Doctor of Philosophy

dissertationThis study explores the ways in which ethnographic data might be represented within a hypertext; format. It begins with an analysis of the historical roots of the technology to determine key characteristics that differentiate it from other media. Three characteristics surface through this analysis: multilinearity, multivocality, and multimodality. The current study examines these characteristics from a more critical stance to determine what is possible in practice. To this end, three ethnographic hypertext;s are analyzed to determine strengths and weaknesses. From this analysis, a set of design implications emerge that provides a framework for a case study entitled The Congo Prototype. The Congo Prototype is built from an extensive study of a museum located in Belgium, The Royal Museum for Central Africa (RMCA), along with interviews with colonial veterans who served in the Congo up until Independence. This work offers the reader specific techniques that might be incorporated into future works, and at the same time, provides a stand alone ethnographic study of numerous narratives revolving around the Belgian Congo. In the final sections of this dissertation, several suggestions are outlined for future research. It is suggested that practitioners might consider database driven ethnographies as a means of creating a more dynamic reading experience; cross linked studies to achieve a higher degree of multivocality; and integration of a "play around" feature that would allow readers to determine the amount of data that could be viewed in support of specific claims. The study concludes with a brief discussion of some of the intractable issues that cannot be solved through technological means, such as the crisis of representation, the importance of being in the field, and the politics of web publishing

Tight Size-Degree Bounds for Sums-of-Squares Proofs

We exhibit families of $4$-CNF formulas over $n$ variables that have sums-of-squares (SOS) proofs of unsatisfiability of degree (a.k.a. rank) $d$ but require SOS proofs of size $n^{\Omega(d)}$ for values of $d = d(n)$ from constant all the way up to $n^{\delta}$ for some universal constant$\delta$. This shows that the $n^{O(d)}$ running time obtained by using the Lasserre semidefinite programming relaxations to find degree-$d$ SOS proofs is optimal up to constant factors in the exponent. We establish this result by combining $\mathsf{NP}$-reductions expressible as low-degree SOS derivations with the idea of relativizing CNF formulas in [Kraj\'i\v{c}ek '04] and [Dantchev and Riis'03], and then applying a restriction argument as in [Atserias, M\"uller, and Oliva '13] and [Atserias, Lauria, and Nordstr\"om '14]. This yields a generic method of amplifying SOS degree lower bounds to size lower bounds, and also generalizes the approach in [ALN14] to obtain size lower bounds for the proof systems resolution, polynomial calculus, and Sherali-Adams from lower bounds on width, degree, and rank, respectively

Fractional Pseudorandom Generators from Any Fourier Level

We prove new results on the polarizing random walk framework introduced in recent works of Chattopadhyay {et al.} [CHHL19,CHLT19] that exploit $L_1$ Fourier tail bounds for classes of Boolean functions to construct pseudorandom generators (PRGs). We show that given a bound on the $k$-th level of the Fourier spectrum, one can construct a PRG with a seed length whose quality scales with $k$. This interpolates previous works, which either require Fourier bounds on all levels [CHHL19], or have polynomial dependence on the error parameter in the seed length [CHLT10], and thus answers an open question in [CHLT19]. As an example, we show that for polynomial error, Fourier bounds on the first $O(\log n)$ levels is sufficient to recover the seed length in [CHHL19], which requires bounds on the entire tail. We obtain our results by an alternate analysis of fractional PRGs using Taylor's theorem and bounding the degree-$k$ Lagrange remainder term using multilinearity and random restrictions. Interestingly, our analysis relies only on the \emph{level-k unsigned Fourier sum}, which is potentially a much smaller quantity than the $L_1$ notion in previous works. By generalizing a connection established in [CHH+20], we give a new reduction from constructing PRGs to proving correlation bounds. Finally, using these improvements we show how to obtain a PRG for $\mathbb{F}_2$ polynomials with seed length close to the state-of-the-art construction due to Viola [Vio09], which was not known to be possible using this framework

Simultaneous Source Localization and Polarization Estimation via Non-Orthogonal Joint Diagonalization with Vector-Sensors

Joint estimation of direction-of-arrival (DOA) and polarization with electromagnetic vector-sensors (EMVS) is considered in the framework of complex-valued non-orthogonal joint diagonalization (CNJD). Two new CNJD algorithms are presented, which propose to tackle the high dimensional optimization problem in CNJD via a sequence of simple sub-optimization problems, by using LU or LQ decompositions of the target matrices as well as the Jacobi-type scheme. Furthermore, based on the above CNJD algorithms we present a novel strategy to exploit the multi-dimensional structure present in the second-order statistics of EMVS outputs for simultaneous DOA and polarization estimation. Simulations are provided to compare the proposed strategy with existing tensorial or joint diagonalization based methods

Assessment of the structural validity of three foot and ankle specific patient-reported outcome measures

