The department keeps a web archive of containing past newsletters, details of past colloquia, and other useful information.
The archive is currently in the process of being reorganized. Once complete, the newly organized archive will appear here. However, in the interim it can still be accessed in its original form here.
Fall 2013
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Tuesday October 15 2013, 2:30pm  3:30pm, Location 111 DSC
Dr. Chris True University of Nebraska  Lincoln
Using Geogebra to demonstrate the relationship among f, f'and f'' graphically and constructing antiderivatives
Abstract
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Geogebra is a free program that has many applications. Most often, people consider the use of the program to algebra and geometry problems. The demonstration will show how to successfully use the package in a calculus classroom to engage students in discussions and provide insight into the underlying concepts with derivatives and antiderivatives.
Speaker Biography
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Chris True is an Adjunct Professor in the Mathematics Dept. at UNL. He is also an Advanced Placement Consultant for College Board and is a Regional Instructor for Texas Instruments.
Tuesday November 12 2013, 2:30pm  3:30pm, Location 111 DSC (Cool Math Talk)
Dr. Pari Ford, University of Nebraska at Kearney
All Tied Up: Ropes, Tangles, and Fractions
Abstract
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The activity comes from John Conway and the idea is that we can associate a number with a tangle of two ropes, and with only two types of moves, the ropes can be tangled and untangled in a straightforward way. The calculations associated with the rope moves involve arithmetic with fractions and working with positive and negative numbers.
Speaker Biography
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Dr. Ford is an assistant professor at the University of Nebraska at Kearney. Her research interests are in graph theory and the mathematical concept knowledge of preservice elementary school teachers. She is the founder and coorganizer for the Central Nebraska Math Teachers Circle which meets regularly in Kearney. Pari is also the Past President of the Nebraska Association of Teachers of Mathematics and Section Governor for the Mathematical Association of America. When not involved with research, teaching, or service, she likes to spend time with her husband and 2 kids, Olivia and Nathan.
Friday November 15 2013, 11:00am  12:00pm, Location 110 DSC (Cool Math Talk)
Dr. Mahbubul Majumder, University of Nebraska at Omaha
How can we (not) ruin the power of statistical data visualization
Abstract
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We often use a statistical data plot to visualize the pattern in the
data. But, improper use of graphics can ruin the power of statistical
data visualization. This presentation will demonstrate how easily that
can be done. On the other hand, appropriate use of graphics can reveal a
strong message that would otherwise be hidden, no matter how the data
is presented. This talk will demonstrate new methods called lineup and
Rorschach protocols that can be used to test the significance of
visual findings. A human subjects experiment is conducted using
simulated data to provide controlled conditions. Results suggest that
the power of lineup protocol is higher than even the conventional
statistical inference. This opens up new areas of research involving
statistical data visualization, triggers new uses of data graphics, and
bridges the gulf between exploratory data analysis (EDA) and
inferential statistics.
Spring 2013
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Tuesday January 29 2013, 2:30pm  3:30pm, Location 116 DSC (Cool Math Talk)
Dr. Neal Grandgenett Haddix Community Chair of STEM Education, University of Nebraska at Omaha
Five Minute Challenges for Reinforcing Mathematical Topics
Abstract
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Sometimes it is nice to do a quick five minute activity to introduce or reinforce mathematical topics in algebra, geometry, probability, statistics, or calculus, as well to illustrate mathematical connections to other disciplines. Simple activities such as envelope cutting, paper folding, yarn knots, and mirror reflections actually have lots of underlying mathematical connections, and can build significant student interest across science, technology, engineering, and mathematics (STEM). This cool math talk will illustrate some of these quick mathematical challenges and strategies, that are useful in a wide range of K16 mathematics courses. Dr. Neal Grandgenett, the Haddix Community Chair of STEM Education at UNO will demonstrate (and distribute) some of these quick five minute challenges to help build student mathematical interest.
Tuesday February 26 2013, 2:30pm  3:30pm, Location 116 DSC
Karen Rhea, University of Michigan
StudentCentered Coursework
Abstract
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When thinking about inquirybased learning (IBL), there are many things to consider: the necessary syllabus of the courses, the expertise and training of instructors, the goals and expectations of the students, and the institution. In this talk, we will explore a class model that has shown to successfully encourage an interactiveengaged classroom. We will discuss how the style is supported and the reasons why we believe that model is an important support for the goals of our courses. This talk is intended for a variety of audiences including preservice teachers, university instructors (both experienced and novice to IBL), and people interested in learning more about IBL.
Speaker Biography
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Karen Rhea is a Lecturer Emeritus at the University of Michigan and she was named the Patricia Shure Collegiate Lecturer in 2012 for her contributions to U of M education. In 2011, she was the recipient of the MAA’s Deborah and Franklin Tepper Haimo Award for Distinguished College or University Teaching of Mathematics for her contributions to changes in the calculus curriculum nationally and for her work developing other outstanding teachers. In 2010 she was the recipient of the Matthews Underclass Teaching Award from the College of Literature, Science, and Arts for her distinctive contribution to teaching in courses in first or secondyear level math courses and her enthusiasm and dedication to undergraduate education
Friday March 8 2013, 2:30pm  3:30pm, Location 116 DSC
Dr. George Avalos, Professor, University of NebraskaLincoln
Concerning Rational Decay Properties of Certain Coupled PDE Systems
Abstract
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In this talk, we shall demonstrate how delicate frequency domain relations and estimates, derived for certain coupled systems of partial differential equation models (PDE's), may be exploited so as to establish results of uniform and rational decay. In particular, our focus will be upon decay properties of coupled PDE systems of different characteristics; e.g., hyperbolic versus parabolic characteristics. For such PDE systems of contrasting dynamics, the attainment of explicit decay rates is known to be a difficult problem, inasmuch as there has not been an established methodology to handle hyperbolicparabolic systems. For uncoupled wave equations or uncoupled heat equations, there are specific Carleman's multiplier methods in the time domain, wherein the exponential weights in each Carleman's multiplier carefully take into account the particular dynamics involved, be it hyperbolic or parabolic. But for coupled PDE systems which involve hyperbolic dynamics interacting with parabolic dynamics, typically across some boundary interface, Carleman's multipliers are not readily applicable. Given that such coupled PDE systems occur frequently in nature and in engineering applications; e.g., fluidstructure and structural acoustic interactions, there is a patent need to devise broadly implementable techniques by which one can infer uniform decay for a given PDE system. In this connection, our talk shall center on a novel frequency domain methodology.
