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A review of the literature suggests that few studies use formative indicator measurement models, even though they should. Therefore, the purpose of this research is to (a) discuss the distinction between formative and reflective measurement models, (b) develop a set of conceptual criteria that can be used to determine whether a construct should be modeled as having formative or reflective indicators, (c) review the marketing literature to obtain an estimate of the extent of measurement model misspecification in the field, (d) estimate the extent to which measurement model misspecification biases estimates of the relationships between constructs using a Monte Carlo simulation, and (e) provide recommendations for modeling formative indicator constructs. [ABSTRACT FROM AUTHOR]

The use of thermal time is essential in plant studies and crop growth modeling because correcting time for temperature allows working in fluctuating conditions as if temperature was constant. However, thermal time is often seen as a loose concept because of a multitude of thermal functions and case-specific parameter values. Our hypothesis is that these different formalisms and parameterization could emerge from common principles and a common response of plant development to temperature, but with several counfounding factors which are not taken into account. We first show that these calculations of thermal time are based on sound common principles and mathematical formalisms. We test, via a modelling exercise of nine case studies using maize plants grown in three field sites, how a given "ground truth" response of plant development rate to temperature can be affected if an experimenter either considers or ignores confounding factors. We also show that apparent differences in temperature responses between phenological stages of the growth cycle, between day and night, or between plant genotypes may be due to the confounding effects of evaporative demand, the range of temperatures, and the time interval at which measurements are taken. On the basis of our findings, we propose that the critical point in the use of a given formalism of thermal time calculation is to ensure that the chosen model is compatible with the temporal definition, temperature range, and environmental scenario in the considered dataset. [ABSTRACT FROM AUTHOR]

Recent contributions to the financial econometrics literature exploit high-frequency (HF) data to improve models for daily asset returns. This paper proposes a new class of dynamic extreme value models that profit from HF data when estimating the tails of daily asset returns. Our realized peaks-over-threshold approach provides estimates for the tails of the time-varying conditional return distribution. An in-sample fit to the S&P 500 index returns suggests that HF data convey information on daily extreme returns beyond that included in low frequency (LF) data. Finally, out-of-sample forecasts of conditional risk measures obtained with HF measures outperform those obtained with LF measures. [ABSTRACT FROM AUTHOR]

Recent maps of the halo using RR Lyrae from Pan-STARRS1 depict the spatial structure of the Sagittarius stream, showing the leading and trailing stream apocentres differ in Galactocentric radius by a factor of 2, and also resolving substructure in the stream at these apocentres. Here we present dynamical models that reproduce these features of the stream in simple Galactic potentials. We find that debris at the apocentres must be dynamically young, being stripped off in pericentric passages either one or two orbital periods ago. The ratio of the leading and trailing apocentres is sensitive to both dynamical friction and the outer slope of the Galactic rotation curve. These dependencies can be understood with simple regularities connecting the apocentric radii, circular velocities, and orbital period of the progenitor. The effect of dynamical friction can be constrained using substructure within the leading apocentre. Our models are far from final; the errors allowed when sampling parameter space are deliberately generous, not every stream feature is reproduced, and we explore a limited set of potentials. Still, it is interesting that we consistently find the mass within 100 kpc to be |${\sim } \! 7 \times 10^{11} \, {\rm M}_{\odot}$|⁠, with a nearly flat rotation curve between 50 and 100 kpc. This points to a more extended Galactic halo than assumed in some current models. We show one example model in various observational dimensions. A plot of velocity versus distance separates younger from older debris, and suggests that the young trailing debris will serve as an especially useful probe of the outer Galactic potential. [ABSTRACT FROM AUTHOR]

This article applies the theory of rate-independent systems to model the locomotion of bio-mimetic soft crawlers. We prove the well-posedness of the approach and illustrate how the various strategies adopted by crawlers to achieve locomotion, such as friction anisotropy, complex shape changes and control on the friction coefficients, can be effectively described in terms of stasis domains. Compared to other rate-independent systems, locomotion models do not present any Dirichlet boundary condition, so that all rigid translations are admissible displacements, resulting in a non-coercivity of the energy term. We prove that existence and uniqueness of solution are guaranteed under suitable assumptions on the dissipation potential. Such results are then extended to the case of time-dependent dissipation potential. [ABSTRACT FROM AUTHOR]

The article presents the pioneering study of a linear system of equilibrium equations of elastic bodies with double porosity when the rigid skeleton of the body is a mixture of two isotropic materials. The general solutions of this system of equations are represented by means of harmonic functions and a metaharmonic function. Based on the constructed general solution, the class of boundary value problems of porous elasticity for the rectangular parallelepiped is solved analytically using the method of separation of variables. The corresponding boundary-contact problems for the multilayer rectangular parallelepiped are also considered. [ABSTRACT FROM AUTHOR]

In the present article, a spectral model is developed for residually stressed electro-elastic bodies. The model uses a total energy function that depends on the right stretch tensor, residual stress tensor and one of the electric variables. Some boundary value results with cylindrical symmetry are given. Results for the inflation of a hollow sphere, where the residual stress is assumed to depend only on the radial position, are also given. The constitutive formulation contains spectral invariants that have an immediate physical interpretation which is useful in a rigorous construction of a specific form of the total energy function via an appropriate experiment [ABSTRACT FROM AUTHOR]

