2006-2007 Academic Year Colloquium Schedule

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August 24, 2006

Title:A Hierarchy of Graph Search Algorithms
Speaker:Richard Krueger, Ph.D.
Department of Computer Science
University of Toronto

Abstract:Graph search algorithms, such as breadth-first search or depth-first search, are widely used for problems ranging from solving mazes, to traversing graphs, to evaluating artificial intelligence search trees. Graph search algorithms visit the vertices of a graph in a particular order, which can reveal structure in the graphs. Despite the wide-spread use of these algorithms, many structural properties of these vertex orderings have not been studied.

In this work, we consider the answer to a simple question: in the various types of graph search vertex orderings, how can a nonneighbouring vertex be visited before a neighbouring vertex? The surprising answers turn out to characterize a variety of known search algorithms, and leads to the identification of two new types of graph searches, completing our graph search hierarchy.

We will show how this new view of graph search vertex orderings lead to applications, such as recognition of classes of graphs, finding orderings of powers of graphs, and computing minimal triangulations of graphs.

Portions of this work is joint with Derek Corneil, Anne Berry and Genevieve Simonet.
Location:Palenske 227
Time:3:10 PM
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August 31, 2006

Title:Generating Hypothetical Explanations of Genetic Linkage Observations
Speaker:Ben Keller
Assistant Professor
Department of Computer Science
Eastern Michigan University

Abstract:Several human diseases are thought to have complex genetic causes, where mutations of several genes are necessary to lead to the occurrence of the disease. Unfortunately, the affected genes are difficult to detect using clinical studies alone. I will discuss an approach we are developing at the National Center for Integrative Biomedical Informatics (U. Michigan) that allows us to generate possible molecular interactions that could explain the clinical results. We will look especially at Bipolar Disorder as a motivating example.
Location:Palenske 227
Time:3:10 PM
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September 7, 2006

Title:Planning for Graduate Study in Mathematics and Computer Science
Speaker:David Reimann
Associate Professor and Chair
Department of Mathematics and Computer Science
Albion College

Abstract:TBA
Location:Palenske 227
Time:3:10 PM
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September 14, 2006

Title:The Sound of Algebra
Speaker:Michele Intermont
Associate Professor
Department of Mathematics and Computer Science
Kalamazoo College

Abstract:Can you really hear algebra? One place to try is in a bell tower. Change ringing uses permutation groups to give order to the ringing of the bells. This talk will give a little background on change ringing and use algebra to ease the task of composing for the bells by answering the question of whether or not understanding falseness for one method (aka song) translates to understanding it for other methods. This talk grew out of an undergraduate senior thesis.
Location:Palenske 227
Time:3:10 PM
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September 21, 2006

Title:The Fundamental Theorem of Algebra: History, Proofs, and Applications
Speaker:Ryan Higginbottom
Visiting Assistant Professor
Department of Mathematics and Computer Science
Kalamazoo College

Abstract:The Fundamental Theorem of Algebra dates back to the mid-17th century, and it can be stated quite easily: every polynomial with complex coefficients has a complex number as a root. There are numerous modern proofs of this theorem, drawing on such diverse fields as complex analysis, abstract algebra, and topology. In this talk, we will discuss at least two of these proofs, and we will touch on some of the theoretical applications. This presentation should be accessible to anyone who has completed Calculus I.
Location:Palenske 227
Time:3:10 PM
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September 28, 2006

Title:Opportunites and Challenges of Wireless Sensor Networks: A Systems Perspective
Speaker:Weisong Shi
Assistant Professor
Department of Computer Science
Wayne State University

Abstract:As new fabrication and integration technologies reduce the cost and size of wireless sensors, the observation and control of our physical world will expand dramatically using the temporally and spatially dense monitoring afforded by wireless sensor networks technology. Several applications such as habitat monitoring, counter-sniper system, environment sampling, and structure monitoring, have been launched, showing the promising future of wide range of applications of networked wireless sensors. In this talk, I will discuss both the opportunites andremaining challenges we are facing from the perspective of computer systems, including hardware design, operatingsystems, cross-layer design, topology/network management, security and privacy, reliability, and programmability. Finally, I will present some ongoing sensors-related projects at Wayne State University.
Location:Palenske 227
Time:3:10 PM
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October 5, 2006

Title:Geometric Sculpture
Speaker:George Hart
Professor
Department of Computer Science
SUNY Stony Brook

