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Articles 1 - 30 of 102
Full-Text Articles in Physical Sciences and Mathematics
Combinatorial Proofs Of Fibonomial Identities, Arthur Benjamin, Elizabeth Reiland
Combinatorial Proofs Of Fibonomial Identities, Arthur Benjamin, Elizabeth Reiland
All HMC Faculty Publications and Research
We provide a list of simple looking identities that are still in need of combinatorial proof.
Review: Crystal Bases Of Q-Deformed Kac Modules Over The Quantum Superalgebras Uq(Gl(Mln)), Gizem Karaali
Review: Crystal Bases Of Q-Deformed Kac Modules Over The Quantum Superalgebras Uq(Gl(Mln)), Gizem Karaali
Pomona Faculty Publications and Research
No abstract provided.
Op-Ed: Solve This Math Problem: The Gender Gap, Francis Su
Op-Ed: Solve This Math Problem: The Gender Gap, Francis Su
All HMC Faculty Publications and Research
Women may not face such blatant impediments to doing math and science today. But Mirzakhani's achievement aside, we are still a long way from adequately recognizing the outstanding work of women.
Math Talk: Preparing Your Conference Presentation, Gizem Karaali
Math Talk: Preparing Your Conference Presentation, Gizem Karaali
Pomona Faculty Publications and Research
If you are a typical reader of this blog, then you recently wrapped up your finals week and then dutifully made a summer plan. And then came the summer. Your plan may have involved working on a manuscript, preparing for a qualifying exam or a new course coming up in the fall, drafting a grant proposal, learning a new language (human or machine), eating kale in four different forms, and perhaps some fun times under the sun. Some, like me, also made plans to travel to conferences and give talks. Gearing up to get ready for my first conference of …
Exponential Decay Of Reconstruction Error From Binary Measurements Of Sparse Signals, Richard Baraniuk, Simon Foucart, Deanna Needell, Yaniv Plan, Mary Wootters
Exponential Decay Of Reconstruction Error From Binary Measurements Of Sparse Signals, Richard Baraniuk, Simon Foucart, Deanna Needell, Yaniv Plan, Mary Wootters
CMC Faculty Publications and Research
Binary measurements arise naturally in a variety of statistical and engineering applications. They may be inherent to the problem—e.g., in determining the relationship between genetics and the presence or absence of a disease—or they may be a result of extreme quantization. A recent influx of literature has suggested that using prior signal information can greatly improve the ability to reconstruct a signal from binary measurements. This is exemplified by onebit compressed sensing, which takes the compressed sensing model but assumes that only the sign of each measurement is retained. It has recently been shown that the number of one-bit measurements …
Four Quotient Set Gems, Stephan Ramon Garcia, Michael Someck '14, Bob Lutz '13, Bryan Brown '15, Michael Dairyko '13
Four Quotient Set Gems, Stephan Ramon Garcia, Michael Someck '14, Bob Lutz '13, Bryan Brown '15, Michael Dairyko '13
Pomona Faculty Publications and Research
Our aim in this note is to present four remarkable facts about quotient sets. These observations seem to have been overlooked by the MONTHLY, despite its intense coverage of quotient sets over the years.
Near Oracle Performance And Block Analysis Of Signal Space Greedy Methods, Raja Giryes, Deanna Needell
Near Oracle Performance And Block Analysis Of Signal Space Greedy Methods, Raja Giryes, Deanna Needell
CMC Faculty Publications and Research
Compressive sampling (CoSa) is a new methodology which demonstrates that sparse signals can be recovered from a small number of linear measurements. Greedy algorithms like CoSaMP have been designed for this recovery, and variants of these methods have been adapted to the case where sparsity is with respect to some arbitrary dictionary rather than an orthonormal basis. In this work we present an analysis of the so-called Signal Space CoSaMP method when the measurements are corrupted with mean-zero white Gaussian noise. We establish near-oracle performance for recovery of signals sparse in some arbitrary dictionary. In addition, we analyze the block …
Jhm Contents Word Puzzle, Robert Haas
Jhm Contents Word Puzzle, Robert Haas
Journal of Humanistic Mathematics
This is a word-search puzzle based on the contents page of the previous (Volume 4 Issue 1-January 2014) issue of the Journal of Humanistic Mathematics.
The Physicist's Basement, Nora Culik
The Physicist's Basement, Nora Culik
Journal of Humanistic Mathematics
No abstract provided.
Jeffery's Equation, Sandra J. Stein
Jeffery's Equation, Sandra J. Stein
Journal of Humanistic Mathematics
No abstract provided.