The key object in the Ehrhart theory of lattice polytopes is the numerator polynomial of the rational generating series of the Ehrhart polynomial, called $$h^*$$ -polynomial. In this article, we prove a new result on the vanishing of its coefficients. As a consequence, we get that $$h^*_i =0$$ implies $$h^*_{i+1}=0$$ if the lattice points of the lattice polytope affinely span the ambient lattice. This generalizes a recent result in algebraic geometry due to Blekherman, Smith, and Velasco, and implies a polyhedral consequence of the Eisenbud–Goto conjecture. We also discuss how this study is motivated by unimodality questions and how it relates to decomposition results on lattice polytopes of given degree. The proof methods involve a novel combination of successive modifications of half-open triangulations and considerations of number-theoretic step functions. [ABSTRACT FROM AUTHOR]

The coffee industry relies on fundamental research to improve the techniques and processes related to its products. While recent theoretical and modelling work has focused on the heat and mass transfer processes within roasting coffee beans, modelling and analysis of chemical reactions in the context of multiphase models of roasting beans has not been well studied. In this paper, we incorporate modified evaporation rates and chemical reaction groups to improve existing mathematical models of roasting coffee beans. We model the phase change from liquid to vapour water within the bean during roasting using first-order Arrhenius-like global reactions, and for other components of the bean, we consider a three-component solid phase model which includes sucrose, reducing sugars and other organic compounds, which allows for porosity of the solid matrix to vary during the roasting process. We non-dimensionalize and then solve the multiphase model numerically, comparing the simulations with data we have collected through full bean and chopped bean experiments. We demonstrate that numerical solutions of the enhanced multiphase model with global water reactions and three-component solid phase reactions agree with experimental data for the average moisture content in whole beans and small chunks of bean, but that the data allows for a range to possible parameter values. We discuss other experimental data that might be collected to more firmly determine the parameters and hence the behaviour more generally. The indeterminacy of the parameters ensures that the additional effects included in the model will enable better understanding the coffee bean roasting process. [ABSTRACT FROM AUTHOR]

The low Reynolds number fluid flow through a channel with varying elliptic cross section is studied, with the inclusion of slip on the fluid–solid interface. An analytical expression for the flux through the channel is obtained, assuming that the slip length is small in comparison to the width of the channel, and a simplified expression for the flux in the limit of small eccentricity is also derived. Numerical results show that there is excellent agreement between the analytical expressions and the finite element solution for three examples presented in this paper. The expression for the flux is reformulated in terms of the semi-major and semi-minor radii, and the area and circumference, in order to estimate the flow through irregular channels. It is shown that the resulting expressions are extensions to existing estimation methods, the 'Aissen approximation' and 'hydraulic radius' methods, to include the effect of slip flow through channels with non-uniform cross section. Numerical results show that there is good agreement between the suggested flux estimation methods and the finite element solution for a pore throat extracted from a Berea sandstone. Furthermore, the suggested methods significantly outperform two common methods used to estimate the flux through an irregular channel, the 'volume matching' and 'minimum radius' methods. [ABSTRACT FROM AUTHOR]

Mendelian randomization studies employ genotypes as experimental handles to infer the effect of genetically modified exposures (e.g. vitamin D exposure) on disease outcomes (e.g. mortality). The statistical analysis of these studies makes use of the standard instrumental variables framework. Many of these studies focus on elderly populations, thereby ignoring the problem of left truncation, which arises due to the selection of study participants being conditional upon surviving up to the time of study onset. Such selection, in general, invalidates the assumptions on which the instrumental variables analysis rests. We show that Mendelian randomization studies of adult or elderly populations will therefore, in general, return biased estimates of the exposure effect when the considered genotype affects mortality; in contrast, standard tests of the causal null hypothesis that the exposure does not affect the mortality rate remain unbiased, even when they ignore this problem of left truncation. To eliminate "survivor bias" or "truncation bias" from the effect of exposure on mortality, we next propose various simple strategies under a semi-parametric additive hazard model. We examine the performance of the proposed methods in simulation studies and use them to infer the effect of vitamin D on all-cause mortality based on the Monica10 study with the genetic variant filaggrin as instrumental variable. [ABSTRACT FROM AUTHOR]

Modern epidemiological studies collect data on time-varying individual-specific characteristics, such as body mass index and blood pressure. Incorporation of such time-dependent covariates in time-to-event models is of great interest, but raises some challenges. Of specific concern are measurement error, and the non-synchronous updating of covariates across individuals, due for example to missing data. It is well known that in the presence of either of these issues the last observation carried forward (LOCF) approach traditionally used leads to bias. Joint models of longitudinal and time-to-event outcomes, developed recently, address these complexities by specifying a model for the joint distribution of all processes and are commonly fitted by maximum likelihood or Bayesian approaches. However, the adequate specification of the full joint distribution can be a challenging modeling task, especially with multiple longitudinal markers. In fact, most available software packages are unable to handle more than one marker and offer a restricted choice of survival models. We propose a two-stage approach, Multiple Imputation for Joint Modeling (MIJM), to incorporate multiple time-dependent continuous covariates in the semi-parametric Cox and additive hazard models. Assuming a primary focus on the time-to-event model, the MIJM approach handles the joint distribution of the markers using multiple imputation by chained equations, a computationally convenient procedure that is widely available in mainstream statistical software. We developed an R package "survtd" that allows MIJM and other approaches in this manuscript to be applied easily, with just one call to its main function. A simulation study showed that MIJM performs well across a wide range of scenarios in terms of bias and coverage probability, particularly compared with LOCF, simpler two-stage approaches, and a Bayesian joint model. The Framingham Heart Study is used to illustrate the approach. [ABSTRACT FROM AUTHOR]

