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A Model of Relative Thinking
No full textFixed differences loom smaller when compared to large differences. We propose a model of relative thinking where a person weighs a given change along a consumption dimension by less when it is compared to bigger changes along that dimension. In deterministic settings, the model predicts context effects such as the attraction effect but predicts meaningful bounds on such effects driven by the intrinsic utility for the choices. In risky environments, a person is less likely to sacrifice utility on one dimension to gain utility on another that is made riskier. For example, a person is less likely to exert effort for a fixed monetary return if there is greater overall income uncertainty. We design and run experiments to test basic model predictions and find support for these predictions.Author's Origina
At Love's Hearth: An Original One-Act Musical Exploring the Intersection of Music and Spiritual Care
No full textThis 45-minute original piece explored the intersection of music and spiritual care in both its content and in the rehearsal process for a performance that involved 25 musicians. Synopsis: Tragedy strikes on Rosie’s sixth birthday when her mother, Rachel, falls ill. As the family gathers around the hospital bed, reeling as they try to metabolize the situation, a visitor slips in and offers a simple but profound gift. Late October. Late 1960’s. The midwest, US. Inspired by a true story
Statistical Perspectives on Algorithmic Fairness: Quantifying Group Fairness in Thresholding Decisions
No full textMachine learning algorithms have become increasingly entrusted with consequential, high-impact decisions over the past few decades; however, numerous examples of the unfairness of their outcomes spawned the creation of the research field of algorithmic fairness over the past decade. Most of the work in algorithmic fairness has primarily focused on rigorously defining fairness as it relates to machine learning procedures and outcomes, and proposing a robust set of methods for correcting for unfairness; however, there still remains a gap in rigorously identifying and quantifying the extent of unfairness in a statistical sense. In this thesis, we provide novel derivations for the distributions of five of the most fundamental group fairness metrics—accuracy, acceptance rate, false positive rate, false negative rate, and positive predictive value—and the distributions of their differences across protected groups. These ultimately serve as the bases for the construction of confidence intervals, which provide a principled framework for rigorously assessing uncertainty and the extent of unfairness with respect to the disparity of group fairness quantities between protected groups. We hope these statistical tools contribute new perspectives and understanding to this highly multidisciplinary field of algorithmic fairness
Circuit Lower Bounds for Low-Energy States of Quantum Code Hamiltonians
No full textThe No Low-energy Trivial States (NLTS) conjecture of Freedman and Hastings, 2014 -- which posits the existence of a local Hamiltonian with a super-constant quantum circuit lower bound on the complexity of all low-energy states -- identifies a fundamental obstacle to the resolution of the quantum PCP conjecture. In this work, we provide new techniques, based on entropic and local indistinguishability arguments, that prove circuit lower bounds for all the low-energy states of local Hamiltonians arising from quantum error-correcting codes.
For local Hamiltonians arising from nearly linear-rate or nearly linear-distance LDPC stabilizer codes, we prove super-constant circuit lower bounds for the complexity of all states of energy o(n). Such codes are known to exist and are not necessarily locally testable, a property previously suspected to be essential for the NLTS conjecture. Curiously, such codes can also be constructed on a two-dimensional lattice, showing that low-depth states cannot accurately approximate the ground-energy even in physically relevant systems.Accepted Manuscrip
The Politics of Karameh: Palestinian Dignity and Defiance Against the Necrocarceral State
No full textFor decades, Israel has systematically confiscated and withheld the bodies of slain Palestinians as a form of punishment and control over the living. The bodies are deposited without proper identification in secret military-controlled gravesites or in police morgue refrigerators where they lie frozen indefinitely. As their families are forced to negotiate in Israeli courts for the retrieval and burial of their children, their grief is compounded by the denial of traditional burial rites. Thus, Israel’s corpse confiscation policy has become synonymous with the intergenerational dehumanization and criminalization of Palestinians from birth into death. This dissertation centers the politics of Palestinian death, grief and mourning as critical sites for exploring questions of Indigenous rights, sovereignty and belonging in contexts of ongoing settler colonialism. Drawing on long-term engagement with the Palestinian grassroots movement to return the dead to their families, each chapter explores a different mode of Israel’s corpse confiscation policy over seven decades of entrenched Israeli settler colonial occupation. I use ethnographic research, in-depth interviews, and archival and legal research to examine the intersections of carceral, border