Proposals
Below are some proposals for talks from the past (and current). By clicking on the ID number, more details are shown. By default, these are sorted chronologically (recent first) and by then by last name. The data can be sorted by alternate means by using the links at the top right, each allowing ascending or descending orders.
Displaying 101-120 of 471 results.
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ID:
388
Year: 2014
Name: Morgan Fonley
Institution: University of Iowa
Subject area(s):
Title of Talk: Amplification and damping of an oscillating streamflow signal in a river network
Abstract: When river flow is observed under dry conditions (such as late summer), a daily fluctuation can be seen. Without the addition of precipitation, the source of these fluctuations is understood to be evapotranspiration of water from the riparian zone of trees near the river network. The flow at any point in the river network exhibits a time delay between the time of maximal evaporation (around midday) and the minimal streamflow. Several hypotheses suggest reasons for this time delay including different methods by which water moves through the soil. An alternative hypothesis is that the time delay instead comes from constructive and destructive interference that occurs when the oscillating flows of river links undergo different phase shifts and combine their signals. In this way, the flow at a downstream river link can be amplified or damped. I present an analytic solution to the transport equation, a linear ordinary differential equation that can be used to determine the flow at any point in a river network when all hillslopes are assumed to have uniform parameters. I use this solution to demonstrate the extent of amplification or damping that can occur when different parameter values are varied.
Year: 2014
Name: Morgan Fonley
Institution: University of Iowa
Subject area(s):
Title of Talk: Amplification and damping of an oscillating streamflow signal in a river network
Abstract: When river flow is observed under dry conditions (such as late summer), a daily fluctuation can be seen. Without the addition of precipitation, the source of these fluctuations is understood to be evapotranspiration of water from the riparian zone of trees near the river network. The flow at any point in the river network exhibits a time delay between the time of maximal evaporation (around midday) and the minimal streamflow. Several hypotheses suggest reasons for this time delay including different methods by which water moves through the soil. An alternative hypothesis is that the time delay instead comes from constructive and destructive interference that occurs when the oscillating flows of river links undergo different phase shifts and combine their signals. In this way, the flow at a downstream river link can be amplified or damped. I present an analytic solution to the transport equation, a linear ordinary differential equation that can be used to determine the flow at any point in a river network when all hillslopes are assumed to have uniform parameters. I use this solution to demonstrate the extent of amplification or damping that can occur when different parameter values are varied.
ID:
147
Year: 2006
Name: Scott Wood
Institution: University of Iowa
Subject area(s): Bayesian statistics, spatial statistics, medical geography
Title of Talk: Model Fitting and Selection for County-Level Depression Hospitalization Rates Using Bayesian Statistical Methods
Abstract: Researchers in the health sciences are interested in identifying and modeling the risk factors that are associated with high rates of hospitalization for depression. Being able to identify U.S. counties with high standardized hospitalization rates (SHR) would be useful in allocating federal resources. This project analyzes and critiques three potential Bayesian statistical models that can be implemented using WinBUGS software. Ordinary least squares, Poisson regression, and Bayesian conditional autoregressive (CAR) models are considered in detail. Though each has its advantages and disadvantages, qualitative and quantitative evidence suggest that the Bayesian CAR model is the optimal choice for this data. While a Bayesian CAR model will be shown to account for spatial autocorrelation and Poisson response variables, it was not as reliable as hoped for making accurate predictions at the county level.
Year: 2006
Name: Scott Wood
Institution: University of Iowa
Subject area(s): Bayesian statistics, spatial statistics, medical geography
Title of Talk: Model Fitting and Selection for County-Level Depression Hospitalization Rates Using Bayesian Statistical Methods
Abstract: Researchers in the health sciences are interested in identifying and modeling the risk factors that are associated with high rates of hospitalization for depression. Being able to identify U.S. counties with high standardized hospitalization rates (SHR) would be useful in allocating federal resources. This project analyzes and critiques three potential Bayesian statistical models that can be implemented using WinBUGS software. Ordinary least squares, Poisson regression, and Bayesian conditional autoregressive (CAR) models are considered in detail. Though each has its advantages and disadvantages, qualitative and quantitative evidence suggest that the Bayesian CAR model is the optimal choice for this data. While a Bayesian CAR model will be shown to account for spatial autocorrelation and Poisson response variables, it was not as reliable as hoped for making accurate predictions at the county level.