Abstract:George W. Hart will show slides of some of his mathematically informedsculptures. These include works made of metal, wood, acrylic, or foundobjects, and often use laser-cutting or rapid prototyping technologies intheir realization. Also shown will be brief videos of the assembly ofthree large commissions: a six-foot sculpture constructed from 642 CDROMsin the Computer Science building at U.C. Berkeley, a five-foot sculptureconstructed at a community "barn raising" event, and a "Salamanders"sculpture assembled by students when he was artist in residence at MIT.Mathematical and computer science aspects of these designs will bediscussed. For examples of Hart's work, see www.georgehart.com.
Location:Norris 101
Time:3:10 PM
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October 19, 2006

Title:Mathematical Typesetting with TEX
Speaker:Robert Messer
Associate Professor
Department of Mathematics and Computer Science
Albion College

Abstract:You can create beautiful documents with the TEX typesettingsystem. This was developed by Donald Knuth to utilize the power of computers in handling the detailsof fine typesetting. In particular, TEX knows the rules for choosing the correct font sizes and spacing between characters in typesetting mathematical formulas. Bring the solution to one of your homework assignments, and we will go to the computer lab to see how easy this is.
Location:Palenske 251
Time:3:10 pm
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October 26, 2006

Title:Combinatorial Identities
Speaker:George Grossman
Associate Professor
Department of Mathematics
Central Michigan University

Abstract:Combinatorial identities have a fascinating history inmathematics many of which involve binomial coefficients which arerecursive in nature. Numerous identities are derived fromgenerating functions or proven by recurrence equations. We examine acertain interesting combinatorial identity found in a text ofPolya and Szego, 1924. We show a derivation and proof of thisidentity. We also show a generalization of the identity.
Location:Palenske 227
Time:3:10 PM
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November 2, 2006

Title:The Role of Computer Science in Geoinformatics
Speaker:Patrick Kinnicutt
Assistant Professor
Department of Computer Science / Geology
Central Michigan University

Abstract:The geosciences have made significant advances during the past few decades, with the aid of computer technologies in such areas as scientific computing and visualization, telemetry and data acquisition, massively parallel supercomputer simulations, large-scale databases and the cyberinfrastructure in general. Immersive environments enable geoscientists to visualize geologic formations in 3D, virtual reality environments enable things like real-time geosteering of deep boreholes, and real-time telemetry enable the ability to transmit data acquired from downhole data acquisition sensors. The use of this and other computer technology to solve real-world problems in the geosciences is part of a discipline called geoinformatics.

This talk describes what geoinformatics is and how information and computer technology are used in the geosciences. A general overview of geoinformatics will be given, followed by specific examples via source code and case studies. The use of geographic information systems (GIS), web services, knowledge representation, and geostatistical modeling and simulation will be presented. In particular, a case study examining the use of non-Euclidean distance metrics to model surficial dioxin distributions near Midland, MI will be presented. Current developments in cyberinfrastructure development for the geosciences will be presented as well, with a focus on the technologies used to build the cyberinfrastructure. Lastly, the use of asset teams will be discussed at oilfield software companies like Schlumberger and Halliburton, highlighting the importance of teamwork and communication in the solution of domain-specific problems.
Location:Palenske 227
Time:3:10 PM
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November 9, 2006

Title:Exaggerating Data
Speaker:Jack Kalbfleisch
Professor and Chair
Department of Biostatistics
University of Michigan

Abstract:We will look at a number of examples where the way in which the data arise is biased so that care must be exercised in drawing conclusions. These examples include the famous bus paradox of Feller and some more practical situations which arise, for example, in the analysis of early detection programs for disease, or in the analysis of data on patient survival in studies of organ transplants. Some elementary statistical aspects will be considered and developed with a view to finding ways to carry out a correct analysis of the data.
Location:Palenske 227
Time:3:10 PM
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November 16, 2006

Title:When Does Inversion Preserve Convexity?
Speaker:David E. Blair
Professor Emeritus
Department of Mathematics
Michigan State University

Abstract:Given a smooth closed convex curve in the plane, what is the setof points in the plane as centers of inversion for which the image of thegiven curve will again be a convex curve? This question has an attractive answer. After reviewing the geometry of curve theory and of inversion theory (reflection in circles), we will give a proof of the answer. If time permits, we will discuss the corresponding question for convex bodies in 3-space.
Location:Palenske 227
Time:3:10 PM
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November 30, 2006