and legal systems that underpin a form of settler colonial governance I term necrocarcerality. Ultimately, this dissertation shows how Israel’s corpse confiscation policy manifests as a tool of settler colonial expansion on the body, as well as how Palestinians have resisted its intention to punish through the diverse ways they respond to being denied burial rites. I argue that their varied, yet interconnected strategies comprise a “politics of karameh (dignity)” that must be understood as a collective expression of anticolonial defiance against Israel’s necrocarcerality. Thus, the captive dead body becomes a critical site of Indigenous sovereign expression under the precarious conditions of life in the settler colonial state. By centering the criminalization and incarceration of the Palestinian corpse, alongside Indigenous practices of grief and mourning, this dissertation shows how the politics of death may inform a liberated Palestinian future
Love and Grief: An Evening of Jazz Improvisation
No full textMy project is a performance of jazz improvisation that explores songs of love and grief. I have experienced a loss in my life and have decided to channel my thoughts and feelings into a creative project. My belief is that one way to deal with grief is to practice being completely present. To play jazz improvisation requires radical presence and jazz is a music of praise for the present. Jazz bands are a community of "yes." As I describe in my paper, the evening was a wonderful surprise on many levels. It was the first time I met the accompanying musicians (the bass player and drummer). It was the first time I led a piano trio
The Impact of the ‘Open’ Workspace on Human Collaboration
No full textOrganizations’ pursuit of increased workplace collaboration has led managers to transform traditional office spaces into ‘open’, transparency-enhancing architectures with fewer walls, doors and other spatial boundaries, yet there is scant direct empirical research on how human interaction patterns change as a result of these architectural changes. In two intervention-based field studies of corporate headquarters transitioning to more open office spaces, we empirically examined—using digital data from advanced wearable devices and from electronic communication servers—the effect of open office architectures on employees' face-to-face, email and instant messaging (IM) interaction patterns. Contrary to common belief, the volume of face-to-face interaction decreased significantly (approx. 70%) in both cases, with an associated increase in electronic interaction. In short, rather than prompting increasingly vibrant face-to-face collaboration, open architecture appeared to trigger a natural human response to socially withdraw from officemates and interact instead over email and IM. This is the first study to empirically measure both face-to-face and electronic interaction before and after the adoption of open office architecture. The results inform our understanding of the impact on human behaviour of workspaces that trend towards fewer spatial boundaries.Version of Recor
Yours, Mine, and Ours: The Effects of Post-2011 School Finance Reforms on Student Outcomes and the Redistribution of K-12 Education Funding
No full textIt is a principal interest of the state to provide a quality public education to all students within its jurisdiction, as education at the K-12 level is essential for access to social mobility and other opportunities in adulthood. Significant disparities in the public education system, however, have existed and continue to persist across income lines. A major question in education legislation, then, is whether or not increasing funding to underprivileged schools will enhance students’ academic and economic outcomes. This paper investigates post-2011 school finance reforms, implemented at the state level, to determine if they have any substantive effect on student outcomes and to examine their impact on the redistribution of K-12 public education funding. Through event study analyses, no significant effect on standardized test scores, graduation rates, or teen birth rates is found of school finance reforms in the period from 2011-2022. Redistribution, which would increase low-income school budgets relative to their non-low-income peers, is also unfounded. Substitution effects, where low-income local governments reallocate local funds toward other endeavors after receiving increased state funding for education, are found in both event study analyses and in public school budget reports from several counties, and provide an explanation for this lack of redistribution and the stagnation of student achievement
Sparsity Bounds for Spectral Approximations of Graphs
No full textGraph sparsification is the concept of using a sparse graph to approximate a much denser one --- a powerful tool for improving the complexity of graph algorithms. In this thesis, we focus on the setting of \emph{spectral sparsification}, which requires our sparsifiers to roughly preserve the original graph's linear-algebraic nature. Specifically, the central goal is to understand and obtain existence results for the level of sparsity achievable under spectral approximation. Given an arbitrary graph and an approximation factor we would like to achieve, we ask: how few edges can we hope for a spectral sparsifier to have? We present a blend of expository material and novel contributions throughout this thesis to this end.