ID:
148
Year: 2006
Name: Alfredo Villanueva
Institution: University of Iowa
Subject area(s): Differential Geometry
Title of Talk: Prolongations on a Riemannian Manifold
Abstract: Traditionally the method of prolongations is carry out by algebraic manipulations which become very complex, especially in cases of partial differential equations on curved spaces, here we are applying some results from representation theory and differential operators to have a systematic method that allow us to close some overdetermined systems on a Riemannian manifold.
Year: 2006
Name: Alfredo Villanueva
Institution: University of Iowa
Subject area(s): Differential Geometry
Title of Talk: Prolongations on a Riemannian Manifold
Abstract: Traditionally the method of prolongations is carry out by algebraic manipulations which become very complex, especially in cases of partial differential equations on curved spaces, here we are applying some results from representation theory and differential operators to have a systematic method that allow us to close some overdetermined systems on a Riemannian manifold.
ID:
410
Year: 2014
Name: Jennifer Good
Institution: University of Iowa
Subject area(s):
Title of Talk: What did J.S. Bach know about fractals?
Abstract: The mathematical term 'fractal', coined in the late 20th century, is used to describe detailed mathematical objects with certain repeating patterns. Bach's 3rd cello suite, composed 250 years earlier, contains evidence of a fractal embedded in one of its movements. Come learn about fractals as we see (and hear) how one appears in this famous piece of music!
Year: 2014
Name: Jennifer Good
Institution: University of Iowa
Subject area(s):
Title of Talk: What did J.S. Bach know about fractals?
Abstract: The mathematical term 'fractal', coined in the late 20th century, is used to describe detailed mathematical objects with certain repeating patterns. Bach's 3rd cello suite, composed 250 years earlier, contains evidence of a fractal embedded in one of its movements. Come learn about fractals as we see (and hear) how one appears in this famous piece of music!
ID:
417
Year: 2015
Name: Catherine Patterson
Institution: University of Iowa
Subject area(s): Mathematical biology, applied math, modeling
Title of Talk: Modeling the Effects of Multiple Myeloma Bone Disease
Abstract: Cancer is a lot like a hurricane; you can see it coming, but you don't know exactly where it will go or how much damage it will do. However, by combining a mathematical model with patient data, we can make predictions about the development of a patient's cancer. My research focuses on multiple myeloma, a plasma cell cancer that disrupts the bone remodeling process. In multiple myeloma patients, bone destruction outpaces bone replacement, producing bone lesions. This talk will describe the cell dynamics that regulate bone remodeling and explain how they are impacted by multiple myeloma. I will then discuss techniques used to model this system, including Savageau's power law approximations.
Year: 2015
Name: Catherine Patterson
Institution: University of Iowa
Subject area(s): Mathematical biology, applied math, modeling
Title of Talk: Modeling the Effects of Multiple Myeloma Bone Disease
Abstract: Cancer is a lot like a hurricane; you can see it coming, but you don't know exactly where it will go or how much damage it will do. However, by combining a mathematical model with patient data, we can make predictions about the development of a patient's cancer. My research focuses on multiple myeloma, a plasma cell cancer that disrupts the bone remodeling process. In multiple myeloma patients, bone destruction outpaces bone replacement, producing bone lesions. This talk will describe the cell dynamics that regulate bone remodeling and explain how they are impacted by multiple myeloma. I will then discuss techniques used to model this system, including Savageau's power law approximations.
ID:
162
Year: 2006
Name: Giovanna Llosent
Institution: University of Iowa
Subject area(s): Modular Representation Theory
Title of Talk: The stable endomorphism group of non-simple string modules over a very particular finite dimensional algebra.
