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Articles 1 - 30 of 69
Full-Text Articles in Physical Sciences and Mathematics
Newton’S Third Law In Karmic Warfare, Kazmier Maślanka
Newton’S Third Law In Karmic Warfare, Kazmier Maślanka
The STEAM Journal
A work entitled "Newton's Third Law in Karmic Warfare" is a mathematical visual poem which is a perfect example of a technique, that I call The Paradigm Poem. This piece makes a direct connection with the concept of karma and Newton’s Third Law of motion. I will introduce the concept of “The Mathematical Paradigm Poem” to illuminate an example of how metaphor is used in mathematical visual poetry. I will also discuss much of the process in making this aesthetic expression.
Race, Space, And The Conflict Inside Us, Francis Su
Race, Space, And The Conflict Inside Us, Francis Su
All HMC Faculty Publications and Research
Talking about race is hard. Our nation is wrestling with some open wounds about race. These sores have been around a while, but they have been brought to light recently by technology, politics, and an increasingly diverse population. And regardless of the outcome of the U.S. presidential election, we will all need to work at healing these sores, not just in our personal lives, but in our classrooms and in our profession.
A Sampling Kaczmarz-Motzkin Algorithm For Linear Feasibility, Jesus A. De Loera, Jamie Haddock, Deanna Needell
A Sampling Kaczmarz-Motzkin Algorithm For Linear Feasibility, Jesus A. De Loera, Jamie Haddock, Deanna Needell
CMC Faculty Publications and Research
We combine two iterative algorithms for solving large-scale systems of linear inequalities, the relaxation method of Agmon, Motzkin et al. and the randomized Kaczmarz method. We obtain a family of algorithms that generalize and extend both projection-based techniques. We prove several convergence results, and our computational experiments show our algorithms often outperform the original methods.
Biquasiles And Dual Graph Diagrams, Deanna Needell, Sam Nelson
Biquasiles And Dual Graph Diagrams, Deanna Needell, Sam Nelson
CMC Faculty Publications and Research
We introduce dual graph diagrams representing oriented knots and links. We use these combinatorial structures to define corresponding algebraic structures we call biquasiles whose axioms are motivated by dual graph Reidemeister moves, generalizing the Dehn presentation of the knot group analogously to the way quandles and biquandles generalize the Wirtinger presentation. We use these structures to define invariants of oriented knots and links. In particular, we identify an example of a finite biquasile whose counting invariant distinguishes the chiral knot 9-32 from its mirror image, demonstrating that biquasile counting invariants are distinct from biquandle counting invariants.
Batched Stochastic Gradient Descent With Weighted Sampling, Deanna Needell, Rachel Ward
Batched Stochastic Gradient Descent With Weighted Sampling, Deanna Needell, Rachel Ward
CMC Faculty Publications and Research
We analyze a batched variant of Stochastic Gradient Descent (SGD) with weighted sampling distribution for smooth and non-smooth objective functions. We show that by distributing the batches computationally, a significant speedup in the convergence rate is provably possible compared to either batched sampling or weighted sampling alone. We propose several computationally efficient schemes to approximate the optimal weights, and compute proposed sampling distributions explicitly for the least squares and hinge loss problems. We show both analytically and experimentally that substantial gains can be obtained
Tolerant Compressed Sensing With Partially Coherent Sensing Matrices, Tobias Birnbaum, Yonina C. Eldar, Deanna Needell
Tolerant Compressed Sensing With Partially Coherent Sensing Matrices, Tobias Birnbaum, Yonina C. Eldar, Deanna Needell
CMC Faculty Publications and Research
We consider compressed sensing (CS) using partially coherent sensing matrices. Most of CS theory to date is focused on incoherent sensing, that is, columns from the sensing matrix are highly uncorrelated. However, sensing systems with naturally occurring correlations arise in many applications, such as signal detection, motion detection and radar. Moreover, in these applications it is often not necessary to know the support of the signal exactly, but instead small errors in the support and signal are tolerable. In this paper, we focus on d-tolerant recovery, in which support set reconstructions are considered accurate when their locations match the true …
A Practical Study Of Longitudinal Reference Based Compressed Sensing For Mri, Samuel Birns, Bohyun Kim, Stephanie Ku, Kevin Stangl, Deanna Needell
A Practical Study Of Longitudinal Reference Based Compressed Sensing For Mri, Samuel Birns, Bohyun Kim, Stephanie Ku, Kevin Stangl, Deanna Needell
CMC Faculty Publications and Research
Compressed sensing (CS) is a new signal acquisition paradigm that enables the reconstruction of signals and images from a low number of samples. A particularly exciting application of CS is Magnetic Resonance Imaging (MRI), where CS significantly speeds up scan time by requiring far fewer measurements than standard MRI techniques. Such a reduction in sampling time leads to less power consumption, less need for patient sedation, and more accurate images. This accuracy increase is especially pronounced in pediatric MRI where patients have trouble being still for long scan periods. Although such gains are already significant, even further improvements can be …
Freedom Through Inquiry, Francis Su
Freedom Through Inquiry, Francis Su
All HMC Faculty Publications and Research
I delivered this speech at the Inquiry‐Based Learning Forum & 19th Annual Legacy of R.L. Moore Conference on August 4, 2016. It is partly an homage to an influential teacher, partly an excuse to articulate what makes some styles of teaching so effective, and partly an excuse to talk about difficult issues facing our nation and our classrooms today.