Speaker Biography
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George Avalos received the Ph.D. in Applied Mathematics from the University of Virginia. He is currently a Professor at the University of NebraskaLincoln. His research interests include Control Theory for Partial Differential Equations.
Tuesday March 26 2013, 2:30pm  3:30pm, Location 116 DSC (Cool Math Talk)
Ron Taylor, Berry College
An introduction to the mathematical theory of knots
Abstract
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Knot theory was born out of an interest in cataloging the elements and was derailed by the discovery of the speed of light. Subsequently it was revived both as an area of mathematics, but one with scientific implications. In this talk we will discuss the history of knot theory along with some interesting results and applications.
Friday March 29 2013, 2:30pm  3:30pm, Location 116 DSC
Jun Kawabe, Faculty of Engineering, Shinshu University
The study of Riesz spacevalued nonadditive measures
Abstract
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In 1974, Sugeno [2] introduced the notion of fuzzy measures and integrals to evaluate nonadditive or nonlinear quality in systems engineering. In the same year, Dobrakov [1] independently introduced the notion of submeasures to refine measure theory further. Both fuzzy measures and submeasures are special kinds of nonadditive measures, and their studies have stimulated engineers’ and mathematicians’ interest in nonadditive measure theory; see Wang and Klir [3].
The classical theorems, such as the Egoroff theorem, the Alexandroff theorem, and some convergence theorems of integrals, are fundamental and important to develop measure theory. Therefore many researchers continue to try to obtain their successful analogues in nonadditive measure theory.
When we try to develop nonadditive measure theory in Riesz space, along with the nonadditivity of measures, we confront some tougher problems due to the epsilonargument, which is useful in measure theory, not working well in a general Riesz space. In this talk, instead of the epsilonargument, we introduce and impose some new smoothness conditions on a Riesz space (the asymptotic Egoroff property, the monotone function continuity property, and so on) to obtain successful analogues of some important results in realvalued nonadditive measure theory.
This work is supported by GrantinAid for Scientific Research No. 20540163, Japan Society for the Promotion of Science (JSPS).
References
[1] I. Dobrakov, On submeasures I, Dissertationes Math. (Rozprawy Mat.) 112, Warszawa, 1974.
[2] M. Sugeno, Theory of fuzzy integrals and its applications, Doctoral Thesis, Tokyo Institute of Technology, 1974.
[3] Z. Wang, G.J. Klir, Generalized Measure Theory, Springer, Berlin Heidelberg, New York, 2009.
Speaker Biography
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Prof. Jun Kawabe received his PhD in Information Sciences, from Tokyo Institute of Technology, Tokyo, Japan, in 1986. Then he worked as a lecturer and associate professor in Shinshu University, Nagano, Japan. He has been serving as a full professor in Shinshu University since 2003. He was a visiting researcher in Massachusetts Institute of Technology in 1996 and 200506. Prof. Kawabe has published 48 research papers and 2 books. His research interests are: nonAdditive Measure Theory, weak convergence of vector measures with values in Riesz space, fuzziness and uncertainty, fuzzy set, fuzzy number, and probability theory.
Wednesday April 3 2013, 2:30pm  3:30pm, Location 116 DSC
Melanie DeVries, Graduate Student, UNL
Unknotting Mathematical Knots
Abstract
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Knot theory is a subfield of mathematics that concentrates on objects called knots – embeddings of the circle in a 3dimensional balls – which can be thought of as endlessly elastic and frictionless strings that are tangled around themselves before their ends are glued together. The main question of this field is when are two knots equivalent, a deceptively simple question that has spawned the study of several different intrinsic properties of knots. One we will look at in particular is the study of unknotting numbers, the number of times a move called an unknotting operation needs to be applied to untangle a knot. We will also look at unknotting operations and unknotting numbers in a generalization of knot theory – virtual knot theory – that looks at embeddings of knots in more complicated surfaces.
Friday April 5 2013, 1:00pm  2:00pm, Location 401 RH (Cool Math Talk)
John Konvalina, Department of Mathematics, UNO
A Mathematical Adventure from Combinatorics to Fractal Geometry to Brain Tumor Growth
Abstract
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This talk will take you on a quick journey in discovery and amazement of the power of mathematical thinking from a simple counting problem arising in mathematical biology to the emergence of a new fractal, and then, finally, coming back around to biology with an application to brain tumor growth.
Speaker Biography
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Dr. Konvalina is Professor and Chair of the Department of Mathematics. His interests are in combinatorics, number theory, mathematics education, fractals, chaos theory, mathematical biology, data science, math anxiety, and more! He has published three textbooks and dozens of papers in pure and applied mathematics.
Wednesday April 17 2013, 2:30pm  3:30pm, Location 116 DSC
Ginger McKee, Wolfram Research, Inc
Mathematica 9 in Education and Research
Abstract
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During this free seminar, we will explore Mathematica's use for a wide variety of practical and theoretical applications across a variety of disciplines. Attendees will not only see new features in Mathematica 9, but will also receive examples of this functionality to begin using immediately. No Mathematica experience is required, and students are encouraged to attend.
