A high-order accurate scheme for solving the time-domain dispersive Maxwell's equations and material interfaces is described. Maxwell's equations are solved in second-order form for the electric field. A generalized dispersive material (GDM) model is used to represent a general class of linear dispersive materials and this model is implemented in the time-domain with the auxiliary differential equation

Abstract High-dimensional changepoint analysis is a growing area of research and has applications in a wide range of fields. The aim is to accurately and efficiently detect changepoints in time series data when both the number of time points and dimensions grow large. Existing methods typically aggregate or project the data to a smaller number of dimensions, usually one. We present a high-dimensional

Abstract The increased availability of high-dimensional data, and appeal of a “sparse” solution has made penalized likelihood methods commonplace. Arguably the most widely utilized of these methods is ℓ1 regularization, popularly known as the lasso. When the lasso is applied to high-dimensional data, observations are relatively few; thus, each observation can potentially have tremendous influence on

Tuning parameter selection is of critical importance for kernel ridge regression. To date, a data-driven tuning method for divide-and-conquer kernel ridge regression (d-KRR) has been lacking in the literature, which limits the applicability of d-KRR for large datasets. In this article, by modifying the generalized cross-validation (GCV) score, we propose a distributed generalized cross-validation (dGCV)

We address the component-based regularization of a multivariate Generalized Linear Mixed Model (GLMM) in the framework of grouped data. A set Y of random responses is modelled with a multivariate GLMM, based on a set X of explanatory variables, a set A of additional explanatory variables, and random effects to introduce the within-group dependence of observations. Variables in X are assumed many and

We propose a Bayesian procedure for simultaneous variable and covariance selection using continuous spike-and-slab priors in multivariate linear regression models where q possibly correlated responses are regressed onto p predictors. Rather than relying on a stochastic search through the high-dimensional model space, we develop an ECM algorithm similar to the EMVS procedure of Ročková and George targeting

Abstract The ridge inverse covariance estimator is generalized to allow for entry-wise penalization. An efficient algorithm for its evaluation is proposed. Its computational accuracy is benchmarked against implementations of specific cases the generalized ridge inverse covariance estimator encompasses. The proposed estimator shrinks toward a user-specified, nonrandom target matrix and is shown to be

Numerical Cherenkov radiation is a well-known problem of FDTD PIC codes caused by numerical dispersion errors creating spurious radiation around accelerated particles. It is usually dealt with by complex numerical schemes and low-pass filters. In this study we look at a simple way to circumvent this problem for wakefield accelerators simulations by only modifying the field interpolation algorithm.

This paper focuses on the fast evaluation of the matrix-vector multiplication (matvec) g=Kf for K∈CN×N, which is the discretization of a multidimensional oscillatory integral transform g(x)=∫K(x,ξ)f(ξ)dξ with a kernel function K(x,ξ)=e2πiΦ(x,ξ), where Φ(x,ξ) is a piecewise smooth phase function with x and ξ in Rd for d=2 or 3. A new framework is introduced to compute Kf with O(Nlog⁡(N)) time and memories

This paper studies the statistical behavior of a switched variable step size Normalized Least Mean Square adaptive filter. The purpose of the switching is to obtain a Normalized Least Mean Square adaptive filter combination with fast convergence and small steady-state mean-square weight deviation (MSD). Previous works studied variable step-size Least Mean Square (LMS) and Normalized Mean Square (NLMS)

The paper proposes a density gradient based approach to topology optimization under design-dependent boundary loading. Since there is no explicit boundary representation in density-based topology optimization, the design-dependent boundary loads are implicitly imposed through a domain integration of spatial gradient of the density field. The density gradient based loading is formally derived and justified

In this paper, a face-averaged nodal-gradient approach is proposed as an efficient gradient method for a second-order cell-centered finite-volume discretization on triangular grids. The gradients needed in the linear reconstruction are computed in two steps: (1) compute gradients at nodes from solutions stored at cells, and (2) compute the gradient at each face by averaging the nodal gradients over

We develop a well-balanced central-upwind scheme for rotating shallow water model with horizontal temperature and/or density gradients—the thermal rotating shallow water (TRSW). The scheme is designed using the flux globalization approach: first, the source terms are incorporated into the fluxes, which results in a hyperbolic system with global fluxes; second, we apply the Riemann-problem-solver-free

Concerns over women's safety on public transport systems are commonly reported in the media. We develop statistical models to test for gender differences in the perception of safety and satisfaction on urban metros and buses by using large‐scale unique customer satisfaction data for 28 world cities over the period 2009–2018. Results indicate a significant gender gap in the perception of safety, with

The study of conditions under which a two-dimensional random variable (X, Y) will have the property that X/(X+Y)=dY/(X+Y) was initiated by Bhattacharjee and Dhar. Some additional perhaps unexpected examples related to this phenomenon are provided. Discrete and absolutely continuous cases are discussed in detail. Singular continuous cases are briefly mentioned.