Teaching Differential Equations Through A Modeling First Approach, Brian Winkel
Teaching Differential Equations Through A Modeling First Approach, Brian Winkel
Journal of Humanistic Mathematics
No abstract provided.
Menger Sponge, E Laura Golberg
Menger Sponge, E Laura Golberg
Journal of Humanistic Mathematics
No abstract provided.
Quantitative Literacy, Thomas L. Moore
Quantitative Literacy, Thomas L. Moore
Journal of Humanistic Mathematics
No abstract provided.
The Greatest Integer Function, Alanna Rae
The Greatest Integer Function, Alanna Rae
Journal of Humanistic Mathematics
No abstract provided.
Teaching The Quandary Of Statistical Jurisprudence: A Review-Essay On Math On Trial By Schneps And Colmez, Noah Giansiracusa
Teaching The Quandary Of Statistical Jurisprudence: A Review-Essay On Math On Trial By Schneps And Colmez, Noah Giansiracusa
Journal of Humanistic Mathematics
This review-essay on the mother-and-daughter collaboration Math on Trial stems from my recent experience using this book as the basis for a college freshman seminar on the interactions between math and law. I discuss the strengths and weaknesses of this book as an accessible introduction to this enigmatic yet deeply important topic. For those considering teaching from this text (a highly recommended endeavor) I offer some curricular suggestions.
Book Review: A New Index For Predicting Catastrophes: Poems By Madhur Anand, Joanne Growney
Book Review: A New Index For Predicting Catastrophes: Poems By Madhur Anand, Joanne Growney
Journal of Humanistic Mathematics
This review explores Madhur Anand’s recent poetry collection from several points of view. One involves consideration of mathematical concepts and imagery in her poems. A second viewpoint takes into consideration Anand’s own field – she is a professor of environmental science with a focus on ecology. A third view considers the poems as art objects – words building pictures that offer to readers both insights and pleasures.
Fuzzy Logic In Health Care Settings: Moral Math For Value-Laden Choices, Sarah Voss
Fuzzy Logic In Health Care Settings: Moral Math For Value-Laden Choices, Sarah Voss
Journal of Humanistic Mathematics
This essay is intended as an example of “moral math”, i.e., ideas culled from mathematics which can positively impact social behavior. Specifically, it combines fuzzy logic with the ethical decisions which hospital staff and others are sometimes forced to make about health care (e.g., euthanasia issues following Hurricane Katrina). The assumption is that such decisions involve value-laden choices which lend themselves to “fuzzy” or “smart” protocols. The article discusses the history of fuzzy logic – what it is, how it is used, and how it might be even better-used as a support basis for making difficult choices …
Stop Ruining Math! Reasons And Remedies For The Maladies Of Mathematics Education, Rachel M. Steinig
Stop Ruining Math! Reasons And Remedies For The Maladies Of Mathematics Education, Rachel M. Steinig
Journal of Humanistic Mathematics
Did you love math as a kid? Or was it ruined for you? Sadly, many people have had math ruined for them for various reasons. Some might say that it was because of not understanding what was going on, being bored in class, parental or societal pressure to achieve in math, not seeing a point in learning math, wrong amount of homework, grades, curriculum, physical concerns, mean teachers, or any number of things. This article delves into the many common reasons why math is ruined for so many kids, and offers solutions so that math can be enjoyable for everyone. …
Al-Khwarizmı And The Hermeneutic Circle: Reflections On A Trip To Samarkand, Asuman G. Aksoy
Al-Khwarizmı And The Hermeneutic Circle: Reflections On A Trip To Samarkand, Asuman G. Aksoy
Journal of Humanistic Mathematics
In this paper we discuss al-Khwarzmi's life and aspects of his work and suggest a possible hermeneutic avenue into his contribution to mathematics.
Patterns Formed By Coins, Andrey M. Mishchenko
Patterns Formed By Coins, Andrey M. Mishchenko
Journal of Humanistic Mathematics
This article is a gentle introduction to the mathematical area known as circle packing, the study of the kinds of patterns that can be formed by configurations of non- overlapping circles. The first half of the article is an exposition of the two most important facts about circle packings, (1) that essentially whatever pattern we ask for, we may always arrange circles in that pattern, and (2) that under simple conditions on the pattern, there is an essentially unique arrangement of circles in that pattern. In the second half of the article, we consider related questions, but where we …
Combinatorics Of The Sonnet, Terry S. Griggs
Combinatorics Of The Sonnet, Terry S. Griggs
Journal of Humanistic Mathematics
Using a definition of a sonnet, the number of basic rhyming schemes is enumerated. This is then used to discuss the 86 sonnets which appear in John Clare's The Rural Muse.