Speaker Biography
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To find out more, please contact Ginger McKee at ginger@wolfram.com or 18009653726 ext. 3492
Tuesday April 23 2013, 2:30pm  3:30pm, Location 116 DSC (Cool Math Talk)
Dr. Dana Ernst, Assistant Professor, Department of Mathematics and Statistics, Northern Arizona University
Impartial Games for Generating Groups
Abstract
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Given a single element from a group G, we can create new elements of the group by raising the element to various powers. Some finite number of elements will "generate" all of group G. In the game DO GENERATE, the goal is to generate the all of G. In DO NOT GENERATE, the loser is the player who generates all of G. In this talk, Dr. Dana Ernst will help us explore both games and discuss winning strategies. Time permitting, he will also relay some of the current research related to both games.
Speaker Biography
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 Assistant Professor in the Department of Mathematics and Statistics at Northern Arizona University in Flagstaff, AZ
 Special Projects Coordinator for the Academy of InquiryBased Learning
 Research interests include combinatorics, algebraic structures, inquirybased learning, and the Moore method for teaching mathematics
Fall 2012
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Tuesday September 18 2012, 2:30pm  3:30pm, Location 116 DSC (Cool Math Talk)
Dr. James Tanton
Some Fibonacci Surprises
Abstract
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The Fibonacci numbers 1,1,2,3,5,8,13,... have been studied and probed and generalized and analyzed in most every possible way for centuries (well, for 810 years to be precise; well, ... longer actually if you read Sanskrit) and one might think there is little more to say about them. Let me surprise you then with a whole host of new appearances of the Fibonacci numbers. (And this talk comes with an invitation for you to find more of your own!)
Speaker Biography
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Believing that mathematics really is accessible to all, James Tanton (PhD, Mathematics, Princeton 1994) is committed to sharing the delight and the beauty of the subject. In 2004 James founded the St. Mark's Institute of Mathematics, an outreach program promoting joyful and effective mathematics education. He worked as a fulltime high school teacher at St. Mark's School in Southborough MA,(20042012) and he conducted, and continues to conduct, mathematics graduate courses for teachers though Northeastern University and American University. He also gives professional development workshops across the nation and Canada.
James recently relocated to Washington D.C. and is working with the Math For America program in D.C. and with the Mathematical Association of America.
James is the author of SOLVE THIS: MATH ACTIVITIES FOR STUDENTS AND CLUBS (MAA, 2001), THE ENCYCLOPEDIA OF MATHEMATICS (Facts on File, 2005), MATHEMATICS GALORE! (MAA, 2012) and twelve selfpublished texts. He is the 2005 recipient of the Beckenbach Book Prize, the 2006 recipient of the Kidder Faculty Prize at St. Mark's School, and a 2010 recipient of a Raytheon Math Hero Award for excellence in school teaching.
He also publishes research and expository articles, and through his extracurricular research classes for students has helped high school students purse research projects and also publish in mathematical journals.
More about James can be garnered from his website www.jamestanton.com
Friday September 28 2012, 2:30pm  3:30pm, Location 116 DSC (Cool Math Talk)
Kyle Duckert, Instructor, Mathematics Department, University of Nebraska at Omaha
The physics of a sandbox: An introduction to granular hydrodynamics
Abstract
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We study interactions between shocks and standing wave patterns in continuum simulations of vertically oscillated granular layers. Layers of grains atop a plate with sinusoidal oscillations in the vertical direction leave the plate at some time during the cycle if the accelerational amplitude of oscillation is greater than the acceleration of gravity. Above a critical acceleration, standing waves form stripe patterns. In these same shaken layers, shocks are produced when layers collide with the plate after leaving the plate earlier in the cycle. We simulate vertically shaken layers using numerical solutions of continuum equations to NavierStokes order to find number density, average velocity, and granular temperature as functions of time and location within the cell. We compare shocks and standing waves coexisting in this system; pressure gradients produced by shocks play a significant role in the formation of standing wave patterns.
Tuesday October 9 2012, 2:30pm  3:30pm, Location 116 DSC (Cool Math Talk)
Dr. Elliott Ostler, Professor, Teacher Education, University of Nebraska at Omaha
Mathematics, Measurement, and Machines
Abstract
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The National Council of Teachers of Mathematics has called measurement the forgotten standard. You might ask, how could something so important be so easily forgotten? Simple, like so many other things, we take for granted what we assume is easily understood, but did you know you can measure time, roots, rational exponents, and other complex mathematical quantities with a standard ruler? It's true! This informative session will take you through a series of measurement techniques and even show you how to build machines for measuring and calculating using measurement.
Speaker Biography
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Elliott Ostler is a former Junior High and High School mathematics and science teacher in Nebraska, Iowa, and Washington. He has been a professor of STEM Education at UNO for 18 years and specializes in creating manipulative geometric applications and representations for common numeric and algebraic concepts. He is also active in brining mobile technology into classrooms to help students better understand STEM concepts. He has worked directly with some of the nation’s leading education service and support institutions such as the College Board, Texas Instruments, NASA, Jet Propulsion Laboratories, and the NCTM. His current research in STEM learning is related to helping students understand how machines are engineered through careful measurements and geometric concepts we see so often but regularly take for granted.
Friday November 9 2012, 1:00pm  2:00pm, Location 254 DSC (Cool Math Talk)
Kathryn Haymaker, Mathematics Department, University of Nebraska Lincoln
Combinatorics and the game SET
Abstract
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SET is a multiperson card game in which the goal is to collect particular sets of three cards from a group of 12 (or more). The person with the most SETs by the end of the game wins. It turns out that a SET corresponds to a line in a 4dimensional version of TicTacToe! I'll explain how that game works, and we will use the correspondence along with some counting techniques to answer interesting questions about the game, including: what is the size of the largest group of cards that does not contain a SET?, and, what is the most likely type of SET?