Abstract The Weibull-tail class of distributions is a sub-class of the Gumbel extreme domain of attraction, and it has caught the attention of a number of researchers in the last decade, particularly concerning the estimation of the so-called Weibull-tail coefficient. In this paper, we propose an estimator of this Weibull-tail coefficient when the Weibull-tail distribution of interest is censored from

In this work, we present a novel nonlocal nonlinear coarse grid approximation using a machine learning algorithm. We consider unsaturated and two-phase flow problems in heterogeneous and fractured porous media, where mathematical models are formulated as general multicontinuum models. We construct a fine grid approximation using the finite volume method and embedded discrete fracture model. Macroscopic

This paper presents a novel CFD-driven machine learning framework to develop Reynolds-averaged Navier-Stokes (RANS) models. The CFD-driven training is an extension of the gene expression programming method Weatheritt and Sandberg (2016) [8], but crucially the fitness of candidate models is now evaluated by running RANS calculations in an integrated way, rather than using an algebraic function. Unlike

We consider the estimation of the relative median poverty gap (RMPG) at the level of Italian provinces by using data from the European Union Survey on Income and Living Conditions. The overall sample size does not allow reliable estimation of income‐distribution‐related parameters at the provincial level; therefore, small area estimation techniques must be used. The specific challenge in estimating

A brief survey on methods to handle non‐proportional hazards in survival analysis is given with emphasis on short‐term and long‐term hazard ratio modelling. A drawback of the existing model of this nature is that except at time zero or infinity, the hazard ratio for a unit increase in the value of a covariate depends on the starting value. With two or more covariates, the hazard ratio for a unit increase

Abstract We study non-stationary random length sequences of random variables with regularly varying tails. Tail and extremal indexes of their maxima and linear combinations are found. We obtain conditions when both sums and maxima of these sequences have the same tail and extremal indexes. Their extremal index corresponds to the tail index of the most heavy-tailed random variable in the sequence.

Abstract We introduce a general technique for proving estimates for certain random planar maps which belong to the \(\gamma \)-Liouville quantum gravity (LQG) universality class for \(\gamma \in (0,2)\). The family of random planar maps we consider are those which can be encoded by a two-dimensional random walk with i.i.d. increments via a mating-of-trees bijection, and includes the uniform infinite

In causal inference, and specifically in the causes‐of‐effects problem, one is interested in how to use statistical evidence to understand causation in an individual case, and in particular how to assess the so‐called probability of causation. The answer involves the use of potential responses, which describe what would have happened to the outcome if we had observed a different value for the exposure

The paper analyses temperature data from 96 selected weather stations world wide, and from reconstructed northern hemisphere temperature data over the last two millennia. Using a non‐parametric test, we find that the stationarity hypothesis is not rejected by the data. Subsequently, we investigate further properties of the data by means of a statistical model known as the fractional Gaussian noise

Unmeasured, spatially structured factors can confound associations between spatial environmental exposures and health outcomes. Adding flexible splines to a regression model is a simple approach for spatial confounding adjustment, but the spline degrees of freedom do not provide an easily interpretable spatial scale. We describe a method for quantifying the extent of spatial confounding adjustment

Multiple‐systems estimation is a key approach for quantifying hidden populations such as the number of victims of modern slavery. The UK Government published an estimate of 10000–13000 victims, constructed by the present author, as part of the strategy leading to the Modern Slavery Act 2015. This estimate was obtained by a stepwise multiple‐systems method based on six lists. Further investigation shows

Several Organisation for Economic Co‐operation and Development countries have recently implemented an automatic link between the statutory retirement age and life expectancy for the total population to ensure sustainability in their pension systems due to increasing life expectancy. As significant mortality differentials are observed across socio‐economic groups, future changes in these differentials

Given the increasing prevalence of adult obesity, furthering understanding of the determinants of measures such as the body mass index (BMI) remains high on the policy agenda. We contribute to existing literature on modelling the BMI by proposing an extension to latent class modelling, which serves to unveil a more detailed picture of the determinants of BMI. Interest here lies in latent class analysis

