South Dakota School of Mines & Technology

*— Science and Engineering since 1885 —*

SD MINES

South Dakota School of Mines & Technology

The Department of Math and Computer Science presents a seminar series each semester. The department colloquium is traditionally held on Tuesdays at 11 am and the Graduate Seminar is held on Mondays at 4 pm. All Colloquia are open to the SD Mines campus and also to the general public.

Check this page for dates, speakers, and topics.

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We studied the connection between Linear Algebra and Graph Theory. By defining a matrix representation of a graph, we are able to talk about things like eigenvalues and determinants. In some cases it was found that certain graphs have eigenvalues symmetric about zero and others have repeating determinants based on size.

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We will present the emulation of a machine using ternary logic. 3-value logic and associated gates will be discussed, as well as how they may be composed into a ternary based system. An emulator for ternary machine will be demonstrated.

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Maximum likelihood is an estimation technique in statistics which, roughly speaking, has optimal properties when the sample size is not small. So what proportion, for example of M&Ms made by Mars are blue? Also, how can we characterize raindrop size?

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In the summer of 2015, the South Dakota School of Mines and Technology (SDM&T) embarked on a new student success initiative that focused on mathematics. The first component of this student success program was the initiation of an online summer program to engage students in preparing for their mathematics course before the start of fall classes. MathSpark is the summer review program provided by the math faculty at SDSM&T. Intended for incoming freshmen, SDSM&T provides free access to online materials to help sharpen student math skills and better prepare student for their first year math courses. Using Pearson's MyMathTest software, Mines math faculty built Diagnostic Exams for College Algebra, Trigonometry, Calculus 1 and Calculus 2 courses.

These exams identify weaknesses each individual student should target over the summer. This program has been delivered over multiple platforms including social media, texting, live chat, online videos, and on campus sessions. This presentation will outline these components, discuss student responses, and possible changes to the program.

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Bring your laptop! After downloading R and R studio participants will play with calculus and/or probability apps run via the R Shiny package inside R Studio. The R Shiny package allows for the creation of very flexible apps without extensive programming skill. Some limited details will be given on the structure of the app code for those who may consider creating their own apps.

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The Pade approximation method deals with the problem of analytic continuation of a convergent power series. In fact, it is a nonlinear method of summation of that power series outside its disk of convergence. In some partial forms this method was known since the time of Jacobi and Gauss as continued fraction expansion (or J-fraction expansion named after Jacobi). It was recognized that J-fraction expansions give the single- valued continuation of a germ of a multi-valued function from the origin into an unknown domain which could be much larger than the initial disk of convergence. By the reason of nonlinear character of a Pade approximants method, it was very difficult to construct a rather general theory of the convergence of this method. This was done relatively recently, in 1985-1986, by prominent German mathematician, Herbert Stahl. The basic concept of Stahl's seminal theory is the convergence of Pade approximants in capacity inside the so-called Stahl's domain. It is a domain in which the given germ of multi-valued function possesses the holomorphic (i.e., analytical and single-valued) property. This domain is defined in relation to its complement which consists of finite number of analytic arcs andi is called the Stahl's compact set. Both zeros and poles of Pade approximants accumulate to the Stahl's compact set as the degree of Pade approximation tends to infinity. These remarkable properties of Pade approximants make them very useful for numerical analysis of multi-valued analytic functions, in particular, algebraic functions.

The focus of the talk would be on the critical application of Pade approximants and their zero-pole distribution in the voltage collapse analysis of the electricity networks.

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When the solar system is modeled using the Kepler equations, you get the orbits that we all know and love. However, these orbits do not account for small changes in the center of mass of an object. Also, this model does not accurately predict the orbits of planets with moons. The accuracy can be improved through numerical techniques. We model the solar system using two numerical methods, the Leapfrog method and the Predictor-Corrector method. We will compare the accuracy and efficiency of these two methods.

