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Constraints arise naturally in many scientific experiments/studies such as in, epidemiology, biology, toxicology, etc. and often researchers ignore such information when analyzing their data and use standard methods such as the analysis of variance (ANOVA). Such methods may not only result in a loss of power and efficiency in costs of experimentation but also may result poor interpretation of the data. In this paper we discuss constrained statistical inference in the context of linear mixed effects models that arise naturally in many applications, such as in repeated measurements designs, familial studies and others. We introduce a novel methodology that is broadly applicable for a variety of constraints on the parameters. Since in many applications sample sizes are small and/or the data are not necessarily normally distributed and furthermore error variances need not be homoscedastic (i.e. heterogeneity in the data) we use an empirical best linear unbiased predictor (EBLUP) type residual based bootstrap methodology for deriving critical values of the proposed test. Our simulation studies suggest that the proposed procedure maintains the desired nominal Type I error while competing well with other tests in terms of power. We illustrate the proposed methodology by re-analyzing a clinical trial data on blood mercury level. The methodology introduced in this paper can be easily extended to other settings such as nonlinear and generalized regression models. [ABSTRACT FROM AUTHOR]

Prophylactic interventions such as vaccine allocation are some of the most effective public health policy planning tools. The supply of vaccines, however, is limited and an important challenge is to optimally allocate the vaccines to minimize epidemic impact. This resource allocation question (which we refer to as VID) has multiple dimensions: when, where, to whom, etc. Most of the existing literature in this topic deals with the latter (to whom), proposing policies that prioritize individuals by age and disease risk. However, since seasonal influenza spread has a typical spatial trend, and due to the temporal constraints enforced by the availability schedule, the when and where problems become equally, if not more, relevant. In this paper, we study the VID problem in the context of seasonal influenza spread in the United States. We develop a national scale metapopulation model for influenza that integrates both short and long distance human mobility, along with realistic data on vaccine uptake. We also design GA, a greedy algorithm for allocating the vaccine supply at the state level under temporal constraints and show that such a strategy improves over the current baseline of pro-rata allocation, and the improvement is more pronounced for higher vaccine efficacy and moderate flu season intensity. Further, the resulting strategy resembles a ring vaccination applied spatiallyacross the US. [ABSTRACT FROM AUTHOR]

The social functions of urbanized areas are highly dependent on and supported by the convenient access to public transportation systems, particularly for the less privileged populations who have restrained auto ownership. To accurately evaluate the public transit accessibility, it is critical to capture the spatiotemporal variation of transit services. This can be achieved by measuring the shortest paths or minimum travel time between origin-destination (OD) pairs at each time-of-day (e.g. every minute). In recent years, General Transit Feed Specification (GTFS) data has been gaining popularity for between-station travel time estimation due to its interoperability in spatiotemporal analytics. Many software packages, such as ArcGIS, have developed toolbox to enable the travel time estimation with GTFS. They perform reasonably well in calculating travel time between OD pairs for a specific time-of-day (e.g. 8:00 AM), yet can become computational inefficient and unpractical with the increase of data dimensions (e.g. all times-of-day and large network). In this paper, we introduce a new algorithm that is computationally elegant and mathematically efficient to address this issue. An open-source toolbox written in C++ is developed to implement the algorithm. We implemented the algorithm on City of St. George’s transit network to showcase the accessibility analysis enabled by the toolbox. The experimental evidence shows significant reduction on computational time. The proposed algorithm and toolbox presented is easily transferable to other transit networks to allow transit agencies and researchers perform high resolution transit performance analysis. [ABSTRACT FROM AUTHOR]

Atherosclerosis, the leading death in the United State, is a disease in which a plaque builds up inside the arteries. As the plaque continues to grow, the shear force of the blood flow through the decreasing cross section of the lumen increases. This force may eventually cause rupture of the plaque, resulting in the formation of thrombus, and possibly heart attack. It has long been recognized that the formation of a plaque relates to the cholesterol concentration in the blood. For example, individuals with LDL above 190 mg/dL and HDL below 40 mg/dL are at high risk, while individuals with LDL below 100 mg/dL and HDL above 50 mg/dL are at no risk. In this paper, we developed a mathematical model of the formation of a plaque, which includes the following key variables: LDL and HDL, free radicals and oxidized LDL, MMP and TIMP, cytockines: MCP-1, IFN-γ, IL-12 and PDGF, and cells: macrophages, foam cells, T cells and smooth muscle cells. The model is given by a system of partial differential equations with in evolving plaque. Simulations of the model show how the combination of the concentrations of LDL and HDL in the blood determine whether a plaque will grow or disappear. More precisely, we create a map, showing the risk of plaque development for any pair of values (LDL,HDL). [ABSTRACT FROM AUTHOR]