Speaker Biography
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Kathryn Haymaker, of Hellertown, PA, is a Ph.D. student in mathematics at UNL. She studies coding theory, which originated with the need to send information reliably and efficiently over a communication or storage channel. Her dissertation research includes the use of mathematical structures to design codes for flash memories and writeonce memories. In fall 2011, she spent two months at a thematic program on coding theory at a technical institute in Lausanne, Switzerland. She received the G.C. Young and W.H. Young Award for scholarship in the UNL math department, and the 20122013 Presidential Graduate Fellowship. She graduated with honors in mathematics from Bryn Mawr College in 2007.
Monday November 12 2012, 2:30pm  3:30pm, Location 116 DSC (Cool Math Talk)
Howard Alcosser, Diamond Bar High School, California
How to Succeed in Teaching Calculus to Students  MOTIVATE
Abstract
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High school students take Calculus for many different reasons  most of them have nothing to do with the love of math! I'll talk about some of these reasons and how I motivate students to be successful both in my class and at the universitydespite their wide range of mathematical abilities.
Speaker Biography
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Howard Alcosser has taught AP Calculus AB and BC and IB Higher Level Math in Diamond Bar, California for 30 years where he has been the architect of the AP Calculus program that was designated "Best in the World" in 2005 and "Best in the Nation" in 2007 by the College Board in their Report to the Nation and California's Best by the Siemens Foundation in 2008. The College Board named Howard in 2006 as one of 20 Exemplary AP Teachers in the Western Region.
Howard has been an AP Calculus Reader for the past 11 years and has led workshops across the country.
Howard is also referred to as "Mister Calculus", as he has a website for teachers and students to access much information regarding Calculus via "Ask Mister Calculus": http://home.roadrunner.com/~askmrcalculus/index.html
Thursday November 15 2012, 2:30pm  3:30pm, Location 256 DSC (Cool Math Talk)
Ivars Peterson, Director of Publications at the Mathematical Association of America
The Jungles of Randomness
Abstract
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From slot machines and amusement park rides to dice games and shuffled cards, chance and chaos pervade everyday life. Sorting through the various meanings of randomness and distinguishing between what we can and cannot know with certainty proves to be no simple matter. Inside information on how slot machines work, the perils of believing random number generators, and the questionable fairness of dice, tossed coins, and shuffled cards illustrate how tricky randomness can be.
Speaker Biography
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Ivars Peterson is an awardwinning mathematics writer. He is currently Director of Publications for Journals and Communications at the Mathematical Association of America. He worked for 25 years as a columnist and online editor at Science News and continues as a longstanding columnist for the children's magazine Muse. He wrote the weekly online column Ivars Peterson’s MathTrek. He is the author of a number of popular mathematics and related books. Ivars Peterson received the Joint Policy Board for Mathematics Communications Award in 1991 for "exceptional skill in communicating mathematics to the general public over the last decade". For the spring 2008 semester, he accepted the Wayne G. Basler Chair of Excellence for the Integration of the Arts, Rhetoric and Science at East Tennessee State University. He gave a series of lectures on how math is integral in our society and our universe. He also taught a course entitled "Communicating Mathematics".
Monday November 26 2012, 2:30pm  4:00pm, Location 115 DSC
Ginger McKee, Wolfram Research, Inc
Mathematica in Education and Research
Abstract
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This talk illustrates capabilities in Mathematica that are directly applicable for use in teaching on campus. Topics of this technical talk include: Free form input, 2D and 3D visualization, Dynamic interactivity, Ondemand scientific data, Exampledriven course materials, Symbolic interface construction, Practical and theoretical applications.
Friday November 30 2012, 2:30pm  3:30pm, Location 116 DSC (Cool Math Talk)
Dr. Doug Downey, Assistant Professor, EECS, Northwestern University
Web Information Extraction: Theory and Applications
Abstract
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Search engines are extremely useful tools for answering simple questions.
However, for more complex questions  e.g., "which nanotechnology companies are hiring on the West Coast?"  existing search engines are less effective, because the answers are not contained on just a single page. Answering these questions requires extracting and synthesizing information across multiple documents. Currently, this is a tedious and errorprone manual process.
In this talk, I will describe my research toward automating the extraction of information from the Web. I will present a theoretical model of the redundancy inherent in the Web, and show how the model enables the autonomous extraction of facts from Web text. I will then highlight our ongoing work toward more powerful information extraction capabilities and applications.
Speaker Biography
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Doug Downey is an assistant professor in the EECS Department of Northwestern University. He obtained his PhD from the University of Washington, where he was advised by Oren Etzioni. His research interests are in the areas of natural language processing, machine learning, and artificial intelligence, with a particular interest in utilizing the Web to autonomously extract large knowledge bases.
Spring 2012
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Tuesday January 24 2012, 2:30pm  3:30pm, MBSC Dodge Rooms
Dr. Michael Matthews, Assistant Professor, Mathematics Department, University of Nebraska at Omaha
Mathemagic: Magic in the Mathematics Classroom
Abstract
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We will be presenting several different magic tricks that are based on mathematical principals or "Mathemagic". Magic can be a powerful tool for mathematics teachers if used properly. Of course, since it is entertainment, it can be used to dazzle the students. Thus it makes a great hook into a particular lesson. Or of course, it could be used as another "5 minute fillers". However, used properly mathemagic can be used to teach concepts as a core part of a lesson. Such magic tricks can also be a basis for good questions for homework or projects. Magical Tricks will be presented that are appropriate for grades 312.
