Super-Resolution Via Superset Selection And Pruning,
2013
Massachusetts Institute of Technology
Super-Resolution Via Superset Selection And Pruning, Laurent Demanet, Deanna Needell, Nam Nguyen
CMC Faculty Publications and Research
We present a pursuit-like algorithm that we call the "superset method" for recovery of sparse vectors from consecutive Fourier measurements in the super-resolution regime. The algorithm has a subspace identification step that hinges on the translation invariance of the Fourier transform, followed by a removal step to estimate the solution's support. The superset method is always successful in the noiseless regime (unlike L1-minimization) and generalizes to higher dimensions (unlike the matrix pencil method). Relative robustness to noise is demonstrated numerically.
Poincaré Polynomial Of Fjrw Rings And The Group-Weights Conjecture,
2013
Brigham Young University - Provo
Poincaré Polynomial Of Fjrw Rings And The Group-Weights Conjecture, Julian Boon Kai Tay
Theses and Dissertations
FJRW-theory is a recent advancement in singularity theory arising from physics. The FJRW-theory is a graded vector space constructed from a quasihomogeneous weighted polynomial and symmetry group, but it has been conjectured that the theory only depends on the weights of the polynomial and the group. In this thesis, I prove this conjecture using Poincaré polynomials and Koszul complexes. By constructing the Koszul complex of the state space, we have found an expression for the Poincaré polynomial of the state space for a given polynomial and associated group. This Poincaré polynomial is defined over the representation ring of a group …
Energy Flux Streamlines Versus Acoustic Rays For Modeling Interaction With Rigid Boundaries: Near Field Of Sound From A Circular Loudspeaker,
2013
Georgia Southern University
Energy Flux Streamlines Versus Acoustic Rays For Modeling Interaction With Rigid Boundaries: Near Field Of Sound From A Circular Loudspeaker, Cleon Dean, James Braselton
Mathematical Sciences: Faculty Presentations (1991-2022)
Sound emitted by a circular loudspeaker can be treated as equivalent to a plane wave diffracted by a circular aperture in a rigid, sound absorbing screen. Axial symmetry leads one to expect constructive interference along the symmetry axis in the near field (the Poisson-Arago spot). An energy flux streamline model was developed to help visualize this and other features of the nearsound field. The model is used to draw out similarities and differences between energy flux streamlines and acoustic rays, particularly in the transition to the far field.
Hilbert Space Theory And Applications In Basic Quantum Mechanics,
2013
California Polytechnic State University, San Luis Obispo
Hilbert Space Theory And Applications In Basic Quantum Mechanics, Matthew Gagne
Mathematics
We explore the basic mathematical physics of quantum mechanics. Our primary focus will be on Hilbert space theory and applications as well as the theory of linear operators on Hilbert space. We show how Hermitian operators are used to represent quantum observables and investigate the spectrum of various linear operators. We discuss deviation and uncertainty and briefly suggest how symmetry and representations are involved in quantum theory.
Σary,
2013
Minnesota State University Moorhead
Σary, Minnesota State University Moorhead, Mathematics Department
Math Department Newsletters
No abstract provided.
√(X2 + Μ) Is The Most Computationally Efficient Smooth Approximation To |X|: A Proof,
2013
The University of Texas at El Paso
√(X2 + Μ) Is The Most Computationally Efficient Smooth Approximation To |X|: A Proof, Carlos Ramirez, Reinaldo Sanchez, Vladik Kreinovich, Miguel Argaez
Departmental Technical Reports (CS)
In many practical situations, we need to minimize an expression of the type |c1| + ... + |cn|. The problem is that most efficient optimization techniques use the derivative of the objective function, but the function |x| is not differentiable at 0. To make optimization efficient, it is therefore reasonable to approximate |x| by a smooth function. We show that in some reasonable sense, the most computationally efficient smooth approximation to |x| is the function √(x2 + μ), a function which has indeed been successfully used in such optimization.