Abstract: Let A be a finite dimensional algebra over an algebraic closed field k of characteristic 2 with a quiver representation and relations. Consider all non-simple string modules for this algebra which do not lie in the Auslander-Reiten component of the simple modules. Is there a non-simple string module M for which the group of stable endomorphisms is isomorphic to k? Under the hypothesis above we were able to prove that the underlying string S of the string module M has a substring S' and there is an endomorphism that does not factor through a projective A-module and lies in S'. The maximun lenght of the underlying string of a string module needed for completing the study of all stable endomorphism groups of non-simple string modules was 17. In particular, the cases needed for complete generalization are 54.
Year: 2006
Name: Giovanna Llosent
Institution: University of Iowa
Subject area(s): Modular Representation Theory
Title of Talk: The stable endomorphism group of non-simple string modules over a very particular finite dimensional algebra.
Abstract: Let A be a finite dimensional algebra over an algebraic closed field k of characteristic 2 with a quiver representation and relations. Consider all non-simple string modules for this algebra which do not lie in the Auslander-Reiten component of the simple modules. Is there a non-simple string module M for which the group of stable endomorphisms is isomorphic to k? Under the hypothesis above we were able to prove that the underlying string S of the string module M has a substring S' and there is an endomorphism that does not factor through a projective A-module and lies in S'. The maximun lenght of the underlying string of a string module needed for completing the study of all stable endomorphism groups of non-simple string modules was 17. In particular, the cases needed for complete generalization are 54.
ID:
418
Year: 2015
Name: Kevin Gerstle
Institution: University of Iowa
Subject area(s): Algebra
Title of Talk: Algebras and Coalgebras
Abstract: While algebra is widely recognized as an important branch of mathematics, most people do not know how the objects called algebras play a vital role in our understanding of many commonly used number systems such as the real and complex numbers. In addition, the dual notion of coalgebras give us a way to introduce a new type of structure to these systems allowing us novel, exciting ways to talk about numbers. In this talk, we will explore the interplay between algebras and coalgebras, and I will show what information these algebraic structures give us about some of our favorite number systems.
Year: 2015
Name: Kevin Gerstle
Institution: University of Iowa
Subject area(s): Algebra
Title of Talk: Algebras and Coalgebras
Abstract: While algebra is widely recognized as an important branch of mathematics, most people do not know how the objects called algebras play a vital role in our understanding of many commonly used number systems such as the real and complex numbers. In addition, the dual notion of coalgebras give us a way to introduce a new type of structure to these systems allowing us novel, exciting ways to talk about numbers. In this talk, we will explore the interplay between algebras and coalgebras, and I will show what information these algebraic structures give us about some of our favorite number systems.
ID:
427
Year: 2015
Name: Julia Walk
Institution: University of Iowa
Subject area(s): Mathematical Biology
Title of Talk: Building a Model of the Effects of Multiple Myeloma on Kidney Function
Abstract: Multiple myeloma is a type of plasma cell cancer associated with many health challenges, including damage to the kidney. When a patient's kidneys are damaged, waste builds up in the bloodstream and the body begins to shut down. We would like to model what happens as the cancer affects the proximal tubule cells in the kidney, to eventually create a model that doctors can use as a predictive tool to catch problems early. We will explore an initial model that captures the biology of the interaction between kidney cells and proteins produced by the myeloma cells. The discussion will emphasize the development of the model using power law approximations in a system of ODEs.
Year: 2015
Name: Julia Walk
Institution: University of Iowa
Subject area(s): Mathematical Biology
Title of Talk: Building a Model of the Effects of Multiple Myeloma on Kidney Function
Abstract: Multiple myeloma is a type of plasma cell cancer associated with many health challenges, including damage to the kidney. When a patient's kidneys are damaged, waste builds up in the bloodstream and the body begins to shut down. We would like to model what happens as the cancer affects the proximal tubule cells in the kidney, to eventually create a model that doctors can use as a predictive tool to catch problems early. We will explore an initial model that captures the biology of the interaction between kidney cells and proteins produced by the myeloma cells. The discussion will emphasize the development of the model using power law approximations in a system of ODEs.