Shipping freight rates are notoriously volatile and shipping investors are perceived to be risk loving. The paper explores the stochastic properties of freight rates in the shipping industry and derives the analytical equations for their moments in downside and upside markets by using a two‐piece extension of the generalized error distribution. Pricing equations developed across shipping segments show

We propose a multilevel structural equation model to investigate the interrelationships between childhood socio‐economic circumstances, partnership formation and stability, and mid‐life health, using data from the 1958 British birth cohort. The structural equation model comprises latent class models that characterize the patterns of change in four dimensions of childhood socio‐economic circumstances

Among the many disparities for which Brazil is known is the difference in performance across students who attend the three administrative levels of Brazilian public schools: federal, state and municipal. Our main goal is to investigate whether student performance in the Brazilian Mathematical Olympics for Public Schools is associated with school administrative level and student gender. For this, we

Causal directed acyclic graphs (DAGs) are naturally tailored to represent biological signalling pathways. However, a causal DAG is only identifiable up to Markov equivalence if only observational data are available. Interventional data, based on exogenous perturbations of the system, can greatly improve identifiability. Since the gain of an intervention crucially depends on the intervened variables

We consider the problem of quantifying the degree of association between pairs of discrete event time series, with potential applications in forensic and cybersecurity settings. We focus in particular on the case where two associated event series exhibit temporal clustering such that the occurrence of one type of event at a particular time increases the likelihood that an event of the other type will

Current estimation methods for the probability of causation ‘PC’ make strong parametric assumptions or are inefficient. We derive a non‐parametric influence‐function‐based estimator for a projection of PC, which allows for simple interpretation and valid inference by making weak structural assumptions. We apply our estimator to real data from an experiment in Kenya. This experiment found, by estimating

Coal burning power plants are a frequent target of regulatory programmes because of their emission of chemicals that are known precursors to the formation of ambient particulate air pollution. Health impact assessments of emissions from coal power plants typically rely on assumed causal relationships between emissions, ambient pollution and health, many of which have never been empirically verified

The paper addresses the task of forming a prior distribution to represent expert opinion about a multinomial model that contains covariates. The task has not previously been addressed. We suppose that the sampling model is a multinomial logistic regression and represent expert opinion about the regression coefficients by a multivariate normal distribution. This logistic–normal model gives a flexible

A common problem in educational evaluation is estimating causal effects of interventions from non‐experimental data on students. Scores from standardized achievement tests often are used to adjust for differences in background characteristics of students in different non‐experimental groups. An open question is whether, and how, these adjustments should account for the errors in test scores as measures

In social science research, interference between units is the rule rather than the exception. Contagion represents one key causal mechanism of such spillover effects, where one's treatment affects the outcome of another individual indirectly by changing the treated unit's own outcome. Alternatively, the treatment of one individual can affect the outcome of another person through other mechanisms. We

Institutions in healthcare, education and other public services are under constant pressure to perform to high standards and with efficiency. Assessment of their performance is often problematic because it either ignores important background variables of their patients, students or clients (the casemix), or adjusts for them in a way that is not equitable or transparent. We apply a method of indirect

Comparison group selection is paramount for health policy evaluations, where randomization is seldom practicable. Rolling enrolment is common in these evaluations, introducing challenges for comparison group selection and inference. We propose a novel framework, GroupMatch, for comparison group selection under rolling enrolment, founded on the notion of time agnosticism: two subjects with similar outcome

The population attributable fraction (PAF) is a popular epidemiological measure for the burden of a harmful exposure within a population. It is often interpreted causally as the proportion of preventable cases after an elimination of exposure. Originally, the PAF was defined for cohort studies of fixed length with a baseline exposure or cross‐sectional studies. An extension of the definition to complex

Instrumental variable methods, subject to appropriate identification assumptions, enable consistent estimation of causal effects in the presence of unobserved confounding. Near–far matching has been proposed as one analytic method to improve inference by strengthening the effect of the instrument on the exposure and balancing observable characteristics between groups of subjects with low and high values

Many well‐known problems with two‐sided p‐values are due to their use in hypothesis tests, with ‘reject–accept’ conclusions about point null hypotheses. We present an alternative motivation for p‐value‐based tests, viewing them as assessments of only the sign of an underlying parameter, where we can conclude that the parameter is positive or negative, or simply say nothing either way. Our approach

A new standard is proposed for the evidential assessment of replication studies. The approach combines a specific reverse Bayes technique with prior‐predictive tail probabilities to define replication success. The method gives rise to a quantitative measure for replication success, called the sceptical p‐value. The sceptical p‐value integrates traditional significance of both the original and the replication

