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Quantum Algorithms for Symmetric Cones
No full textQuantum algorithms for optimization often achieve speedups in the problem dimension. Yet, their error dependence and sensitivity to scale makes it challenging to identify broad classes of optimization problems for which their is a clear advantage over classical algorithms. This dissertation is comprised of multiple projects spanning three parts that seek to reduce this gap.Part I concerns quantum linear algebra. We provide a construction for implementing matrix arithmetic operations, such as Kronecker and Hadamard products, on a quantum computer. Then, we demonstrate how Iterative Refinement can be leveraged to exponentially improve the dependence on precision in the overall running time associated with classically solving linear systems of equations using quantum computers.Part II concerns Quantum Interior Point methods (QIPMs) for Semidefinite and Second-order conic optimization. QIPMs attempt to speedup the bottleneck of the classical IPM by substituting the classical solution of the Newton linear system with the combined use of a quantum linear systems algorithm and quantum state tomography (with some classical computation between iterates). We present the first provably convergent QIPMs for Semidefinite and Second-order conic optimization, by properly symmetrizing the Newton linear system, and utilizing an orthogonal subspace representation of the search directions to ensure feasibility of the sequence of iterates generated by our algorithms. Using the techniques we develop in Part I, we obtain a speedup in the dimension over classical IPMs, and recover their polylogarithmic dependence on precision.Part III concerns quantum frameworks for semidefinite optimization based on matrix exponentials and Gibbs states. By combining state of the art quantum computing algorithms with iterative refinement techniques we provide evidence of genuine end-to-end asymptotic speedups for solving the semidefinite approximation of Quadratic Unconstrained Binary Optimization (QUBO) problems. We also show that dequantizing our approach yields a classical algorithm that (up to polylogarithmic factors) runs in matrix multiplication time
Contact seaweeds II: type C
No full textThis paper is a continuation of earlier work on the construction of contact
forms on seaweed algebras. In the prequel to this paper, we show that every
index-one seaweed subalgebra of is contact by
identifying contact forms that arise from Dougherty\u27s framework. We extend this
result to include index-one seaweed subalgebras of .
Our methods are graph-theoretic and combinatorial
Seaweed algebras
No full textThe index of a Lie algebra is an important algebraic invariant, but it is
notoriously difficult to compute. However, for the suggestively-named seaweed
algebras, the computation of the index can be reduced to a combinatorial
formula based on the connected components of a "meander": a planar graph
associated with the algebra. Our index analysis on seaweed algebras requires
only basic linear and abstract algebra. Indeed, the main goal of this
survey-type article is to introduce a broader audience to seaweed algebras with
minimal appeal to specialized language and notation from Lie theory. This said,
we present several results that do not appear elsewhere and do appeal to more
advanced language in the Introduction to provide added context
Nitrogenous Altered Volcanic Glasses as Targets for Mars Sample Return
No full textMars exploration is focused on seeking evidence of habitable environments and microbial life. Terrestrial glassy basalts may be the closest Mars‐surface weathering analog and observations increasingly indicate their potential to preserve biogeochemical records. The textures, major and trace element geochemistry, and N concentrations and isotopic compositions of subaerial, subglacial and continental lacustrine hyaloclastites from Antarctica, Iceland, and Oregon, respectively, were studied using micro‐imaging and chemical methods, including gas‐source mass spectrometry. Alteration by meteoric‐sourced waters occurred in circum‐neutral, increasingly alkaline low‐temperature conditions of ∼60°C–100°C (Iceland) and ∼60°C–170°C (Antarctica). Incompatible large ion lithophile element (LILE) enrichments compared to mid‐ocean ridge basalt (MORB) are consistent with more advanced alteration in Antarctic breccias consisting of heulandite‐clinoptilolite, calcite, erionite, quartz, and fluorapophyllite. Granular and tubular alteration textures and radial apatite represent possible microbial traces. Most samples contain more N than fresh MORB or ocean island basalt reflecting enrichment beyond concentrations attributable to igneous processes. Antarctic samples contain 52–1,143 ppm N and have δ 15 Ν air values of −20.8‰ to −7.1‰. Iceland‐Oregon basalts contain 1.6–172 ppm N with δ 15 Ν of −6.7‰ to +7.3‰. Correlations between alteration extents, N concentrations, and concentrations of K 2 O, other LILEs, and Li and B, reflect the siting of secondary N likely