ID:
428
Year: 2015
Name: Christine Caples
Institution: University of Iowa
Subject area(s): Knot Theory
Title of Talk: Tangle Classification
Abstract: A knot can be thought of as a knotted piece of string with the ends glued together. A tangle is formed by intersecting a knot with a 3-dimensional ball. The portion of the knot in the interior of the ball along with the fixed intersection points on the surface of the ball form the tangle. Tangles can be used to model protein-DNA binding, so another way to think of a tangle is in terms of segments of DNA (the strings) bounded by the protein complex (the 3-dimensional ball). Like knots, the same tangle can be represented by multiple diagrams which are equivalent under deformations (no cutting or gluing allowed). A tangle invariant is a value that is the same for equivalent tangles. Tangles can be classified into families which allows one to study properties of tangles that may be useful for solving tangle equations. This talk will be an introduction to knot theory and will investigate how tangle invariants can be used to classify tangles.
Year: 2015
Name: Christine Caples
Institution: University of Iowa
Subject area(s): Knot Theory
Title of Talk: Tangle Classification
Abstract: A knot can be thought of as a knotted piece of string with the ends glued together. A tangle is formed by intersecting a knot with a 3-dimensional ball. The portion of the knot in the interior of the ball along with the fixed intersection points on the surface of the ball form the tangle. Tangles can be used to model protein-DNA binding, so another way to think of a tangle is in terms of segments of DNA (the strings) bounded by the protein complex (the 3-dimensional ball). Like knots, the same tangle can be represented by multiple diagrams which are equivalent under deformations (no cutting or gluing allowed). A tangle invariant is a value that is the same for equivalent tangles. Tangles can be classified into families which allows one to study properties of tangles that may be useful for solving tangle equations. This talk will be an introduction to knot theory and will investigate how tangle invariants can be used to classify tangles.
ID:
437
Year: 2016
Name: Keith Stroyan
Institution: University of Iowa
Subject area(s): Vector Calculus
Title of Talk: Advanced Calculus using Mathematica
Abstract: Advanced Calculus using Mathematica is a complete text on calculus of several variables written in Mathematica NoteBooks. The eText has large movable figures and interactive programs to illustrate things like “zooming in” to see “local linearity.” In addition to lots of traditional style exercises, the eText also has sections on computing with Mathematica. We will discuss some of the novel features of the text including the explicit, implicit, parametric organization and topics often omitted from "regular" texts (like "vector potentials.") We use the text in a second semester multivariable calculus course and a more advanced course.
Year: 2016
Name: Keith Stroyan
Institution: University of Iowa
Subject area(s): Vector Calculus
Title of Talk: Advanced Calculus using Mathematica
Abstract: Advanced Calculus using Mathematica is a complete text on calculus of several variables written in Mathematica NoteBooks. The eText has large movable figures and interactive programs to illustrate things like “zooming in” to see “local linearity.” In addition to lots of traditional style exercises, the eText also has sections on computing with Mathematica. We will discuss some of the novel features of the text including the explicit, implicit, parametric organization and topics often omitted from "regular" texts (like "vector potentials.") We use the text in a second semester multivariable calculus course and a more advanced course.
ID:
447
Year: 2016
Name: Richard Ligo
Institution: University of Iowa
Subject area(s): Differential geometry
Title of Talk: Escaping Flatland: An Introduction to Surface Curvature
Abstract: What if I told you that the majority of ideas conveyed in high school geometry classes are thousands of years old? What if I told you that your understanding of geometry was tremendously incomplete? Believe it or not, one can argue that the first true departure from ancient Greek geometry wasn't published until 1826! In this talk, we describe one such departure and its implications. We begin by describing the curvature of a curve, use this to define the curvature of a surface, and conclude by visiting a famous egregious result. This talk even includes snacks!