This paper is a selective study of the mathematics and people involved with a specific space mission, namely the Mars Exploration Rover (MER) mission launched in 2003. The specific mathematics of the MER mission are sought uncovered through interviews with applied scientists who worked with different aspects of the mission at the Jet Propulsion Laboratory (JPL). Some of the more specific questions attempted answered through this article for instance concerns if the aerospace industry, exemplified by the MER mission, calls for new developments in mathematics or if it mostly relies on well established theories; how much independence the scientists have in their daily work and in their choosing of solutions to problems and whether or not this variate within different areas of the mission; how ready the aerospace industry is for new solutions and new ideas; and to what extent the economics of the missions play a part in this. [ABSTRACT FROM AUTHOR]

This paper summarizes the findings of a workshop convened in the United States in 2018 to discuss methods in coastal and estuarine modeling and to propose key areas of research and development needed to improve their accuracy and reliability. The focus of this paper is on physical processes, and we provide an overview of the current state-of-the-art based on presentations and discussions at the meeting, which revolved around the four primary themes of parameterizations, numerical methods, in-situ and remote-sensing measurements, and high-performance computing. A primary outcome of the workshop was agreement on the need to reduce subjectivity and improve reproducibility in modeling of physical processes in the coastal ocean. Reduction of subjectivity can be accomplished through development of standards for benchmarks, grid generation, and validation, and reproducibility can be improved through development of standards for input/output, coupling and model nesting, and reporting. Subjectivity can also be reduced through more engagement with the applied mathematics and computer science communities to develop methods for robust parameter estimation and uncertainty quantification. Such engagement could be encouraged through more collaboration between the forward and inverse modeling communities and integration of more applied math and computer science into oceanography curricula. Another outcome of the workshop was agreement on the need to develop high-resolution models that scale on advanced HPC systems to resolve, rather than parameterize, processes with horizontal scales that range between the depth and the internal Rossby deformation scale. Unsurprisingly, more research is needed on parameterizations of processes at scales smaller than the depth, including parameterizations for drag (including bottom roughness, bedforms, vegetation and corals), wave breaking, and air–sea interactions under strong wind conditions. Other topics that require significantly more work to better parameterize include nearshore wave modeling, sediment transport modeling, and morphodynamics. Finally, it was agreed that coastal models should be considered as key infrastructure needed to support research, just like laboratory facilities, field instrumentation, and research vessels. This will require a shift in the way proposals related to coastal ocean modeling are reviewed and funded. • Standards are needed for I/O, benchmarks, coupling/nesting, grids, and validation. • Methods for robust parameter estimation and uncertainty quantification are needed. • Models should resolve scales between the depth and the Rossby deformation scale. • Models for bottom drag, wave breaking, and air–sea interactions should be improved. • Improved sediment transport, nearshore circulation, morphodynamics models are needed. [ABSTRACT FROM AUTHOR]

In commemoration of the 40th Anniversary of the Quarterly Journal of Mechanics and Applied Mathematics, Professor C. W. Jones wrote a fine account of its inauguration and history, replete both with facts and amusing anecdotes. Here his account is extended to cover the last ten years and to take note of the 50th Anniversary. [ABSTRACT FROM AUTHOR]

We conduct a detailed investigation of correlations between real-time expressions of individuals made across the United States and a wide range of emotional, geographic, demographic, and health characteristics. We do so by combining (1) a massive, geo-tagged data set comprising over 80 million words generated in 2011 on the social network service Twitter and (2) annually-surveyed characteristics of all 50 states and close to 400 urban populations. Among many results, we generate taxonomies of states and cities based on their similarities in word use; estimate the happiness levels of states and cities; correlate highly-resolved demographic characteristics with happiness levels; and connect word choice and message length with urban characteristics such as education levels and obesity rates. Our results show how social media may potentially be used to estimate real-time levels and changes in population-scale measures such as obesity rates. [ABSTRACT FROM AUTHOR]