Tuesday February 28 2012, 2:30pm  3:30pm, MBSC Dodge Rooms
Dr. Dana C. Ernst, Assistant Professor, Mathematics Department, Plymouth State University
The Futurama Theorem
Abstract
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In the episode "The Prisoner of Benda" of the television show Futurama, Professor Farnsworth and Amy create a mind switching machine, only to afterwards realize that when two people have switched minds, they can never switch back with each other. Throughout the episode, the Professor, with the help of the Globetrotters, try to find a way to solve the problem using two or more additional bodies. The solution to this problem is now called the Futurama Theorem, and is a reallife mathematical theorem, invented by Futurama writer Ken Keeler, who holds a PhD in applied mathematics. In this talk, we will introduce the mathematics behind the Futurama Theorem and present its proof.
Friday March 9 2012, 12:00pm  1:00pm, 261 PKI (Joint colloquium with PKI)
Dr. Mahboub Baccouch, Assistant Professor, Mathematics Department, University of Nebraska at Omaha
Superconvergence and a posteriori error estimation for the local discontinuous Galerkin method applied to the secondorder wave equation
Abstract
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Discontinuous Galerkin (DG) methods have gained in popularity during the last fifteen years because of their ability to address problems having discontinuities, such as those that arise in hyperbolic problems. DG methods allow discontinuous bases, which simplify both h refinement (mesh refinement and coarsening) and prefinement (method order variation). However, for DG methods to be used in an adaptive framework one needs a posteriori error estimates to guide adaptivity and stop the refinement process. The solution space consists of piecewise continuous polynomial functions relative to a structured or unstructured mesh. As such, it can sharply capture solution discontinuities relative to the computational mesh. It maintains local conservation on an elemental basis. The success of the DG method is due to the following properties: (i) does not require continuity across element boundaries, (ii) is locally conservative, (iii) is well suited to solve problems on locally refined meshes with hanging nodes, (iv) exhibits strong superconvergence that can be used to estimate the discretization error, (v) has a simple communication pattern between elements with a common face that makes it useful for parallel computation and (vi) it can handle problems with complex geometries to high order.
The local discontinuous Galerkin (LDG) finite element method is an extension of the DG method aimed at solving ordinary and partial differential equations containing higher than firstorder spatial derivatives. In this talk, we present new superconvergence results for the LDG method applied to the secondorder scalar wave equation in one space dimension. We show that the leading terms of the spatial discretization errors for the pdegree LDG solution and its spatial derivative are proportional to the (p + 1)degree right Radau and (p + 1)degree left Radau polynomials, respectively. More precisely, we prove that the global discretization error for the LDG solution is O(hp+3/2) superconvergent at the roots of the right Radau polynomial of degree p + 1 and the solution’s derivative converges as O(hp+3/2) at the roots of the (p + 1)degree left Radau polynomial while a local error analysis and computational results and show higher O(hp+2) convergence rates at the roots of Radau polynomials of degree p + 1 on each element for both the solution and its derivative. These results are used to construct asymptotically correct a posteriori error estimates. We further show that the LDG discretization error estimates converge to the true spatial errors under mesh refinement. Finally, we prove that the global effectivity indices, for both the solution and its derivative, in the L2norm converge to unity at O(h1/2) rates. Several numerical simulations are performed to validate the theory.
Thursday April 12 2012, 2:30pm  3:30pm, 115 DSC, Math Awareness Month Keynote Speaker
David W. Tyner, U.S. Strategic Command
Mathematics and Operations Research at USSTRATCOM
Abstract
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Located at Offutt Air Force Base near Omaha, Neb., U.S. Strategic Command (USSTRATCOM) is one of nine unified commands in the Department of Defense. USSTRATCOM integrates and coordinates the necessary command and control capability to provide accurate and timely information for the President, the Secretary of Defense, other National Leadership and regional combatant commanders.
Its responsibilities include space operations; Defense Department information operations; global missile defense; and combating weapons of mass destruction.
This presentation will include information on operations research and general mathematical applications at USSTRATCOM. Specific focus will be on reliability testing and the use of Mann Grubbs in confidence interval determinations.
Also presented will be information on mathematical programs and careers at USSTRATCOM and the US Department of Defense.
Fall 2011
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Wednesday October 5 2011, 2:30pm  3:30pm, 115 DSC
Dr. Jing Chu, CAS Research Center on Fictitious Economy & Data Science, Beijing, China
Identification of LambdaMeasures Based on Partial Information
Abstract
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In information science, we cannot get rid of incomplete information or information with errors. When the information appears as a set function, one eligible method to deal with such kind of information is to identify it with a lambdameasure, which is a typical nonadditive measure placing a historical important role in information science. In this paper, by using a genetic algorithm, a general identification of lambdameasure based on partial and/or imprecise information is discussed. The method and strategy developed in this paper are also available for the identification of other types of nonadditive measures, such as kinteractive measures and belief measures.
Wednesday October 12 2011, 2:30pm  3:30pm, 115 DSC (Cool Math Talk)
Dr. Andrew W. Swift, Assistant Professor, Mathematics Department, University of Nebraska at Omaha
Statistics in Action: ESPN and the Mystery of the US Open Draw
Abstract
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On August 15 2011, the ESPN program “Outside the Lines” ran a segment about the annual US Open tennis tournament. Their claim was that the tournament draw was favoring the top seeds even beyond the advantage gained by the seeding process. They backed their claim with statistical analysis of the tournament drawings from the past 10 years.
In this talk, a deeper look at ESPN’s analysis will be presented, as well as a discussion of statistical decision making in general. No prior understanding of statistical analysis is required.
