Mathematics Symposium: "Mathematics Awareness Month at UNO"
Bronson Wacker, in conjunction with the Wilda Stephenson Internship
and Dr. Griff Elder
History of Cosmology
In the last century, cosmologists have begun the search for the answer … and it’s not forty-two, as of yet. Many dedicated scientists have made it their life work to ponder the imponderable, question the unquestionable, and reach for the unreachable. Through their endurance and curiosity, we are now beginning to understand life, the universe and everything.
Marie Spilde, UNO - Mathematics, KRMP
Solving nonlinear optimization problems with nondifferentiable objective function by pseudo gradient search and genetic algorithms
The talk provides an overview of the steps used to optimize nonlinear multiregressions based on Choquet integrals, as well as an introduction to genetic algorithms and the pseudo gradient search. The computer program that was written as part of the project is demonstrated on a data set taken from the United Nations.
Naomi Kochi, UNO - Mathematics
Fractals in cellular automata
Our research goal is to model a living system with cellular automata. We believe life happens on the edge of chaos where nontrivial dynamics are going on. This presentation will cover basic aspects of elementary cellular automata and some properties of fractals which can be found in the state of nontrivial dynamics.
Huimin Geng, UNO - Computer Science, KRMP
Dynamics of Random Boolean Networks with
Constant Number of Parents and Asynchrony
generated by Stochastic Processes
In this talk we consider a simple Boolean
network with N nodes, each node's state at time t being
determined by a constant number k of parent nodes. The nodes are
asynchronously updated based on various stochastic processes. We
study the dynamics of the models and show that the system has a
behavior that ranges from order to chaos depending on the type and
the parameter combinations of the stochastic processes used.
Xutao Deng, UNO - Computer Science, KRMP
Dynamics of Random Boolean Networks with
Non-Constant Number of Parents and Asynchrony
generated by Stochastic Processes
We consider a simple
asynchronous Boolean network with N nodes, each node's state at
time t being determined by a certain number of parent nodes,
which may vary from one node to another. The number of nodes to be
updated is generated by certain stochastic processes. Studying the dynamics of
the model, we find that the system is ordered as long as it is
asynchronous. For some parameter combinations, the system may
eventually become synchronous and we show that it may exhibit order or chaos, depending on the underlying parameters.
Jin Hui, UNO - Mathematics, KRMP
Nonlinear Multiregressions Based On Choquet Integral For Data With Both Numerical And Categorical Attributes
Based on Choquet integrals with respect to generalized fuzzy measures, a model of nonlinear multiregression that can catch the interaction among mixed-type predictive attributes toward the objective attribute has been established recently. This paper improves the previous relative works in three aspects.
Stacy Peterson, UNO - Mathematics
Finding the Median in an Unsorted List of Data
Many computerized algorithms have been created to find the median in a large set of numbers. Most use randomization and have a relatively small running time based on the number of elements in the set. This talk will present those algorithms used and discuss the number of comparisons that are needed for each algorithm in the worst case. It will also present the open problem of the number of comparisons needed without a randomized algorithm.
Vladimir Ufimtsev, UNO - Mathematics, KRMP
Generation of DNA Codes
Deoxyribonucleic acid (DNA) is an acid within the nucleus that is enriched with genetic codes used by living organisms for their physical development. We can use a branch of Mathematics that was initiated around the same time as DNA research, known as Coding Theory, to study the similarity between different DNA strands. Codes built on spaces of "DNA sequences" can be implemented in Biomolecular computing and could have other important applications. The insertion deletion metric (built from the longest common subsequence), commonly used for DNA codes, will be discussed. A new metric based on the longest common block subsequence (D'Yachkov, Macula, Pogozelski, Renz, Rykov, Torney) will be introduced. As always we will present bounds on such codes.
Bob Slaughter, UNO - Mathematics, KRMP
An Improved Metric for Generation of Codes for DNA Computing
For DNA computing, it is desired to generate codes of large size and large distance. A common distance metric is the familiar longest common subsequence (LCS). The work of Rykov and Macula suggests the use of a related metric, block LCS, which imposes an additional adjacency requirement, with the goal of more accurately modeling actual bonding energies. The traditional dynamic programming algorithm for the conventional LCS no longer applies. Two new algorithms were developed, the first maximizing efficiency, running in O(n^2) and using O(n) memory; and a second more intuitive algorithm, running in O(n^3), and using O(n^2) memory. Code size using the new metric for various length and distance parameters is explored.
Adam Walling, UNO - Mathematics (joint work with Vladimir Ufimtsev), KRMP
Elementary Topology From Scratch
Topology is an area of Mathematics that is closely connected to set theory and which provides language and methods for many other Mathematical disciplines. The main objective of our project was to create an introductory text in elementary topology and related topics that would serve as a manual for future UNO topology courses. The manual will be available for free online. In the presentation we will be covering just a small part of the topics that were discussed during the construction of the manual. First we will introduce the notion of Hausdorff measure and define what a 'fractal' is. Then we will conclude the presentation by presenting the first fractal; the Peano curve.
Tuesday, April 5, 4:00PM, DSC256, Gary Beck, UNO - Mathematics
Parametric Model Selection Techniques
Many statistical models are available for modelling lifetime data. Given a data set of lifetimes, which may or may not be censored, which parametric model should be used to conduct statistical tests? In only a few cases can analytical expressions be found to answer this question in some optimal fashion. Various measures of discrepancy and other functionals of the distribution function will be considered for a finite number of competing parametric statistical models. Utilizing techniques developed by Linhart and Zucchini, survival data from pediatric patients who have received stem cell transplants will be analyzed to determine if models for random samples represent the actual model for the population.