Abstract: Mathematical ballistics in the United States until the First World War was largely dependent on the work of European authors such as Francesco Siacci of Italy. The war brought with it a call to the American mathematical community for participation in ballistics problems. The community responded by sending mathematicians to work at newly formed ballistics research facilities at Aberdeen Proving Grounds and Washington, D.C. This paper focuses on the efforts of Forest Ray Moulton and details how he dealt with various aspects of a single problem: differential variations in the ballistic trajectory due to known factors. [Copyright &y& Elsevier]

Financial literacy is ideally suited to be integrated into mathematics courses and taught in an interdisciplinary manner. Students learn best and are motivated when tackling real-world meaningful questions. This article shares how elementary mathematics was applied to better understand the debate about raising the minimum wage and the United States National Debt. To serve as a guide for other teachers who wish to incorporate financial literacy into their mathematics courses and take an interdisciplinary approach, this article suggests readings, data sets, and pedagogical practices. Students were engaged and enthusiastic to work on problems that challenged their thinking about financial issues. [ABSTRACT FROM AUTHOR]

We aim to determine whether a game-theoretic model between an insurer and a healthcare practice yields a predictive equilibrium that incentivizes either player to deviate from a fee-for-service to capitation payment system. Using United States data from various primary care surveys, we find that non-extreme equilibria (i.e., shares of patients, or shares of patient visits, seen under a fee-for-service payment system) can be derived from a Stackelberg game if insurers award a non-linear bonus to practices based on performance. Overall, both insurers and practices can be incentivized to embrace capitation payments somewhat, but potentially at the expense of practice performance. [ABSTRACT FROM AUTHOR]

Objective: The Centers for Disease Control and Prevention (CDC) coordinates a labor-intensive process to measure the prevalence of autism spectrum disorder (ASD) among children in the United States. Random forests methods have shown promise in speeding up this process, but they lag behind human classification accuracy by about 5%. We explore whether more recently available document classification algorithms can close this gap. Materials and methods: Using data gathered from a single surveillance site, we applied 8 supervised learning algorithms to predict whether children meet the case definition for ASD based solely on the words in their evaluations. We compared the algorithms’ performance across 10 random train-test splits of the data, using classification accuracy, F1 score, and number of positive calls to evaluate their potential use for surveillance. Results: Across the 10 train-test cycles, the random forest and support vector machine with Naive Bayes features (NB-SVM) each achieved slightly more than 87% mean accuracy. The NB-SVM produced significantly more false negatives than false positives (P = 0.027), but the random forest did not, making its prevalence estimates very close to the true prevalence in the data. The best-performing neural network performed similarly to the random forest on both measures. Discussion: The random forest performed as well as more recently available models like the NB-SVM and the neural network, and it also produced good prevalence estimates. NB-SVM may not be a good candidate for use in a fully-automated surveillance workflow due to increased false negatives. More sophisticated algorithms, like hierarchical convolutional neural networks, may not be feasible to train due to characteristics of the data. Current algorithms might perform better if the data are abstracted and processed differently and if they take into account information about the children in addition to their evaluations. Conclusion: Deep learning models performed similarly to traditional machine learning methods at predicting the clinician-assigned case status for CDC’s autism surveillance system. While deep learning methods had limited benefit in this task, they may have applications in other surveillance systems. [ABSTRACT FROM AUTHOR]

