Seminar Series
Fall 2009
All talks are at 3:30 in Bakeless 205.
Subversion is a popular version control software system that has many benefits and different uses. In this talk we will introduce the Subversion system and demonstrate how it can be used in a Software Engineering Course. This includes using Subversion to evaluate students.
A perfect distance tree is a weighted tree with n vertices in which the set of distances between vertices is {1, 2, 3, ..., s}, where s = n(n-1)/2. We define a tree with n vertices to be a Perfect Distance Tree mod m if all distances {1, 2, 3, ..., s} (mod m) can be obtained. The talk will show that every star with m + 1 vertices, where m is odd, is a perfect distance tree mod m. And the stars obtained from this star by removing the edge labeled 0 or by changing the weight 0 to another weight are also perfect distance trees mod m. By combining stars, we will show that every star with km vertices can be labeled to be a perfect distance tree mod m. Finally, we show that certain twin-stars (trees of diameter 3) can be labeled as perfect distance trees mod m. This is joint work with Dr. William Calhoun.
Device drivers, the code that allows an operating system to communicate with its hardware, are currently written in C. This forces any information concerning how a driver should communicate with hardware into comments rather than code. As a result, driver code may break a specification without anyone noticing until the hardware misbehaves. This talk will present a possible solution using a specification language and a type-safe intermediate language which forces the driver to obey its specification. No prior knowledge of operating systems or C is required for this talk.
My presentation introduces elliptic curves through their applications to Fermat’s Last Theorem and cryptography. First I will talk a little about the life of Andrew Wiles and his famous proof of Fermat’s Last Theorem. Then I will describe a geometric/algebraic interpretation of elliptic curves and relate it to the proof of Wiles. Our focus then shifts to cryptography. I will highlight the differences between public key and symmetric cryptography, show how elliptic curves are used in this area, and compare elliptic curve cryptography with other public key cryptosystems such RSA and the Diffie-Hellman protocol. My talk will emphasize how elliptic curves often show up in unexpected places and prove to be quite useful.
Spring 2009
All talks are at 3:30 in CEH-218.
Genetic algorithms are computer simulations that apply the principles of natural selection and genetic mutation to solve hard optimization problems. They have been used for everything from investment analysis to airplane wing design. This project deals with the use of genetic algorithms to find small sorting networks — electronic circuits that sort sequences of numbers by combining components that can sort a single pair of numbers. Our focus is the fitness measure used to determine the likelihood of survival and reproduction for individual "chromosomes" (digital representations of the circuits). In particular, our refined view of fitness confers a survival benefit on circuits that do a good job of partially sorting their inputs, allowing useful sub-structures to be passed on to the next generation.
All integers are divisible by the product of their primes factors. Some, like 30, are not prime powers yet are also divisible by the sum of their prime factors. In this talk, we will take a closer look at such integers as well as at integers satisfying related divisibility conditions. For example, we will see that for every positive integer k there are in nitely many positive integers n having more than two distinct prime factors and which are divisible by the sum of their prime factors, by the sum of the squares of their prime factors, and so on up to the sum of the kth powers of their prime factors. The proofs use variations of Vinogradov's Three Primes Theorem. Many of the results presented in the talk have been obtained jointly with Jean-Marie De Koninck.
The talk will introduce a general method for constructing generalized p-value via fiducial inference. Furthermore, the frequency properties of the generalized test are discussed. As illustrations, the two-parameter exponential model and unbalanced two-fold nested design are researched. Furthermore, the power properties of the generalized test are discussed. It is shown that the resulting generalized p-value has good frequency properties.
Mathematicians love a good problem. Mathematics journals such as Math Horizons and the American Mathematical Monthly publish interesting problems and solicit solutions from their readers. Some are easy, but others are quite challenging. Intriguing sample problems involving geometry, graph theory and modular arithmetic will be discussed, and students will be encouraged to participate in problem solving.
