- Scholarly Works, Mathematics

# Scholarly Works, Mathematics

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- Electronic Health Record: Comparative analysis of HL7 and open EHR approachesNestor, Mamani Macedo; Garcia Hilares, Nilton Alan; Julio, Pariona Quispe; R, Alarcon Matutti (IEEE, 2010-06-01)
Show more This paper presents a comparative analysis of the main proposals to automatize a Patient’s Health Record in any Medical Center: HL7 and OpenEHR. The methodology includes analyzing each approach, defining some criteria of evaluation, doing a comparative chart, and showing the main conclusions.Show more - Resilient s-ACD for Asynchronous Collaborative Solutions of Systems of Linear EquationsErlandson, Lucas; Atkins, Zachary; Fox, Alyson; Vogl, Christopher; Miedlar, Agnieszka; Ponce, Colin (IEEE, 2023-09-26)
Show more Solving systems of linear equations is a critical component of nearly all scientific computing methods. Traditional algorithms that rely on synchronization become prohibitively expensive in computing paradigms where communication is costly, such as heterogeneous hardware, edge computing, and unreliable environments. In this paper, we introduce an s-step Approximate Conjugate Directions (s-ACD) method and develop resiliency measures that can address a variety of different data error scenarios. This method leverages a Conjugate Gradient (CG) approach locally while using Conjugate Directions (CD) globally to achieve asynchronicity. We demonstrate with numerical experiments that s-ACD admits scaling with respect to the condition number that is comparable with CG on the tested 2D Poisson problem. Furthermore, through the addition of resiliency measures, our method is able to cope with data errors, allowing it to be used effectively in unreliable environments.Show more - Detection of passageways in natural foliage using biomimetic sonarWang, Ruihao; Liu, Yimeng; Müller, Rolf (IOP Publishing, 2022-08-10)
Show more The ability of certain bat species to navigate in dense vegetation based on trains of short biosonar echoes could provide for an alternative parsimonious approach to obtaining the sensory information that is needed to achieve autonomy in complex natural environments. Although bat biosonar has much lower data rates and spatial (angular) resolution than commonly used human-made sensing systems such as LiDAR or stereo cameras, bat species that live in dense habitats have the ability to reliably detect narrow passageways in foliage. To study the sensory information that the animals may have available to accomplish this, we have used a biomimetic sonar system that was combined with a camera to record echoes and synchronized images from 10 different field sites that featured narrow passageways in foliage. The synchronized camera and sonar data allowed us to create a large data set (130 000 samples) of labeled echoes using a teacher-student approach that used class labels derived from the images to provide training data for echo-based classifiers. The performance achieved in detecting passageways based on the field data closely matched previous results obtained for gaps in an artificial foliage setup in the laboratory. With a deep feature extraction neural network (VGG16) a foliage-versus-passageway classification accuracy of 96.64% was obtained. A transparent artificial intelligence approach (class-activation mapping) indicated that the classifier network relied heavily on the initial rising flank of the echoes. This finding could be exploited with a neuromorphic echo representation that consisted of times where the echo envelope crossed a certain amplitude threshold in a given frequency channel. Whereas a single amplitude threshold was sufficient for this in the previous laboratory study, multiple thresholds were needed to achieve an accuracy of 92.23%. These findings indicate that despite many sources of variability that shape clutter echoes from natural environments, these signals contain sufficient sensory information to enable the detection of passageways in foliage.Show more - Characteristics of departments with high-use of active learning in introductory STEM courses: implications for departmental transformationLau, Alexandra C.; Henderson, Charles; Stains, Marilyne; Dancy, Melissa; Merino, Christian; Apkarian, Naneh; Raker, Jeffrey R.; Johnson, Estrella (2024-02-12)
Show more Background: It is well established in the literature that active learning instruction in introductory STEM courses results in many desired student outcomes. Yet, regular use of high-quality active learning is not the norm in many STEM departments. Using results of a national survey, we identified 16 departments where multiple instructors reported using high levels of active learning in their introductory chemistry, mathematics, or physics courses. We conducted interviews with 27 instructors in these 16 departments to better understand the characteristics of such departments. Results: Using grounded theory methodology, we developed a model that highlights relevant characteristics of departments with high use of active learning instruction in their introductory courses. According to this model, there are four main, interconnected characteristics of such departments: motivated people, knowledge about active learning, opportunities, and cultures and structures that support active learning. These departments have one or more people who are motivated to promote the use of active learning. These motivated people