Loops And Their Permutation Groups,
2013
University of Denver
Loops And Their Permutation Groups, Mark Greer
Electronic Theses and Dissertations
This dissertation uses the connections between loops and their associated permutation groups to study certain varieties of loops. We first define a variety of loops generalizing commutative automorphic loops and show this new variety is power associative. We show a correspondence to Bruck loops of odd order and use this correspondence to give structural results for our new variety, which in turn hold for commutative automorphic loops. Next, we study a variety of loops that generalize both Moufang and Steiner loops. We extend on known results for Moufang loops and then extend two different doubling constructions for creating Moufang and …
Insights On The Neyman - Pearson Lemma: Alternative Critical Regions, And Their Power.,
2013
Taylor University
Insights On The Neyman - Pearson Lemma: Alternative Critical Regions, And Their Power., David E. Wetzell
ACMS Conference Proceedings 2013
The Neyman-Pearson Lemma is a powerful fundamental lemma in the area of hypothesis testing in Statistics. It gives the best test when testing simple vs. simple hypotheses. In this talk we would like to investigate testing a population mean H0 μ = μ0 vs. H1 μ = μ1 > μ0. As a result of the N-P Lemma, the best test is of the form, “Reject H0 if x>c” , where c is chosen so that the Type I error probability is a. Let n be small. What are some alternative decision rules of size a, what …
Service-Learning Panel,
2013
Trinity Christian College
Service-Learning Panel, Dave Klanderman, Josh Wilkerson, Maria Zack
ACMS Conference Proceedings 2013
Many of us have wanted to incorporate service experiences in courses, or are being asked by our institutions to do so. Service-learning is a way of looking at service as being a partner with and leading to learning for our students. But in math, there are not a lot of resources to use! Our panelists will present classroom-tested ideas from several different levels of course, and we will end with a short time for more brainstorming among all participants.
Pedagogical Enhancements To The Desymbol Logic Translator,
2013
Rowan University
Pedagogical Enhancements To The Desymbol Logic Translator, Darren F. Provine, Nancy Lynn Tinkham
ACMS Conference Proceedings 2013
DeSymbol is a program that translates first-order predicate logic expressions into English. It is intended to be a practice tool for students who are learning logic for the first time or who are trying to refresh their memories if they need to use symbolic logic for an upper-level course. Students start with an English sentence and translate it by hand into symbolic logic notation; then they can check their work by using DeSymbol to translate their notation back into English. If the English sentence produced by DeSymbol differs significantly from the original English sentence, this helps the student to see …
Mapping Biblical Commandments To An Iterated Prisoner’S Dilemma Framework,
2013
Bethel University
Mapping Biblical Commandments To An Iterated Prisoner’S Dilemma Framework, Nathan Gossett, Adam Johnson
ACMS Conference Proceedings 2013
In his writings on Game Theory, an d the Iterated Prisoner’s Dilemma in particular, Robert Axelrod outlined four properties that are predictors of a successful strategy: Niceness, Reciprocity, Forgiveness, and Understandability. On the topic of Reciprocity, Axelrod makes the claim that not only does The Golden Rule lead to a suboptimal strategy, but that one of the most successful strategies (Tit for Tat) shows that a command of “An eye for an eye” leads to a much more optimal strategy. In this paper, we will discuss the details of Axelrod’s four properties, outline Biblical support for all four, and discuss …
Open Source Software: What Is It, And Why Should We Care?,
2013
Gordon College
Open Source Software: What Is It, And Why Should We Care?, Karl-Dieter Crisman
ACMS Conference Proceedings 2013
This paper examines the distinctions in talking about computer software that has implications for both mathematics and moral thought.
Teaching Complex Analysis As A Lab-Type Course With A Focus On Geometric Interpretations Using Mathematics,
2013
Taylor University
Teaching Complex Analysis As A Lab-Type Course With A Focus On Geometric Interpretations Using Mathematics, William M. Kinney
ACMS Conference Proceedings 2013
I taught complex analysis for the first time in my career during the spring of 2013. I decided to do something “radical” and teach it as a lab-type course with a focus on geometric interpretations using the computer program Mathematica. The students and I met in a computer lab and, during most meetings, we spent a large portion of our time experimenting and exploring using Mathematica to visualize key concepts in complex analysis. Because of this, there was a heavy emphasis on viewing analytic functions as conformal mappings as well as considering associated vector fields and flows. Mathematica was used …
Faith Integration Projects For First-Year Students,
2013
Messiah College
Faith Integration Projects For First-Year Students, Doug Phillippy
ACMS Conference Proceedings 2013
This talk will consider the use of projects to motivate students to think deeply about how their faith connects with mathematics. This talk will begin by describing what a faith integration project is, including the goals and objectives of such a project. The talk will briefly describe a number of projects written by the speaker, with a more detailed look at one of those projects. The talk will conclude by discussing how these projects are being used to assess how students are doing at articulating a maturing understanding of the connection between faith and mathematics
Philosophy Motivates Undergraduates In Mathematics,
2013
Highland Community College
Philosophy Motivates Undergraduates In Mathematics, Dustin Wilson
ACMS Conference Proceedings 2013
A talk on how elective seminars on the philosophy of mathematics can inspire undergraduate students to pursue and persist in mathematics.
