.

Apr
27
Thu
MFC Seminar: The Joy of FP in Haskell @ Keller 401
Apr 27 @ 3:00 pm – 4:15 pm

Title: The Joy of Functional Programming in Haskell

Speaker: Jake Fennick

Time: 3pm Tuesday April 18, 2017

Location: Keller 401

Abstract:

The goal of this talk is to convey to you the experience of pure joy
and excitement when using Haskell, and to help you actually get
started programming in Haskell. After a basic introduction to the
language, we will cover

1. The development environment and getting set up
2. More advanced language features
3. Some mathematical patterns and functional programming idioms
4. Lots of fancy demos such as plotting/visualization, LaTeX,
algorithmic music generation, high performance computing, etc.
5. A little bit of theory

This will be a coding talk, so we will primarily be walking through
code and actually getting set up. The code (including installation
scripts) is at https://github.com/TypeFunc/uh-mfc I hope to cover a
lot of material, so I encourage you to check it out but it isn’t
strictly necessary.

Apr
28
Fri
MA defense: Mirza Baig
Apr 28 @ 7:30 am – 8:30 am

Inverting the Radon Transform using Summability Kernels

Link to Master’s project

Abstract. We study an inversion technique of the Radon Transform using Summability Kernels and consider the problem of numerically implementing this algorithm. In doing so we investigate the tradeoff between the various analytical and discretization parameters involved and propose a simple framework using recent results in literature for integrating over $mathbb{S}^{n-1}$ to estimate the rate of convergence of our numerical implementation to the analytical inversion technique as well as offer a heuristic in parameter selection which would considerably reduce a brute force search over a large search space. We also discuss how the smoothness of the phantom to be estimated controls the convergence in the numerical inversion algorithm and have numerical experiments to validate our theoretical findings.

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Logic Seminar: Jack Yoon @ Keller 404
Apr 28 @ 2:30 pm – 3:30 pm

Jack Yoon will continue his explication of Proof Mining.

May
3
Wed
Colloquium: Yuriy Zinchenko (U. Calgary) @ Keller 401
May 3 @ 3:00 pm – 4:00 pm

TITLE
Dose-volume requirements modeling for radiotherapy optimization

ABSTRACT
Radiation therapy is an important modality in cancer treatment. To find a good treatment plan, optimization models
and methods are typically used, while dose-volume requirements play an important role in plan’s quality evaluation.
We compare four different optimization approaches to incorporate the so-called dose-volume constraints into the
fluence map optimization problem for intensity modulated radiotherapy. Namely, we investigate (1) conventional
emph{Mixed Integer Programming} (MIP) approach, (2) emph{Linear Programming} (LP) approach to partial volume
constraints, (3) emph{Constrained Convex Moment} (CCM) approach, and (4) emph{Unconstrained Convex Moment
Penalty} (UCMP) approach. The performance of the respective optimization models is assessed using anonymized data
corresponding to eight previously treated prostate cancer patients. Several benchmarks are compared, with the goal
to evaluate the relative effectiveness of each method to quickly generate a good initial plan, with emphasis on
conformity to DVH-type constraints, suitable for further, possibly manual, improvement.

BIO
Dr. Zinchenko received his PhD from Cornell University on 2005 under supervision of Prof. James Renegar.
From 2005 to 2008 he held a PDF position at the Advanced Optimization Lab at McMaster University, working
with Prof. Tamas Terlaky and Prof. Antone Deza, and spent portion of his fellowship with radiation oncology group
at the Princess Margaret Hospital in Toronto. Currently, Yuriy is an Associate Professor of Mathematics & Stat at the
University of Calgary.
Dr. Zinchenko’s primary research interest lies in convex optimization, and particularly, the curvature of the central path for
interior-point methods, and applications. Yuriy’s work on optimal radiotherapy design was recognized by 2008 MITACS
Award for Best Novel Use of Mathematics in Technology Transfer, and in 2012-2015 he served as one of the PIs for
PIMS Collaborative Research Group grant on optimization.

May
4
Thu
MA defense: Sean Sanford
May 4 @ 9:30 am – 10:30 am

Smooth Actions of Compact Lie Groups on $S^2$ are Smoothly Equivalent to Linear Actions:

Link to Master’s project

Abstract:

Mathematicians have been interested in group actions on spheres since before the algebraic description of a group was defined. The rotational and reflective symmetries of the circle and of S^2 were naturally among the first to be considered. When we restrict attention to a compact topological group, there is a classic theorem of Kerekjártó to the effect that for S^2 , these are essentially the only actions:

Theorem 1 (Kerekjártó, [3]). Every continuous, effective action of a compact topological group G on S^2 is topologically conjugate to a linear action (to the standard action of a subgroup of O(3) on S^2 as a subset of R^3 ).

Thus in the topological category, in order to understand all effective actions of compact groups on S^2 , it is enough to understand the subgroups G ≤ O(3) and their actions via matrix multiplication on S^2 ⊆ R^3 (so called linear actions).

The goal of this paper is to extend this result to the smooth category. In other words, we show that every smooth, effective action of a compact Lie group, on S^2 is smoothly conjugate (i.e. conjugate through a diffeomorphism) to a linear action.

The main theorem of the paper is helpful for studying the topology of the space of actions of compact Lie groups on S^2 and we present a corollary as an example of this. We also explicitly determine all compact subgroups of O(3) up to conjugacy within O(3), and use this information to construct explicit G-CW decompositions for preferred representatives of each of these conjugacy classes. The G-CW decompositions are useful in other areas for example in the classification of G-equivariant vector bundles over S^2, and in determining whether such bundles have algebraic models.

University of Hawaiʻi at Mānoa