The Discipline Of History And The “Modern Consensus In The Historiography Of Mathematics”, Michael N. Fried
The Discipline Of History And The “Modern Consensus In The Historiography Of Mathematics”, Michael N. Fried
Journal of Humanistic Mathematics
Teachers and students of mathematics often view history of mathematics as just mathematics as they know it, but in another form. This view is based on a misunderstanding of the nature of history of mathematics and the kind of knowledge it attempts to acquire. Unfortunately, it can also lead to a deep sense of disappointment with the history of mathematics itself, and, ultimately, a misunderstanding of the historical nature of mathematics. This kind of misunderstanding and the disappointment following from it--both raised to the level of resentment--run through the paper "A Critique of the Modern Consensus in the Historiography of …
A Critique Of The Modern Consensus In The Historiography Of Mathematics, Viktor Blåsjö
A Critique Of The Modern Consensus In The Historiography Of Mathematics, Viktor Blåsjö
Journal of Humanistic Mathematics
The history of mathematics is nowadays practiced primarily by professional historians rather than mathematicians, as was the norm a few decades ago. There is a strong consensus among these historians that the old-fashioned style of history is “obsolete,” and that “the gains in historical understanding are incomparably greater” in the more “historically sensitive” works of today. I maintain that this self-congratulatory attitude is ill-founded, and that the alleged superiority of modern historiographical standards ultimately rests on a dubious redefinition of the purpose of history rather than intrinsic merit.
How Do I Love Thee? Let Me Count The Ways For Syllabic Variation In Certain Poetic Forms, Mike Pinter
How Do I Love Thee? Let Me Count The Ways For Syllabic Variation In Certain Poetic Forms, Mike Pinter
Journal of Humanistic Mathematics
The Dekaaz poetic form, similar to haiku with its constrained syllable counts per line, invites a connection between poetry and mathematics. Determining the number of possible Dekaaz variations leads to some interesting counting observations. We discuss two different ways to count the number of possible Dekaaz variations, one using a binary framework and the other approaching the count as an occupancy problem. The counting methods described are generalized to also count variations of other poetic forms with syllable counts specified, including haiku. We include Dekaaz examples and suggest a method that can be used to randomly generate a Dekaaz variation.
Fields In Math And Farming, Susan D'Agostino
Fields In Math And Farming, Susan D'Agostino
Journal of Humanistic Mathematics
A young woman’s search for a a contemplative, insightful experience leads her from farming to mathematics.
Being Reasonable: Using Brainteasers To Develop Reasoning Ability In Humanistic Mathematics Courses, Gary Stogsdill
Being Reasonable: Using Brainteasers To Develop Reasoning Ability In Humanistic Mathematics Courses, Gary Stogsdill
Journal of Humanistic Mathematics
Developing reasoning ability is often cited as one of the principal justifications of a mathematics requirement for liberal arts undergraduates. Humanistic math courses have become recognized as a paradigm for liberal arts mathematics, but such courses may not provide the opportunity to develop reasoning ability. The author describes his procedure for using brainteasers to promote reasoning in a humanistic math course for liberal arts undergraduates.
Joining ``The Mathematician's Delirium To The Poet's Logic'': Mathematical Literature And Literary Mathematics, Rita Capezzi, Christine Kinsey
Joining ``The Mathematician's Delirium To The Poet's Logic'': Mathematical Literature And Literary Mathematics, Rita Capezzi, Christine Kinsey
Journal of Humanistic Mathematics
This paper describes our team-taught interdisciplinary mathematics and literature course, Mathematical Literature and Literary Mathematics, which invites students to consider Raymond Queneau's challenge: "Why shouldn't one demand a certain effort on the reader's part? Everything is always explained to him. He must eventually tire of being treated with such contempt.'' We study works by Berge, Borges, Calvino, Perec, Queneau, Robbe-Grillet and Stoppard, among others. From a literary critical perspective, the course highlights the play of language rather than the primacy of meaning. We choose texts where mathematical concepts are subjects or structuring elements of the literature, and ideally both. …
Some Effects Of The Human Genome Project On The Erdős Collaboration Graph, Chris Fields
Some Effects Of The Human Genome Project On The Erdős Collaboration Graph, Chris Fields
Journal of Humanistic Mathematics
The Human Genome Project introduced large-scale collaborations involving dozens to hundreds of scientists into biology. It also created a pressing need to solve discrete mathematics problems involving tens of thousands of elements. In this paper, we use minimal path lengths in the Erdős Collaboration Graph between prominent individual researchers as a measure of the distance between disciplines, and we show that the Human Genome Project brought laboratory biology as a whole closer to mathematics. We also define a novel graph reduction method and a metric that emphasizes the robustness of collaborative connections between researchers; these can facilitate the analysis of …