Cohort data are often incomplete because some subjects drop out of the study, and inverse probability weighting (IPW), multiple imputation (MI), and linear increments (LI) are methods that deal with such missing data. In cohort studies of ageing, missing data can arise from dropout or death. Methods that do not distinguish between these reasons for missingness typically provide inference about a hypothetical cohort where no one can die (immortal cohort). It has been suggested that inference about the cohort composed of those who are still alive at any time point (partly conditional inference) may be more meaningful. MI, LI, and IPW can all be adapted to provide partly conditional inference. In this article, we clarify and compare the assumptions required by these MI, LI, and IPW methods for partly conditional inference on continuous outcomes. We also propose augmented IPW estimators for making partly conditional inference. These are more efficient than IPW estimators and more robust to model misspecification. Our simulation studies show that the methods give approximately unbiased estimates of partly conditional estimands when their assumptions are met, but may be biased otherwise. We illustrate the application of the missing data methods using data from the 'Origins of Variance in the Old-old' Twin study. [ABSTRACT FROM AUTHOR]

Distributed lag models (DLMs) have been widely used in environmental epidemiology to quantify the lagged effects of air pollution on an outcome of interest such as mortality or cardiovascular events. Generally speaking, DLMs can be applied to time-series data where the current measure of an independent variable and its lagged measures collectively affect the current measure of a dependent variable. The corresponding distributed lag (DL) function represents the relationship between the lags and the coefficients of the lagged exposure variables. Common choices include polynomials and splines. On one hand, such a constrained DLM specifies the coefficients as a function of lags and reduces the number of parameters to be estimated; hence, higher efficiency can be achieved. On the other hand, under violation of the assumption about the DL function, effect estimates can be severely biased. In this article, we propose a general framework for shrinking coefficient estimates from an unconstrained DLM, that are unbiased but potentially inefficient, toward the coefficient estimates from a constrained DLM to achieve a bias-variance trade-off. The amount of shrinkage can be determined in various ways, and we explore several such methods: empirical Bayes-type shrinkage, a hierarchical Bayes approach, and generalized ridge regression. We also consider a two-stage shrinkage approach that enforces the effect estimates to approach zero as lags increase. We contrast the various methods via an extensive simulation study and show that the shrinkage methods have better average performance across different scenarios in terms of mean squared error (MSE).We illustrate the methods by using data from the National Morbidity, Mortality, and Air Pollution Study (NMMAPS) to explore the association between PM$_{10}$, O$_3$, and SO$_2$ on three types of disease event counts in Chicago, IL, from 1987 to 2000. [ABSTRACT FROM AUTHOR]

Dependent data arise frequently in applied research and several approaches to adjusting for the dependence among observations have been proposed in quantile regression. Cluster bootstrap is generally inefficient and computationally demanding, especially when the number of clusters is large. When the primary interest is on marginal quantiles, estimating equations have been proposed that estimate a working correlation matrix from the regression residuals' sign. However, the Pearson's correlation coefficient is an inadequate measure of dependence between binary variables because its range depends on their marginal probabilities. Instead, we propose to model the working correlation matrix through odds ratios. Different working structures can be easily estimated by suitable logistic regression models. These structures can be parametrized to depend on covariates and clusters. Simulations show that the proposed estimator has similar behavior to that of generalized estimating equations applied to regression for the mean. We study marginal quantiles of cognitive behavior with data from a randomized trial for treatment of obsessive compulsive disorder. [ABSTRACT FROM AUTHOR]

In neuroimaging, hundreds to hundreds of thousands of tests are performed across a set of brain regions or all locations in an image. Recent studies have shown that the most common family-wise error (FWE) controlling procedures in imaging, which rely on classical mathematical inequalities or Gaussian random field theory, yield FWE rates (FWER) that are far from the nominal level. Depending on the approach used, the FWER can be exceedingly small or grossly inflated. Given the widespread use of neuroimaging as a tool for understanding neurological and psychiatric disorders, it is imperative that reliable multiple testing procedures are available. To our knowledge, only permutation joint testing procedures have been shown to reliably control the FWER at the nominal level. However, these procedures are computationally intensive due to the increasingly available large sample sizes and dimensionality of the images, and analyses can take days to complete. Here, we develop a parametric bootstrap joint testing procedure. The parametric bootstrap procedure works directly with the test statistics, which leads to much faster estimation of adjusted p-values than resampling-based procedures while reliably controlling the FWER in sample sizes available in many neuroimaging studies. We demonstrate that the procedure controls the FWER in finite samples using simulations, and present region- and voxel-wise analyses to test for sex differences in developmental trajectories of cerebral blood flow. [ABSTRACT FROM AUTHOR]

Mediation analysis explores the degree to which an exposure's effect on an outcome is diverted through a mediating variable. We describe a classical regression framework for conducting mediation analyses in which estimates of causal mediation effects and their variance are obtained from the fit of a single regression model. The vector of changes in exposure pathway coefficients, which we named the essential mediation components (EMCs), is used to estimate standard causal mediation effects. Because these effects are often simple functions of the EMCs, an analytical expression for their model-based variance follows directly. Given this formula, it is instructive to revisit the performance of routinely used variance approximations (e.g., delta method and resampling methods). Requiring the fit of only one model reduces the computation time required for complex mediation analyses and permits the use of a rich suite of regression tools that are not easily implemented on a system of three equations, as would be required in the Baron-Kenny framework. Using data from the BRAIN-ICU study, we provide examples to illustrate the advantages of this framework and compare it with the existing approaches. [ABSTRACT FROM AUTHOR]