Title:Summer and Off-Campus Programs
Speaker:Darren E. Mason
Associate Professor
Department of Mathematics and Computer Science
Albion College

Abstract:Have you ever wondered if you can study mathematics and/or computer science off-campus? Either during the summer or during the academic year? Each year a number of high-quality academic opportunities are availableto Albion College students. Options include research/study internships at
  • academic institutions both within the United States and abroad,
  • numerous federal government agencies, and
  • a number of government scientific laboratories.
In this presentation we will tour a new portion of the Albion College Math/CS website that illustrates these various opportunities as well as provide adviceon how to apply, deadlines, any other pertinent information.
Location:Palenske 227
Time:3:10 PM
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February 1, 2007

Title:The Classical Problems of the Calculus of Variations
Speaker:Charles R. MacCluer
Professor
Department of Mathematics
Michigan State University

Abstract:One of the earliest uses of the calculus was to attack "variational problems," where the objective is to minimize certain path integrals. These first problems were proposed by Johann Bernoulli, Newton, von Leibniz, and others --- in certain cases as challenges to smoke out their competition. We will tour (but not solve) a collection of these early problems on least time, geodesics, bluff bodies, isoperimetric problems, hanging cable, etc, as well as the modern Nobel-winning Mirrlees formulation of optimal tax structure.

If time permits, we will also sketch the derivation of the Euler-Lagrange equation for solving variational problems and its application to conservative mechanical systems. Finally, we will formulate a representative optimal control problem.
Location:Palenske 227
Time:3:10 PM
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February 8, 2007

Title:A Combinatorial Gauss-Bonnet Theorem
Speaker:Robert W. Bell
Assistant Professor
Department of Mathematics and
Lyman Briggs School of Science
Michigan State University

Abstract:The classical Gauss - Bonnet theorem for a closed surface S says thatintegral of the curvature over S depends only on the topological type ofS. For instance, although the unit sphere x2 + y2 + z2 = 1 and theellipsoid 3x2 + 5y2 + 7z2 = 1 are curved differently, if we integratetheir curvatures, we obtain the same value in both cases because thesphere and the ellipsoid are topologically the same surface.

We will prove a combinatorial generalization of the Gauss - Bonnet theoremfor two dimensional polyhedra. As a corollary, we will deduce theclassical theorem. No background is required for core of the talk;however, relating the combinatorial theorem to the classical one requiressome acquaintance with vector calculus.
Location:Palenske 227
Time:3:10 PM
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February 15, 2007

Title:When Good Rings Go Bad, or: How I Learned to Stop Worrying and Love Non-commutativity
Speaker:Cayley Pendergrass
Assistant Professor
Department of Mathematics and Computer Science
Albion College

Abstract:Despite overwhelmingly popular knowledge, there are worlds in which ab is not equal to ba and, sometimes, (ab)c is not equal to a(bc). It's fascinating what can or cannot happen when we relax the rules for multiplication, and I hope to share a little about this aspect of algebra and why I find it interesting.

This peculiar behavior is described by mathematicians in terms of axioms; we begin by assuming particular conditions to be true and use only these to build an elaborate structure of theorems and properties. Despite the esoteric idea of stating some properties and studying what happens, these sets, called algebras, turn up in (arguably) real life. Even though these are certainly interesting and entertaining ideas in their own right, mathematicians aren't just making them up for fun; these types of structures are used model to specific physical applications, particularly in particle and quantum physics.

This talk will begin in the integers and end up in sets where our standard notions of multiplication do not work. We'll discuss the axioms required for rings and algebras, see some examples of rings with elements that behave badly, and discuss how these rings differ from our familiar ideas of numbers. Because I'll focus on examples, very little prerequisite knowledge will be required.
Location:Palenske 227
Time:3:10 PM
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February 22, 2007

Title:Is my Smartcard Secure? Side Channel Attacks on the Advanced Encryption Standard
Speaker:Kevin Compton
Associate Professor
Electrical Engineering and Computer Science
University of Michigan