Linear Convergence Of Stochastic Iterative Greedy Algorithms With Sparse Constraints, Nam Nguyen, Deanna Needell, Tina Woolf
Linear Convergence Of Stochastic Iterative Greedy Algorithms With Sparse Constraints, Nam Nguyen, Deanna Needell, Tina Woolf
CMC Faculty Publications and Research
Motivated by recent work on stochastic gradient descent methods, we develop two stochastic variants of greedy algorithms for possibly non-convex optimization problems with sparsity constraints. We prove linear convergence in expectation to the solution within a specified tolerance. This generalized framework applies to problems such as sparse signal recovery in compressed sensing, low-rank matrix recovery, and co-variance matrix estimation, giving methods with provable convergence guarantees that often outperform their deterministic counterparts. We also analyze the settings where gradients and projections can only be computed approximately, and prove the methods are robust to these approximations. We include many numerical experiments which …
Lattices From Elliptic Curves Over Finite Fields, Lenny Fukshansky, Hiren Maharaj
Lattices From Elliptic Curves Over Finite Fields, Lenny Fukshansky, Hiren Maharaj
CMC Faculty Publications and Research
In their well known book Tsfasman and Vladut introduced a construction of a family of function field lattices from algebraic curves over finite fields, which have asymptotically good packing density in high dimensions. In this paper we study geometric properties of lattices from this construction applied to elliptic curves. In particular, we determine the generating sets, conditions for well-roundedness and a formula for the number of minimal vectors. We also prove a bound on the covering radii of these lattices, which improves on the standard inequalities.
Block Kaczmarz Method With Inequalities, Jonathan Briskman, Deanna Needell
Block Kaczmarz Method With Inequalities, Jonathan Briskman, Deanna Needell
CMC Faculty Publications and Research
The randomized Kaczmarz method is an iterative algorithm that solves overdetermined systems of linear equations. Recently, the method was extended to systems of equalities and inequalities by Leventhal and Lewis. Even more recently, Needell and Tropp provided an analysis of a block version of the method for systems of linear equations. This paper considers the use of a block type method for systems of mixed equalities and inequalities, bridging these two bodies of work. We show that utilizing a matrix paving over the equalities of the system can lead to significantly improved convergence, and prove a linear convergence rate as …
Energy Driven Pattern Formation In Planar Dipole-Dipole Systems In The Presence Of Weak Noise, Jaron P. Kent-Dobias '14, Andrew Bernoff
Energy Driven Pattern Formation In Planar Dipole-Dipole Systems In The Presence Of Weak Noise, Jaron P. Kent-Dobias '14, Andrew Bernoff
All HMC Faculty Publications and Research
We study pattern formation in planar fluid systems driven by intermolecular cohesion (which manifests as a line tension) and dipole-dipole repulsion which are observed in physical systems including ferrofluids in Hele-Shaw cells and Langmuir layers. When the dipolar repulsion is sufficiently strong, domains undergo forked branching reminiscent of viscous fingering. A known difficulty with these models is that the energy associated with dipole-dipole interactions is singular at small distances. Following previous work, we demonstrate how to ameliorate this singularity and show that in the macroscopic limit, only the relative scale of the microscopic details of a system are relevant, and …
Two-Part Reconstruction With Noisy-Sudocodes, Yanting Ma, Dror Baron, Deanna Needell
Two-Part Reconstruction With Noisy-Sudocodes, Yanting Ma, Dror Baron, Deanna Needell
CMC Faculty Publications and Research
We develop a two-part reconstruction framework for signal recovery in compressed sensing (CS), where a fast algorithm is applied to provide partial recovery in Part 1, and a CS algorithm is applied to complete the residual problem in Part 2. Partitioning the reconstruction process into two complementary parts provides a natural trade-off between runtime and reconstruction quality. To exploit the advantages of the two-part framework, we propose a Noisy-Sudocodes algorithm that performs two-part reconstruction of sparse signals in the presence of measurement noise. Specifically, we design a fast algorithm for Part 1 of Noisy-Sudocodes that identifies the zero coefficients of …
Why You Need A Summer Plan, Gizem Karaali
Why You Need A Summer Plan, Gizem Karaali
Pomona Faculty Publications and Research
In the last decade, for many times, I have tasted first-hand the end-of-summer blues I described above. I have spent many early spring months dreaming of all that I would be doing when the summer arrives, only to realize that it was already September and I had not much to show for for the months in between. I have also observed many of my peers going through similar things, and I just assumed for years that this was how it had to be. But then some time in the middle of the tenure track, I decided to try approaching my …
Biodynamic Agriculture: A Valuable Alternative To The Industrial Farming System, Eden K. Olsen