We consider the problem of individual-specific medication level recommendation (initiation, removal, increase, or decrease) for asthma sufferers. Asthma is one of the most common chronic diseases in both adults and children, affecting 8% of the US population and costing $37-63 billion/year in the United States of America. Asthma is a complex disease, whose symptoms may wax and wane, making it difficult for clinicians to predict outcomes and prognosis. Improved ability to predict prognosis can inform decision making and may promote conversations between clinician and provider around optimizing medication therapy. Data from the US Medical Expenditure Panel Survey (MEPS) years 2000-2010 were used to fit a longitudinal model for a multivariate response of adverse events (Emergency Department or in-patient visits, excessive rescue inhaler use, and oral steroid use). To reduce bias in the estimation of medication effects, medication level was treated as a latent process which was restricted to be consistent with prescription refill data. This approach is demonstrated to be effective in the MEPS cohort via predictions on a validation hold out set and a synthetic data simulation study. This framework can be easily generalized to medication decisions for other conditions as well. [ABSTRACT FROM AUTHOR]

Until recently, high-throughput gene expression technology, such as RNA-Sequencing (RNA-seq) required hundreds of thousands of cells to produce reliable measurements. Recent technical advances permit genome-wide gene expression measurement at the single-cell level. Single-cell RNA-Seq (scRNA-seq) is the most widely used and numerous publications are based on data produced with this technology. However, RNA-seq and scRNA-seq data are markedly different. In particular, unlike RNA-seq, the majority of reported expression levels in scRNA-seq are zeros, which could be either biologically-driven, genes not expressing RNA at the time of measurement, or technically-driven, genes expressing RNA, but not at a sufficient level to be detected by sequencing technology. Another difference is that the proportion of genes reporting the expression level to be zero varies substantially across single cells compared to RNA-seq samples. However, it remains unclear to what extent this cell-to-cell variation is being driven by technical rather than biological variation. Furthermore, while systematic errors, including batch effects, have been widely reported as a major challenge in high-throughput technologies, these issues have received minimal attention in published studies based on scRNA-seq technology. Here, we use an assessment experiment to examine data from published studies and demonstrate that systematic errors can explain a substantial percentage of observed cell-to-cell expression variability. Specifically, we present evidence that some of these reported zeros are driven by technical variation by demonstrating that scRNA-seq produces more zeros than expected and that this bias is greater for lower expressed genes. In addition, this missing data problem is exacerbated by the fact that this technical variation varies cell-to-cell. Then, we show how this technical cell-to-cell variability can be confused with novel biological results. Finally, we demonstrate and discuss how batch-effects and confounded experiments can intensify the problem. [ABSTRACT FROM AUTHOR]

We extend our analysis on the Oldroyd-B model in Barrett & Boyaval (2011, Math. Models Methods Appl. Sci. 21, 1783–1837) to consider the finite element approximation of the FENE-P system of equations, which models a dilute polymeric fluid, in a bounded domain $$\mathscr{D} \subset {\mathbb R}^d$$, $$d=2$$ or $$3$$, subject to no-flow boundary conditions. Our schemes are based on approximating the pressure and the symmetric conformation tensor by either (a) piecewise constants or (b) continuous piecewise linears. In case (a), the velocity field is approximated by continuous piecewise quadratics ($$d=2$$) or a reduced version, where the tangential component on each simplicial edge ($$d=2$$) or face ($$d=3$$) is linear. In case (b), the velocity field is approximated by continuous piecewise quadratics or the mini-element. We show that both of these types of schemes, based on the backward-Euler-type time discretization, satisfy a free energy bound, which involves the logarithm of both the conformation tensor and a linear function of its trace, without any constraint on the time step. Furthermore, for our approximation (b) in the presence of an additional dissipative term in the stress equation, the so-called FENE-P model with stress diffusion, we show (subsequence) convergence in the case $$d=2$$, as the spatial and temporal discretization parameters tend to zero, towards global-in-time weak solutions of this FENE-P system. Hence, we prove existence of global-in-time weak solutions to the FENE-P model with stress diffusion in two spatial dimensions. [ABSTRACT FROM AUTHOR]

This article deals with the numerical analysis of a coupled two-fluid Reynolds-averaged Navier–Stokes (RANS) turbulence model, such as atmosphere–ocean flow. Each fluid is modeled by the coupled steady Stokes equations with the equation for the turbulent kinetic energy (TKE). In this model, the eddy viscosities for velocity and TKE depend on the TKE, the production (source) term for the TKEs is only in $$L^1$$ and the boundary condition for the TKEs on the interface between the two flows depends quadratically on the difference of velocities. To overcome the lack of regularity, we approximate the initial system by a regularized system, in which the eddy viscosities and source terms for the TKEs are regularized by convolution. We perform a full finite element discretization of the regularized model, combined with a decoupled iterative linearization procedure. We prove that the discrete scheme converges to the continuous scheme for large enough eddy viscosities in natural norms. Finally, we present some numerical tests where we study the accuracy of the procedure, and simulate a realistic flow in which an imposed wind in the upper atmosphere generates an upwelling in the oceanic flow. [ABSTRACT FROM AUTHOR]

