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In this paper, we draw on recent research on so-called Fermi problems and situate the fundamental principles underlying this type of tasks and their use from a task design perspective. We use the models and modelling perspective on teaching and learning to elaborate on aspects related to the design of single-use, as well as sequences of, Fermi problems. In addition, we discuss a framework (called the Fermi problem activity template [FPAT] framework) for supporting the design and use of Fermi problems to facilitate students' learning within particular mathematics content areas and/or aimed at particular concepts or higher-order thinking skills. We also illustrate how the FPAT framework can be used to (i) facilitate interdisciplinary collaborations with other subjects such as the social sciences, but in particular with the other STEM subjects; and (ii) support teachers in adapting and implementing Fermi problems in their classrooms. [ABSTRACT FROM AUTHOR]

Maximal lactate steady state (MLSS) is accepted as the gold standard method to determine the upper boundary of heavy exercise domain, while critical power (CP) is one of the most practical ways to estimate the lower boundary of severe exercise domain. However, it has been recently discussed that the upper boundary of heavy-intensity exercise domain does not equal to lower boundary of severe-intensity exercise domain. Conversely, the best individual fit method (CP fit) has recently been suggested as an accurate estimation of CP. However, there has not been a comparative evaluation of CP fit versus MLSS. The aim of this study was, therefore, to focus on the comparison of CP fit with MLSS. Eleven well-trained male cyclists participated in this study. Following the determination of maximal oxygen uptake, MLSS was determined through the performance of standard 30-minute constant work rate exercises performed on separate days. Cyclists performed four constant-load exercises lasting 2–15 minutes on different days. The data were then fitted to mathematical models to obtain CP fit. Bland-Altman plot with 95% limits of agreement (LoA) was used to measure agreement between CP fit and MLSS. According to the findings, CP fit overestimated the work rate corresponding to MLSS (300 ± 38 W vs. 265 ± 39 W; P = 0.001; effect size = 3.28). Bland-Altman results showed high LoA (14 to 55.9 W) and very high bias (bias = 35 ± 10.7 W; P = 0.001; r : 0.96) between CP fit and MLSS. CP fit was not identical for MLSS. [ABSTRACT FROM AUTHOR]

The performance of a sensor-based rotor flux-oriented vector control induction machine drive is highly influenced by the estimated value of the rotor time constant/rotor resistance which varies continuously with temperature when it is driven with the variable loads. Therefore, to achieve accurate torque control, online tunning of the rotor time constant is necessary. This article proposes a novel and simple adaption technique to estimate the rotor time constant. In this proposed method, the reference model of the rotor flux vector is derived using the voltage model of the induction machine, which is independent of the rotor time constant. The current controller uses the model of the rotor flux vector that is derived using the current model of the induction machine. This current model is dependent on the rotor time constant. The error between the rotor flux vectors derived using the current model and the voltage model is minimized using the least-squares method. In this process, the rotor time constant is always tuned to its actual value. The article also presents a simple approach to estimate the parameters of induction machine like the stator resistance, the net leakage inductance, and the initial value of the rotor time constant in an offline mode at a standstill condition. To validate the proposed algorithm, two experimental prototypes are developed for two different power ratings of 3.7 and 67 kW. Experimental results from these prototypes confirm the effectiveness, reliability, and stability of the proposed algorithm both in the motoring and regenerative modes of operation. This method of the adaptation of the rotor time constant is simple and, therefore, useful for practicing engineers. [ABSTRACT FROM AUTHOR]