A link to the ESPN story can be found here: http://tinyurl.com/3e6ra4d
Wednesday October 26 2011, 2:30pm  3:30pm, 115 DSC
Dr. Stephen R. Dunbar, University of Nebraska, Lincoln and MAA American Mathematics Competitions
The Common Core State Standards and Math on the AMC Contests
Abstract
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I will discuss the setting and content of the new Common Core State Standards in Mathematics along with their short history. I will then take problems from the middleschool and highschool level competitions from the MAA and map them back to the Common Core Standards. The goal is to find the match between math that mathematicians find interesting and challenging for students and the Standards. In the process I will show that the Common Core Standards fail to contain some fundamental topics and often underestimate the grade level difficulty of topics that are covered.
Friday November 4 2011, 3:30pm  4:30pm, Old Gym 306, Creighton University (Joint colloquium with CU)
Dr. Ellen Gethner, Associate Professor, University of Colorado
To the Moon and Beyond
Abstract
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If Earth colonizes its Moon, and cartographers elect to color the corresponding map, they are faced with two planar maps (the map of Earth and the map of its Moon) with an extra coloring constraint: a country and its colony are to be assigned the same color; such a map is called an "EarthMoon Map."
More generally, the thickness of a graph G, denoted Theta(G), is the smallest integer t such that G can be represented as the edgedisjoint union of t planar graphs. We say that G has thickness t or that G is a thicknesst graph and write Theta(G)=t. Thus if G is planar, then Theta(G)=1. And the graph corresponding to an EarthMoon map has thickness at most two. In 1959 Gerhard Ringel asked: what is the largest chromatic number of any thicknesstwo graph? An exact answer continues to be elusive, and the folklore amongst graph colorers is
that finding that answer is at least as hard as the proof of the Four Color Theorem, if not harder.
But there are other related problems that are reasonable and interesting to investigate. For example, the rinflation of a graph G, denoted by G[r], is the graph obtained by replacing each vertex of G with a K_r and then taking the join of neighboring (K_r )s. If chi(G)=k, then chi(G[r]) <= rk and the bound is sharp. What can be said about the thickness of G[r] when, for example, G is planar? This problem and others will be discussed, with open problems given along the way.
Friday November 11 2011, 2:30pm  4:00pm, 115 DSC
Christopher Goodrich, GTA, University of Nebraska, Lincoln
Partial Hölder Continuity for Minimizers of Functionals with Continuous Coefficients
Abstract
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In this talk we shall discuss some recent regularity results for minimizers of the
functional
u >  ⌠ ⌡

_{}
Ω

a(x,u) g(Du) dx, 

where u : Ω⊆ℝ^{n} →ℝ^{N} with n,N ≥ 2,in the case where g is only assumed to be asymptotically convex and to satisfy standard growth, and a ∈ L^{∞} (Ω × ℝ^{N}) satisfies a continuity condition. We shall begin by giving an introduction to the calculus of variations and then to the regularity problem. After developing this preliminary material and placing it into an appropriate historical context, we shall discuss our new results for the problem above. We shall conclude by briefly suggesting how our results may be able to be extended to the setting of a Riemannian manifold.
Thursday December 8, 2:30pm  4:00pm, 402 RH
Judith Covington , Louisiana State University in Shreveport
The game of SET and Geometry
Abstract
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What exactly does the game of SET have to do with geometry? The game of Set deals with matching or not matching four different characteristics. Geometry deals with points, lines and planes. This talk will briefly describe the game of set and discuss how to use the SET cards to describe a finite geometry model.
2012/2013
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Student: Li Westman. Advisor: Zhenyuan Wang
Ranking Fuzzy Numbers by their Left and Right Wingspans.
Description
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Based on the area between the curve of the membership function and the horizontal real axis, concepts of left and right wingspans are introduced. By them, a new index, called the wcenter for fuzzy numbers is proposed. It is continuous with respect to the convergence of fuzzy number sequence. An intuitive and reasonable ranking method for fuzzy numbers based on their wcenter is also established. This new ranking method is useful in fuzzy decision making and fuzzy data mining. The paper also points out that, in literature, some ranking methods based on the centroid of fuzzy numbers are not reasonable.
Final Project Report Awarded First Prize
Student: Amanda Ludes. Advisor: Dora Matache
Average Influence of Threshold Boolean Functions and Heterogeneous Kauffman Networks.
Description
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For this project we wish to find a formula for the average influence of threshold Boolean functions and then use it to model the influence and find the critical values for combinations of different types of Boolean functions in a heterogeneous random Boolean network. Besides threshold functions which are the main focus, other functions considered in the heterogeneous model fall in the categories of: canalizing functions with one canalizing input, canalizing functions with two canalizing inputs, and biased functions. While recent research has focused on finding phase transitions for homogeneous network ensembles with just one type of underlying Boolean function, real biological networks are comprised of a number of different types of Boolean functions, potentially with links between nodes of different classes. Here, we find the average influence of functions for the heterogeneous network in terms of the parameters for the network. This will allow us to find the critical condition, which divides the phase space into ordered and chaotic regions. We plot this influence and use it to find the critical condition in phase diagrams for both networks consisting only of threshold functions, and networks of ensembles of the four different types of functions.
Final Project Report Awarded Second Prize
Student: Balagbo Lawson. Advisor: Mahboub Baccouch
A posteriori error estimates for a discontinuous Galerkin method for onedimensional linear hyperbolic problems.
Description
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The discontinuous Galerkin (DG) finite element method provides an appealing approach to address problems having discontinuities, such as those that arise in hyperbolic conservation laws. In this talk, we study the global convergence of the implicit residualbased a posteriori error estimates for a DG method applied to onedimensional linear hyperbolic conservation laws. We use a recent superconvergence result [Y. Yang and C.W. Shu, SIAM J. Numer. Anal., 50 (2012), pp. 31103133] to prove that these error estimates at a fixed time converge to the true spatial errors in the L2norm under mesh refinement. The order of convergence is proved to be p+3/2, when pdegree piecewise polynomials are used. Finally, we prove that the global effectivity indices in the L2norm converge to unity under mesh refinement. The order of convergence is proved to be 1. These results improve upon our previously published work in which the order of convergence for the a posteriori error estimates and the global effectivity indices are proved to be p+5/4 and 1/2, respectively. Several numerical simulations are performed to validate the theory.