have knowledge about active learning as well as access to opportunities to promote the use of active learning. Finally, these departments have cultures and structures that support the use of active learning. In these departments, there is a positive feedback loop that works iteratively over time, where motivated people shape cultures/structures and these cultures/structures in turn increase the number and level of commitment of the motivated people. A second positive feedback loop was found between the positive outcome of using active learning instruction and the strengthening of cultures/structures supportive of active learning. Conclusions: According to the model, there are two main take-away messages for those interested in promoting the use of active learning. The first is that all four components of the model are important. A weak or missing component may limit the desired outcome. The second is that desired outcomes are obtained and strengthened over time through two positive feedback loops. Thus, there is a temporal aspect to change. In all of the departments that were part of our study, the changes took at minimum several years to enact. While our model was developed using only high-use of active learning departments and future work is needed to develop the model into a full change theory, our results do suggest that change efforts may be made more effective by increasing the robustness of the four components and the connections between them.Show more - Domain truncation, absorbing boundary conditions, Schur complements, and Padé approximationGander, Martin J.; Jakabčin, Lukáš; Outrata, Michal (Osterreichische Akademie der Wissenschaften, Verlag, 2024)
Show more We show for a model problem that the truncation of an unbounded domain by an artificial Dirichlet boundary condition placed far away from the domain of interest is equivalent to a specific absorbing boundary condition placed closer to the domain of interest. This specific absorbing boundary condition can be implemented as a truncation layer terminated by a Dirichlet condition. We prove that the absorbing boundary condition thus obtained is a spectral Padé approximation about infinity of the transparent boundary condition. We also study numerically two improvements for this boundary condition, the truncation with an artificial Robin condition placed at the end of the truncation layer and a Padé approximation about a different point than infinity. Both of these give new and substantially better results compared to using the artificial Dirichlet boundary condition at the end of the truncation layer. We prove our results in the context of linear algebra, using spectral analysis of finite and infinite Schur complements, which we relate to continued fractions. We illustrate our results with numerical experiments.Show more - Spectral analysis of implicit 2 stage block Runge-Kutta preconditionersGander, Martin J.; Outrata, Michal (Elsevier, 2023-01-01)
Show more We analyze the recently introduced family of preconditioners in [15] for the stage equations of implicit Runge-Kutta methods for two stage methods. We give explicit formulas for the eigenvalues and eigenvectors of the preconditioned systems for a general method and use these to give explicit convergence estimates of preconditioned GMRES for some common choices of the implicit Runge-Kutta methods. This analysis also allows us to qualitatively predict and explain the main observed features of the GMRES convergence behavior, not only bound it. We illustrate our analysis with numerical experiments. We also consider the direction of numerical optimization for improving the preconditioners performance, as suggested in [15]. We consider two different ways – both distinct to the one introduced in [15] – and numerically optimize these, using the explicit bounds obtained beforehand.Show more - Why Similar Policies Resulted In Different COVID-19 Outcomes: How Responsiveness And Culture Influenced Mortality RatesLim, Tse Yang; Xu, Ran; Ruktanonchai, Nick; Saucedo, Omar; Childs, Lauren M.; Jalali, Mohammad S.; Rahmandad, Hazhir; Ghaffarzadegan, Navid (Health Affairs, 2023-12)
Show more In the first two years of the COVID-19 pandemic, per capita mortality varied by more than a hundredfold across countries, despite most implementing similar nonpharmaceutical interventions. Factors such as policy stringency, gross domestic product, and age distribution explain only a small fraction of mortality variation. To address this puzzle, we built on a previously validated pandemic model in which perceived risk altered societal responses affecting SARS-CoV-2 transmission. Using data from more than 100 countries, we found that a key factor explaining heterogeneous death rates was not the policy responses themselves but rather variation in responsiveness. Responsiveness measures how sensitive communities are to evolving mortality risks and how readily they adopt nonpharmaceutical interventions in response, to curb transmission.We further found that responsiveness correlated with two cultural constructs across countries: uncertainty avoidance and power distance. Our findings show that more responsive adoption of similar policies saves many lives, with important implications for the design and implementation of responses to future outbreaks.Show more - Extraordinary parasite multiplication rates in human malaria infectionsGreischar, Megan A.; Childs, Lauren M. (Cell Press, 2023-08)