Connections, Mark Huber, Gizem Karaali
Connections, Mark Huber, Gizem Karaali
Journal of Humanistic Mathematics
No abstract provided.
The Problems Of Contemporariness And Voice: Review Of Literacy & Mathematics: A Contemporary Approach To Quantitative Literacy By Jay P. Abramson And Matthew A. Isom (2005), Gizem Karaali
Pomona Faculty Publications and Research
The book under review covers the traditional content of a typical mathematical literacy text. After a brief overview of the book contents, the review then focuses on two specific challenges that QL textbooks have to meet: the timeliness of the contexts used and the subjective author voice that inevitably colors any contextualized discussion. Both issues noticeably arise in the text reviewed. Nonetheless instructors may find it a helpful resource.
One-Bit Compressive Sensing Of Dictionary-Sparse Signals, Richard Baraniuk, Simon Foucart, Deanna Needell, Yaniv Plan, Mary Wootters
One-Bit Compressive Sensing Of Dictionary-Sparse Signals, Richard Baraniuk, Simon Foucart, Deanna Needell, Yaniv Plan, Mary Wootters
CMC Faculty Publications and Research
One-bit compressive sensing has extended the scope of sparse recovery by showing that sparse signals can be accurately reconstructed even when their linear measurements are subject to the extreme quantization scenario of binary samples—only the sign of each linear measurement is maintained. Existing results in one-bit compressive sensing rely on the assumption that the signals of interest are sparse in some fixed orthonormal basis. However, in most practical applications, signals are sparse with respect to an overcomplete dictionary, rather than a basis. There has already been a surge of activity to obtain recovery guarantees under such a generalized sparsity model …
Optimizing Quantization For Lasso Recovery, Xiaoyi Gu, Shenyinying Tu, Hao-Jun Michael Shi, Mindy Case, Deanna Needell, Yaniv Plan
Optimizing Quantization For Lasso Recovery, Xiaoyi Gu, Shenyinying Tu, Hao-Jun Michael Shi, Mindy Case, Deanna Needell, Yaniv Plan
CMC Faculty Publications and Research
This letter is focused on quantized Compressed Sensing, assuming that Lasso is used for signal estimation. Leveraging recent work, we provide a framework to optimize the quantization function and show that the recovered signal converges to the actual signal at a quadratic rate as a function of the quantization level. We show that when the number of observations is high, this method of quantization gives a significantly better recovery rate than standard Lloyd-Max quantization. We support our theoretical analysis with numerical simulations.
Math Education: A Messy Problem, Gizem Karaali
Math Education: A Messy Problem, Gizem Karaali
Pomona Faculty Publications and Research
The current state of math education in America is certainly not ideal, writes Gizem Karaali, but mathematicians, researchers, policy makers and others are working on it -- and it is definitely a problem worth working on.
Collaboration And Creativity In Southern Califonia: An Offering, Gizem Karaali, Ami Radunskaya
Collaboration And Creativity In Southern Califonia: An Offering, Gizem Karaali, Ami Radunskaya
Pomona Faculty Publications and Research
WiMSoCal (Women in Math in Southern California) is a regional conference in its ninth incarnation. The conference is the result of the efforts of Professor Cymra Haskell (USC) to create a supportive local community for women mathematicians. At our first meeting in 2007, a confluence of Ami’s EDGE regional cluster and Cymra’s WISE group at USC, we socialized, got to know each other and brainstormed about what we, as a group, would like to see happen. It was clear that our younger colleagues wanted to meet as mathematicians, sharing intellectual ideas as well as anecdotes from the trenches.
The Power Of Two: Two Tips For Mathematicians, Gizem Karaali
The Power Of Two: Two Tips For Mathematicians, Gizem Karaali
Pomona Faculty Publications and Research
This post is about two great tips involving the number 2 that I learned along the way. They will perhaps not double your happiness or fortune, but I promise you that you will not regret it if you do decide to take them along for the ride.
Review: On Complex Symmetric Toeplitz Operators, Stephan Ramon Garcia
Review: On Complex Symmetric Toeplitz Operators, Stephan Ramon Garcia
Pomona Faculty Publications and Research
No abstract provided.
Multi-Year Optimization Of Malaria Intervention: A Mathematical Model, Harry J. Dudley, Abhishek Goenka '15, Cesar J. Orellana '17, Susan E. Martonosi
Multi-Year Optimization Of Malaria Intervention: A Mathematical Model, Harry J. Dudley, Abhishek Goenka '15, Cesar J. Orellana '17, Susan E. Martonosi
All HMC Faculty Publications and Research
Malaria is a mosquito-borne, lethal disease that affects millions and kills hundreds of thousands of people each year, mostly children. There is an increasing need for models of malaria control. In this paper, a model is developed for allocating malaria interventions across geographic regions and time, subject to budget constraints, with the aim of minimizing the number of person-days of malaria infection.
Review: On Rank One Perturbations Of Complex Symmetric Operators, Stephan Ramon Garcia
Review: On Rank One Perturbations Of Complex Symmetric Operators, Stephan Ramon Garcia
Pomona Faculty Publications and Research
No abstract provided.