Year: 2016
Name: Richard Ligo
Institution: University of Iowa
Subject area(s): Differential geometry
Title of Talk: Escaping Flatland: An Introduction to Surface Curvature
Abstract: What if I told you that the majority of ideas conveyed in high school geometry classes are thousands of years old? What if I told you that your understanding of geometry was tremendously incomplete? Believe it or not, one can argue that the first true departure from ancient Greek geometry wasn't published until 1826! In this talk, we describe one such departure and its implications. We begin by describing the curvature of a curve, use this to define the curvature of a surface, and conclude by visiting a famous egregious result. This talk even includes snacks!
ID:
466
Year: 2017
Name: Ranthony A.C. Edmonds
Institution: University of Iowa
Subject area(s): Blended learning; flipped instruction; trigonometry
Title of Talk: A Case for Blended Learning: A Partially Flipped Trigonometry Course
Abstract: Blended learning is an instructional approach that combines online digital media with traditional classroom methods. Blended courses are sometimes known as hybrid courses in that some of the introduction is occurring outside of the classroom, and it has gained recent attention as a method to address remediation and student motivation in introductory math courses in higher education. Flipped instruction is a type of blended learning that has gained a lot of attention as an alternative to lecture based instruction in its own right. However, common pitfalls of this technique include resistance from instructors due to the perceived amount of time to create instructional videos and materials, and from students due to the amount of independent learning required outside of class. Partially flipped instruction addresses these concerns by incorporating both independent and face-to-face instruction. It can also alleviate the amount of time spent on additional materials by instructors, while still holding students accountable for their own learning outside of class. This talk will give a brief introduction to blending learning, what is it, and what it is not. Next, we will focus on a particular type of blended learning, flipped instruction, and subsequently a partially flipped model used in the Spring of 2017 at the University of Iowa for a College Trigonometry course. The main features of this model included instructional videos, created with Doceri for iPad, which were viewed outside of class once a week by students, coupled with a short assessment based on that instruction. The following ‘flipped’ period involved individual and/or group activities expanding upon concepts introduced in the videos. Canvas by Instructure was used heavily throughout the course. Motivation and implementation of the design will be described, quantitative data with regards to course assessments will be given, and the results of a qualitative survey given to students about their experience in the course will be shared. Last, we will describe some specific efforts of certain math departments to incorporate blended learning in their curricula.
Year: 2017
Name: Ranthony A.C. Edmonds
Institution: University of Iowa
Subject area(s): Blended learning; flipped instruction; trigonometry
Title of Talk: A Case for Blended Learning: A Partially Flipped Trigonometry Course
Abstract: Blended learning is an instructional approach that combines online digital media with traditional classroom methods. Blended courses are sometimes known as hybrid courses in that some of the introduction is occurring outside of the classroom, and it has gained recent attention as a method to address remediation and student motivation in introductory math courses in higher education. Flipped instruction is a type of blended learning that has gained a lot of attention as an alternative to lecture based instruction in its own right. However, common pitfalls of this technique include resistance from instructors due to the perceived amount of time to create instructional videos and materials, and from students due to the amount of independent learning required outside of class. Partially flipped instruction addresses these concerns by incorporating both independent and face-to-face instruction. It can also alleviate the amount of time spent on additional materials by instructors, while still holding students accountable for their own learning outside of class. This talk will give a brief introduction to blending learning, what is it, and what it is not. Next, we will focus on a particular type of blended learning, flipped instruction, and subsequently a partially flipped model used in the Spring of 2017 at the University of Iowa for a College Trigonometry course. The main features of this model included instructional videos, created with Doceri for iPad, which were viewed outside of class once a week by students, coupled with a short assessment based on that instruction. The following ‘flipped’ period involved individual and/or group activities expanding upon concepts introduced in the videos. Canvas by Instructure was used heavily throughout the course. Motivation and implementation of the design will be described, quantitative data with regards to course assessments will be given, and the results of a qualitative survey given to students about their experience in the course will be shared. Last, we will describe some specific efforts of certain math departments to incorporate blended learning in their curricula.