Show more For pathogenic organisms, faster rates of multiplication promote transmission success, the potential to harm hosts, and the evolution of drug resistance. Parasite multiplication rates (PMRs) are often quantified in malaria infections, given the relative ease of sampling. Using modern and historical human infection data, we show that established methods return extraordinarily – and implausibly – large PMRs. We illustrate how inflated PMRs arise from two facets of malaria biology that are far from unique: (i) some developmental ages are easier to sample than others; (ii) the distribution of developmental ages changes over the course of infection. The difficulty of accurately quantifying PMRs demonstrates a need for robust methods and a subsequent re-evaluation of what is known even in the well-studied system of malaria.Show more - Squares of bivariate Goppa codesBasener, Wesley; Cotardo, Giuseppe; Krebs, Jenna; Liu, Yihan; Matthews, Gretchen L.; Ufferman, Eric (2023-10-13)
Show more In this paper, we study squares of bivariate Goppa codes, as they relate to the Goppa code distinguishing problem for bivariate Goppa codes. Introduced in 2021, multivariate Goppa codes are subfield subcodes of certain evaluation codes defined by evaluating polynomials in m variables. The evaluation codes are augmented Cartesian codes, a generalization of Reed-Muller codes. Classical Goppa codes are obtained by taking m=1. The multivariate Goppa code distinguishing problem is to distinguish efficiently a generator matrix of a multivariate Goppa code from a randomly drawn one. Because a randomly drawn code has a large square, codes with small squares may be considered distinguishable, revealing structure which facilitates private key recovery in a code-based cryptosystem.Show more - Quantum distance to uncontrollability and quantum speed limitsBurgarth, Daniel; Borggaard, Jeffrey T.; Zimboras, Zoltan (American Physical Society, 2022-04-04)
Show more Distance to uncontrollability is a crucial concept in classical control theory. Here, we introduce quantum distance to uncontrollability as a measure of how close a universal quantum system is to a nonuniversal one. This allows us to provide a quantitative version of the quantum speed limit, decomposing the bound into geometric and dynamical components. We consider several physical examples including globally controlled solid state qubits, scrambling of quantum information, and a cross-Kerr system, showing that the quantum distance to uncontrollability provides a precise meaning to spectral crowding, weak interactions, and other bottlenecks to universality. We suggest that this measure should be taken into consideration in the design of quantum technology.Show more - Performance assessment of energy-preserving, adaptive time-step variational integratorsSharma, Harsh; Borggaard, Jeffrey T.; Patil, Mayuresh; Woolsey, Craig A. (Elsevier, 2022-11)
Show more A fixed time-step variational integrator cannot preserve momentum, energy, and symplectic form simultaneously for nonintegrable systems. This barrier can be overcome by treating time as a discrete dynamic variable and deriving adaptive time-step variational integrators that conserve the energy in addition to being symplectic and momentum-preserving. Their utility, however, is still an open question due to the numerical difficulties associated with solving the discrete governing equations. In this work, we investigate the numerical performance of energy-preserving, adaptive time-step variational integrators. First, we compare the time adaptation and energy performance of the energy-preserving adaptive algorithm with the adaptive variational integrator for Kepler's two-body problem. Second, we apply tools from Lagrangian backward error analysis to investigate numerical stability of the energy-preserving adaptive algorithm. Finally, we consider a simple mechanical system example to illustrate the backward stability of this energy-preserving, adaptive time-step variational integrator.Show more - A statistical framework for domain shape estimation in Stokes flowsBorggaard, Jeffrey T.; Glatt-Holtz, Nathan E.; Krometis, Justin (IOP Publishing, 2023-08-01)
Show more We develop and implement a Bayesian approach for the estimation of the shape of a two dimensional annular domain enclosing a Stokes flow from sparse and noisy observations of the enclosed fluid. Our setup includes the case of direct observations of the flow field as well as the measurement of concentrations of a solute passively advected by and diffusing within the flow. Adopting a statistical approach provides estimates of uncertainty in the shape due both to the non-invertibility of the forward map and to error in the measurements. When the shape represents a design problem of attempting to match desired target outcomes, this ‘uncertainty’ can be interpreted as identifying remaining degrees of freedom available to the designer. We demonstrate the viability of our framework on three concrete test problems. These problems illustrate the promise of our framework for applications while providing a collection of test cases for recently developed Markov chain Monte Carlo algorithms designed to resolve infinite-dimensional statistical quantities.Show more - Optimization-Based Parametric Model Order Reduction Via
