■ February 3, 9 a.m. - 10 a.m. AS 105Eric Weber (Iowa State)
Title: Spectral Theory of Small Hadamard Matrices
Abstract: We prove that if $A$ and $B$ are Hadamard matrices which are both of size $4 \times 4$ or $5 \times 5$ and in dephased form, then $tr(A) = tr(B)$ implies that $A$ and $B$ have the same eigenvalues, including multiplicity. We calculate explicitly the spectrum for these matrices. We also extend these results to larger Hadamard matrices which are permutations of the Fourier matrix and calculate their spectral multiplicities.
■ March 5, 4 p.m. - 5 p.m. AS 106
Mike Janssen (Dordt College)
Title: Symbolic Powers of Ideals: Problems and Progress
Abstract: Symbolic powers of ideals have been the focus of much recent study in commutative algebra and algebraic geometry. Problems in algebraic geometry (e.g., Waring’s problem) and commutative algebra (e.g., the question of containment in ordinary powers of ideals) have motivated much of this work, but symbolic powers also have applications to other fields, such as computer science, combinatorics, and graph theory. We will explore the questions that have motivated the study of symbolic powers of ideals and share recent results in this direction.
■ April 23, 4 p.m. - 5 p.m. AS 106
Edoardo Persichetti (Dakota State)
Title: Post-Quantum Cryptography
Abstract: In this talk I will present the latest development in the post-quantum cryptography area. The talk will include mathematical content related to the major areas of interest, such as multivariate equations, linear codes and lattices, but will be aimed at a general audience. Everybody is welcome!
■ October 16, 4:15 p.m. - 5:15 p.m., AS 105
Harry Freeman (Counseling & Psychology in Education, USD)
Title: How strong is our love for one person?
Abstract: I am interested in comparing the level of support we expect from our most significant relationship relative to others in our support network. Under what conditions can we make the claim that individuals value a single individual more than all others in their support networks. Can a probability be computed for a non-parametric distribution, or is it better to set an effect size based on the sample using inferential stats?
Abstract: Many applications such as compression and data representation in the area of signal processing are based on Hilbert spaces and their orthonormal bases. In this talk, we explore old (classic) and new orthonormal bases in the Hilbert space L2[0,1], as well as some of their applications to signal processing. It is well-known that the classic Walsh functions serve as an orthonormal basis for the L2[0,1] space; in a recent paper published by Dutkay, Picioroaga, and Song, the authors developed a generalized form of this basis. In my talk I will discuss convergence and continuity properties of the generalized Walsh series. I will also show how unitary N x N matrices, along with the quadrature mirror filters that implement them, give rise to representations of Cuntz isometries on L2[0,1]. In this setting, a signal can be encoded or encrypted on N-channels according to filters generated by the unitary matrix. Partial results will be presented on the security of an encryption scheme that implements these Cuntz isometries.
■ November 5, 4 p.m. - 5 p.m., AS 107
Steven Nathan Harding (Mathematical Sciences, USD)
Title: Generalized Walsh transforms, Cuntz algebras representations and applications in signal processing
■ November 20, 4 p.m. - 5 p.m., AS 105
■ January 29, 4 p.m. - 5 p.m., AS 107
Nathan Tintle (Dordt College)
Title: The use of randomization methods in teaching introductory statistics
Abstract: A growing movement in statistics education is to use permutation, bootstrapping and simulation methods (broadly defined as ‘randomization methods’) when teaching introductory statistics to non-math majors (Stat 101). I will provide a history of this movement, with particular attention to a textbook under development by myself and six others (Beth Chance, George Cobb, Allan Rossman, Soma Roy, Todd Swanson and Jill VanderStoep; http://math.hope.edu/isi). I will compare and contrast our approach with the traditional sequence of topics in Stat 101 and a few other randomization-based curriculum projects underway, summarize published assessment data on these approaches and discuss implementation details.
October 2, AS, Room 107, 4 p.m. - 5 p.m.
■ December 4, AS, Room 105, 4 p.m. - 5 p.m.
Abstract: Are there an infinite number of primitive Pythagorean triples? Using number theory I will show the answer to this question and how to find these triples. I will prove what numbers can and cannot be used in the triples and prove the method that will be demonstrated.
This should be an interest to all secondary math education majors and next semesters number theory students.
20, AS, Room 104B, 4 p.m. - 5 p.m.
Abstract: link to pdf
3, AS, Room 105, 4 p.m. - 5 p.m.