ID:
468
Year: 2017
Name: Maria Gommel
Institution: University of Iowa
Subject area(s):
Title of Talk: The Shape of Data: An Introduction to Topological Data Analysis
Abstract: What does it mean for data to have "shape"? Can this idea of "shape" help us better analyze data? In this talk, I will introduce some basic ideas of algebraic topology that allow us to describe the "shape" of a data set, and discuss how these ideas can help us analyze data. We'll also see an example of how these techniques have been applied to fMRI brain data. This talk is entirely self-contained and appropriate for undergraduates at any level.
Year: 2017
Name: Maria Gommel
Institution: University of Iowa
Subject area(s):
Title of Talk: The Shape of Data: An Introduction to Topological Data Analysis
Abstract: What does it mean for data to have "shape"? Can this idea of "shape" help us better analyze data? In this talk, I will introduce some basic ideas of algebraic topology that allow us to describe the "shape" of a data set, and discuss how these ideas can help us analyze data. We'll also see an example of how these techniques have been applied to fMRI brain data. This talk is entirely self-contained and appropriate for undergraduates at any level.
ID:
217
Year: 2007
Name: Dennis Roseman
Institution: University of Iowa
Subject area(s):
Title of Talk: How likely is a lattice link?
Abstract: Lattice points in space are points with integer coordinates. A unit lattice edge is a line segment of unit length between lattice points. A lattice link is a finite collection union of lattice edges whose union is topologically equivalent to a union of disjoint circles. We define a notion of probability for lattice knots and links and use this to frame the question: which is more ``likely'', the square knot or the granny knot. A square knot is obtained by tying a right hand trefoil and a left had trefoil together; the granny knot is obtained by using two identical trefoils. We also discuss our progress towards calculation of these probabilities.
Year: 2007
Name: Dennis Roseman
Institution: University of Iowa
Subject area(s):
Title of Talk: How likely is a lattice link?
Abstract: Lattice points in space are points with integer coordinates. A unit lattice edge is a line segment of unit length between lattice points. A lattice link is a finite collection union of lattice edges whose union is topologically equivalent to a union of disjoint circles. We define a notion of probability for lattice knots and links and use this to frame the question: which is more ``likely'', the square knot or the granny knot. A square knot is obtained by tying a right hand trefoil and a left had trefoil together; the granny knot is obtained by using two identical trefoils. We also discuss our progress towards calculation of these probabilities.
ID:
473
Year: 2017
Name: Kevin Bombardier
Institution: University of Iowa
Subject area(s): cryptography, algebra, number theory
Title of Talk: Cryptography - Secure Communication
Abstract: Essential to our modern technological world, cryptography is the study of secure communication. In this talk we will discuss some of the basic ideas in cryptography, explain the differences between symmetric and asymmetric-key cryptosystems, and explore some basic examples of cryptosystems. As an illustration of the mathematics involved, we will do a simplified computational example by computing keys using the RSA algorithm. This talk will be self-contained; no prior knowledge of cryptography will be assumed.
Year: 2017
Name: Kevin Bombardier
Institution: University of Iowa
Subject area(s): cryptography, algebra, number theory
Title of Talk: Cryptography - Secure Communication
Abstract: Essential to our modern technological world, cryptography is the study of secure communication. In this talk we will discuss some of the basic ideas in cryptography, explain the differences between symmetric and asymmetric-key cryptosystems, and explore some basic examples of cryptosystems. As an illustration of the mathematics involved, we will do a simplified computational example by computing keys using the RSA algorithm. This talk will be self-contained; no prior knowledge of cryptography will be assumed.