*H*_{2}⊗*L*_{2}First-Order Necessary ConditionsHund, Manuela; Mitchell, Tim; Mlinaric, Petar; Saak, Jens (SIAM Publications, 2022-06-16)Show more In this paper, we generalize existing frameworks for H2 ⊗ L2-optimal model order reduction to a broad class of parametric linear time-invariant systems. To this end, we derive first-order necessary optimality conditions for a class of structured reduced-order models and then, building on those, propose a stability-preserving optimization-based method for computing locally H2 ⊗ L2-optimal reduced-order models. We also make a theoretical comparison to existing approaches in the literature and, in numerical experiments, show how our new method, with reasonable computational effort, produces stable optimized reduced-order models with significantly lower approximation errors.Show more - A Unifying Framework for Interpolatory ℒ2-Optimal Reduced-Order ModelingMlinaric, Petar; Gugercin, Serkan (SIAM, 2023-09-15)
Show more We develop a unifying framework for interpolatory L2-optimal reduced-order modeling for a wide class of problems ranging from stationary models to parametric dynamical systems. We first show that the framework naturally covers the well-known interpolatory necessary conditions for H2-optimal model order reduction and leads to the interpolatory conditions for H2L-0-optimal model order reduction of multi-inputmulti-output parametric dynamical systems. Moreover, we derive novel interpolatory optimality conditions for rational discrete least-squares minimization and for L2-optimal model order reduction of a class of parametric stationary models. We show that bitangential Hermite interpolation appears as the main tool for optimality across different domains. The theoretical results are illustrated in two numerical examples.Show more - ℒ2-Optimal Reduced-Order Modeling Using Parameter-Separable FormsMlinaric, Petar; Gugercin, Serkan (SIAM Publications, 2023-04-26)
Show more We provide a unifying framework for L-optimal reduced-order modeling for linear time-invariant dynamical systems and stationary parametric problems. Using parameter-separable forms of the reduced-model quantities, we derive the gradients of the L cost function with respect to the reduced matrices, which then allows a nonintrusive, data-driven, gradient-based descent algorithm to construct the optimal approximant using only output samples. By choosing an appropriate measure, the framework covers both continuous (Lebesgue) and discrete cost functions. We show the efficacy of the proposed algorithm via various numerical examples. Furthermore, we analyze under what conditions the data-driven approximant can be obtained via projection.Show more - The Effect of Spatially Correlated Errors on Sea Surface Height Retrieval from SWOT AltimetryYaremchuk, Max; Beattie, Christopher; Panteleev, Gleb; D’Addezio, Joseph M.; Smith, Scott (MDPI, 2023-08-31)
Show more The upcoming technology of wide-swath altimetry from space will enable monitoring the ocean surface at 4–5 times better spatial resolution and 2–3 times better accuracy than traditional nadir altimeters. This development will provide a chance to directly observe submesoscale sea surface height (SSH) variations that have a typical magnitude of a few centimeters. Taking full advantage of this opportunity requires correct treatment of the correlated SSH errors caused by uncertainties in environmental conditions beneath the satellite and in the geometry and orientation of the on-board interferometer. These observation errors are highly correlated both along and across the surface swath scanned by the satellite, and this presents a significant challenge for accurate processing. In particular, the SWOT precision matrix has off-diagonal elements that are too numerous to allow standard approaches to remain tractable. In this study, we explore the utility of a block-diagonal approximation to the SWOT precision matrix in order to reconstruct SSH variability in the region east of Greenland. An extensive set of 2dVar assimilation experiments demonstrates that the sparse approximation proposed for the precision matrix provides accurate SSH retrievals when the background-to-observation error ratio*ν*does not exceed 3 and significant wave height is below 2.5 m. We also quantify the range of*ν*and significant wave heights over which the retrieval accuracy of the exact spatially correlated SWOT error model will outperform the uncorrelated model. In particular, the estimated range is found to be substantially wider (ν<10 with significant wave heights below 8–10 m), indicating the potential benefits of further improving the accuracy of approximations for the SWOT precision matrix.Show more - Examining whether and how instructional coordination occurs within introductory undergraduate STEM coursesCouch, Brian A.; Prevost, Luanna B.; Stains, Marilyne; Whitt, Blake; Marcy, Ariel E.; Apkarian, Naneh; Dancy, Melissa H.; Henderson, Charles; Johnson, Estrella; Raker, Jeffrey R.; Yik, Brandon J.; Earl, Brittnee; Shadle, Susan E.; Skvoretz, John; Ziker, John P. (Frontiers, 2023-04)
