Contributors

Rachel Traylor, Ph.D.Founder and Lead Researcher

Jason HathcockResearcher and Designer

Jonathan Johnson

Kevin Gibson
Bio
 Ph.D. Mathematics, University of Texas at Arlington, 2016
 M.S. Statistics, Georgia Institute of Technology, 2013
 B.S. Applied Mathematics, Georgia Institute of Technology, 2011
Dr. Traylor is the founder and lead mathematician at the Math Citadel, and a Research Assistant Professor at Marquette University. She is a former Senior Research Scientist in Mathematics and Analytics for Dell EMC, producing 6 patents during her 2 year tenure. She has also worked for Lockheed Martin Aeronautics as a DBA and quality control analyst. Her academic experience includes working as an instructor at 4 different institutions throughout the US, as well as pure and applied mathematics research focusing on probability theory, queueing, and reliability theory. She has given numerous lectures, webinars, seminars, and conference talks across the country in both academic settings and industrial conferences. Beyond her experience in the technology, aerospace, and manufacturing sectors, she has university training and background in logistics, operations research, and chemistry.
Lectures, Seminars, and Conference Talks
 “The Keystones of Queueing” — UC Riverside Mathematics Seminar — Riverside, CA (2019)
 “Chemical Kinetics in Computer Networks” — CHINOG 09 — Chicago, IL (2019)
 “Counterexamples, Subtleties, and Paradoxes in Probability” — Marquette Mathematics Seminar — Milwaukee, WI (2019)
 “Vertical Dependency Structures in Sequences of Discrete Random Variables” — Marquette Mathematics Seminar — Milwaukee, WI (2018)
 “Some New Thoughts on Anomaly Detection and Time Series Modeling” — SNIA Storage Developer’s Conference — Santa Clara, CA (2018)
 “Modeling Network Reliability More Simply Using Probability” — CHINOG 08 — Chicago, IL (2018)
 “Dynamic Reliability Methods for a Clustered Task Server” — SNIA Storage Developer’s Conference — Santa Clara, CA (2017)
 “The Business of Stochastic Multilevel Disk Risk Modeling for Storage Arrays” — SNIA Storage Developer’s Conference — Santa Clara, CA (2017)
 “The Gravity of Mathematics” — Tech Field Day Exclusive — Santa Clara, CA (2017)
 “Modeling Disk Failures with Absorbing Markov Chains” — SNIA Storage Developer’s Conference — Santa Clara, CA (2016)
 “Coherent Systems Analysis” — Professional Lecture — ipSpace.net
 “Reliability Basics” — Professional Lecture — ipSpace.net
 “Queueing Theory Basics” — Professional Lecture — ipSpace.net
 “Graph Theory: Connectivity and Reliability” — Professional Lecture — ipSpace.net
 “Graph Theory: Trees” — Professional Lecture — ipSpace.net
Issued Patents
 Method for Dynamically Modeling Medium Error Evolution to Predict Disk Failure, US 10,191,668
 Prediction of Disk Failure, US 9,612,896
Publications
 Generalizing the Negative Binomial Distribution Via FirstKind Dependence  Traylor, R. Journal of The Math Citadel
 On Permuted FirstKind Dependence of Categorical Random Variables  Traylor, R.  Journal of The Math Citadel
 A Generalized Geometric Distribution From Vertically Dependent Bernoulli Random Variables  Traylor, R.  Journal of The Math Citadel

Stochastic Reliability of a Server under a Random Workload Traylor, R.  AACTO Vol 1, Issue 2

Vertical Dependency in Sequences of Categorical Random Variables Traylor, R. and Hathcock, J.  AACTO Vol. 1, Issue 2

Reliability of a ClusteredTask Server Under Modulated Correlation  Traylor, R. & Korzeniowski, A.  International Journal of Statistics and Probability, Vol. 6, No. 2

A Generalized Multinomial Distribution from Dependent Categorical Random Variables  Traylor, R.  AACTO, Vol. 1. Issue 1, pp 115

Dynamic Reliability of a Cluster Server  Korzeniowski, A. & Traylor, R.  International Journal of Statistics and Probability, Vol. 5, No. 4, pp 4551

RAIDShield: Characterizing, Monitoring, and Proactively Protecting Against Disk Failures  Ma. A, et. al  ACM Transactions on Storage, Vol. 11, Issue 4
 Stochastic Reliability Models for a General Server and Related Networks  Traylor, R.  Ph.D. Dissertation, University of Texas at Arlington
Courses Taught
 Statistical Methods (Fall 2019) — Marquette University, Milwaukee, WI
 Calculus 4 (Winter 2018) — Foothills College, Los Altos Hills, CA
 Calculus 2 (Spring 2015) — University of Texas at Arlington, Arlington, TX
 Statistical Inference (Fall 2014) – University of Texas at Arlington, Arlington, TX
 Multivariate Data Analysis (Spring 2014) –University of Texas at Arlington, Arlington, TX
 Elementary Statistical Analysis (Fall 2013, summer 2014) — University of Texas at Arlington, Arlington, TX
 Calculus 13 (Fall 2008 – Spring 2011) — Georgia Institute of Technology, Atlanta, GA
Bio
 B.S. Mathematics, Minor Chemistry, University of Texas at Arlington, 2013
Jason Hathcock studied mathematics and chemistry at the University of Texas at Arlington, receiving an Honors B.S. in Mathematics with a minor in Chemistry. He continued to study mathematics under Dr. Andrzej Korzeniowski at the graduate level, with an emphasis in applied probability. He produces the photographs, and musical numbers for the videos of the Research Cortex, and assists Dr. Traylor in her research endeavors.
His hobbies include composition for the guitar, beautiful typesetting, and quietly critiquing film.
Publications

Vertical Dependency Structures in Sequences of Categorical Random Variables  Traylor, R. and Hathcock, J.  AACTO Vol. 1. Issue 2
Research Interests and Specializations
Jonathan Johnson
Bio
 M.S. Mathematics, University of Texas at Arlington
 B.S. Mathematics, University of Texas at Dallas
I am a mathematics PhD student at the University of Texas at Austin. I love to learn and study all kinds of math, but mostly, I research knot theory and 3dimensional manifolds. I received B.S. in mathematics from the University of Texas at Dallas, and a M.S. in mathematics from the University of Texas at Arlington. When I’m not studying math, I like to design board games and play sports.
Publications
 Summation Chains of Sequences Part 3: Sequence Chains from Linear Functions. AACTO, Vol. 1, Issue 2
 Summation Chains of Sequences Part 2: Relationships between Sequences via Summation Chains. AACTO, Vol. 1, Issue 2
 Summation Chains of Sequences Part 1: Introduction, Generation, and Key Definitions. AACTO, Vol 1, Issue 1
Kevin Gibson
Bio
 M.S. Computer Science, University of Toronto
 B.ASc. Mathematics and Engineering, Queen’s University, Kingston
Kevin is a software engineer at Microsoft, working on augmented and virtual reality, focusing on surface reconstruction. In the past I have done work in softbody simulation, and am interested in any math that can be used in computer graphics generally. In particular, I am currently looking at discrete exterior calculus and perturbation methods for solving differential equations. In my spare time, I play guitar, play video games, and is learning to bake bread.