To reduce operational costs and to ensure security of supply, gas distribution networks require accurate forecasts of the demand for gas. Among domestic and commercial customers, demand relates primarily to the weather and patterns of life and work. Public holidays have a pronounced effect which often spreads into neighbouring days. We call this spread the ‘proximity effect’. Traditionally, the days

Theories predict that the timing of childbearing and number of children born are determined by multiple socio‐economic factors. Despite this, many methods cannot investigate the interrelationships between these determinants, including the direct and indirect influence that they have on fertility over the life course. Here we use the parametric g‐formula to examine the interdependent influences of time‐varying

When developing a new medicine for children, the potential to extrapolate from adult efficacy data is well recognized. However, significant assumptions about the similarity of adults and children are needed for extrapolations to be biologically plausible. One such assumption is that of similar exposure–response (E–R‐) relationships. Motivated by applications to antiepileptic drug development, we consider

Motivated by the Australian National University poll, we consider a situation where survey data have been collected from respondents for several categorical variables and a primary geographic classification, e.g. postcode. Here, a common and important problem is to obtain estimates for a second target geography that overlaps with the primary geography but has not been collected from the respondents

We investigate the hot hand hypothesis in professional darts in a nearly ideal setting with minimal to no interaction between players. Considering almost 1 year of tournament data, corresponding to 167492 dart throws in total, we use state space models to investigate serial dependence in throwing performance. In our models, a latent state process serves as a proxy for a player's underlying form, and

Information asymmetry reflects the risk and uncertainty faced by investors and is a measure of a firm's transparency. High information asymmetry could increase the cost of external financing, which in turn impedes a firm's leverage (debt–asset ratio) adjustment. The paper studies the adjustment speed towards the target leverage in the presence of information asymmetry by using microlevel data from

Trial‐based economic evaluations are typically performed on cross‐sectional variables, derived from the responses for only the completers in the study, using methods that ignore the complexities of utility and cost data (e.g. skewness and spikes). We present an alternative and more efficient Bayesian parametric approach to handle missing longitudinal outcomes in economic evaluations, while accounting

Rejection inference aims to reduce sample bias and to improve model performance in credit scoring. We propose a semisupervised clustering approach as a new rejection inference technique. K‐prototype clustering can deal with mixed types of numeric and categorical characteristics, which are common in consumer credit data. We identify homogeneous acceptances and rejections and assign labels to part of

Crimes against women in India have been continuously increasing lately as reported by the National Crime Records Bureau. Gender‐based violence has become a serious issue to such an extent that it has been catalogued as a high impact health problem by the World Health Organization. However, there is a lack of spatiotemporal analyses to reveal a complete picture of the geographical and temporal patterns

There is an extensive literature on the causes of educational inequalities, and the life course consequences of educational attainment. Mendelian randomization, where genetic variants associated with exposures of interest are used as proxies for those exposures, often within an instrumental variables framework, has proven highly effective at elucidating the causal effects of several risk factors in

This paper investigates the construction and optimization of multidimensional summation-by-parts (SBP) operators. The optimization of free parameters in the cubature rule, the interpolation/extrapolation operator R, and in the skew-symmetric matrix Sξ, is investigated and a methodology to optimize the operators is presented. It is demonstrated that increasing the degree of the cubature rule from 2p−1

Pseudospectral numerical schemes for solving the Dirac equation in general static curved space are derived using a new pseudodifferential representation of the Dirac equation along with a simple Fourier-basis technique. Owing to the presence of non-constant coefficients in the curved space Dirac equation, convolution products usually appear when the Fourier transform is performed. To circumvent this

This work extends the concepts of algebraic flux correction and convex limiting to continuous high-order Bernstein finite element discretizations of scalar hyperbolic problems. Using an array of adjustable diffusive fluxes, the standard Galerkin approximation is transformed into a nonlinear high-resolution scheme which has the compact sparsity pattern of the piecewise-linear or multilinear subcell

Solving general high-dimensional partial differential equations (PDE) is a long-standing challenge in numerical mathematics. In this paper, we propose a novel approach to solve high-dimensional linear and nonlinear PDEs defined on arbitrary domains by leveraging their weak formulations. We convert the problem of finding the weak solution of PDEs into an operator norm minimization problem induced from

In digital histopathological image analysis, two conflicting objectives are often pursued: closeness to the original tissue and high classification performance. The former objective tries to recover images (stains) that are as close as possible to the ones obtained by staining the tissue with a single dye. The latter objective requires images that allow the extraction of better features for an improved