Background: The structural validity of the Lower extremity functional scale (LEFS), the Visual analogue scale foot and ankle (VAS-FA), and the Western Ontario and McMaster Universities osteoarthritis index (WOMAC) has not been compared earlier in patients after foot and ankle surgery. Methods: Altogether 165 previously operated patients completed the foot and ankle specific instruments, the 15D health-related quality of life (HRQoL) instrument, and general health (VAS). Results: The LEFS, the VAS-FA and the WOMAC had slight differences in their measurement properties. The VAS-FA had the best targeting and coverage. All three foot and ankle measures accounted for mobility and usual activities when compared to the different aspects of generic HRQoL. Conclusions: The LEFS, the VAS-FA and the WOMAC have relatively similar psychometric properties among foot and ankle patients, yet the VAS-FA provides the best targeting and coverage. (C) 2019 European Foot and Ankle Society. Published by Elsevier Ltd. All rights reserved.Peer reviewe

Efficient deterministic approximate counting for low-degree polynomial threshold functions

We give a deterministic algorithm for approximately counting satisfying assignments of a degree-$d$ polynomial threshold function (PTF). Given a degree-$d$ input polynomial $p(x_1,\dots,x_n)$ over $R^n$ and a parameter $\epsilon> 0$, our algorithm approximates $\Pr_{x \sim \{-1,1\}^n}[p(x) \geq 0]$ to within an additive $\pm \epsilon$ in time $O_{d,\epsilon}(1)\cdot \mathop{poly}(n^d)$. (Any sort of efficient multiplicative approximation is impossible even for randomized algorithms assuming $NP\not=RP$.) Note that the running time of our algorithm (as a function of $n^d$, the number of coefficients of a degree-$d$ PTF) is a \emph{fixed} polynomial. The fastest previous algorithm for this problem (due to Kane), based on constructions of unconditional pseudorandom generators for degree-$d$ PTFs, runs in time $n^{O_{d,c}(1) \cdot \epsilon^{-c}}$ for all $c > 0$. The key novel contributions of this work are: A new multivariate central limit theorem, proved using tools from Malliavin calculus and Stein's Method. This new CLT shows that any collection of Gaussian polynomials with small eigenvalues must have a joint distribution which is very close to a multidimensional Gaussian distribution. A new decomposition of low-degree multilinear polynomials over Gaussian inputs. Roughly speaking we show that (up to some small error) any such polynomial can be decomposed into a bounded number of multilinear polynomials all of which have extremely small eigenvalues. We use these new ingredients to give a deterministic algorithm for a Gaussian-space version of the approximate counting problem, and then employ standard techniques for working with low-degree PTFs (invariance principles and regularity lemmas) to reduce the original approximate counting problem over the Boolean hypercube to the Gaussian version

Habitat Characteristics and Nesting Ecology of Golden Eagles in Arizona

Golden Eagles (Aquila chrysaetos) have a broad range globally and in general are well-studied. However, Arizona’s Golden Eagle population remained essentially unstudied until 2011, when Arizona Game and Fish Department (AZGFD) began nest surveys for cliff nesting Golden Eagles throughout the state. As a result of this data collection, the natural history of Arizona’s Golden Eagles is finally revealing itself. This dissertation outlined a reliable description of their nesting phenology that provides a framework for timing surveys and a baseline to monitor the effects of climate change on Golden Eagles. The mean date for egg-laying was February 14 and pairs nesting in the high desert initiate nesting about ten days later than their southern counterparts. A brief study collecting prey remains determined that Black-tailed Jack Rabbit (Lepus californicus) was the central prey species for Golden Eagles in northern Arizona. The results of a multiscale habitat suitability model (HSM) determined that slope between 18º-28º was the most important habitat characteristics for Golden Eagles and the sagebrush landcover was the least important. The multiscale productivity prediction model did not predict with high accuracy; however, the results did reveal some data gaps and provided guidance for adjustments in the future. The results of this entire dissertation can guide future research priorities for Golden Eagles in Arizona. For example, more research on Golden Eagle prey dynamics is needed to determine the impact prey have on their nesting success. Additional research should focus on adding human impact factors such as recreational activity or elemental mining as possible factors that negatively influence nesting productivity. Finally, quantifying climate features on a finer temporal scale should be considered and continued nest site data collection will increase the sample size for more informative results

On the Interplay between Social Welfare and Tractability of Equilibria

Computational tractability and social welfare (aka. efficiency) of equilibria are two fundamental but in general orthogonal considerations in algorithmic game theory. Nevertheless, we show that when (approximate) full efficiency can be guaranteed via a smoothness argument \`a la Roughgarden, Nash equilibria are approachable under a family of no-regret learning algorithms, thereby enabling fast and decentralized computation. We leverage this connection to obtain new convergence results in large games -- wherein the number of players $n \gg 1$ -- under the well-documented property of full efficiency via smoothness in the limit. Surprisingly, our framework unifies equilibrium computation in disparate classes of problems including games with vanishing strategic sensitivity and two-player zero-sum games, illuminating en route an immediate but overlooked equivalence between smoothness and a well-studied condition in the optimization literature known as the Minty property. Finally, we establish that a family of no-regret dynamics attains a welfare bound that improves over the smoothness framework while at the same time guaranteeing convergence to the set of coarse correlated equilibria. We show this by employing the clairvoyant mirror descent algortihm recently introduced by Piliouras et al.Comment: To appear at NeurIPS 202