ID:
474
Year: 2017
Name: Aqeeb Sabree
Institution: University of Iowa
Subject area(s): Advanced Calculus would be helpful
Title of Talk: Research Topics from Reproducing Kernel Hilbert Spaces
Abstract: Reproducing Kernel Hilbert Spaces (RKHS) have applications to statistics, machine learning, differential equations, and more. The goal of this presentation is to introduce the concept of a RKHS, and discuss it’s applications to many research areas. The amazing thing about this research area is that there are many research questions/topics for dissertations or undergraduate research experiences. I will give a brief history of RKHSs, highlighting where it has appeared and how it has been applied. Then I will present the theoretical foundation(s) of the subject; from here I will go into its applications. Below, you will find highlights of the theory that I will present, and some highlights of its application. You can discuss the existence of RKHSs in different ways: one, you can prove that the evaluation functional is bounded; or, two, you can prove that (given a Hilbert space) the Hilbert space has a reproducing kernel function. A nice property of the reproducing kernel is that it is unique. Thus, every RKHS has exactly one reproducing kernel; furthermore, every reproducing kernel is the reproducing kernel for a unique RKHS (Moore--Aronszajn). The process of recreating the RKHS from the kernel function is termed the it reconstruction problem, and is an interesting research area. The usefulness of the theory of RKHSs can be seen in the fact that the finite energy Fourier, Hankel, sine, and cosine transformed band-limited signals are specific realizations of the abstract reproducing kernel Hilbert space (RKHS). Sampling Theory: Sampling theory deals with the reconstruction of functions (or signals) from their values (or samples) on an appropriate set of points. When given a reproducing kernel Hilbert space, H; one asks: What are some (suitable) sets of points which reproduce (or interpolate) the full values of functions from H? And when given points in a set S, one asks: What are the RKHSs for which S is a complete set of sample points? Meaning the values of functions from H are reproduced by interpolation from S.
Year: 2017
Name: Aqeeb Sabree
Institution: University of Iowa
Subject area(s): Advanced Calculus would be helpful
Title of Talk: Research Topics from Reproducing Kernel Hilbert Spaces
Abstract: Reproducing Kernel Hilbert Spaces (RKHS) have applications to statistics, machine learning, differential equations, and more. The goal of this presentation is to introduce the concept of a RKHS, and discuss it’s applications to many research areas. The amazing thing about this research area is that there are many research questions/topics for dissertations or undergraduate research experiences. I will give a brief history of RKHSs, highlighting where it has appeared and how it has been applied. Then I will present the theoretical foundation(s) of the subject; from here I will go into its applications. Below, you will find highlights of the theory that I will present, and some highlights of its application. You can discuss the existence of RKHSs in different ways: one, you can prove that the evaluation functional is bounded; or, two, you can prove that (given a Hilbert space) the Hilbert space has a reproducing kernel function. A nice property of the reproducing kernel is that it is unique. Thus, every RKHS has exactly one reproducing kernel; furthermore, every reproducing kernel is the reproducing kernel for a unique RKHS (Moore--Aronszajn). The process of recreating the RKHS from the kernel function is termed the it reconstruction problem, and is an interesting research area. The usefulness of the theory of RKHSs can be seen in the fact that the finite energy Fourier, Hankel, sine, and cosine transformed band-limited signals are specific realizations of the abstract reproducing kernel Hilbert space (RKHS). Sampling Theory: Sampling theory deals with the reconstruction of functions (or signals) from their values (or samples) on an appropriate set of points. When given a reproducing kernel Hilbert space, H; one asks: What are some (suitable) sets of points which reproduce (or interpolate) the full values of functions from H? And when given points in a set S, one asks: What are the RKHSs for which S is a complete set of sample points? Meaning the values of functions from H are reproduced by interpolation from S.