We begin by developing the basic theory and motivations behind spectral approximation for undirected, weighted graphs. Then, we present a few existing algorithms for obtaining spectral sparsifiers, including one which attains the state-of-the-art \emph{linear size} bound, meaning the sparsifiers produced have number of edges linear in the number of vertices . Next, we present our joint work with Phevos Paschalidis, in which give a constructive proof for recovering the existence of linear-sized sparsifiers from the proof by Marcus, Spielman, and Srivastava of the long-standing \emph{Kadison-Singer} conjecture, formalizing deep connections between these two results. Finally, we expand our view to stronger definitions of spectral approximation in the literature that allow for sparsifying directed graphs and provide more preservation guarantees, and we unify our view on these through the lens of \emph{graph lifts}. Lifts encode the local structure of a graph into a larger graph with a new global structure, and they have been shown to be a promising technique for reductions both within and between these different spectral approximation definitions. While only O(n \polylog n) size bounds are generally known for these stronger spectral sparsifiers, we give a proof for obtaining linear-sized \emph{unit-circle} sparsifiers in the special case of undirected regular graphs using lifts. Lastly, we outline a path to generalizing this lift perspective for directed unit-circle sparsification, proving some original results and stating interesting open problems toward this goal
Order by Disorder in Topological Quantum Materials
No full textTopological materials are a promising platform for next-generation devices, ranging from optoelectronics to interconnects. In these materials, the interplay between magnetic, electronic, and lattice degrees of freedom presents an opportunity to discover new phases with enhanced tunability and performance. In this thesis, I discuss the role of fluctuations — deviations from global order in space and time— in promoting incipient phases in topological materials, such as incommensurate magnetism and nematicity, which are probed through an ensemble of experimental techniques, including electrical and thermal transport as well as time-resolved X-ray scattering.
In the first part of the dissertation, I explore the role of thermally-activated, geometrically frustrated carriers in driving rotational symmetry-breaking. Geometric frustration from the kagomé lattice localizes modes onto specific crystallographic regions in real-space, leading to flat-bands with quenched kinetic energy in reciprocal space. These electronic flat-bands are so sensitive to any lattice perturbation that they can drive a profound reconstruction of the entire crystal. When the temperature is raised such that electronic flat-bands below the Fermi-level are activated, the localized electrons conspire to form nematic state where rotational symmetry is broken. At lower temperatures, these carriers are not active and thus no nematic state is formed. In contrast to systems in which interactions with the lattice actually slow down quasiparticle transport, here we find that the flat-electrons are actually mobilized by their interaction with the lattice. These findings have the potential to lead to highly entropic carriers for thermoelectric applications.
In the second part of the thesis, I discuss the way in which thermally enabled scattering amongst topological electrons fundamentally change the interactions in magnetic domains, leading to their enhanced stability. Unlike conventional electrons, which have a doubly degenerate parabolic dispersion for each spin, topological fermions in Weyl semimetals are characterized by the chiral, linear dispersion dictated by the relativistic Weyl equation. The properties of these Weyl fermions propagate through to the exchange interactions experienced by a material's magnetic moments, leading to small domains of incommensurate magnetism which are locally stable but globally unstable. These domains have a distinct impact on the thermal and electronic transport through the crystal, showing how deviations from the global order can still strongly affect macroscopic properties of the material.
Finally, in the last chapter of the thesis, I explore new techniques for observing fluctuations with time-resolved X-ray scattering. Technological advancements in the time-resolution, repetition rate, and brilliance of X-ray scattering sources--chiefly among them X-ray Free Electron Lasers (XFELs)-- are enabling observations of time-dependent phenomena from timescales of femtoseconds all the way to minutes. While these experiments promise to elucidate new physical behavior of systems ranging from biological proteins to topological magnets, a key challenge in their execution is analyzing the massive troves of data that result from taking a time-series of detector images. In parallel with the rise of time-resolved X-ray scattering, there have been numerous machine learning techniques that have the potential to revolutionize the way these massive troves of time-series data are analyzed. I demonstrate the utility and promise of non-linear embedding methods popularized in machine learning communities by applying them to nano-second resolution data from the EU-XFEL. These methods are a departure from typical analysis methods based on statistical correlation functions, and unveil distinct fluctuations of magnetic-stripes in a topological magnet.
Taken together, these results point to the unexpected ways in which quantum materials can be engineered such that their characteristic thermal fluctuations aid, rather than hinder, their performance in applications such as spintronics and thermoelectrics. Furthermore, by utilizing a wide array of experimental and computational techniques accessible through National Laboratory User facilities, I hope to show how productive it can be to approach scientific problems from as many angles as possible, leading to robust inductive discoveries