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This presentation will show how Level 1 Basic Linear Algebra Subprograms (BLAS) lend themselves to parallelization through the use of a GPGPU implemented using C++/CUDA for NVIDIA graphics cards. As well as, a thread-safe implementation of a linear congruential pseudo-random number generator. This presentation will show how Level 1 Basic Linear Algebra Subprograms (BLAS) lend themselves to parallelization through the useof a GPGPU implemented using C++/CUDA for NVIDIA graphics cards. As well as, a thread-safe implementation of a linear congruential pseudo-random number generator.

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Until recently there was no algorithm that could tell if any number was prime in polynomial time (based on the number of digits) with 100% accuracy. This changed in 2002 with the discovery of the AKS algorithm. This talk will discuss the basics of the AKS algorithm and how to apply the algorithm to a number.

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With a grant from the NSF, five K-12 school districts in the Black Hills have added a yearlong computer science class to their high school curriculum. Now in its second year of implementation, *Expanding Pathways into Computer Science* has generated interesting
findings related to curriculum adoption, student recruitment, student outcomes, and the effectiveness of various teacher supports. The presentation will provide an overview of the new curriculum, successes and challenges related to its adoption, and plans for scaling up.

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The International Chamber of Commerce estimated that the global value of counterfeit goods would rise from $650 billion in 2008 to $1.8 trillion in 2015. Illicit trade is occurring across virtually all sectors, including aerospace and electronics. Drivers are complex, including increasing use of global supply chains and ease of procurement through the internet. In 2013, the NSF supported the Security Printing & Anti-Counterfeiting Technology Research Experience for Undergraduates Site. The REU Site was renewed by NSF in 2016. In 2014, the state of South Dakota supported the creation of the Center for Security Printing and Anti-Counterfeiting Technology (C-SPACT), collaboration center in partnership with SDSM&T, SDSU, and USD. The research conducted under the auspices of C-SPACT and the REU Site will be reviewed during the colloquium. Future research efforts, with a particular emphasis on computer science involvement, will also be discussed.

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Mathematics is the language of physics, and advances in physics often require a physical interpretation of new areas of mathematics. This talk is an informal exploration of the creative leaps of two prominent physicists of 20th century, Paul Dirac and Richard Feynman. Their quest was for an understanding of our universe on a fundamental level. Their creativity brought in strikingly novel fields of mathematics as weapons to further this quest.

The discussion will focus on the Dirac equation of relativistic quantum mechanics, and the revolutionary Feynman path integral formulation of quantum mechanical amplitudes. Some knowledge of quantum mechanics will be helpful for students attending this talk, but students with no familiarity with this subject should still find the topics covered to be of mathematical interest.

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Bessel function are commonly encountered in the solution of differential equations. Though Bessel was not the first to introduce these functions, he developed them to a much greater extent than others before him. The first use of Bessel function by Bessel himself came in his solution to a classic problem in celestial mechanics, which he communicated in an 1818 letter to his friend and colleague Wihelm Olbers. In this talk, I will examine his work on that problem, and offer a correction to an American Mathematical Monthly article on the subject.

The differential equation that models the motion of the mass on an aging spring can be solved using a power series. Series methods can also be used to solve a classic problem in celestial mechanics, which expresses the angular position of a planet as a function of time. These two seemingly different problems are actually related. By looking at Bessel's work on these problems in the early 1800's, we will show that they are closely related.

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There is an authentication plague upon the land. We have to claim and assert our identity repeatedly to a host of authentication trolls, each jealously guarding an Internet service whose importance to us varies widely. Each troll has varying rules for password complexity, and these rules are often incompatible with each other.

This dog's breakfast of authentication rules grow from password advice given at the dawn of the Internet, but is now hopelessly inappropriate. There are many proposed solutions: pass faces, pass gestures, pass artwork, devices, biometrics, etc. All these have their problems, so the eye-of-newt password rules persist.

I will discuss various solutions that can get us out of this swamp. Including my recent explorations of trying to remember strong keys.