About Existence of Solutions of Differential Equations
Abstract: A more than a hundred years old result (the celebrated Picard-Lindelöf theorem) asserts that if an autonomous vector field f(x) is Lipschitz, then the Cauchy problem X(0)=x of the differential equation X'(t)=f(X) has a unique solution. People wondered if the Lipschitz condition can be weakened. This proved to be a very resistant problem, but with serious theoretical and practical implications. There are two milestone steps in this development: the 1989 DiPerna –Lions paper and the 2004 Ambrosio's article, both in Inventiones Mathematicae. I will briefly present the main innovations brought by these two papers, with a focus on the Ambrosio's concept of Lagrangian flow. Then I will show why if the vector field is only bounded measurable, one can find a vector field with no solutions on a set of positive Lebesgue measure. On the other hand, if the vector field is only bounded measurable and with components staying away from zero, it is believed that the existence theorem still holds almost everywhere, but this seems to be a difficult problem in dimension higher than one. This talk wants to be a discussion revolving around the concept of solution of an ODE/PDE.
3, AS, Room 107, 4 p.m. - 5 p.m.
Abstract: A ratio-dependent predator-prey model with double Allee effect on the prey is proposed. The presentation includes a parametric analysis of the stability properties of the dynamics of the system in which the functional response is a function of the ratio of prey and predator. The model is studied analytically as well as numerically, including stability and bifurcation analysis. We also discuss the biological relevance of the method regarding both coexistence (conservation) and extinction (biological control) issues.
■ October, 24, AS, Room 107, 4 p.m. - 5 p.m.
Ionut Chifan (University of Iowa)
Rigidity in von Neumann algebras
Abstract: In this talk I will survey some very recent and exciting developments in the classification of von Neumann algebras associated with group actions on measure spaces.
■ November, 7, AS, Room 107, 4 p.m. - 5 p.m.
Gabriel Picioroaga (USD)
Processing and encrypting images with Maple
Abstract: Whenever we use a mobile phone or take pictures with a digital camera and process them with a photo editor or shop online we indirectly use built in software based on Linear Algebra, Finite Group Theory, and even College Algebra. In the first part of my talk I will show how with simple Maple programs and insights from basic mathematics courses we can build a photo editor. The prerequisites are a little knowledge of common algebra operations and understanding how an image file is stored as a matrix. I will survey (with lots of picture examples) types of transformations one can apply to an original image to obtain a filtered image, or a smaller image, or a zoom in and out of the image. Also, the known film photography technique of multi-exposure can be adapted digitally and with better results (blending) using a simple algorithm based on number multiplication and roots. For the second part of the talk and if time permits I will explain how Abstract Algebra (Group Theory, Finite Fields) is used in modern encryption algorithms (RSA, AES) and propose a few simple schemes for image encryption which combined could prove stronger. The theoretical framework where these algorithms and their weaknesses are to be investigated is provided by a large group of invertible functions defined on sets of matrices.
Abstract: Failing a component in a composite system often causes more load on survival components and enhances the hazard rate. Assuming that component lifetimes in a composite system have a Burr type-XII distribution with a power-trend hazard rate function, point estimates of Burr type-XII distribution parameters and interval estimates of the baseline survival function are obtained by using the maximum-likelihood estimation method and Fisher information matrix. A testing procedure is provided to test whether the hazard rate function would change along with the number of failed components. An intensive simulation has been conducted to evaluate the performance of the proposed estimation procedure, and an example is given for illustration.
SPRING 2012■ March 28, AS, Room 105, 4 p.m. - 5 p.m.
Ginger McKee (Wolfram Research)
Mathematica in Education and Research
This talk illustrates capabilities in Mathematica 8 that are directly applicable for use in teaching and research on campus. Topics of this technical talk include:
* Free forum input
* 2D and 3D visualization
* Dynamic interactivity
* On-demand scientific data
* Example-driven course materials* Symbolic interface construction
* Practical and theoretical applications.
Whether or not you're familiar with Mathematica, you'll find this seminar worthwhile--so don't forget to pass the invitation on to your colleagues and students. All attendees will receive an electronic copy of the examples, which can be adapted to individual projects.
■ September 21, AS, Room 107, 4 p.m. - 5 p.m.