Final Project Report Awarded Third Prize
Student: Bo Guo. Advisor: Zhenyuan Wang
On Pseudo Gradient Search for Solving Nonlinear Multiregression with the Choquet Integral.
Description
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The objective function in some real optimization problems may not be differentiable with respect to the unknown parameters at some points such that the gradient does not exist at those points. Replacing the classical gradient search, the method of pseudo gradient search has been proposed and used for solving nonlinear optimization problems, such as nonlinear multiregression based on the Choquet integral with a linear core. It is a local search with rapid search speed. To improve the search tactics, a random angle search in randomly selected dimensions is also involved. Our experiments show that the proposed pseudo gradient search is effective and efficient. It can be widely used for solving nonlinear optimization problems with continuous objective function.
Final Project Report
Student: Joonhee Lee. Advisor: Mahboub Baccouch
Superconvergence and a posteriori error estimation for the local discontinuous Galerkin method for solving convectiondiffusion problems in one space dimension.
Description
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The discontinuous Galerkin (DG) method is a class of finite element methods using discontinuous piecewise polynomials as the solution and the test spaces. DG method is a powerful tool for approximating some partial differential equations which model problems in physics, especially in fluid dynamics or electrodynamics. DG combines many attractive features of the classical finite element, finite volume, and finite difference methods. The local discontinuous Galerkin (LDG) finite element method is an extension of the DG method aimed at solving ordinary and partial differential equations containing higher than firstorder spatial derivatives. In this talk we study the superconvergence properties of the LDG method applied to transient convectiondiffusion problems in one space dimension. We show that the leading terms of the local spatial discretization errors for the pdegree LDG solution and its spatial derivative are proportional to (p+1)degree right Radau and (p+1)degree left Radau polynomials, respectively. Thus, the local discretization errors for the pdegree LDG solution and its spatial derivative achieve (p+2)th order superconvergent at the roots of the right and left Radau polynomials of degree p+1, respectively. These results are used to construct asymptotically correct a posteriori error estimates. Several numerical simulations are performed to validate the theory.
Final Project Report
Student: Teng Li. Advisor: Valentin Matache
Complex Dynamics, Geometric Function Theory, and a Fixed Point Theorem.
Description
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Geometric function theory is a body of knowledge that covers the geometric properties of analytic functions. Conformal transforms and their properties are among the most popular topics belonging to it. We will present aspects less known to the general public, such as the behavior of the sequence of iterates of analytic selfmaps of the unit disc, which leads to the famous DenjoyWolff theorem, and based on that theorem, to a recent fixed point theorem, whose message is that families of analytic selfmaps of the disc simultaneously have a fixe point in that set (not the same for all of them), if they interpolate between select interpolation data sets. The study of iterates of analytic selfmaps is designated by the term complex dynamics.
Final Project Report
Student: Celeste Mott. Advisor: Dora Matache
Simulation of a heterogeneous boolean network.
Description
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A Boolean network is a system of nodes linked to one another, each node capable of two states, active or inactive. As time passes, each node examines the state of its input nodes and determines its own state according to a specific rule, or Boolean function. As the network evolves, it can either regress into a cycle of repeating states or erupt into chaos under certain conditions. This paper examines a computer simulation that creates a Boolean network of n nodes where each node has a connectivity (number of input nodes), k, drawn from a uniform distribution, and one of four general function typescanalyzing with one canalyzing input, canalyzing with two canalyzing inputs, threshold, or bias functions. The goal is to estimate the probability that the network returns to its original behavior after a small disturbance. The main purpose of this computer simulation is a means of reference. Since the program has a great number of editable parameters, one can use the simulation to estimate how modifying a parameter will affect the stability of a network or compare that with mathematical models or real data against the simulation.
Final Project Report
Student: Nguyen Nguyen. Advisor: Valentin Matache
Hyperbolic composition operators and the invariant subspace problem.
Description
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About 20 years ago, three mathematicians proved that the Invariant Subspace Problem, which is still open for Hilbert space operators, can be reduced to the study of the invariant subspace lattice of a single operator: a hyperbolic composition operator acting on the Hilbert Hardy space H2 of all functions analytic in the open unit disc, having square sumable Maclaurin coefficients. We will show how this approach leads to the problem of deciding if the only minimal invariant subspaces of a hyperbolic composition operator are the 1dimensional eigenspaces or not, and report on several results obtained in this direction.
Final Project Report
2011/2012
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Student: Rodney Tembo. Advisor: Dora Matache
Boolean network modeling of social networks as distributed prediction markets.
Description
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Random Boolean Networks are networks of nodes that can be in one of two possible states ON or OFF, and whose evolution from one time point to another is governed by given Boolean rules. Each node's evolution is influenced by the state of other nodes called its parents. We consider a social network of traders and marketers. The marketers aggregate trader information and share it with other marketers and traders. The traders use this information, as well as outside information from media and their own beliefs to model their dynamics from one time step to another. At the same time the traders can be considered part of a social network of traders in which they make predictions of the other traders' behavior and use them to make their own decisions or to influence the marketers and consequently the entire market.
Final Project Report Awarded First Prize
Student: Andrew Tew. Advisor: Robert Todd
4move reducibility of cables of (2p+1,2) torus knots.