Strongly regular graphs and symmetric designs are mathematical structures with many applications in the modern world. R.E.A.C. Paley discovered many of the most elegant examples of these objects in 1933, and in particular has a graph named after him, the Paley graph. Many years elapsed, and still his graphs were the only ones known possessing certain properties. In fact, all of these graphs had number of vertices equal to a prime power. Last year, some examples were found having number of vertices that is not a prime power. We will discuss Paley's work as well as recent results. Most of the talk should be accessible to students and faculty alike.
We study a certain non-linear second order differential equation and establish some criteria for its solutions to be oscillatory. The method used is elementary so students with solid differentiation and integration skills should have no problem understanding.
Fall 2008
All talks are at 3:30 in CEH-218.
Students in Advanced Java (56.221) will present two internet-based Java applications that they developed for the course: a chat room and an electronic banking system.
The study of dose-response modeling, and in particular, the favorable biological responses to low exposures to chemicals known as hormesis, can be used to determine the best dose level for maximal benefit. The study of hormesis has become very popular over the past decade. Gaylor (2004) used a single quadratic to model the hormesis curve. Here, we argue that using a double quadratic (one for the down trend and one for the up trend), will result in a better description of the process. The maximum likelihood method is used to estimate model parameters. In order to solve the nonlinear likelihood equations, the EM (Expectation-Maximazation) algorithm is utilized to convert the nonlinearity to a linear problem. We then use an example with real data to illustrate our methodology.
A holistic approach to detecting bottlenecks and hotspots is necessary when optimizing games that run on modern hardware. Moore's law no longer predicts transistor count in single-core processor performance; processors now focus on multi-core and throughput architectures such as the GPU. Our processors are evolving &mdash so have our techniques for optimizing software.
This talk describes one use of the Python programming language to introduce programming concepts to non-majors. A visual, graphical animation of a bouncing ball demonstrates some fundamental algorithmic concepts such as looping and "if-else" processing in a context that offers an intuitive basis and something more engaging than the classic text outputs. This example is evolved into a simple, if somewhat lame, game in an attempt to relate programming to the more enjoyable uses of today's computers.
What's the shortest path an ant can take to get from one point to another in a funnel?
This talk is a high-level non-technical survey of Artificial Life (ALife), an area of computer science that links biology, physics and philosophy. The field was initiated in the late 1940s by John von Neumann, one of the giants of 20th century science and mathematics, who worked out the logical form of a self-replicating machine. Today it is devoted to the study of living systems through the use of computers to simulate biological phenomena. The main theme of this talk is the emergence of complex behaviors from the local interactions of simple, autonomous components, as when individual ants self-organize into highly sophisticated ant colonies without any external guidance or centralized control. In particular, I would like to discuss lifeforms in Conway's Game of Life, self-replicating computer programs that adapt and evolve, and algorithms that find solutions to computational problems by mimicking the processes of natural selection. I would also like to survey ideas about ALife that philosophers have started to consider, such as the prospect of genuine life emerging from artificial systems.
Many earth scientists think that in a great deal of mathematical modeling in seismology, the emphasis has been mathematics with little or no attempt to tie together the mathematical results with geological facts. They view this approach of modeling essentially a mathematical exercise with a bit of geological justification. In contrast they consider a situation in which a geological problem is investigated with mathematical tools, but the mathematics is considered of purely secondary interest. The objective is to derive geological conclusions which are testable, not to develop elegant mathematics, though that may indeed occur. The goal of this presentation is to describe a step in a "right" direction and develop a model for ground displacement due to earthquakes based on deterministic formulations proposed by seismologists.
Pick a positive integer — for example, 45. Write down all its positive integer divisors: 1, 3, 5, 9, 15, 45. Now write down the number of divisors of each of these: 1, 2, 2, 3, 4, 6. Add these up and square the sum: 324. Now add up the cubes of the numbers of that list: 324. Are these always the same? Why? This is a beginning for talking about integer solutions of (a + b + c + ...)2 = a3 + b3 + c3 +..., known to insiders as "square of sum equals sum of cubes". Along the way we find easy solutions, old old solutions, square and triangular solutions, and statements about when solutions do and don't exist. No advanced mathematical knowledge required to understand what's going on.
Spring 2008
All of the talks this semester are in BCH 107 unless otherwise noted.