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 361-380 of 471 results.
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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
ID:
236
Year: 2008
Name: Fengrong Wei
Institution: University of Iowa
Subject area(s):
Title of Talk: variable selection in high dimensional regression
Abstract: My research work studies statistical regression models for data sets with a small sample but huge number of variables. For example, we may wish to study the same 5000 genes in only 200 individuals with the goal of predicting whether they will develop a certain rare cancer. A classical linear regression for the cancer outcome in terms of the 5000 genes does not work with only 200 data points because the associated linear equations are not full rank. We might choose 200 of the genes and do a regression, but there are over 10^363 such choices. My work uses "penalty functions" add to the linear equations which will make the problem solvable. Theoretically, we can show that the result have the "oracle" property which means it will give us the baseline true model with probability going to 1.
Year: 2008
Name: Fengrong Wei
Institution: University of Iowa
Subject area(s):
Title of Talk: variable selection in high dimensional regression
Abstract: My research work studies statistical regression models for data sets with a small sample but huge number of variables. For example, we may wish to study the same 5000 genes in only 200 individuals with the goal of predicting whether they will develop a certain rare cancer. A classical linear regression for the cancer outcome in terms of the 5000 genes does not work with only 200 data points because the associated linear equations are not full rank. We might choose 200 of the genes and do a regression, but there are over 10^363 such choices. My work uses "penalty functions" add to the linear equations which will make the problem solvable. Theoretically, we can show that the result have the "oracle" property which means it will give us the baseline true model with probability going to 1.
ID:
237
Year: 2008
Name: Fengrong Wei
Institution: University of Iowa
Subject area(s): biomathematics
Title of Talk: variable selection in high dimensional regression
Abstract: My research work studies statistical regression models for data sets with a small sample but huge number of variables. For example, we may wish to study the same 5000 genes in only 200 individuals with the goal of predicting whether they will develop a certain rare cancer. A classical linear regression for the cancer outcome in terms of the 5000 genes does not work with only 200 data points because the associated linear equations are not full rank. We might choose 200 of the genes and do a regression, but there are over 10^363 such choices. My work uses "penalty functions" add to the linear equations which will make the problem solvable. Theoretically, we can show that the result have the "oracle" property which means it will give us the baseline true model with probability going to 1.
Year: 2008
Name: Fengrong Wei
Institution: University of Iowa
Subject area(s): biomathematics
Title of Talk: variable selection in high dimensional regression
Abstract: My research work studies statistical regression models for data sets with a small sample but huge number of variables. For example, we may wish to study the same 5000 genes in only 200 individuals with the goal of predicting whether they will develop a certain rare cancer. A classical linear regression for the cancer outcome in terms of the 5000 genes does not work with only 200 data points because the associated linear equations are not full rank. We might choose 200 of the genes and do a regression, but there are over 10^363 such choices. My work uses "penalty functions" add to the linear equations which will make the problem solvable. Theoretically, we can show that the result have the "oracle" property which means it will give us the baseline true model with probability going to 1.
ID:
238
Year: 2008
Name: Le Gui
Institution: University of Iowa
Subject area(s): 94A12
Title of Talk: Digitalization in the signal processing
Abstract: In real life when we store and transmit analog audio or video signals, we first obtain a digital representation of the signal. This process is called Digitalization or Analog-to-Digital (A/D) conversion and consists of two steps: sampling and quantization. In the "sampling" step we restrict time to a discrete sample of the continuous times. In the "quantization" step we discretize the real values of the time-discrete sample of the first step. We will discuss different quantization methods based on binary expansion or Beta-expansion and compare their "accuracy." "Accuracy" means that we can re-construct a good approximation of the original signal from its digitalization. Or "can you hear me now?"
Year: 2008
Name: Le Gui
Institution: University of Iowa
Subject area(s): 94A12
Title of Talk: Digitalization in the signal processing
Abstract: In real life when we store and transmit analog audio or video signals, we first obtain a digital representation of the signal. This process is called Digitalization or Analog-to-Digital (A/D) conversion and consists of two steps: sampling and quantization. In the "sampling" step we restrict time to a discrete sample of the continuous times. In the "quantization" step we discretize the real values of the time-discrete sample of the first step. We will discuss different quantization methods based on binary expansion or Beta-expansion and compare their "accuracy." "Accuracy" means that we can re-construct a good approximation of the original signal from its digitalization. Or "can you hear me now?"