We establish the error estimates of a conservative finite difference method (CFDM) for the Klein–Gordon–Zakharov (KGZ) system with a dimensionless parameter $${\varepsilon} \in (0,1]$$, which is inversely proportional to the speed of sound. When $${\varepsilon} \rightarrow 0^+$$, the KGZ system collapses to the Klein–Gordon (KG) equation. In the subsonic limit regime, i.e. $$0<{\varepsilon}\ll1$$, the solution propagates waves with wavelength $$O({\varepsilon})$$ and $$O(1)$$ in time and space, respectively, with amplitude at $$O({\varepsilon}^{\alpha^\dagger})$$, where $$\alpha^\dagger=\min\{\alpha,1+\beta,2\}$$, $$\alpha\ge 0$$ and $$\beta\ge-1$$ are two parameters describing the incompatibility of the initial data of the KGZ system with respect to the limiting KG equation. This oscillation in time brings difficulties in designing numerical methods and establishing their error estimates in the subsonic limit regime. We propose a CFDM and analyse the error bounds in this article. By applying the energy method and the limiting KG equation, we obtain two independent error bounds at $$O(h^2/{\varepsilon}^{1-\alpha^*}+\tau^2/{\varepsilon}^{3-\alpha^\dagger})$$ and $$O(h^2+\tau^2+{\varepsilon}^{\alpha^*})$$ with $$h$$ mesh size, $$\tau$$ time step and $$\alpha^*=\min\{1,\alpha,1+\beta\}$$. Hence, we obtain uniform error bounds at $$O(h^2+\tau^{{2}/{4-\alpha^\dagger}})$$ when $$\alpha\ge1$$ and $$\beta\ge 0$$. While for $$\alpha=0$$ or $$\beta=-1$$, the result suggests the meshing strategy requirement of the CFDM is $$h=O({\varepsilon}^{1/2})$$ and $$\tau=O({\varepsilon}^{3/2})$$ for $$0<{\varepsilon}\ll1$$. [ABSTRACT FROM AUTHOR]

This work discusses the main analogies and differences between the deterministic approach underlying most cosmological N -body simulations and the probabilistic interpretation of the problem that is often considered in mathematics and statistical mechanics. In practice, we advocate for averaging over an ensemble of S independent simulations with N particles each in order to study the evolution of the one-point probability density Ψ of finding a particle at a given location of phase space $$({\boldsymbol x},{\boldsymbol v})$$ at time t. The proposed approach is extremely efficient from a computational point of view, with modest CPU and memory requirements, and it provides an alternative to traditional N -body simulations when the goal is to study the average properties of N -body systems, at the cost of abandoning the notion of well-defined trajectories for each individual particle. In one spatial dimension, our results, fully consistent with those previously reported in the literature for the standard deterministic formulation of the problem, highlight the differences between the evolution of the one-point probability density Ψ(x, v, t) and the predictions of the collisionless Boltzmann (Vlasov–Poisson) equation, as well as the relatively subtle dependence on the actual finite number N of particles in the system. We argue that understanding this dependence with N may actually shed more light on the dynamics of real astrophysical systems than the limit N → ∞. [ABSTRACT FROM AUTHOR]

Summary: Precision medicine is an emerging scientific topic for disease treatment and prevention that takes into account individual patient characteristics. It is an important direction for clinical research, and many statistical methods have been proposed recently. One of the primary goals of precision medicine is to obtain an optimal individual treatment rule (ITR), which can help make decisions on treatment selection according to each patient's specific characteristics. Recently, outcome weighted learning (OWL) has been proposed to estimate such an optimal ITR in a binary treatment setting by maximizing the expected clinical outcome. However, for ordinal treatment settings, such as individualized dose finding, it is unclear how to use OWL. In this article, we propose a new technique for estimating ITR with ordinal treatments. In particular, we propose a data duplication technique with a piecewise convex loss function. We establish Fisher consistency for the resulting estimated ITR under certain conditions, and obtain the convergence and risk bound properties. Simulated examples and an application to a dataset from a type 2 diabetes mellitus observational study demonstrate the highly competitive performance of the proposed method compared to existing alternatives. [ABSTRACT FROM AUTHOR]

Summary: In multivariate recurrent event data regression, observation of recurrent events is usually terminated by other events that are associated with the recurrent event processes, resulting in informative censoring. Additionally, some covariates could be measured with errors. In some applications, an instrumental variable is observed in a subsample, namely a calibration sample, which can be applied for bias correction. In this article, we develop two non‐parametric correction approaches to simultaneously correct for the informative censoring and measurement errors in the analysis of multivariate recurrent event data. A shared frailty model is adopted to characterize the informative censoring and dependence among different types of recurrent events. To adjust for measurement errors, a non‐parametric correction method using the calibration sample only is proposed. In the second approach, the information from the whole cohort is incorporated by the generalized method of moments. The proposed methods do not require the Poisson‐type assumption for the multivariate recurrent event process and the distributional assumption for the frailty. Moreover, we do not need to impose any distributional assumption on the underlying covariates and measurement error. Both methods perform well, but the second approach improves efficiency. The proposed methods are applied to the Nutritional Prevention of Cancer trial to assess the effect of selenium treatment on the recurrences of basal cell carcinoma and squamous cell carcinoma. [ABSTRACT FROM AUTHOR]

Summary: We suggest a wild bootstrap resampling technique for nonparametric inference on transition probabilities in a general time‐inhomogeneous Markov multistate model. We first approximate the limiting distribution of the Nelson–Aalen estimator by repeatedly generating standard normal wild bootstrap variates, while the data is kept fixed. Next, a transformation using a functional delta method argument is applied. The approach is conceptually easier than direct resampling for the transition probabilities. It is used to investigate a non‐standard time‐to‐event outcome, currently being alive without immunosuppressive treatment, with data from a recent study of prophylactic treatment in allogeneic transplanted leukemia patients. Due to non‐monotonic outcome probabilities in time, neither standard survival nor competing risks techniques apply, which highlights the need for the present methodology. Finite sample performance of time‐simultaneous confidence bands for the outcome probabilities is assessed in an extensive simulation study motivated by the clinical trial data. Example code is provided in the web‐based Supplementary Materials. [ABSTRACT FROM AUTHOR]