Background: Risk prediction is crucial in many areas of medical practice, such as cardiac transplantation, but existing clinical risk-scoring methods have suboptimal performance. We develop a novel risk prediction algorithm and test its performance on the database of all patients who were registered for cardiac transplantation in the United States during 1985-2015. Methods and findings: We develop a new, interpretable, methodology (ToPs: Trees of Predictors) built on the principle that specific predictive (survival) models should be used for specific clusters within the patient population. ToPs discovers these specific clusters and the specific predictive model that performs best for each cluster. In comparison with existing clinical risk scoring methods and state-of-the-art machine learning methods, our method provides significant improvements in survival predictions, both post- and pre-cardiac transplantation. For instance: in terms of 3-month survival post-transplantation, our method achieves AUC of 0.660; the best clinical risk scoring method (RSS) achieves 0.587. In terms of 3-year survival/mortality predictions post-transplantation (in comparison to RSS), holding specificity at 80.0%, our algorithm correctly predicts survival for 2,442 (14.0%) more patients (of 17,441 who actually survived); holding sensitivity at 80.0%, our algorithm correctly predicts mortality for 694 (13.0%) more patients (of 5,339 who did not survive). ToPs achieves similar improvements for other time horizons and for predictions pre-transplantation. ToPs discovers the most relevant features (covariates), uses available features to best advantage, and can adapt to changes in clinical practice. Conclusions: We show that, in comparison with existing clinical risk-scoring methods and other machine learning methods, ToPs significantly improves survival predictions both post- and pre-cardiac transplantation. ToPs provides a more accurate, personalized approach to survival prediction that can benefit patients, clinicians, and policymakers in making clinical decisions and setting clinical policy. Because survival prediction is widely used in clinical decision-making across diseases and clinical specialties, the implications of our methods are far-reaching. [ABSTRACT FROM AUTHOR]

Recent research has produced a number of methods for forecasting seasonal influenza outbreaks. However, differences among the predicted outcomes of competing forecast methods can limit their use in decision-making. Here, we present a method for reconciling these differences using Bayesian model averaging. We generated retrospective forecasts of peak timing, peak incidence, and total incidence for seasonal influenza outbreaks in 48 states and 95 cities using 21 distinct forecast methods, and combined these individual forecasts to create weighted-average superensemble forecasts. We compared the relative performance of these individual and superensemble forecast methods by geographic location, timing of forecast, and influenza season. We find that, overall, the superensemble forecasts are more accurate than any individual forecast method and less prone to producing a poor forecast. Furthermore, we find that these advantages increase when the superensemble weights are stratified according to the characteristics of the forecast or geographic location. These findings indicate that different competing influenza prediction systems can be combined into a single more accurate forecast product for operational delivery in real time. [ABSTRACT FROM AUTHOR]

Time spent fishing is the effort metric often studied in fisheries but it may under-represent the effort actually expended by fishers. Entire fishing trips, from the time vessels leave port until they return, may prove more useful for examining trends in fleet dynamics, fisher behavior, and fishing costs. However, such trip information is often difficult to resolve. We identified ~30,000 trips made by vessels that targeted walleye pollock (Gadus chalcogrammus) in the Eastern Bering Sea from 2008–2014 by using vessel monitoring system (VMS) and landings data. We compared estimated trip durations to observer data, which were available for approximately half of trips. Total days at sea were estimated with < 1.5% error and 96.4% of trip durations were either estimated with < 5% error or they were within expected measurement error. With 99% accuracy, we classified trips as fishing for pollock, for another target species, or not fishing. This accuracy lends strong support to the use of our method with unobserved trips across North Pacific fisheries. With individual trips resolved, we examined potential errors in datasets which are often viewed as “the truth.” Despite having > 5 million VMS records (timestamps and vessel locations), this study was as much about understanding and managing data errors as it was about characterizing trips. Missing VMS records were pervasive and they strongly influenced our approach. To understand implications of missing data on inference, we simulated removal of VMS records from trips. Removal of records straightened (i.e., shortened) vessel trajectories, and travel distances were underestimated, on average, by 1.5–13.4% per trip. Despite this bias, VMS proved robust for trip characterization and for improved quality control of human-recorded data. Our scrutiny of human-reported and VMS data advanced our understanding of the potential utility and challenges facing VMS users globally. [ABSTRACT FROM AUTHOR]

We study gender representation on the editorial boards of 435 journals in the mathematical sciences. Women are known to comprise approximately 15% of tenure-stream faculty positions in doctoral-granting mathematical sciences departments in the United States. Compared to this group, we find that 8.9% of the 13067 editorships in our study are held by women. We describe group variations within the editorships by identifying specific journals, subfields, publishers, and countries that significantly exceed or fall short of this average. To enable our study, we develop a semi-automated method for inferring gender that has an estimated accuracy of 97.5%. Our findings provide the first measure of gender distribution on editorial boards in the mathematical sciences, offer insights that suggest future studies in the mathematical sciences, and introduce new methods that enable large-scale studies of gender distribution in other fields. [ABSTRACT FROM AUTHOR]

