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.

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.

Inverting the Radon Transform using Summability Kernels

**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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Jack Yoon will continue his explication of Proof Mining.

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.

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

**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.

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