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Evolutionary algorithms provide biologically inspired, random search approaches to problem solving in artificial intelligence. Genetic algorirthms (GAs) are evolutionary algorithms that apply principles from genetics to evolve problem solutions. In this talk, the fundamental principles of FAs will be introduced, along with two seemingly-related applications: string guessing and Sudoku.

General purpose computing on graphics processing units (GPGPU) makes use of graphics processing units (GPUs) to perform computations that are traditionally handled by central processing unit (CPU). Modern graphics cards provide thousands of GPUs for the cost of a single CPU, making massively parallel hardware affordable. Little work has been done to speed up GA computations using GPGPU. Although GAs are inherntly sequential, a significant amoutn of parallel processing may be performed within each generation. A framework for GPGPU acceleration of GAs will be presented, showing substantial speedups are possible with this approach.

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Chronic Wasting Disease (CWD) is a fatal prion disease that affects Cervids. Infections in deer and elk have been well document since the mid 1900s, but it was not until 2005 that it was found in moose. Many models for CWD transmisison within elk and deer exist, but the disease is not well modeled in moose. Previous CWD models may not apply to mosse, because their social structure varies from that of deer and elk. In this talk, we examine the differences between moose and other Cervids in order to create a CWD model specific to moose. To do this, we start with a standard SI disease model for CWD in mule deer. We then explore variations on this model and discuss the feasibility of each model given emperical data on moose populations and CWD infection rates in Colorado.

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The Cubli is a self-balancing robotic cube invented by a graduate student in Zurich, Switzerland. The self-balancing cube is classified as a an inverted pendulum, which means the center of gravity of the object is above the pivot point. For this robot to achieve a stable balance, a state space control system known as the Linear Quadratic Regulator (LQR) and is used to optimize the controller of the problem. The LQR uses the fields of discrete mathematics and linear algebra in its derivation of finding the optimal control along with complex analysis to confirm that steady state is reachable.

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A scorigami is a mathematical construct made from folding an idealized piece over a sequence of staight-line creases, making a single straight-line cut through the folded paper and then unfolding the paper to determine the types of shapes that result. In this presentation, we formulate a geometric and algebraic model for scorigami using complex geometry. Using this model, we define the notion of a contractive fold, and show that any symmetric, convex polygon can be formed from scorigami through a finite sequence of contractive folds.

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Markov chains can be used to model a number of real-world situations, including sports. In this talk we focus on applications to baseball. Using Markov chains and historic baseball data, conclusions can be drawn for example, as to whether or not sacrifice bunting or base stealing are good strategies.

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The classic Fibonacci rabbit problem involves a population of pairs of rabbits that take one month to mature, and then produce a litter of one breeding pair every month forever after. In this presentation, we examine the effects of changing three parameters of these rabbits: the rate of maturation, the size of the litters, and their total life expectancy. We devise a recursion relation for the population of Fibonacci rabbits in terms of these parameters. We also investigate whether or not it is possible to uniquely determin these parameters given only data on the total monthly population of rabbits after a specific (but unknown) duration of time.

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Gitbook is an online or desktop editor that can be used to author books. Built on Node.js framework, Gitbook uses markdown language to build your book. Writing a Gitbook is very straight forward and not much different from using standard word processor except that it has the ability to incorporate LaTeX within your document. Available output formats include html, pdf, eBook and JSON. This talk will focus on the basics of Gitbook and how to get started writing your own book. In addition, I will cover bookdown which is an adaptation of Gitbook that can be used with R statistical software. Bring your notebook computer to this talk so you can start building a simput book using Gitbook! You can view a sample from the Math 382 book at at this link.