ID:
222
Year: 2008
Name: K Stroyan
Institution: University of Iowa
Subject area(s): Trig, Calculus, and Vision
Title of Talk: A new formula for depth perception
Abstract: When you are moving, such as walking, and fix your gaze at an object ahead, but off to the side, say a tree, stationary objects behind the tree seem to move in the same direction as you, while objects in front seem to move in the opposite direction. This is a monocular cue to depth, as opposed to binocular disparity - the difference in the images in your two (separated) eyes. Working with a vision researcher, we have found a simple new formula for depth in terms of motion. Work is in progress in his laboratory to see how much of the geometric information contained in the formula is actually used by humans. The proof of the formula is a very simple application of trigonometry and infinitesimal calculus. We were led to discover it through experimental intuition and some interactive programs that we will demonstrate.
Year: 2008
Name: K Stroyan
Institution: University of Iowa
Subject area(s): Trig, Calculus, and Vision
Title of Talk: A new formula for depth perception
Abstract: When you are moving, such as walking, and fix your gaze at an object ahead, but off to the side, say a tree, stationary objects behind the tree seem to move in the same direction as you, while objects in front seem to move in the opposite direction. This is a monocular cue to depth, as opposed to binocular disparity - the difference in the images in your two (separated) eyes. Working with a vision researcher, we have found a simple new formula for depth in terms of motion. Work is in progress in his laboratory to see how much of the geometric information contained in the formula is actually used by humans. The proof of the formula is a very simple application of trigonometry and infinitesimal calculus. We were led to discover it through experimental intuition and some interactive programs that we will demonstrate.
ID:
225
Year: 2008
Name: Yi Li
Institution: University of Iowa
Subject area(s):
Title of Talk: REU 2007 at University of Iowa--A Personal Experience
Abstract: This talk is about the summer '07 REU work I supervised. I want to tell you about work of three wonderful visiting undergraduate students and the paper they recently submitted: "Chaotic Dynamics, Fractals and Billiards." I also want to tell you about my experience as a first time REU mentor.
Year: 2008
Name: Yi Li
Institution: University of Iowa
Subject area(s):
Title of Talk: REU 2007 at University of Iowa--A Personal Experience
Abstract: This talk is about the summer '07 REU work I supervised. I want to tell you about work of three wonderful visiting undergraduate students and the paper they recently submitted: "Chaotic Dynamics, Fractals and Billiards." I also want to tell you about my experience as a first time REU mentor.
ID:
229
Year: 2008
Name: Benjamin Galluzzo
Institution: University of Iowa
Subject area(s):
Title of Talk: The Mathematical Contest in Modeling: An Advisor's Perspective
Abstract: This past February, The University of Iowa participated in The Mathematical Contest in Modeling (MCM) for the first time. This talk will focus on the organizational challenges we encountered while preparing for MCM as well as ideas that we hope to implement for future contests.
Year: 2008
Name: Benjamin Galluzzo
Institution: University of Iowa
Subject area(s):
Title of Talk: The Mathematical Contest in Modeling: An Advisor's Perspective
Abstract: This past February, The University of Iowa participated in The Mathematical Contest in Modeling (MCM) for the first time. This talk will focus on the organizational challenges we encountered while preparing for MCM as well as ideas that we hope to implement for future contests.
ID:
231
Year: 2008
Name: Ian Besse
Institution: University of Iowa
Subject area(s): Mathematical Biology/Physiology; ODEs
Title of Talk: A model of cardiac action potential incorporating caveolae-associated ion currents
Abstract: The contraction of a cardiac cell is initiated by a transient depolarization of the cell membrane called an action potential. Action potentials result from the rapid movement of ions across the membrane through pores called ion channels. Recent electrophysiological data regarding caveolae, small invaginations of the cell membrane, reveal that caveolae are reservoirs of
Year: 2008
Name: Ian Besse
Institution: University of Iowa
Subject area(s): Mathematical Biology/Physiology; ODEs
Title of Talk: A model of cardiac action potential incorporating caveolae-associated ion currents
Abstract: The contraction of a cardiac cell is initiated by a transient depolarization of the cell membrane called an action potential. Action potentials result from the rapid movement of ions across the membrane through pores called ion channels. Recent electrophysiological data regarding caveolae, small invaginations of the cell membrane, reveal that caveolae are reservoirs of