Rodica Curtu (Department of Mathematics, University of Iowa)
Selection of mixed-mode oscillations in a neuronal competition model
Abstract: Mixed-mode oscillations (MMOs) are temporal periodic activity patterns characterized by notable changes in amplitude: during each cycle, there is an alternation between small-amplitude oscillations and large, fast excursions of relaxation type. MMOs arise in a variety of physical systems; in particular, they were observed in in-vitro experiments at both individual neuron and neuronal population levels and, more recently, they were also found in computational neuroscience models. This talk will show the existence of MMOs in a neuronal competition model that involves slow negative feedback and gain function nonlinearities, and depends on a control parameter associated with external constant stimuli. Analytical and numerical investigation of the system uncover an interesting, novel property of the MMOs: they are periodic canards, but their small amplitude oscillations result from a combined effect of the folded node funnel (canard-induced rotations) and the spiraling unstable manifold of a nearby equilibrium (Hopf-induced rotations). One distinctive feature of the model is that the MMOs are periodic solutions that exhibit small amplitude oscillations and canard behavior twice per cycle; this is due to the fact that transition between the dynamics on the slow manifold and that along the fast fibers occurs near a folded node on both lower and upper branches of the slow manifold.
October 21, AS, Room 107, 4 p.m. - 5 p.m.
Recurrent Events: Modeling and Statistical Inference
Abstract: In various field such as reliability, economics, sociology, biomedical studies, it is often of interest to monitor occurrence of an event. Such event could be the failure of an electronic system, outbreak of a disease, claim filing, etc…. These events recur and so it is of interest to describe their recurrence behavior through a stochastic model. This talk pertains to the modeling and statistical inference with recurrent event data. I will first discuss some results in the single event setting and show how that translate into recurrent events. I will then summarize some important inference and asymptotic results pertaining to the estimation of the distribution function of the gap-time in recurrent event models. These results are based on important aspects of recurrent events that are not accounted for in the current literature. The discussions on the estimation of the distribution function of the gap-time will be followed by the development of chi-squared type test for testing a simple parametric null model. I will next investigate small sample and asymptotic properties of the test as well as power analysis against a sequence of Pitman's alternatives. Application to some real datasets will be demonstrated. Finally some open problems pertaining to recurrent events will be indicated.
Keywords: Recurrent events; Sum-quota constraint; Informative monitoring; Martingales; Gaussian process; Weak convergence; Pitman's alternatives; Goodness of fit.
14, AS, Room 104B, 1 p.m. - 3 p.m.
Fall 2010■ November 10, AS, Room 107, 4 p.m. - 5 p.m.
Dmitri S. Kilin (Department of Chemistry, University of South Dakota)
Computational modeling of physical and chemical properties of nanostructured silicon surfaces for electronics and photovoltaics
Abstract: A new method combining ab initio electronic structure and density matrix approaches has been developed to simulate photo-excited dynamics in silicon-based energy materials. The interaction of electrons with thermalized lattice vibrations provides the dissipative terms in the equation of motion (EOM) for the reduced density matrix of the silicon surface and describes line broadening of optical excitations, dephasing, and population relaxation from the photoexcited state towards thermalized electronic state. The steady state solutions of the EOM in a basis of Kohn-Sham orbitals provide the electronic charge density for excited states responsible for the induction of a photovoltage at the surfaces , while time dependent solutions of the EOM provide rates for carrier relaxation induced by lattice vibrations . Our simulations predict that absorption and photovoltage spectra of the silicon surfaces are drastically affected by presence of adsorbates on the surface or by p- or n- doping. The results obtained by our atomistic approach provide insight on trends relevant to the absorption of near IR, visible, and near UV light, which is of interest in measurements of photovoltages and in the utilization of solar energy.
1. D. S. Kilin and D. A. Micha, "Surface Photovoltage at Nanostructures on Si Surfaces: Ab Initio Results" J. Phys. Chem. 113, 3530 (2009).
2. D. S. Kilin and D. A. Micha, "Electronic Relaxation at a Photoexcited Nanostructured Si(111)Surface" J. Phys. Chem. Lett. 1, 1073 (2010).
■ December 1, AS, Room 107, 4 p.m. - 5 p.m.
Catalin Georgescu (USD)
Abstract: In a broad sense, a dynamical system is given by the action of a group upon a topological space. How the structure (and topology) of the group influences the dynamics of the action generated a large body of mathematical work. Among the many tools used, topological entropy proved to be one of the most important. Originated from the standard concept of entropy of a physical system, topological entropy is notoriously difficult to compute and most of the open problems related to entropy revolved around this issue and around its dependence on the parameters of the system. I will present the basic properties of entropy and its connections to algebraic and measure entropy, some examples and a brief overview of the relation that exists between entropy and Lyapunov exponents.