ID:
497
Year: 2018
Name: Kevin Bombardier
Institution: University of Iowa
Subject area(s): Commutative Ring Theory, Algebra
Title of Talk: An Exploration of Factorization: Mathematical Atoms
Abstract: The mathematical system of the integers has many useful properties. One of these is unique factorization. For example, we can write the number 14 in a unique way: 14 = 2 * 7. However, the numbers 2 and 7 cannot be factored into "smaller pieces" in a nontrivial way. So in this sense, they could be called atoms of this mathematical system. Other mathematical systems usually do not have all of the nice properties that the integers do. Some useful properties can still be salvaged in certain cases. An atomic domain is a special mathematical system where its members have a factorization into a product of atoms. However, despite the ability to still factor elements into atoms, some are not as well-behaved as the integers were. For example, there are atomic domains where elements have an infinite number of distinct factorizations! We will discuss some important cases of these atomic domains. Of particular interest will be an atomic domain that only has finitely many atoms.
Year: 2018
Name: Kevin Bombardier
Institution: University of Iowa
Subject area(s): Commutative Ring Theory, Algebra
Title of Talk: An Exploration of Factorization: Mathematical Atoms
Abstract: The mathematical system of the integers has many useful properties. One of these is unique factorization. For example, we can write the number 14 in a unique way: 14 = 2 * 7. However, the numbers 2 and 7 cannot be factored into "smaller pieces" in a nontrivial way. So in this sense, they could be called atoms of this mathematical system. Other mathematical systems usually do not have all of the nice properties that the integers do. Some useful properties can still be salvaged in certain cases. An atomic domain is a special mathematical system where its members have a factorization into a product of atoms. However, despite the ability to still factor elements into atoms, some are not as well-behaved as the integers were. For example, there are atomic domains where elements have an infinite number of distinct factorizations! We will discuss some important cases of these atomic domains. Of particular interest will be an atomic domain that only has finitely many atoms.
ID:
242
Year: 2008
Name: Palle Jorgensen
Institution: University of Iowa
Subject area(s): Analysis
Title of Talk: Matrix functions
Abstract: When I was little my father, for reasons unbeknownst to me, told me about low-pass and high-pass filters. He was a telephone engineer and worked on filters in signal processing. The 'high' and 'low' part of the story refers to frequency bands. Not that this meant much to me at the time. Rather, I was fascinated by the pictures of filter designs in the EE journals stacked up on the floor. And it was only many years later I came across this stuff in mathematics: quadrature mirror filters and all that; yet the visual impression still lingered. The talk will cover some of this math, especially wavelets: Subband filters define operators in Hilbert space which satisfy all kinds of abstract relations, and they are terribly useful. They are used in math and in signal processing. Matrix functions from math are called poly-phase matrices by engineers, and they are scattering matrices in other circles, and quantum gates in physics. In fact a lot of the things we do in math are known and used in other fields, but under different names, and known in different ways.
Year: 2008
Name: Palle Jorgensen
Institution: University of Iowa
Subject area(s): Analysis
Title of Talk: Matrix functions
Abstract: When I was little my father, for reasons unbeknownst to me, told me about low-pass and high-pass filters. He was a telephone engineer and worked on filters in signal processing. The 'high' and 'low' part of the story refers to frequency bands. Not that this meant much to me at the time. Rather, I was fascinated by the pictures of filter designs in the EE journals stacked up on the floor. And it was only many years later I came across this stuff in mathematics: quadrature mirror filters and all that; yet the visual impression still lingered. The talk will cover some of this math, especially wavelets: Subband filters define operators in Hilbert space which satisfy all kinds of abstract relations, and they are terribly useful. They are used in math and in signal processing. Matrix functions from math are called poly-phase matrices by engineers, and they are scattering matrices in other circles, and quantum gates in physics. In fact a lot of the things we do in math are known and used in other fields, but under different names, and known in different ways.