# Spring 2022 Department Colloquium

### Tuesday 1/11 at 4:00-4:20

Speaker: None

Title: Organizational meeting

Abstract: Please attend or email Nandor Sieben before the meeting if you or your guest would like to give a talk this semester.

### Tuesday 1/18 at 4:00-4:50

Speaker: Steve Wilson

Title: Families of Regular Hypergraphs in Regular Hypermaps

Abstract: The study of which regular (i.e. symmetric) graphs can be the skeleton of a regular map (an embedding into a surface) has a long-ish history. We have theorems saying for which values of $n$ the complete graph $K_n$ is symmetrically embeddable. Ditto for $K_n,n$ and the $n$-dimensional cube.

The generalizations to HYPERgraphs and HYPERmaps are much less familiar. We will examine symmetry in these more general cases, and we will find, after a suitable introduction, that they have an unexpected charm.

### Tuesday 1/25 at 4:00-4:50

Speaker: Christina

Title: The impact of instructional model and instructor rank on our Precalculus course

Abstract: From Fall 2008 to Spring 2019, NAU utilized four different instructional models to deliver its Precalculus course. This descriptive- comparative study utilized students’ final grade in the Precalculus course to understand the effect of the different instructional models on students’ achievement in our Precalculus course and the subsequent mathematics course, Calculus I, in addition to the effect of instructor rank on students’ achievement.

### Tuesday 2/01 at 4:00-4:50

Speaker: Angie Hodge-Zickerman

Title: Living Proof: Lessons learned from Black mathematicians

Abstract: Historically, Black students have been both underrepresented and marginalized in the field of mathematics. The research project I will talk about seeks to understand the stories of Black Americans who have been successful in the field of mathematics. With an understanding of the obstacles each Black mathematician in this study has faced and the tools that have helped them to overcome these hurdles, I will discuss how the findings can help support Black mathematicians and other underrepresented groups in mathematics programs.

### Tuesday 2/08 at 4:00-4:50

Speaker: Eddie Nijholt

Title: Networks have much more symmetry than you think

Abstract: Symmetry has always played a prominent role in the analysis of network dynamical systems. If nodes can be switched around in the graph, corresponding maps can be found in phase space sending solutions to solutions. At the same time, networks tend to have far more structure than this, and examples abound of network systems without any classical symmetry, yet with surprising dynamical behavior. We will see that many structural properties of network graphs can in fact be seen as a kind of symmetry, provided one expands the definition. As a result, such properties can be preserved in established dynamical techniques, most notably in various reduction methods.

### Tuesday 2/15 at 4:00-4:50

Speaker: Tyler Diggans

Title: The Essential Synchronization Backbone Problem

Abstract: A new optimization problem is defined for the synchronization of networked oscillator systems with applications to power grid hardening and information flow systems. Given a system of networked oscillators that achieves synchronization, we seek a minimal-edge subgraph of the original network such that the synchronization manifold has conjugate stability. In some applications of synchronization, the size of the basin of stability and the average time to synchronization are not as important as whether the system can achieve similar synchronization states. For example, how many transmission lines of a power grid can be disrupted or destroyed, before synchronization is no longer possible under any parameter settings. The solutions to this problem vary widely with the type of oscillators used and coupling implemented: for the most basic oscillator systems, solutions are spanning trees, but for certain linear couplings of chaotic oscillators, we find complicated interwoven central cycles with the potential for pendant vertices as well. I will also use this opportunity to update my former academic family on the progress of my career since leaving NAU and plans for the future.

### Tuesday 2/22 at 4:00-4:50

Speaker: Ye Chen

Title: Rule-based modeling and data assimilation by pyBioNetFit

Abstract: Rule-based modeling is a modeling approach that uses rules to generate a system of ODEs. It was first developed to solve the combinatorial complexity when modeling chemical kinetics in cell signaling systems, and now a general purpose ODE generator that can be applied to other fields, such as epidemiology modeling and land carbon cycle modeling. With rules that generate ODE model, the python package pyBioNetFit can be used to do data assimilation. In this talk, I will demonstrate examples of how to use the rule-based modeling and pyBioNetFit on COVID modeling and land carbon cycle modeling.

### Tuesday 3/01 at 4:00-4:50

Speaker: Bahattin Yildiz

Title: Improving Future Cryptosystems in the Quantum Era

Abstract: In this talk , I will go over some of the recent work I have done on Classical McEliece Cryptosystem and the NTRU cryptosystem, two of the finalists in NIST’s Post-quantum Competition. In the first part of the talk I will talk about how we were able to integrate PUFs into generation of matrices for the McEliece cryptosystem. We also demonstrate how to efficiently generate non-singular matrices using circulant matrices and how significantly this improves the efficiency of the key generation phase for the McEliece Cryptosystem. In the second part of the talk, I will talk about our recent improvement to the security of NTRU, without a computational overhead, inspired by an idea from cyclic codes.