Spring 2010■ February 24, AS, Room 107, 4 p.m. - 5 p.m.
Y.L. Lio (University of South Dakota)
A Novel Estimation Approach for Mixture Transition Distribution Model in High-Order Markov Chains (joint work with D.G. Chen)
Abstract: A transformation is proposed to convert the nonlinear constraints of the parameters in the mixture transition distribution(MTD) model into box-constraints. The proposed transformation removes the difficulties associated with the maximum likelihood estimation (MLE) process in the MTD modeling so that the MLEs of the parameters can be easily obtained via a hybrid algorithm from the evolutionary algorithms and/or quasi-Newton algorithms for global optimization. Simulation studies are conducted to demonstrate MTD modeling by the proposed novel approach through a global search algorithm in R environment. Finally, the proposed approach is used for the MTD modeling of three real data sets.
■ March 3, AS, Room 104B, 4 p.m. - 5 p.m.
Gleb Haynatzki (University of Nebraska Medical Center)
The speaker will give a presentation of the graduate program available at UN Medical Center and discuss career opportunities in Biostatistics and Public Health (data management, pharmaceutical and clinical trials, data analysis, academia and government agencies). The UNMC College of Public Health Biostatistics Department collaborates with scientists, physicians, clinical investigators and other researchers, provides statistical consulting, teaches courses in biostatistics, and conducts methodological research. The Department's expertise includes clinical trials, study design, surviving analysis, general linear models, longitudinal analysis, survey methodology, and analysis of microarray gene-expression data and other high-dimensional data.
March 17 AS, Room 107, 4 p.m. -
Function theory and composition operators on spaces of analytic functions
Abstract: Composition operators are operators acting on spaces of functions on a set S, by composition to the right with a fixed selfmap of S. They have been systematically studied since the late sixties. However, composition operators were implicitly present in the mathematical literature much earlier than that. The theory of composition operators acting on holomorphic function spaces is by far the most developed. In this talk, we will address some major directions of investigation, emphasizing how the research on those topics mixes operator theory and function theory in a harmonious way, and reporting on the speaker’s own contributions.
■ March 26, AS, Room 107, 4 p.m. - 5 p.m.
Il Woo Cho (St. Ambrose University )
Abstract: In this talk, we consider distortions on histories. A Mathematical history is determined by a certain type I von Neumann algebra "M" in a fixed operator algebra B(H), equipped with an automorphism group, which is an one-parameter group satisfying some additional conditions, called an E_0 group. By fixing a finite number of partial isometries in B(H) with a suitable connection with each other, we can show the existence of the distortion of M distorted by the partial isometries. Also, we can characterize the von Neumann algebra distorted by partial isometries.
■ April 14, AS, Room 107, 4 p.m. - 5 p.m.
Nan Jiang (University of South Dakota)
The Convergence of a Class of Methods - semi-discrete case
Abstract: In the talk, we will introduce a class of high resolution schemes, using flux limiters for hyperbolic conservation laws. In the 80's, Sweby [SIAM J. Numer. Anal. 21 (1984)] constructed and predicted the entropy convergence of this family of schemes. However, the convergence issues of these problems have been open. In the last part of this talk, I will present my recent progress in the convergence analysis of this class of schemes, which extends our previous convergence results [Jiang and Yang, Methods and Applications of Analysis, Vol. 12, No. 1 (2005) pp. 089-102]. Remarkably, by showing the the convergence of the schemes with Roe's superbee limiter, our convergence criteria [Yang and Jiang, Methods and Applications of Analysis Vol. 10 (2003), No. 4, 487-512] also guarantee the entropy convergence of any flux limiter method. Thus, the entropy convergence problems of the entire family of Sweby's flux limiter schemes can be put to the rest. The talk is accessible to the senior math major and the graduate students.
Key words and phrases. Conservation law with source terms, schemes with flux limiters, entropy convergence.
Fall 2009■ October 21, AS, Room 16B, 4 p.m. - 5 p.m.
Clare Wagner (USD)
SMART Board and SMART Notebook Basics
Abstract: This presentation will provide an introduction to how to use a SMART Board in a mathematics classroom. Useful features of SMART Notebook software in preparing lecture outlines prior to teaching in a mathematics classroom will also be shared.