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With the increase in the number of available 3D models (digital reprsentation of object in the computer), the ability to accurately and efficiently search for 3D models is crucial in many applications such as Computer Aided Design (CAD), 3D game, movie and animation production. As a result, 3D model retrieveal has become an important research area.M

Sketch-Based 3D model retrieval is an intuitive way to retrieve relevant 3D models given a user sketch. However, it is one of the most challenging research topics in the field of 3D model retrieval due to the big semantic gap between human-drawn sketches and 3D models. Such big semantic gap makes the search based on a direct sketch-model comparison suffer low accuracy and high computation cost.

We have proposed several novel sketch-based 3D model retrieval algorithms that have acheived significant improvements in both search accuracy and efficiency. In addition, we also built three benchmarks for large-scale 3D model retrieval and solicited state of the art algorithms by running three Eurographics Shape Retrieval Contest (SHREC) tracks in 2013, 2014, and 2016, and made related benchmarks, evaluation results and tools publically available on the websites, while some results have been published in top journals.

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Virtual reality for the public has become a reality, with inexpensive headsets like the Oculus Rift. However, prior to the Oculus Rift, virtual reality was used for decades in training. In these early environments, motion sickness-like sypmptoms, or cybersickness, was regularly reported. With the release to the general public, the possibility of this risk has increased, but empirical support for safety and development guidelines is mostly lacking. The current state of the research into cybersickness is examined, and possible models are proposed. Lastly, mitigation strategies are presented for developers.

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The Fast Fourier Transform (FFT) was introduced in 1965 by J. Cooley and J. Tukey, and has become one of the most important algorithms in modern computing. But there is a strong evidence that Carl Friedrich Gauss presented an FFT-like algorithm more than a century earlier.

The first half of the talk will serve as a flying introduction to the FFT, followed by a glimpse into Gauss's work in the second half of the talk

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We have had access to ten years of data of every student that have had contact with the Department of Mathematics and Computer Science. This data includes both demographic records (ACT/SAT scores, HS GPA, enrollment date, graduation year etc), as well as class records (classes taken, when, where, what grade etc). It should be noted that even though the data was extensive it was de-identified, there were no student names, student IDs etc. We will present our findings from the analysis of this data. The focus will be on the classification and association analysis. Some old truths will be confirmed together with some new findings.

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There are many different equations of state available to characterize the relationship between state function. These state function include pressure, temperature, or volumes of fluids. The goal of this project is to find a simpler approach to predict the PH of one specific fluid system, supercritical carbon dioxide and water based on temperature and pressure.

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In recent decades students have increasingly arrived at college unprepared for university-level eduction. Deficiences are regularly seen in both content mastery and study skills. This talk will examine the past one hundred and fifty years of American educational history in an attempt to explain why students are the way they are. The history of American Education is a vast subject, as a result, this talk will focus only on those event in history that have a had a direct impact on students' ability to learn

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General-purpose computing on graphics processing units (GPGPU) makes use of graphics processing units (GPUs) to perform computations that are traditionally handled by the central processing unit. Modern graphics cards provide thousands of GPUs for the cost of a single CPU, bringing massively parallel hardware to the masses. Many applications in mathematics, science and engineering are "embarrassingly parallel", and show dramatic performance increases from GPGPU processing.

This talk will introduce GPGPU programming on NVIDIA graphics cards using the Comon Unified Device Architecture (CUDA) framework. Examples from image processing and computer vision will be provided.

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Your team is in a best of a 2k+1 playoff series (k a non-negative integer). Assuming your team beats the opposing team in individual games with chance p, with game outcomes independent, the chance your team wins the series – call it W_{2k+1}(p) may be readily found.
There are a number of “obvious” properties that are actually fairly difficult to establish analytically about W_{2k+1}(p) unless this chance is rewritten in a non-standard way (a hint is provided by the title of the talk). For example, W_{2k+1}(p) should
be strictly increasing in p.

In addition to discussing how to establish such obvious properties, the expected length of the series will be presented.

