Physical Sciences and Mathematics Commons^™

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

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

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

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

The Pinchot Wire: Private Cash, Public Lands - Why The Katahdin Woods And Waters National Monument Matters, Char Miller

Pomona Faculty Publications and Research

Here’s how President Obama celebrated the National Park Service’s 100th birthday: with the stroke of his pen, he established the Katahdin Woods and Waters National Monument in Maine, one of the most innovative initiatives in U.S. environmental history. That’s because the 87,500-acre park, which encompasses some of the Pine Tree State’s most remarkable forests and waterways, is a gift of the Quimby family and comes with a $40 million endowment, a private-public partnership without parallel.

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

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

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.

Embers, Char Miller

Pomona Faculty Publications and Research

After living in Southern California for nine years, I should be used to fire season—and the fact that there is something called fire season—but I’m not.

My wife and I moved to the Southland in late summer 2007, and within the month we saw some of the region’s most horrific firestorms consume vast stretches of chaparral-cloaked foothills, deep canyons filled with alder and oak and, at higher elevations, thick stands of pine and cedar.

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 View: Fire Fuels Regeneration In Eastern Sierra, Char Miller

Pomona Faculty Publications and Research

Sometimes it’s the small things that can best tell big stories.

Like the Marina Fire, which currently has burned a modest 800 acres to the north of Lee Vining, threatened but did not burn any structures, and whose greatest disruption has been periodically to shut down US 395. It hardly seems worth much attention.

Dead Trees Don’T Mean Catastrophe For California, Char Miller

Pomona Faculty Publications and Research

Nature knows what it’s doing. You’d never know that, though, from the panicked reaction to news that 66 million trees in California have died since 2005, including 26 million said to have perished just in the last few months.

The Erskine Fire And Public-Lands Management In The American West, Char Miller

Pomona Faculty Publications and Research

The Erskine Fire is big, fast and dangerous. Its power is evident in the tragic loss of life, the incineration of an estimated 150 structures and its rapid growth — more than 36,000 acres burned in its first 30 hours.

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 …

Fire Inevitable, Despite Attempts To Tame Chaparral, Char Miller

Pomona Faculty Publications and Research

You didn’t need to fly into Ontario International Airport this past week to know that Southern California’s fire season had begun. But the view from 10,000 feet offered a unique perspective on how wildfires impact the region.

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.

Bioswales For Stormwater Remediation And Infiltration: Assessing Regulatory Climate And Quantifying Filtration Capacity Of A Claremont Bioswale, Skyler Lewis, Boyu Liu, Paul Picciano, Liana Solis, Char Miller

Environmental Analysis Program Senior Projects

Watershed management is critical in ensuring a sustainable water supply. This project is designed to assess the impact of bioswales in the context of Southern California’s climate. The patterns of droughts and floods make these green infrastructure appealing as they offer potential to boost water quality and regenerate local aquifers, while reducing the area of impermeable surfaces in our urban landscape. As bioswales have not been commonly incorporated into infrastructure development, our project focuses on a relatively new bioswale, added in 2012 and located on Pomona College’s campus, to serve as our case study in determining the viability of bioswales …

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.

Rethinking La's Nature Through German Eyes, Char Miller

Pomona Faculty Publications and Research

Los Angeles might be more than 5700 miles from Berlin as a crow (or Luftansa) flies, but German culture—and most notably its varied perceptions of nature—have strongly influenced how those living in the Southland experience their environs.

Oft in the negative, to judge from the enduring legacy of Bertold Brecht’s sharp commentary about the City of Angeles in which he sheltered during the ravages of World War II. “They have nature here,” he jotted down in his diary in August 1941, and as “everything is so artificial, they even have an exaggerated feeling for nature, which becomes alienated.”

Rethinking: Wind, Wende, Wandel, Friederike Von Schwerin-High

Pomona Faculty Publications and Research

No abstract provided.

Umdenken: Von Der Natur Lernen (Rethinking: Learning From Nature): Some Personal Thoughts On The Goethe Institute Traveling Exhibition, Hans J. Rindisbacher

Pomona Faculty Publications and Research

No abstract provided.

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

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

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

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

Pomona Faculty Publications and Research

No abstract provided.

Review: A C*-Algebra Approach To Complex Symmetric Operators, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.

Simulating Surfactant Spreading: Impact Of A Physically Motivated Equation Of State, Dina Sinclair '17, Rachel Levy, Karen E. Daniels

All HMC Faculty Publications and Research

For more than two decades, a single model for the spreading of a surfactant-driven thin liquid film has dominated the applied mathematics literature on the subject. Recently, through the use of fluorescently-tagged lipids, it has become possible to make direct, quantitative comparisons between experiments and models. These comparisons have revealed two important discrepancies between simulations and experiments: the spatial distribution of the surfactant layer, and the timescale over which spreading occurs. In this paper, we present numerical simulations that demonstrate the impact of the particular choice of the equation of state (EoS) relating the surfactant concentration to the surface tension. …

Malheur Occupation In Oregon: Whose Land Is It Really?, Char Miller

Pomona Faculty Publications and Research

The Malheur National Wildlife Refuge, a 187,757-acre haven for greater sandhill cranes and other native birds in eastern Oregon, is usually a pretty peaceful place. But its calm was shattered on Saturday, January 2 when Ammon Bundy and a group of armed men broke into and occupied a number of federal buildings on the refuge, vowing to fight should the government try to arrest them. Their insurrectionary goal appears to be, simply put, to destroy the national system of public lands – our forests, parks and refuges – that was developed in the late 19th century to conserve these …

Review: Transitivity And Bundle Shifts, Stephan Ramon Garcia

Pomona Faculty Publications and Research

No abstract provided.