WIXLIB

Student PresentationsFriday March 4, 2:30 – 3:30Hendrick Room2:30Schur's Theorem in Integer LatticesAndrew Lott, lottal@millsaps.eduMillsaps CollegeA standard proof of Schur’s Theorem yields that any r-coloring of{1, 2, . . . , Rr 1} yields a monochromatic solution to x y z,where Rr is the classical r-color Ramsey number, the minimum Nsuch that any r-coloring of a complete graph on N vertices yields amonochromatic triangle. We explore generalizations andmodifications of this result in higher dimensional integer lattices,showing in particular that if k d 1, then any r-coloring of{1, 2, . . . , Rr (Ck)d 1}d yields a monochromatic solution tox1 · · · xk 1 xk with {x1, . . . , xd} linearly independent, whereRr (Ck) is the analogous Ramsey number in which triangles arereplaced by k-cycles. We also obtain computational results andexamples in the case d 2, k 3, and r {2, 3, 4}.2:50An Exploration of Higher-Order DerivativesSaima Arif, snarif@mc.eduMississippi CollegeThis paper presents the concept of Fractional Derivatives, thehistory behind them and how they were developed. In addition tothat, two different approaches to calculating fractionalderivatives are considered: a modification of the integer orderderivative using the Gamma Function as well as the RiemannLiouville Integral. We explore one application of the fractionalderivative in the field of image processing.

3:10Analysis of COVID-19 and Vaccination Administration inMississippiMegan Sickinger, Megan.Sickinger@usm.eduUniversity of Southern MississippiIn this work, we develop a mathematical model to observe thespread of COVID-19 and vaccine administration in Mississippi.How simplistic can a model be to accurately measure the spreadof COVID-19 in short term observations with a vaccine controlmeasure? From this question arose an eight compartmentASIRD-V model, where asymptomatic cases and recoveredpopulation are split between unvaccinated and vaccinated. Weinvestigate the stability and equilibrium points of this model, andsimulations optimize the model's parameters over short periodsof time using both death data and vaccine data given by theCenters for Disease Control. This model observes the impact ofpolicy changes as well as the vaccine rollout in Mississippi tocombat the spread of COVID-19. This work is an extension ofthe summer research on the ASIRD model in the 2020undergraduate Cross Scholar summer research program at theUniversity of Southern Mississippi.https://xkcd.com/1856

Faculty Presentations IFriday March 4, 2:30 – 4:15Cane River Room2:30A precise probability related to Simpson’s paradoxAlex Rice, riceaj@millsaps.eduMillsaps CollegeSuppose two friends are about to participate in a two-day contest inwhich they repeatedly attempt a task with a clear success/failureoutcome (such as shooting free throws on a basketball court). Wehave no specific prior knowledge of the participants’ skills, or ofhow many attempts they will take each day, so we suppose thateach participant’s success rate for day 1, success rate for day 2, andproportion of attempts that take place on day 1 are all chosenuniformly at random between 0 and 1. What is the probability thatthe same person has a higher success rate each of the twoindividual days, but the other person has a higher success rate forthe two-day period? This can be thought of as a prior probability ofa simple case of Simpson’s Paradox, and we show that thisprobability isπ2 936 .0241556778 . . .2:50w-Polar Decomposition for O(p,q)Edgar Reyes, edgar.reyes@selu.edu,Southeastern Louisiana UniversityThe polar decomposition of a nonsingular real matrix is theproduct of a positive-definite real matrix and an orthogonal matrix.In this talk, we generalize the polar decomposition to the indefiniteorthogonal group O(p, q).

3:10Cycle Index Polynomials and Separability Algorithms inQuantum ComputingZachary P. Bradshaw, zbradshaw@tulane.eduTulane UniversityThe cycle index polynomial of a group is an important object inPólya theory. It is interesting that this combinatorial device makesan appearance in the acceptance probability of certain quantumalgorithms that test for the entanglement of a pure bipartitequantum state, an important resource in the field of quantumcomputing. In this talk we discuss this property and answer aconjecture about the behavior of the cycle index polynomial for thesymmetric groups in this context, showing that the algorithmproposed by LaBorde and Wilde becomes more stringent as theorder of the symmetric group increases. This result follows fromthe relationship between the cycle index polynomial and thecomplete Bell polynomials, which satisfy a desirable recurrencerelation. Finally, we conjecture that a similar behavior holds for thecycle index polynomial of any finite group.3:30Preparing for Praxis ProblemsJessica Bass, bassj@nsula.eduNorthwestern State UniversityTo help our mathematics education students prepare for thePraxis exam, I created a course to meet the needs of thesestudents. Students is in this course review material covered bythe Praxis exam and test taking strategies. This talk will discussthe changes regarding the new mathematics content exam andhow we are preparing our students for the exam and theclassroom.

Faculty Presentations IFriday March 4, 2:30 – 4:15Cane River Room3:50A Successful Approach to Teaching Co-requisite MathCoursesCarrie Maggio, maggioca@nsula.eduNorthwestern State UniversityFor the last several years NSU has offered corequisite courses tostudents meeting the criteria. Many different approaches havebeen implemented. Finding the right balance to help studentssucceed in their first math course and beyond has been achallenge. We have developed a course framework that hasallowed students to receive the extra instruction needed tosucceed and gain confidence in their ability to solve problems.https://xkcd.com/2343/