Description
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Nakanishi conjectured in 1979 that the 4move operation on a knot diagram is an unknotting move. Though the conjecture is consider to be false, no counterexample has been found and it has been show that there is no counterexample with 12 crossings or fewer. For some time it was thought that the 2cable of the trefoil knot was a counterexample, however Askitas presented a sequence of 4moves that reduced it to the unknot. In that paper he mentions that he believes that there is an inductive proof to show that all cable of (2p+1,2) torus knots are 4move reducible. Our goal is to explore this avenue. To do this project a student should be in the later part of their degree having taken 2230 and at least one other proof class, and the student should like drawing pictures.
Final Project Report Awarded Second Prize
Student: Stephen Dodds. Advisor: Mahboub Baccouch
Robotic manipulators: Modeling, Numerical methods, and control.
Description
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Robotic manipulators are a major component in the manufacturing industry. They are used for many reasons including speed, accuracy, and repeatability. Increasingly, robotic manipulators are finding their way into our everyday life. In fact in almost every product we encounter a robotic manipulator has played a part in its production. The goal of this project is to allow the student to apply the techniques of numerical methods to an engineering design problem. Matlab is selected as the programming tool.
In this project, we consider the twolink robotic manipulator which is a classic example studied in introductory robotics courses. The equations of motion for the two arms are described by nonlinear differential equations. Because closedform solutions are not available, the equations of motion are numerically studied using the numerical methods. We propose to apply robust numerical methods to solve these differential equations. Special interest is devoted to determine the motion of the two arms to yield a desired xyposition of the robot hand.
Final Project Report Awarded Third Prize
Student: Benjamin Knutson. Advisor: Mahboub Baccouch
Relation of Shape Equations (ROSE) Analysis: Comparison of Shapes in Weapon Detection Systems.
Description
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A metal detector is a device which responds to concealed metal. Most current metal detectors can infer the approximate size, density, and material composition of detected objects, but cannot discriminate against harmless objects such as metallic watches and jewelry, which must first be removed. It is our goal in this analysis to statistically compare the shapes of detected objects so that metal detectors can quickly and accurately infer the presence of concealed metal weaponry, thereby making them a more practical means of security. Though potentially useful in many areas, this shape analysis will be developed for further implementation of weapon detection systems in public buildings, specifically in schools.
Two shape equations are built from creating a helical mesh which wraps around the surface of each object. One shape equation denotes the coordinates of the surface points as distances from a central axis; the other as distances from the origin. A relation of shape equations (ROSE) compares the detected object's equations with those of other objects in a library to determine the relative amount of work it would take to transform the detected object into each member of the library. An Analysis of Variance test statistically compares the work values. The probability that the detected object is of the same class of objects as those in the library is given by the Ftest.
The shape analysis will be performed on a test prism with respect to a library of prisms. The performance will measure the strength and efficiency of the analysis.
Final Project Report
Student: Mickey Loos. Advisor: Andrew W. Swift
A Statistical Investigation into the Existence of the "Home Run Derby Effect" in Baseball.
Description
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Each July, approximately halfway through the baseball season, Major League Baseball holds an AllStar game. The day before the AllStar game 8 players (4 from each league) take part in a Home Run Derby. The Home Run Derby usually features players that have hit a high number of home runs in the first half of the season. Once the second half of the season resume, if any of the home run derby participants suffer a performance slump it will be usually be followed by media articles stating that performing the derby was the cause. In this project the student will collect and analyize data to investigate whether the is an significant (negative) effect from competing in the home run derby. The student will be expected to collect data from available sources and to analyize it using statistical software. A knowledge of STAT 3800 or MATH 4740/4750 is highly recommended, but all interested students should feel free to contact the project advisor.
Final Project Report
Student: Andrew Montgomery. Advisor: Robert Todd
The hyperbolic Law of Cosines.
Description
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In this project we will read from several sources to understand the hyperbolic upperhalf plane. Then we will develop the tools we need to do some hyperbolic trigonometry with the goal of understanding the hyperbolic Law of Cosines. This project is best suited to an upper level undergraduate who has taken Modern Geometry.
Final Project Report
Student: Li Westman. Advisor: Zhenyuan Wang
A Discussion on the St. Petersburg TwoEnvelope Paradox.
Description
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The St. Petersburg TwoEnvelope Paradox is a widely spread probability problem. It evokes a heated discussion for many years by mathematicians, including some Fields Medal receivers. Is it a real paradox?
Final Project Report
Student: Jason Wohlgemuth. Advisor: Dora Matache
Boolean network modeling of layered social networks.
Description
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Random Boolean Networks are networks of nodes that can be in one of two possible states ON or OFF, and whose evolution from one time point to another is governed by given Boolean rules. Each node's evolution is influenced by the state of other nodes called its parents. This project aims at constructing a Boolean model for a social network in which nodes represent people interacting in a business venture with possibly multiple types of nodes, layers, and interactions (e.g. writers coworking with other writers and people that produce drawings for their books). The precise type of social network under consideration is chosen by the student.
Final Project Report
Student: Vladimir Ufimtsev. Advisor: Vyacheslav Rykov
A Scalable Group Testing Based Algorithm for Finding dhighest Betweenness Centrality Vertices in Large Scale Networks.
Description
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We will study a group testing approach to identify the first d vertices with the highest betweenness centrality. Betweenness centrality (BC) of a vertex is the ratio of shortest paths that pass through it and is an important metric in complex networks. The Brandes algorithm computes the BC cumulatively over all vertices. Approximate BC of a single vertex can be computed by selective vertex sampling. We will discover the method where we will sample a set of vertices and compute their combined BC. For small values of d, the number of tests required to find the dhighest BC vertices is logarithmic in the total number of vertices. This algorithm can be highly scalable since the samples are independently selected and therefore each test can be performed in parallel.
Final Project Report