### Tuesday 3/08 at 4:00-4:50

Speaker: Robert Buscaglia

Title: Clinical DSC for Lung Cancer Diagnosis

Abstract: Differential scanning calorimetry (DSC) is being developed for its potential as a clinical diagnostic. DSC thermograms offer reproducible signatures of the thermal denaturation of human blood plasma. The plasma thermogram has been correlated with disease over a variety of studies in the last decade. The plasma thermogram of healthy patients corresponds with the abundance of proteins within the plasma proteome. Changes from a healthy signature occur when the patient is suffering from an illness. Recent publication and grant work dedicated to developing the field of clinical DSC will be presented. Discussion will focus on statistical results related to analysis of plasma thermograms. A recently published study of Lung Cancer patients found that several thermogram metrics have distinct behaviors dependent on cancer type, stage, and progression. This is one of many studies that has shown the ability for thermograms to differentiate patient status. Exciting new areas of study will be introduced.

### Tuesday 3/22 at 4:00-4:50

Speaker: Paul Phillips

Title: Genome-wide association studies using machine learning to unmask novel antimicrobial resistance mechanisms in B. pseudomallei

Abstract: Genome-wide association studies (GWAS) have been used to uncover the link between genotype and phenotype. While GWAS has been conducted for more than a decade, it is only recently that this method has been applied to bacteria. Here we discuss and analyze a promising machine learning (ML) workflow designed for GWAS. The focus of this method was for identifying antimicrobial-resistant (AMR) mechanisms in Burkholderia pseudomallei. Benchmarking the method on data generated in this study identified an SNP mutation that has been demonstrated to confer amoxicillin/clavulanate acid resistance in B. pseudomallei. Specifically, the ML workflow was able to correctly identify the DNA mutation responsible for the S72F amino-acid mutation in the ambler domain of the penA β-lactamase enzyme associated with amoxicillin/clavulanate acid resistance.

### Tuesday 3/29 4:00-4:50

Speaker: Dana C. Ernst

Title: Some enumeration results for sorting signed permutations by reversals

Abstract: A signed permutation is a permutation of the numbers 1 through $n$ in which each number is signed. A reversal of a signed permutation is the act of swapping the order of a consecutive subsequence of numbers and changing the sign of each number in the subsequence. Given a signed permutation $\pi$, it is always possible to transform $\pi$ into the identity permutation using a sequence of reversals. This process of transforming a signed permutation into the identity permutation is referred to as sorting by reversals. The reversal distance of signed permutation $\pi$ is the minimum number of reversals required to transform $\pi$ into the identity permutation. Signed permutations, and their reversals, are useful tools in the comparative study of genomes. Different species often share similar genes that were inherited from common ancestors. However, these genes have been shuffled by mutations that modified the content of the chromosomes, the order of genes within a particular chromosome, and/or the orientation of a gene. Comparing two sets of similar genes appearing along a chromosome in two different species yields two signed permutations. The reversal distance between these two signed permutations provides a good estimate of the genetic distance between the two species. For example, the genomes for cabbage and turnip differ by three reversals while the genomes for a human and a mouse differ by 251 rearrangements, 149 of which are reversals. In this talk, we will discuss several enumeration results concerning the number of signed permutations of a fixed reversal distance.

### Tuesday 4/05 at 4:00-4:50

Speaker: Shafiu Jibrin

Title: A Weighted Analytic Center for Second-Order Cone Constraints

Abstract: This talk introduces a weighted analytic center for a system of second order cone constraints. We study properties of the weighted analytic center and use conjugate gradient (CG) methods to compute it. The methods considered are the HPRP and ZA with exact and inexact line searches. The exact line search uses Newton’s method and quadratic interpolation is used for the inexact line search. Our numerical methods indicate that ZA is better than HPRP in terms of the number of iterations and time to find the weighted analytic center. Quadratic interpolation line search gives the best success rate and fewest number of iterations for the CG methods considered. On the other hand, the fastest time for the CG methods is found with the Newton’s exact line search.

### Tuesday 4/12 at 4:00-4:50

Speaker: No colloquium.

### Tuesday 4/19 at 4:00-4:50

Speaker: No colloquium.

### Tuesday 4/26 at 4:00-4:50

Speaker: No colloquium.