Second Plenary SessionPólya LecturerFriday March 4, 4:30 – 5:30Student Union BallroomIntroduction of Anderson LecturerJudith CovingtonSection ChairPower in Numbers: Unveiling Hidden FiguresTalithia Williams, Harvey Mudd CollegeThe movie “Hidden Figures” brought visibility to the lives ofAfrican American women who served as NASA “humancomputers” in the 1960s, women who dreamed the impossible in afield where their presence was lacking. Meeting the demands of a21st century STEM workforce requires that we look beyondtraditional talent pools to recruit and train individuals typicallyunderrepresented in math. During this talk, I'll discuss mypersonal journey as a woman of color in statistics and share waysin which we can excite public interest in data science, buildingupon the rich legacy of diverse mathematical scientists that havecome before us.https://xkcd.com/1805/

Faculty Presentations IISaturday March 5, 9:00 – 10:30Student Union Ballroom9:00K1 injectivity of the Paschke Dual algebraArindam Sutradhar, arindam1050@gmail.comUniversity of Louisiana at LafayetteLet B be a nonunital separable simple stable C*-algebra withstrict comparison of positive elements and T(B) having finiteextreme boundary, and let A be a simple unital nuclear C*algebra. We prove that the Paschke dualA DB algebra is K1injective. As a consequence, we obtain interesting KKuniqueness theorems which generalize the Brown–Douglas–Fillmore essential codimension property.9:20Poncelet Quadrilaterals Four WaysTaylor A Poe, tpoe@mc.eduMississippi CollegeA consequence of Poncelet's theorem states that given any twopoints in the unit disk, one can find an ellipse with these pointsas foci circumscribed by infinitely many quadrilaterals, each ofwhich is inscribed in the unit circle. We will connect thisbeautiful geometric fact with finite Blaschke products,orthogonal polynomials on the unit circle, numerical ranges ofmatrices, and Mirman's iterations.

9:40Anomaly Detection Using Principal Component Analysis forIdentification of Cyber-Physical Attacks in the Hardware-inthe-Loop-Based Augmented Industrial Control System (HAI)Dataset.Corwin Stanford, j00928757@students.jsums.eduJackson State UniversityPrincipal component analysis (PCA) is a common dimensionreduction technique in which the eigenvectors of a dataset’scovariance matrix that capture the maximum variance within thedata are used to transform said data. The eigenvectors whichcapture the least variance within the data arediscarded. However, these latter components have been shownto be a valuable tool for detecting cyber-physical attacks inindustrial control systems (ICS). When ICS data is transformedusing these components, normal operating data shows littlevariance, but data collected during attacks can vary greatly,resulting in identifiable anomalies. Unlike supervised machinelearning techniques, this does not require information from priorattacks in order to build a detection model. Here, we examine acollection of attacks contained within the HAI dataset, a HIL(hardware-in-the-loop) augmented ICS. A variety of methodsfor selecting PCA components and identifying anomalies areused, and the results compared.10:00Squares of Repunits and their Associated IdentitiesRandall Gordon Wills, rwills@selu.eduSoutheastern Louisiana UniversityDefine a repunit Rn to be an n digit positive integer whose digitsare all 1s. That is Rn 111.111. In this talk we will developvarious identities which express the squares of repunits in terms ofrepunits. This talk is accessible to undergraduates.

Third Plenary SessionBusiness MeetingSaturday March 5, 10:45 – 12:00Student Union BallroomWelcomeFrank SerioNSU Department of MathematicsOutstanding Teacher AddressLeigh Ann MyersOpening of Business MeetingJudith CovingtonRepresentative’s ReportTreasurer’s ReportLaura ShepherdsonChristy Sue LangleyCompetitions Results / Committee ReportsInvitation to 100th Annual MeetingCatherine PutnamClosing RemarksJudith Covingtonhttps://xkcd.com/1403/

Math Word SearchWords can be found going up, down, left, right, and diagonal.A Q R Q X U I G Z W N E Q A V QI F Y A F S L W B I A B L V K RZ S A M E D T J P L Z O E C L TN Y O X N F O Q K X B H R E W HP I X M D E R I V A T I V E S AR I N A O J U I R G P S E H E NV E C T O R S A B V R S U G T HM C S R E T P J F H G U F X E DS Y L I T G A H V A T L E D S UE S W X U E R O I C H U E H E LU Q P E R D A A P C N C U A R DD U A T E B L O L B W L O G I CJ A L R C O L L N R V A I S E NZ R X E S S E Q U E N C E E S KP E T V O T L C K N V A T J U TS R Z E K O N O Z R M G B S Y EI Y O F D R T G P F F L E L M ML I N E A R E G R E S S I O N Tau

Special ThanksMusic provided by Armadillo Jackal Band

Conference Hotels:Chateau St. Denis751 2nd StreetNatchitoches, LA 71457(318) 951-4105Church Street Inn120 Church StreetNatchitoches, LA 71457(318) 238-8888Fairfield Inn & Suites150 Hayes Ave.Natchitoches, LA 71063(318) 354-8007https://xkcd.com/2207/

Friedman Student Union1st FloorCourtyardEsportsVenueSteak ‘nShakeHendrickRoom 121Lobby2nd FloorPresidents Room221Cane River RoomCourtyardBallroomLobbyVic’s

Friedman Student UnionParking: Parking will be in the large parking lot on Sam SibleyDr. across the street from the flagpole and the 2 commuter lotslocated on Caspari St.Banquet: The banquet will beat Chateau St. Denis hotel on2nd Street. Leaving campusfrom Sam Sibley Dr. or CaspariSt., take a right onto UniversityParkway. Take a left onto 2ndStreet, the train tracks passthrough this intersection.Proceed down until 751 2ndStreet. The hotel will be onyour right shortly after Horn St.https://xkcd.com/982/

member of a number of other Professional Organizations (e.g., AMS, SIAM, IMSI, NU's PSE Industrial Advisory oard). Reading, International travel, Texas Holdem, Blackjack, and golf comprise his primary interests outside work. Bayes' Theorem - Making Rational Decisions in the Face of Uncertainty Allen Butler, Daniel H. Wagner Associates