The talks will typically take place on Tuesdays at 4:00-5:00pm in Adel Room 164. Please contact Nandor Sieben if you would like to give a talk or have a question about the colloquium.

**Speaker:** Jaechoul Lee
**Title:** An efficient least squares algorithm for periodic time series regression

**Abstract:**
Periodic and autoregressive data like daily temperatures or sales of seasonal products can be seen in periods fluctuating between highs and lows throughout the year. Generalized least squares (GLS) estimators are frequently computed for such periodic data, because these estimators are minimum variance unbiased estimators. However, the GLS solution can require extremely demanding computations when the data is large. We develop an efficient GLS algorithm in several periodic regression settings. The algorithm can substantially simplify GLS computations by compressing large sets of data into smaller sets. This is accomplished by constructing a structured matching matrix for dimension reduction. Simulations show that the new computation methods using our algorithm can drastically reduce the GLS computing time. Our algorithm can be easily adapted to many big data that shows periodic characteristics often pertinent to economics, environmental studies, and engineering practices. This talk should be accessible to any audience with knowledge on simple matrix operations.

Most likely no colloquium because of faculty candidate visits. Please enjoy the candidate presentations.

**Speaker:** Shafiu Jibrin
**Title:** On Second-Order Cone Functions

**Abstract:**
We consider the second-order cone function (SOCF) $f: \mathbb{R}^n \to \mathbb{R}$
defined by $f(x)= c^T x + d -|A x + b |$, with parameters
$c \in \mathbb{R}^n$, $d \in \mathbb{R}$, $A \in \mathbb{R}^{m \times n}$, and $b \in \mathbb{R}^m$.
Every SOCF is concave. We give
necessary and sufficient conditions for strict concavity of $f$.
The parameters $A$ and $b$ are not uniquely determined.
We show that every SOCF can be written in the
form
$f(x) = c^T x + d -\sqrt{\delta^2 + (x-x_\star)^TM(x-x_\star)}$.
We give necessary and sufficient conditions for the parameters $c$, $d$, $\delta$,
$M = A^T A$, and $x_*$ to be uniquely determined.
We also give necessary and sufficient conditions for $f$ to be bounded above.

Our results have computational implications for convex optimization problems involving second-order constraints such as the problem of minimizing weighted barrier functions. They would allow one to recognize these optimization problems that can be solved efficiently, or to assist in reformulating those that are hard to solve.

This research is a joint work with Dr. James W. Swift.

**Speaker:** John Neuberger
**Title:** A Bifurcation Lemma for Invariant Subspaces

**Abstract:**
The Bifurcation from a Simple Eigenvalue (BSE) Theorem is the foundation of steady-state
bifurcation theory for one-parameter families of functions. When eigenvalues of multiplicity
greater than one are caused by symmetry, the Equivariant Branching Lemma (EBL) can
often be applied to predict the branching of solutions. The EBL can be interpreted as the
application of the BSE Theorem to a fixed point subspace. There are functions which have
invariant linear subspaces that are not caused by symmetry. For example, networks of
identical coupled cells often have such invariant subspaces. We present a generalization of
the EBL, where the BSE Theorem is applied to nested invariant subspaces. We call this the
Bifurcation Lemma for Invariant Subspaces (BLIS). We give several examples of bifurcations
and determine if BSE, EBL, or BLIS apply. We extend our previous automated bifurcation
analysis algorithms to use the BLIS to simplify and improve the detection of branches
created at bifurcations.

**Speaker:** Jin Wang
**Title:** Depth-Based Minimum Volume Ellipsoid Estimators for Multivariate Location, Spread, Skewness, and Kurtosis

**Abstract:**
Multivariate descriptive measures for location, spread, skewness, and kurtosis are the foundation of multivariate statistics. Almost all multivariate statistical methods are based on them. The classical measures of these concepts are moment-based and are estimated by their sample versions. However, these estimators are not robust and are extremely sensitive to outliers. To eliminate or reduce the effects of outliers, we propose some depth-based minimum volume ellipsoid (DMVE) estimators for multivariate location, spread, skewness, and kurtosis. The important properties of the new estimators are studied.

**Speaker:** Nandor Sieben
**Title:** Problem solving for lazy mathematicians: Jim’s dress code puzzle and the magic of constraint solvers

**Abstract:**
Constraint programming often provides simple formulations of a wide variety of problems. We can simply describe what we want in a solution without knowing how to get it. State-of-the-art solvers can do the rest. We learn how to use a few lines of Python code to easily handle Jim’s dress code puzzle, MAT 232 problems, Diophantine systems of inequalities, the send more money puzzle, and graph coloring. Einstein supposedly claimed that only 2% of the world could solve his zebra puzzle. This is no longer true. With constraint solvers, even lazy mathematicians can figure out who owns the zebra.

**Speaker:** Jeffrey Hovermill
**Title:** STEM Education Partnerships

**Abstract:**
School/University Partnerships allow for a bidirectional flow of information, cooperation, and support. This talk will describe several NAU STEM Education Partnerships including the goals, structure, and impact of these various initiatives.

**Spring break**

**Speaker:** Ye Chen
**Title:**

**Abstract:**

**Speaker:** Rachel Neville
**Title:**

**Abstract:**

**Speaker:** Jayden Chrzanowski (30 min)
**Title:** Machine Learning of Baseball strike zones

**Abstract:**

**Speaker:** Avery Bell (30 min)
**Title:** Unsupervised analysis of mixed thermogram data

**Abstract:**

**Speaker:** Keegan Line
**Title:** Baseline Automation and Analysis of Urine Thermograms

**Abstract:**

**Speaker:** Jeff Uyekawa
**Title:**

**Abstract:**

**Speaker:** Hannah Golab and Ruth Perry
**Title:**

**Abstract:**

**Speaker:** Peter Vadasz
**Title:** Newtonian Gravitational Waves from a Continuum

**Abstract:**
Gravitational waves are being shown to derive directly from Newtonian dynamics for a continuous mass distribution, e.g. compressible fluids or equivalent. It is shown that the equations governing a continuous mass distribution, i.e. the inviscid Navier-Stokes equations for a general variable gravitational field g(t,x), are equivalent to a form identical to Maxwell equations from electromagnetism, subject to a specified condition. The consequence of this equivalence is the creation of gravity waves that propagate at finite speed. The latter implies that Newtonian gravitation is not “spooky action at a distance” but rather is similar to electromagnetic waves propagating at finite speed, despite the apparent form appearing in the integrated field formula. In addition, this proves that in analogy to Maxwell equations the Newtonian gravitation equations are Lorentz invariant for waves propagating at the speed of light. Since gravitational waves were so far derived only from Einstein’s general relativity theory it becomes appealing to check if there is a connection between the Newtonian waves presented in this paper and the general relativity type of waves at least in a certain limit of overlapping validity. The latter is left for a follow-up research.