# Upcoming Events

## Tuesday, August 21, 2018

### Analysis, Dynamics, and Applications Seminar

**Location:**Math 402

**Presenter:**Karl Glasner, Program in Applied Mathematics, University of Arizona

### Quantitative Biology Colloquium

**Location:**Math 402

**Presenter:**Joe Watkins, Department of Mathematices & Tim Secomb Department of Physiology, University of Arizona

## Wednesday, August 22, 2018

## Thursday, August 23, 2018

### Modeling and Computation Seminar

**Location:**Math 402

**Presenter:**Andrew Gillette, Program in Applied Mathematics, University of Arizona

## Friday, August 24, 2018

### Program in Applied Mathematics Brown Bag Seminar

**Location:**Math 402

**Presenter:**Soleh Dib and Ken Yamamoto, Program in Applied Mathematics, University of Arizona

### Program in Applied Mathematics Colloquium

**Location:**Math 402

**Presenter:**Maria Cameron, Department of Mathematics, University of Maryland

## Tuesday, August 28, 2018

### Algebra and Number Theory Seminar

**Location:**ENR2 S395

**Presenter:**Dan Madden, U of A

## Thursday, September 6, 2018

### Modeling and Computation Seminar

**Location:**Math 402

**Presenter:**Alan Garfinkel, Graduate Programs in Bioscience, UCLA

## Friday, September 7, 2018

### Program in Applied Mathematics Colloquium

**Location:**Math 501

**Presenter:**Alan Garfinkel, Graduate Programs in Bioscience, UCLA

## Monday, September 10, 2018

### Statistics GIDP Colloquium

Optimal Penalized Function-on-Function Regression

Many scientific studies collect data where the response and predictor variables are both functions of time, location, or some other covariate. Understanding the relationship between these functional variables is a common goal in these studies. Motivated from two real-life examples, we present a function-on-function regression model that can be used to analyze such kind of functional data. Our estimator of the 2D coefficient function is the optimizer of a form of penalized least squares where the penalty enforces a certain level of smoothness on the estimator. Our first result is the representer theorem which states that the exact optimizer of the penalized least squares actually resides in a data-adaptive finite-dimensional subspace although the optimization problem is defined on a function space of infinite dimensions. This theorem then allows us an easy incorporation of the Gaussian quadrature into the optimization of the penalized least squares, which can be carried out through standard numerical procedures. We also show that our estimator achieves the minimax convergence rate in mean prediction under the framework of function-on-function regression. Extensive simulation studies demonstrate the numerical advantages of our method over the existing ones, where a sparse functional data extension is also introduced. The proposed method is then applied to our motivating examples of the benchmark Canadian weather data and a histone regulation study.

**Location:**ENR2 S395

**Presenter:**Xiaoxiao Sun, University of Arizona

## Friday, September 28, 2018

### Mathematics Education Seminar

**Location:**ENR2 S395

**Presenter:**Sherard Robbins, UA Assistant Director for Equity and Student Engagement

## Friday, October 26, 2018

## Friday, November 30, 2018

### Mathematics Education Seminar

**Location:**ENR2 S395

**Presenter:**Michelle Higgins, Associate Director UA STEM Learning Center