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- An Introduction to Graph Statics by Alexia Mader
- Latin Squares by Anthony Morast

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- Optimizing a Two-stage Rocket by Jessica Gillaspie
- Optimal Zombie Dice by Kjerstin Cosand

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- Equations of State for a Binary Supercritical System by Debra Anderson
- Elliptic Curve Cryptography in Cryptocurrency by Christine Hjelmfelt

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A Comparison of Efficiency and Accuracy for Probabilistic Sonar Models and Update Algorithms for Two-Dimensional Mapping

Thesis Advisor: Dr. Larry Pyeatt

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- Quaternion Based Kinematics by Matthew Richard
- Graphic Statics by Alexia Mader
- Optimal Zombie Dice by Kjerstin Cosand
- Elliptic Curve Cryptography by Christine Hjelmfelt

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Thesis defense for Suiyuan Zhang, Computational Sciences and Robotics

November 20, McLaury 210, 11:00 am

Thesis Advisor: Dr. Mengyu Qiao

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November 18, McLaury 205, 11:00 am

By Dr. John Weiss

This talk introduces concurrency constructs in C++11, including external libraries as well as the new C++ concurrency interfaces. I will demonstrate that significant efficiency gains are achievable for the 2-D Fourier transforms on standard multi-core processor systems. This approach applies to other 2-D transforms (such as wavelet transforms and the discrete cosine transform), and readily generalizes to other separable 2-D operations such as convolution and correlation. Preliminary results indicate that scalability is good, and performance will continue to increase as future multi-core processor systems with additional CPUs become available.

This is a brief introduction to Orange, a free, component-based data mining and machine learning software suite.It allows data mining, data analysis and visualization through visual programming as well as Python scripting. It contains a set of components for data pre-processing, feature scoring and filtering, modeling, model evaluation, and exploration techniques. Orange is maintained and developed at the Bioinformatics Laboratory of the Faculty of Computer and Information Science, University of Ljubljana, Slovenia. This introduction will focus on how to use the visual programming tool to create a classifier, an unsupervised clustering, evaluation, and how to visualize the results.

So long, New York... Howdy, East Orange

This talk is an exploration of the mathematical ideas that go into the act of drawing stars. We start with the observation that while it is easy to draw the five pointed star in a single stroke of the pen, we cannot do the same for a 6 pointed one and ask the vague question, "Just what kinds of stars can we draw in a single stroke?" Our attempt to answer that question will lead us to other questions, and this seemingly pointless question about doodling will take us through number theory, abstract algebra, plan geometry, and even complex analysis. This isn't so much a talk with answers as it is a talk about the questions we ask and how we search for mathematical solutions, a sort of journal of an expedition into the mathematical unknown, in which we discover the footprints of earlier explorers and set off in new directions from their lead. We will pose many questions along the way that might make for an interesting starting point for your own undergraduate mathematical research. .... and we will do a lot of doodles.

From movies to pop music, it seems the undead are taking over the world. The usually staid Centers for Disease Control launched its tongue-in-cheek "Preparedness 101: Zombie Apocalypse" public campaign two years ago to drive home the importance of emergency preparation. Even SDSM&T has been infect as evidenced by the wildly popular, campus-wide "Humans vs. Zombies" war this fall. Anthropologist Krystal D'Costa suggests zombies capture our imagination because they represent modern society and technology gone awry and offer the perfect metaphor for an unstoppable pandemic.

Utah State University Professor Jim Powell expands the zombie metaphor to illustrate concepts and results from mathematical epidemiology. Using storylines from such movies as "Night of the Living Dead", "28 Days Later", "The Walking Dead" and "I am Legend," as well as data from the USU games. Dr. Powell will show how mathematicians model an epidemic. He'll talk about how scientists predict the course and impact of epidemics, discuss how "her immunity" (vaccination levels for disease eradication) works and discuss the evolution of reduced virulence and how it has consequences in university administration. Some of these modeling strategies are used by Dr. Powell and SDSM&T's own Dr. Marti Garlick to understand and predict the spread of Zombie Deer (infected with Chronic Wasting Disease) in southern Utah.