Show more Instructors' interactions can foster knowledge sharing around teaching and the use of research-based instructional strategies (RBIS). Coordinated teaching presents an impetus for instructors' interactions and creates opportunities for instructional improvement but also potentially limits an instructor's autonomy. In this study, we sought to characterize the extent of coordination present in introductory undergraduate courses and to understand how departments and instructors implement and experience course coordination. We examined survey data from 3,641 chemistry, mathematics, and physics instructors at three institution types and conducted follow-up interviews with a subset of 24 survey respondents to determine what types of coordination existed, what factors led to coordination, how coordination constrained instruction, and how instructors maintained autonomy within coordinated contexts. We classified three approaches to coordination at both the overall course and course component levels: independent (i.e., not coordinated), collaborative (decision-making by instructor and others), controlled (decision-making by others, not instructor). Two course components, content coverage and textbooks, were highly coordinated. These curricular components were often decided through formal or informal committees, but these decisions were seldom revisited. This limited the ability for instructors to participate in the decision-making process, the level of interactions between instructors, and the pedagogical growth that could have occurred through these conversations. Decision-making around the other two course components, instructional methods and exams, was more likely to be independently determined by the instructors, who valued this autonomy. Participants in the study identified various ways in which collaborative coordination of courses can promote but also inhibit pedagogical growth. Our findings indicate that the benefits of collaborative course coordination can be realized when departments develop coordinated approaches that value each instructor's autonomy, incorporate shared and ongoing decision-making, and facilitate collaborative interactions and knowledge sharing among instructors.Show more - Decomposition of multicorrelation sequences and joint ergodicityDonoso, Sebastián; Moragues, Andreu Ferré; Koutsogiannis, Andreas; Sun, Wenbo (Cambridge University Press, 2023-05)
Show more We show that, under finitely many ergodicity assumptions, any multicorrelation sequence defined by invertible measure-preserving Z(d) -actions with multivariable integer polynomial iterates is the sum of a nilsequence and a nullsequence, extending a recent result of the second author. To this end, we develop a new seminorm bound estimate for multiple averages by improving the results in a previous work of the first, third, and fourth authors. We also use this approach to obtain new criteria for joint ergodicity of multiple averages with multivariable polynomial iterates on Z(d) -systems.Show more - Spatiotemporal and meteorological relationships in dengue transmission in the Dominican Republic, 2015–2019Robert, Michael A.; Rodrigues, Helena S.; Herrera, Demian; de Mata Donado Campos, Juan; Morilla, Fernando; Del Águila Mejía, Javier; Guardado, María E.; Skewes, Ronald; Colomé-Hidalgo, Manuel (2023-06-02)
Show more Dengue has broadened its global distribution substantially in the past two decades, and many endemic areas are experiencing increases in incidence. The Dominican Republic recently experienced its two largest outbreaks to date with 16,836 reported cases in 2015 and 20,123 reported cases in 2019. With continued increases in dengue transmission, developing tools to better prepare healthcare systems and mosquito control agencies is of critical importance. Before such tools can be developed, however, we must first better understand potential drivers of dengue transmission. To that end, we focus in this paper on determining relationships between climate variables and dengue transmission with an emphasis on eight provinces and the capital city of the Dominican Republic in the period 2015–2019. We present summary statistics for dengue cases, temperature, precipitation, and relative humidity in this period, and we conduct an analysis of correlated lags between climate variables and dengue cases as well as correlated lags among dengue cases in each of the nine locations. We find that the southwestern province of Barahona had the largest dengue incidence in both 2015 and 2019. Among all climate variables considered, lags between relative humidity variables and dengue cases were the most frequently correlated. We found that most locations had significant correlations with cases in other locations at lags of zero weeks. These results can be used to improve predictive models of dengue transmission in the country.Show more - Host movement, transmission hot spots, and vector-borne disease dynamics on spatial networksSaucedo, Omar; Tien, Joseph H. (Keai Publishing, 2022-12)
Show more We examine how spatial heterogeneity combines with mobility network structure to in-fluence vector-borne disease dynamics. Specifically, we consider a Ross-Macdonald-type disease model on n spatial locations that are coupled by host movement on a strongly connected, weighted, directed graph. We derive a closed form approximation to the domain reproduction number using a Laurent series expansion, and use this approxima-tion to compute sensitivities of the basic reproduction number to model parameters. To illustrate how these results can be used to help inform mitigation strategies, as a case study we apply these results to malaria dynamics in Namibia, using published cell phone data and estimates for local disease transmission. Our analytical results are particularly useful for understanding drivers of transmission when mobility sinks and transmission hot spots do not coincide.(c) 2022 The Authors. Publishing services by Elsevier B.V. on behalf of KeAi Communications Co. Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).Show more