Summary: Case‐cohort study design has been widely used for its cost‐effectiveness. In any real study, there are always other important outcomes of interest beside the failure time that the original case‐cohort study is based on. How to utilize the available case‐cohort data to study the relationship of a secondary outcome with the primary exposure obtained through the case‐cohort study is not well studied. In this article, we propose a non‐parametric estimated likelihood approach for analyzing a secondary outcome in a case‐cohort study. The estimation is based on maximizing a semiparametric likelihood function that is built jointly on both time‐to‐failure outcome and the secondary outcome. The proposed estimator is shown to be consistent, efficient, and asymptotically normal. Finite sample performance is evaluated via simulation studies. Data from the Sister Study is analyzed to illustrate our method. [ABSTRACT FROM AUTHOR]

Summary: Motivated by the Medical Expenditure Panel Survey containing data from individuals’ medical providers and employers across the United States, we propose a new semiparametric procedure for predicting whether a patient will incur high medical expenditure. Problems of the same nature arise in many other important applications where one would like to predict if a future response occurs at the upper (or lower) tail of the response distribution. The common practice is to artificially dichotomize the response variable and then apply an existing classification method such as binomial regression or a classification tree. We propose a new semiparametric prediction rule to classify whether a future response occurs at the upper tail of the response distribution. The new method can be considered a semiparametric estimator of the Bayes rule for classification and enjoys some nice features. It does not require an artificially dichotomized response and better uses the information contained in the data. It does not require any parametric distributional assumptions and tends to be more robust. It incorporates nonlinear covariate effects and can be adapted to construct a prediction interval and hence provides more information about the future response. We provide an R package plaqr to implement the proposed procedure and demonstrate its performance in Monte Carlo simulations. We illustrate the application of the new method on a subset of the Medical Expenditure Panel Survey data. [ABSTRACT FROM AUTHOR]

We give a simple proof of absence of point spectrum for the self-dual extended Harper's model. We get a sharp result which improves that of [ 1 ] in the isotropic self-dual regime. [ABSTRACT FROM AUTHOR]

State/event linear temporal logic (SE-LTL) provides a concise and intuitive way to express properties incorporating both states and events. Automata-theoretic LTL model checking can be applied to verify SE-LTL properties. However, as SE-LTL is not preserved under classical stutterequivalence, conventional partial order reduction (POR) cannot be directly used to check them. In this paper, we propose a novel approach to exploit POR for reducing the state space with respect to SE-LTL formulas. This approach detects a 'state part' of a Büchi automaton (BA) translated from an SE-LTL formula. Based on 'state part', we introduce a definition of SPs of BAs and labeled Kripke structures (LKS) with the integration of POR for reducing the state spaces of the products. The integrated POR modifies conventional POR by introducing an identification of visible actions with respect to events. Moreover, in order to apply POR to the full class of SE-LTL, we provide techniques to exploit POR for checking SE-LTL with the nexttime operator. We have implemented our techniques in SPIN model checker. The experimental results illustrate the potential of the techniques for reduction compared with pure state-based model checking and SE-LTL model checking without POR. [ABSTRACT FROM AUTHOR]

In this article, we show that for any deformation of analytic foliations, there exists a maximal analytic singular foliation on the space of parameters along the leaves of which the deformation is integrable. [ABSTRACT FROM AUTHOR]

This work is motivated by the articles [9] and [19] in which the following two problems are solved. Let O be a finitely generated ℤ-algebra that is an integrally closed domain of characteristic zero, consider the following problems: (A) Fix s that is integral over O, describe all t such that O[s]= O[t]. (B) Fix s and t that are integral over O, describe all pairs (m, n) ϵ ℕ² such that O[sm]= O[tn]. In this article, we solve these problems and provide a uniform bound for a certain "discriminant form equation" that is closely related to Problem (A) when O has characteristic p > 0. While our general strategy roughly follows [9] and [19], many new delicate issues arise due to the presence of the Frobenius automorphism x → xp. Recent advances in unit equations over fields of positive characteristic together with classical results in characteristic zero play an important role in this article. [ABSTRACT FROM AUTHOR]

In this paper we introduce the concept of decorated character variety for the Riemann surfaces arising in the theory of the Painlevé differential equations. Since all Painlevé differential equations (apart from the sixth one) exhibit Stokes phenomenon, we show that it is natural to consider Riemann spheres with holes and bordered cusps on such holes. The decorated character variety is considered here as complexification of the bordered cusped Teichmüller space introduced in [11].Weshow that the decorated character variety of a Riemann sphere with s holes and n ≥ 1 bordered cusps is a Poisson manifold of dimension 3s+2n-6 and we explicitly compute the Poisson brackets which are naturally of cluster type. We also show how to obtain the confluence procedure of the Painlevé differential equations in geometric terms. [ABSTRACT FROM AUTHOR]

Let C be a smooth curve which is complete intersection of a quadric and a degree k > 2 surface in P3 and let C(2) be its second symmetric power. In this paper we study the finite generation of the extended canonical ring R(▵ ,K) := ▵ (a,b)∊Z2 H0(C(2), a▵ + bK), where ▵ is the image of the diagonal and K is the canonical divisor. In case the quadric is smooth, we show that R(▵ ,K) is finitely generated if and only if the difference of the two g1k on C is torsion and then show that this holds on an analytically dense locus of the moduli space of such curves. [ABSTRACT FROM AUTHOR]

This paper concerns mathematical modelling of charge transport across a thin poorly conducting layer between two electrodes. We describe and analyse two alternative approaches to model quantum effects within a continuum theory: the density gradient confinement (DGC) and density gradient tunnelling (DGT) theories. In either case, quantum effects are characterized by a small parameter, which we exploit to analyse the problems asymptotically. We thus find simplified approximate solutions which show excellent agreement with numerical solutions of the full models, and demonstrate previously undocumented oscillatory behaviour both in the charge density profile and in the variation of current with applied potential difference. [ABSTRACT FROM AUTHOR]