as NH 4 + replacing K + and potentially as N 2 in phyllosilicates and zeolites. Although much of the N enrichment and isotope fractionation presented here is not definitively biogenic, given several unknown factors, we suggest that a combination of textures, major and trace element alteration and N and other isotope geochemical compositions could constitute a compelling biosignature in samples from Mars\u27 surface/near‐surface. , Plain Language Summary Finding evidence of past or present life beyond Earth involves identifying physical features and/or chemistries preserved within rocks. Our knowledge of how the signs of life are preserved, and how to identify them, depends on our understanding of Earth biology and how similar rocks on other planetary bodies can preserve such evidence. Volcanic rocks containing natural glass that are subject to chemical modification by waters are relevant to studying alteration at/near the surface of Mars. We have analyzed examples from Iceland and Antarctica to identify textures, minerals, and chemistry, particularly nitrogen, because it is required for all life on Earth, and other elements that can become concentrated in minerals during rock alteration. Minerals formed as a result of rock‐water interactions indicate their formation in fluids with pH < 9 and temperatures of <170°C. Relatively high concentrations of nitrogen correlated with those of other elements (i.e., potassium) indicate that nitrogen is stored in these minerals. Although much of the N chemistry here is not definitively the result of biological activity, chemically modified glassy volcanics containing nitrogen‐bearing minerals may be useful targets to aim for, especially with other observations, when selecting samples on Mars in the search for ancient or modern life. , Key Points Antarctic/Iceland glass alteration minerals such as phyllosilicates and zeolites can incorporate and store N during fluid rock interactions Textures, chemistry and N (though here not definitely biogenic) in altered glasses may provide environmental and biogeochemical records Altered hyaloclastites, which are widespread on Mars\u27 surface, should be considered when selecting samples for return to Eart
Thank You to Our 2021 Peer Reviewers
No full textThe editorial board of AGU Advances thanks the individuals who reviewed for the journal in 2021. , Plain Language Summary Thank you to the 164 people who reviewed manuscripts for AGU Advances in 2021. , Key Points The editors thank the 2021 peer reviewer
Chimeric forecasting: combining probabilistic predictions from computational models and human judgment
No full textAbstractForecasts of the trajectory of an infectious agent can help guide public health decision making. A traditional approach to forecasting fits a computational model to structured data and generates a predictive distribution. However, human judgment has access to the same data as computational models plus experience, intuition, and subjective data. We propose a chimeric ensemble—a combination of computational and human judgment forecasts—as a novel approach to predicting the trajectory of an infectious agent. Each month from January, 2021 to June, 2021 we asked two generalist crowds, using the same criteria as the COVID-19 Forecast Hub, to submit a predictive distribution over incident cases and deaths at the US national level either two or three weeks into the future and combined these human judgment forecasts with forecasts from computational models submitted to the COVID-19 Forecasthub into a chimeric ensemble. We find a chimeric ensemble compared to an ensemble including only computational models improves predictions of incident cases and shows similar performance for predictions of incident deaths. A chimeric ensemble is a flexible, supportive public health tool and shows promising results for predictions of the spread of an infectious agent.</jats:p
A unified Gaussian copula methodology for spatial regression analysis
No full textAbstractSpatially referenced data arise in many fields, including imaging, ecology, public health, and marketing. Although principled smoothing or interpolation is paramount for many practitioners, regression, too, can be an important (or even the only or most important) goal of a spatial analysis. When doing spatial regression it is crucial to accommodate spatial variation in the response variable that cannot be explained by the spatially patterned explanatory variables included in the model. Failure to model both sources of spatial dependence—regression and extra-regression, if you will—can lead to erroneous inference for the regression coefficients. In this article I highlight an under-appreciated spatial regression model, namely, the spatial Gaussian copula regression model (SGCRM), and describe said model’s advantages. Then I develop an intuitive, unified, and computationally efficient approach to inference for the SGCRM. I demonstrate the efficacy of the proposed methodology by way of an extensive simulation study along with analyses of a well-known dataset from disease mapping.</jats:p