Mathematical Modeling Of The Regulatory T Cell Effects On Renal Cell Carcinoma Treatment,
2013
Harvey Mudd College
Mathematical Modeling Of The Regulatory T Cell Effects On Renal Cell Carcinoma Treatment, Lisette G. De Pillis, Trevor Caldwell '12, Elizabeth Sarapata '13, Heather Williams '12
All HMC Faculty Publications and Research
We present a mathematical model to study the effects of the regulatory T cells (Treg) on Renal Cell Carcinoma (RCC) treatment with sunitinib. The drug sunitinib inhibits the natural self-regulation of the immune system, allowing the effector components of the immune system to function for longer periods of time. This mathematical model builds upon our non-linear ODE model by de Pillis et al. (2009) [13] to incorporate sunitinib treatment, regulatory T cell dynamics, and RCC-specific parameters. The model also elucidates the roles of certain RCC-specific parameters in determining key differences between in silico patients whose immune profiles allowed them to …
B Cell Chronic Lymphocytic Leukemia - A Model With Immune Response,
2013
Tata Institute of Fundamental Research, Centre for Applicable Mathematics
B Cell Chronic Lymphocytic Leukemia - A Model With Immune Response, Seema Nanda, Lisette G. De Pillis, Ami E. Radunskaya
All HMC Faculty Publications and Research
B cell chronic lymphocytic leukemia (B-CLL) is known to have substantial clinical heterogeneity. There is no cure, but treatments allow for disease management. However, the wide range of clinical courses experienced by B-CLL patients makes prognosis and hence treatment a significant challenge. In an attempt to study disease progression across different patients via a unified yet flexible approach, we present a mathematical model of B-CLL with immune response, that can capture both rapid and slow disease progression. This model includes four different cell populations in the peripheral blood of humans: B-CLL cells, NK cells, cytotoxic T cells and helper T …
Forming The Analytical Society At Cambridge University,
2013
Gordon College
Forming The Analytical Society At Cambridge University, Richard Stout
ACMS Conference Proceedings 2013
The Analytical Society, an organization begun by students at Cambridge, was founded in 1812. Even though it was entirely student-led, the society was responsible for significant changes in the Cambridge mathematics curriculum and in the way mathematics was perceived in Britain throughout the nineteenth century. Its success was likely due to the outstanding students who formed the group, some of whom went on to become leaders in British science and mathematics for the next fifty years. In this paper we will briefly look at several of those who played important roles in forming and leading the society and we will …
The Unity Of Knowledge And The Faithfulness Of God: The Theology Of Mathematical Physicist John Polkinghorne,
2013
Marian University - Indianapolis
The Unity Of Knowledge And The Faithfulness Of God: The Theology Of Mathematical Physicist John Polkinghorne, Matt Delong
ACMS Conference Proceedings 2013
In this paper we will give a brief introduction to Polkinghorne's life and work. We will give an introduction to Polkinghorne's approach to philosophy and theology. We will introduce the two most significant influences on Polkinghorne's development as a theologian and philosopher of science. We will then give a necessarily telegraphic review of some of the topics addressed in Polkinghorne's theology, including his thoughts on science and religion, natural theology, evil, providence, prayer, resurrection, the soul and eschatology. We will then conclude with a few short examples of Polkinghorne's thoughts on mathematics.
Leading A Successful Missions Trip In Your Discipline,
2013
Taylor University
Leading A Successful Missions Trip In Your Discipline, Tom Nurkkala, Darci Nurkkala
ACMS Conference Proceedings 2013
The global missions community goes wanting for skilled workers in almost every discipline. However, even students at a Christian institution that emphasizes global engagement remain largely unaware of the impact they can make in missions by leveraging their own academic specialty. In this paper, we draw on our experience leading discipline-specific missions trips as a means to encourage students to reframe their thinking about personal involvement in missions. We discuss the need for students to experience missions firsthand, and the student outcomes we have observed in intercultural awareness and spiritual formation. A key student outcome is an increased willingness to …