We consider a newapproach to both the forward and inverse problems in post-seismic deformation. We present amethod for forward modelling post-seismic deformation in a self-gravitating, heterogeneous and compressible earth with a variety of linear and nonlinear rheologies. We further demonstrate how the adjoint method can be applied to the inverse problem both to invert for rheological structure and to calculate the sensitivity of a given surface measurement to changes in rheology or time-dependence of the source. Both the forward and inverse aspects are illustrated with several numerical examples implemented in a spherically symmetric earth model. [ABSTRACT FROM AUTHOR]

We present numerical conditions for the existence of natural degree-2 Abel maps for any given nodal curve. These conditions depend only on the dual graph of the curve. CoCoA scripts were implemented to check these conditions and to return resolutions of the rational degree-2 Abel maps of the curve by means of blowups along Weil divisors. So far, the scripts have verified the validity of the conditions for numerous curves. [ABSTRACT FROM AUTHOR]

We consider and solve numerically a mathematical model of tumour growth based on cancer stem cells (CSC) hypothesis with the aim of gaining some insight into the relation of different processes leading to exponential growth in solid tumours and into the evolution of different subpopulations of cells. The model consists of four hyperbolic equations of first order to describe the evolution of four subpopulations of cells. A fifth equation is introduced to model the evolution of the moving boundary. The coefficients of the model represent the rates at which reactions occur. In order to integrate numerically the four hyperbolic equations, a formulation in terms of the total derivatives is posed. A finite element discretization is applied to integrate the model equations in space. Our numerical results suggest the existence of a pseudo-equilibrium state reached at the early stage of the tumour, for which the fraction of CSC remains small. We include the study of the behaviour of the solutions for longer times and we obtain that the solutions to the system of partial differential equations stabilize to homogeneous steady states whose values depend only on the values of the parameters. We show that CSC may comprise different proportions of the tumour, becoming, in some cases, the predominant type of cells within the tumour. We also obtain that possible effective measure to detain tumour progression should combine the targeting of CSC with the targeting of progenitor cells. [ABSTRACT FROM AUTHOR]

Let p be a prime number, and F be a nonarchimedean local field of residual characteristic p. We explore the interaction between the pro-p-Iwahori-Hecke algebras of the group GLn(F) and its derived subgroup SLn(F). Using the interplay between these two algebras, we deduce two main results. The first is an equivalence of categories between Hecke modules in characteristic p over the pro-p-Iwahori-Hecke algebra of SL2(Qp) and smooth mod-p representations of SL2(Qp) generated by their pro-p-Iwahori-invariants. The second is a "numerical correspondence" between packets of supersingular Hecke modules in characteristic p over the pro-p-Iwahori-Hecke algebra of SLn(F), and irreducible, n-dimensional projective Galois representations. [ABSTRACT FROM AUTHOR]

In this paper, we prove refined first-order interpolation inequalities for periodic functions and give applications to various refinements of the Carlson-Landau-type inequalities and to magnetic Schrödinger operators. We also obtain Lieb-Thirring inequalities for magnetic Schrödinger operators on multi-dimensional cylinders. [ABSTRACT FROM AUTHOR]

Stimulated by the recent advances in computational tools for the simulation of seismic wave propagation problems in realistic geological configurations, this paper presents a 3D physicsbased numerical analysis of near-source ground motion during the MW 6.0 2012 May 29 earthquake in the Po Plain, Northern Italy. To reproduce with sufficient accuracy some of the most peculiar features of the near-source strong-motion records and of the spatial variability of damage distribution, this study required a sequence of investigations, starting from the analysis of a wide set of near-source records, to the calibration of an improved kinematic seismic source model, up to the development of a 3D numerical model of the portion of the Po Plain interested by the earthquake. The latter includes the basin geometry, characterized by sediment thickness sharply varying from few tens of metres to some kilometres. The spatial resolution of the numerical model is suitable to propagate frequencies up to about 1.5 Hz. Numerical simulations were performed using the open-source high-performance code SPEED, based on the Discontinuous Galerkin Spectral Elements method. The 3D numerical model, coupled with the updated slip distribution along the rupturing fault, proved successful to reproduce with good agreement, measured through quantitative goodness-of-fit criteria, the most relevant features of the observed ground motion. These include: (i) the large fault normal velocity peaks at the near-source stations driven by updip directivity effects; (ii) the small-scale variability at short distance from the source, resulting in the out-of-phase motion at stations separated by only 3 km distance; (iii) the propagation of prominent trains of surface waves, especially in the Northern direction; (iv) the map of earthquake-induced ground uplift with maximum values of about 10 cm, in substantial agreement with geodetic measurements and (v) the two-lobed pattern of the peak ground velocity map, well correlated with the distribution of macroseismic intensity. [ABSTRACT FROM AUTHOR]

We study various capacities on compact Kähler manifolds which generalize the Bedford–Taylor Monge–Ampère capacity. We then use these capacities to study the existence and the regularity of solutions of complex Monge–Ampère equations. [ABSTRACT FROM AUTHOR]

Generalizations of the point-optimal panel unit root tests of Moon, Perron and Phillips (MPP) are developed to cover cases of serially correlated errors. The resulting statistics involve two modifications relative to those of MPP: (a) the error variance is replaced by the long-run variance; (b) centring of the statistic is adjusted to correct for second-order bias effects induced by the correlation between the error and lagged dependent variable. [ABSTRACT FROM AUTHOR]