Background: Several studies have focused on stratifying patients according to their level of readmission risk, fueled in part by incentive programs in the U.S. that link readmission rates to the annual payment update by Medicare. Patient-specific predictions about readmission have not seen widespread use because of their limited accuracy and questions about the efficacy of using measures of risk to guide clinical decisions. We construct a predictive model for readmissions for congestive heart failure (CHF) and study how its predictions can be used to perform patient-specific interventions. We assess the cost-effectiveness of a methodology that combines prediction and decision making to allocate interventions. The results highlight the importance of combining predictions with decision analysis. Methods: We construct a statistical classifier from a retrospective database of 793 hospital visits for heart failure that predicts the likelihood that patients will be rehospitalized within 30 days of discharge. We introduce a decision analysis that uses the predictions to guide decisions about post-discharge interventions. We perform a cost-effectiveness analysis of 379 additional hospital visits that were not included in either the formulation of the classifiers or the decision analysis. We report the performance of the methodology and show the overall expected value of employing a real-time decision system. Findings: For the cohort studied, readmissions are associated with a mean cost of $13,679 with a standard error of $1,214. Given a post-discharge plan that costs $1,300 and that reduces 30-day rehospitalizations by 35%, use of the proposed methods would provide an 18.2% reduction in rehospitalizations and save 3.8% of costs. Conclusions: Classifiers learned automatically from patient data can be joined with decision analysis to guide the allocation of post-discharge support to CHF patients. Such analyses are especially valuable in the common situation where it is not economically feasible to provide programs to all patients. [ABSTRACT FROM AUTHOR]

We developed linguistics-driven prediction models to estimate the risk of suicide. These models were generated from unstructured clinical notes taken from a national sample of U.S. Veterans Administration (VA) medical records. We created three matched cohorts: veterans who committed suicide, veterans who used mental health services and did not commit suicide, and veterans who did not use mental health services and did not commit suicide during the observation period (n = 70 in each group). From the clinical notes, we generated datasets of single keywords and multi-word phrases, and constructed prediction models using a machine-learning algorithm based on a genetic programming framework. The resulting inference accuracy was consistently 65% or more. Our data therefore suggests that computerized text analytics can be applied to unstructured medical records to estimate the risk of suicide. The resulting system could allow clinicians to potentially screen seemingly healthy patients at the primary care level, and to continuously evaluate the suicide risk among psychiatric patients. [ABSTRACT FROM AUTHOR]

Background: A striking characteristic of the past four influenza pandemic outbreaks in the United States has been the multiple waves of infections. However, the mechanisms responsible for the multiple waves of influenza or other acute infectious diseases are uncertain. Understanding these mechanisms could provide knowledge for health authorities to develop and implement prevention and control strategies. Materials and Methods: We exhibit five distinct mechanisms, each of which can generate two waves of infections for an acute infectious disease. The first two mechanisms capture changes in virus transmissibility and behavioral changes. The third mechanism involves population heterogeneity (e.g., demography, geography), where each wave spreads through one sub-population. The fourth mechanism is virus mutation which causes delayed susceptibility of individuals. The fifth mechanism is waning immunity. Each mechanism is incorporated into separate mathematical models, and outbreaks are then simulated. We use the models to examine the effects of the initial number of infected individuals (e.g., border control at the beginning of the outbreak) and the timing of and amount of available vaccinations. Results: Four models, individually or in any combination, reproduce the two waves of the 2009 H1N1 pandemic in the United States, both qualitatively and quantitatively. One model reproduces the two waves only qualitatively. All models indicate that significantly reducing or delaying the initial numbers of infected individuals would have little impact on the attack rate. Instead, this reduction or delay results in a single wave as opposed to two waves. Furthermore, four of these models also indicate that a vaccination program started earlier than October 2009 (when the H1N1 vaccine was initially distributed) could have eliminated the second wave of infection, while more vaccine available starting in October would not have eliminated the second wave. [ABSTRACT FROM AUTHOR]