■ November 4, AS, Room 16B, 4 p.m. - 5 p.m.
Jose Flores (USD)
A Leslie-Gower predator-prey model with Allee effect on the prey
Abstract: In this paper we study a predator-prey model described by autonomous bi-dimensional differential equations systems in which we considered the following three properties:
(a) The equation for predator is a logistic function of the Leslie-Gower type, (b) the prey population is affected by the Allee effect, and (c) the functional response is linear function or a function of Holling type I. The interest of our work is in establishing the quantity of limit cycles of the system. The study of this type of mathematical model intends to understand the oscillatory behavior of many real world phenomena in nature.
(*) This work is in collaboration with: Eduardo González-Olivares, Betsabe González-Yañez, Jaime Mena-Lorca and Alejandro Rojas-Palma at the Institute of Mathematics at the Pontificia Universidad Católica de Valparaíso, Valparaíso Chile
■ November 9, AS, Room 104B, 4 p.m. - 5 p.m.
Keith Stroyan (University of Iowa)
Visual Depth Perception from Motion Parallax
Abstract: This talk will explain what "motion parallax" is and describe recent work on how it is combined with smooth eye pursuit to perceive depth. Extensions of the basic geometric theory suggest a number of new experiments that we hope to complete in the next few years. In Vision Res. 49, p.1969, 2009, we proposed a quantitative motion/pursuit law (M/PL) that uses the ratio of retinal image motion over pursuit eye movement to calculate relative depth for objects near central vision. The math was suggested by a number of earlier experiments by my co-author, Mark Nawrot. Our first paper also included two psychophysical experiments that confirmed the theory. In Nature 452, 42-645 (2008) Nadler, Angelaki & DeAngelis showed that macaques can not perceive depth from motion parallax without an extra retinal signal, but did not propose a signal. After seeing our preprint, Nadler, Nawrot, Angelaki & DeAngelis showed that "MT neurons combine visual motion with a smooth eye movement signal to code depth sign from motion parallax," Neuron (in press). They did NOT show that the brain implements the motion/pursuit formula, only that it uses pursuit somehow. We extended the math to two dimensions of the horizontal plane and analyzed how the M/P ratio varies across space and with time as an observer translates laterally. The theory suggests a number of new experiments designed to compare actual depth, the motion/pursuit inputs, and human (or primate) perception outside central vision. We are also working on extensions of the theory to non-lateral motion and I hope to show a "movie" that Alys (undergrad), Colin (grad), and I made to illustrate the geometry of "optic flow."
■ November 18 , AS, Room 16B, 4 p.m. - 5 p.m.
Y. L. Lio (USD)
The Implementation of R program for Acceptance Sampling Plans from truncated Life Tests for Birnbaum-Saunders Distribution
Abstract: Time to failure due to fatigue is one of the common quality characteristics in material engineering applications. The Birnbaum-Saunders distribution has been proved to provide a better fitting for the fatigue data set than the Weibull distribution does. In this talk, the comparison for two sampling plans from truncated life tests for Birnbaum-Saunders distribution will be implemented by R program.
■ December 2 , AS, Room 16B, 4 p.m. - 5 p.m.
Gabriel Picioroaga (USD)
C* Dynamical Systems
Abstract: A classical dynamical system consists of a compact Hausdorff space X together with a homeomorphism σ : X → X. The study of the iterates σ◦σ…◦σ often leads to the existence of an attractor A on which σ displays "chaotic" behavior (e.g. Julia sets). There are other ways to generate attractors for example by means of an iterated function system (IFS) where the IFS are contractions: a theorem of Hutchinson provides the attractor. While appealing from the point of view of (fractal) geometry (and quite esthetic) these attractors are ill-behaved. Many a times one studies a space by means of the real or complex (continuous or smooth) valued functions on it. It may seem like that for fractals such study would bring nothing to the table, due to their "monstrous " geometry : every function could be continuous and/or smoothness may make no sense.
In my talk I will give an introduction to C* dynamical systems and justify why it provides a comfortable setting to incorporate fractals into mainstream (Functional) Analysis. In this setting the "ill behavior" of the attractors will mean that "non-commutativity" is at play. In the particular case when A is a Cantor set I will talk about the quantum differential df=[F,f] where F is a Fredholm module over the algebra of real valued functions on A thought of as multiplication operators.