Biodynamic Agriculture: A Valuable Alternative To The Industrial Farming System, Eden K. Olsen
Scripps Senior Theses
Since the Scientific and Industrial revolutions, advancing technologies and cutting-edge science have enabled our society to continually promote a growing global economy. Industrial growth has increasingly become a top priority for most governments, notably in the agricultural realm. The advances towards agricultural industrialization began in the 17th century and escalated during the Green Revolution, which examined the possibility of using synthetic fertilizers and mechanization in farming to decrease labor and improve yields. Although seen as economically beneficial, the shift from an agrarian lifestyle to industrial farming has created an ecological, economic, and ideological crisis to our modern world. This …
The Reclamation Of Public Parks: An Analysis Of Environmental Justice In Los Angeles, Allison Rigby
The Reclamation Of Public Parks: An Analysis Of Environmental Justice In Los Angeles, Allison Rigby
Scripps Senior Theses
People who live in cities are far more likely to suffer the physical and psychological effects of urban environments--high noise levels, automobile emissions, toxic industrial waste, crowded living conditions, and a general scarcity of open space. Combating these issues, public parks do more than provide recreational space. They are fundamental to any efforts focusing on urban revitalization, social justice, and sustainability. In downtown Los Angeles, public parks are rare, especially in low-income communities. Several new public parks have reclaimed abandoned land, unwelcoming spaces, and the City’s brownfields. After years of intense private use and neglect, spent land has been reinvigorated …
Musical Missteps: The Severity Of The Sophomore Slump In The Music Industry, Shane M. Zackery
Musical Missteps: The Severity Of The Sophomore Slump In The Music Industry, Shane M. Zackery
Scripps Senior Theses
This study looks at alternative models of follow-up album success in order to determine if there is a relationship between the decrease in Metascore ratings (assigned by Metacritic.com) between the first and second album for a musician or band and the 1) music genre or 2) the number of years between the first and second album release. The results support the dominant thought, which suggests that neither belonging to a certain genre of music nor waiting more or less time to drop the second album makes an artist more susceptible to the Sophomore Slump. This finding is important because it …
The Pacific Crest Trail: A History Of America’S Relationship With Western Wilderness, Jenn Livermore
The Pacific Crest Trail: A History Of America’S Relationship With Western Wilderness, Jenn Livermore
Scripps Senior Theses
The Pacific Crest Trail has become increasingly popular since Clinton Clarke first envisioned such a trail in the 1930’s. By comparing the original motives and experience of the trail to the realities of the trail today, the trail’s fluid narrative becomes apparent. While this narrative is ever changing, over the course of the trail’s history one theme has remained constant – a notably problematic relationship with wilderness rooted in an exaltation of the sublime and post-frontier ideals. This thesis focuses on how the Pacific Crest Trail’s development over the past eighty years has created an experience that, on the surface, …
Improving Image Clustering Using Sparse Text And The Wisdom Of The Crowds, Anna Ma, Arjuna Flenner, Deanna Needell, Allon G. Percus
Improving Image Clustering Using Sparse Text And The Wisdom Of The Crowds, Anna Ma, Arjuna Flenner, Deanna Needell, Allon G. Percus
CMC Faculty Publications and Research
We propose a method to improve image clustering using sparse text and the wisdom of the crowds. In particular, we present a method to fuse two different kinds of document features, image and text features, and use a common dictionary or “wisdom of the crowds” as the connection between the two different kinds of documents. With the proposed fusion matrix, we use topic modeling via non-negative matrix factorization to cluster documents.
Review: Truncated Toeplitz Operators Of Finite Rank, Stephan Ramon Garcia
Review: Truncated Toeplitz Operators Of Finite Rank, Stephan Ramon Garcia
Pomona Faculty Publications and Research
No abstract provided.
Spreading The Char: The Importance Of Local Compatibility In The Diffusion Of Biochar Systems To The Smallholder Agriculture Community Context, Laura C. V. Munoz
Spreading The Char: The Importance Of Local Compatibility In The Diffusion Of Biochar Systems To The Smallholder Agriculture Community Context, Laura C. V. Munoz
Pomona Senior Theses
This thesis enters the context of smallholder agriculture communities in the developing world. It explores the potentials of biochar and what biochar systems could bring to the smallholder communities while simultaneously bringing environmental benefits. It then acknowledges the challenges of diffusion –the spreading of an unfamiliar innovation. It seeks to answer the question of what will make diffusion of biochar systems more successful in the smallholder context, fixating on the characteristic of compatibility as well as the role local community members can play in making a new biochar system more visible to the rest of the communities.