In this article we study finite element approximations of the time-dependent Stokes system on dynamically changing meshes. Applying the backward Euler method for time discretization we use the discrete Helmholtz or Stokes projection to evaluate the solution at time tn−1 on the new spatial mesh at time tn. The theoretical results consist of a priori error estimates that show a dependence on the time step size not better than (1/Δt). These surprisingly pessimistic upper bounds are complemented by numerical examples giving evidence for a negative convergence rate, at least for a large range of time step sizes, and in this sense backing our theory. These observations imply that using adaptive meshes for incompressible flow problems is delicate and requires further investigation. [ABSTRACT FROM PUBLISHER]

We prove that with high probability, d+1 random Bernoulli polynomials in d variables of degree n () do not possess a common root. [ABSTRACT FROM PUBLISHER]

This work is about the numerical solution of the time-domain Maxwell's equations in dispersive propagation media by a discontinuous Galerkin time-domain method. The Debye model is used to describe the dispersive behaviour of the media. The resulting system of differential equations is solved using a centred-flux discontinuous Galerkin formulation for the discretization in space and a second-order leapfrog scheme for the integration in time. The numerical treatment of the dispersive model relies on an auxiliary differential equation approach similar to that which is adopted in the finite difference time-domain method. Stability estimates are derived through energy considerations and convergence is proved for both the semidiscrete and the fully discrete schemes. [ABSTRACT FROM PUBLISHER]

In the present work, the error behaviour of the first-order Lie–Trotter splitting method for nonlinear evolutionary problems is analysed. In particular, a local error representation that is suitable in the presence of unbounded nonlinear operators and critical parameters is deduced. Such local error expansions together with stability bounds are the basic ingredients in the derivation of convergence estimates. Essential tools in the theoretical analysis are an abstract formulation of differential equations on function spaces and the formal calculus of Lie derivatives. In order to illustrate the general approach, the application of the Lie–Trotter splitting method to Schrödinger equations in the semiclassical regime is studied. From numerical computations presented in the literature, it is expected that exponential operator splitting methods are favourable for the time integration of nonlinear Schrödinger equations, provided that the time-step size is suitably chosen depending on the magnitude of the critical parameter. For the least technical example method, the first-order Lie–Trotter splitting method, this is substantiated by theoretical considerations for the time-dependent Gross–Pitaevskii equation and confirmed by numerical examples. Numerical illustrations for higher-order exponential operator splitting methods complement the considerations. [ABSTRACT FROM PUBLISHER]

This article shows how a non-monotonic rule based system (defeasible logic) can be integrated with numerical computation engines, and how this can be applied to solve the Vehicle Routing Problem. To this end, we have simulated a physical system from which we can obtain numerical information. The physical system perceives information from its environment and generates predicates that can be reasoned by a defeasible logic engine. The conclusions/decisions derived will then be realized by the physical system as it takes actions based on the conclusion derived. Here we consider a scenario where a ‘flock’ of Unmanned Autonomous Vehicles (UAVs) have to navigate within an urban canyon environment. The UAVs are self-autonomous without centralized control. The goal of the UAVs is to navigate to their desired destinations without colliding with each other. In case of possible collision, the UAVs concerned will communicate with each other and use their background knowledge or travel guidelines to resolve the conflicts. [ABSTRACT FROM PUBLISHER]

We have carried out two-dimensional, axisymmetric, hydrodynamic numerical modelling of the evolution of radio galaxy lobes. The emphasis of our work is on including realistic hot-gas environments in the simulations and on establishing what properties of the resulting radio lobes are independent of the choice of environmental properties and of other features of the models such as the initial jet Mach number. The simulated jet power we use is chosen so that we expect the inner parts of the lobes to come into pressure balance with the external medium on large scales; we show that this leads to the expected departure from self-similarity and the formation of characteristic central structures in the hot external medium. The work done by the expanding radio lobes on the external hot gas is roughly equal to the energy stored in the lobes for all our simulations once the lobes are well established. We show that the external pressure at the lobe mid-point is a reasonable estimate of the internal (lobe) pressure, with only a weak dependence on the environmental parameters; on the other hand, the predicted radio emission from a source of a given physical size has a comparatively strong dependence on the environment in which the lobe resides, introducing an order of magnitude of scatter into the jet power versus radio luminosity relationship. X-ray surface brightness and temperature visualizations of our simulations bear a striking resemblance to observations of some well-studied radio galaxies. [ABSTRACT FROM AUTHOR]

We discuss recent improvements in the calculation of the radiative cooling in both collisionally ionized and photoionized plasmas. We are extending the spectral simulation code cloudy so that as much as possible of the underlying atomic data are taken from external data bases, some created by others and some developed by the cloudy team. This paper focuses on recent changes in the treatment of many stages of ionization of iron, and discusses its extensions to other elements. The H- and He-like ions are treated in the isoelectronic approach described previously. Fe ii is a special case treated with a large model atom. Here we focus on Fe iii through Fe xxiv, ions which are important contributors to the radiative cooling of hot (T ∼ 105–107 K) plasmas and for X-ray spectroscopy. We use the Chianti atomic data base to greatly expand the number of transitions in the cooling function. Chianti only includes lines that have atomic data computed by sophisticated methods. This limits the line list to lower excitation, longer wavelength, transitions. We had previously included lines from the Opacity Project data base, which tends to include higher energy, shorter wavelength, transitions. These were combined with various forms of the ‘g-bar’ approximation, a highly approximate method of estimating collision rates. For several iron ions the two data bases are almost entirely complementary. We adopt a hybrid approach in which we use Chianti where possible, supplemented by lines from the Opacity Project for shorter wavelength transitions. The total cooling including the lightest 30 elements differs from some previous calculations by significant amounts. [ABSTRACT FROM AUTHOR]