Abstract:In 2001 the National Institute of Standards and Technology (NIST) selected the block cipher Rijndael as the Advanced Encryption Standard (AES), makingit the standard for symmetric key encryption. One of the NIST selection criteria was that the cipher should be easy to implement on inexpensive computationaldevices such smartcards. This raises the question of how secure these devices are. A smartcard leaks information through voltage fluctuations and electromagnetic signals. Is this enough information to break the cipher? We will describe a Simple Power Analysis attack on an 8-bit implementation of AES that findsthe encryption key using an optimized search strategy. This improves on previous work in terms of speed, flexibility, and handling of data error. We can find a 128-bit cipher key in 16ms on average, with similar results for 192- and 256-bit cipher keys. The attack almost always produces a unique cipher key and performs well even in the presence of substantial measurement error. The talk will be self contained: no previous knowledge of cryptography or smartcards will be assumed.
Location:Palenske 227
Time:3:10 PM
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March 1, 2007

Title:Droplet Evaporation in a Quiescent, Micro-Gravity Atmosphere
Speaker:Indrek Wichman
Professor
Mechanical Engineering
Michigan State University

Abstract:Droplet evaporation spans numerous research fields ranging from the analysis of rocket fuels to crystal growth. In this talk [1] a detailed examination is conducted of the sensitivity of the droplet surface temperature and the droplet radius-squared to physical parameters characteristic of hydrocarbon fuels. An optimization analysis is conducted in which the physical parameters are determined to minimize the droplet evaporation time. The nonlinearity of the governing equations requires a numerical solution. An asymptotic analysis is also carried out and the predictions are compared with the numerical simulations. The applicability of the asymptotic analysis is more restricted than is commonly believed. Interestingly, some pseudo-fixed points arise in one of the solutions. The meaning of these points is not clear and their appearance suggests further mathematical analysis of these equations might be profitable.

1. Based largely on the recent M.S. thesis of Mr. Paul R. Cole.
Location:Palenske 227
Time:3:10 PM
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March 8, 2007

Title:Planck's Unphysical Assumption: The Discretization that Began the Quantum Revolution
Speaker:Aaron Miller
Assistant Professor
Physics
Albion College

Abstract:In this talk I will present a portion of the monumental work of Max Planck in his study of the thermal equilibrium between physical solids and radiation fields. In his work, Planck turned a single integral into a summation in order to get his model to match laboratory measurements. This mathematical assumption was profoundly unsatisfying (from a physical point of view) and Planck only intended it to stay in physics until a more satisfactory theory was developed. However, his assumption has born the test of experiment and spawned the field of "quantum mechanics," easily argued as the most successful physical theory in the history of physics.
Location:Palenske 227
Time:3:10 PM
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March 29, 2007

Title:Wirtinger Inequality and the Theorems of Sturm
Speaker:P.K. Wong
Associate Dean and Professor, Emeritus
College of Natural Science
Michigan State University

Abstract:Colloquium Abstract
Location:Palenske 227
Time:3:10 PM
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April 5, 2007

Title:Imaging the Human Brain
Speaker:David Reimann
Associate Professor and Chair
Department of Mathematics and Computer Science
Albion College

Abstract:Imaging techniques commonly used to assess brain structure and function such as radiography, CT, PET, SPECT will be discussed. An emphasis will be placed on the physics, mathematics, and computer science behind these techniques. This talk is part of the national celebration of April as Mathematics Awareness Month
Location:Palenske 227
Time:3:10 PM
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April 12, 2007

Title:The Naked Truth About The Baire Category Theorem
Speaker:Clifford Weil
Professor
Department of Mathematics
Michigan State University

Abstract:The talk will begin with a narrow discussion of the notion of a metric space. Examples presented will be those used later. Then the Baire Category Theorem will be stated and discussed. Finally the theorem wil be applied to prove the existence of a certain difficult to construct examples such as an everywhere continuous, but no where differentiable function. All will be connected to familiar concepts from calculus and will require theorems from advanced calculus.
Location:Palenske 227
Time:3:10 PM
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May 3, 2007

Title:Analysis of Volumetric Data Sets
Speaker:Paul Albee
Assistant Professor
Department of Computer Science
Central Michigan University

Abstract:Volumetric analysis is the process of extracting useful information from three-dimensional data sets. Two areas of interest are volumetric segmentation and interest detection. Volumetric segmentation can be a difficult problem, particularly when type of structures to expect is unknown. A computationally inexpensive algorithm for segmenting large volumes with minimal a priori knowledge is presented. Interest detection is an essential step for identifying salient regions an a volume. A transform for characterizing potentially interesting regions is presented, along with a larger interest detection framework.
Location:Palenske 227
Time:3:10 PM
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