Potential energy functions including many-body polarization are in widespread use in simulations of aqueous and biological systems, metal-organics, molecular clusters, and other systems where electronically induced redistribution of charge among local atomic sites is of importance. The polarization interactions, treated here via the methods of Thole and Applequist, while long-ranged, can be computed for moderate-sized periodic systems with extremely high accuracy by extending Ewald summation to the induced fields as demonstrated by Nymand, Sala, and others. These full Ewald polarization calculations, however, are expensive and often limited to very small systems, particularly in Monte Carlo simulations, which may require energy evaluation over several hundred-thousand configurations. For such situations, it shall be shown that sufficiently accurate computation of the polarization energy can be produced in a fraction of the central processing unit (CPU) time by neglecting the long-range extension to the induced fields while applying the long-range treatments of Ewald or Wolf to the static fields; these methods, denoted Ewald E-Static and Wolf E-Static (WES), respectively, provide an effective means to obtain polarization energies for intermediate and large systems including those with several thousand polarizable sites in a fraction of the CPU time. Furthermore, we shall demonstrate a means to optimize the damping for WES calculations via extrapolation from smaller trial systems. [ABSTRACT FROM AUTHOR]

In the present paper, we obtain the Voronovaskaja-type results of approximation by a type of Bernstein-Stancu operators with shifted knots. [ABSTRACT FROM AUTHOR]

This paper proposes simple semi-phenomenological models to predict the sound absorption efficiency of highly porous polyurethane foams from microstructure characterization. In a previous paper [J. Appl. Phys. 110, 064901 (2011)], the authors presented a 3-parameter semi-phenomenological model linking the microstructure properties of fully and partially reticulated isotropic polyurethane foams (i.e., strut length l, strut thickness t, and reticulation rate Rw) to the macroscopic non-acoustic parameters involved in the classical Johnson-Champoux-Allard model (i.e., porosity [lowercase_phi_synonym], airflow resistivity σ, tortuosity α∝, viscous Λ, and thermal Λ′ characteristic lengths). The model was based on existing scaling laws, validated for fully reticulated polyurethane foams, and improved using both geometrical and empirical approaches to account for the presence of membrane closing the pores. This 3-parameter model is applied to six polyurethane foams in this paper and is found highly sensitive to the microstructure characterization; particularly to strut's dimensions. A simplified micro-/macro model is then presented. It is based on the cell size Cs and reticulation rate Rw only, assuming that the geometric ratio between strut length l and strut thickness t is known. This simplified model, called the 2-parameter model, considerably simplifies the microstructure characterization procedure. A comparison of the two proposed semi-phenomenological models is presented using six polyurethane foams being either fully or partially reticulated, isotropic or anisotropic. It is shown that the 2-parameter model is less sensitive to measurement uncertainties compared to the original model and allows a better estimation of polyurethane foams sound absorption behavior. [ABSTRACT FROM AUTHOR]

In this article, a generalization of the length biased Lomax distribution called the Marshall Olkin length biased Lomax distribution is introduced. A few statistical and reliability properties of the new distribution is discussed. The parameters of the introduced model are estimated by the method of maximum likelihood estimation. The suitability of the model is verified empirically by applying a real life data set. Also, establish a reliability test plan for acceptance or rejection of a lot of products submitted for inspection with lifetimes directed by this distribution. [ABSTRACT FROM AUTHOR]

We discuss an algorithm for the autoregression (AR) model as a typical time-series model. By analyzing the structure of the AR model, we highlight the shortcomings of traditional algorithms for model parameter estimation and propose an approach to overcome the shortcomings of traditional solutions for the AR model. The errors-in-variables (EIV) model is used to solve an existing problem. There is an obvious difference between the AR model and a traditional model. For the AR model, one observation datum appears repeatedly; hence, the residual of one observation datum is not unique. Furthermore, in theory, the optimal estimation of model parameters cannot be obtained by current solutions. Based on an analysis of the AR model, we focus on how to obtain the optimal estimation when the observation data of the AR model are contaminated by outliers. The median function is used to establish a modified solution for the AR model based on the institute of geodesy & geophysics, Chinese academy of sciences (IGG) weight function by comparison with current algorithms for the robust estimation of the EIV model. We propose an iterative algorithm based on median function. Finally, we apply two numerical instances to compare the proposed algorithm with traditional algorithms and draw conclusions from results of the instances. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach for the conversion of an implicit current–voltage (I–V) expression of a double diode model (DDM) photovoltaic (PV) module to an explicit expression of current in terms of voltage. A new method is proposed for the estimation of maximum power point (MPP) of a DDM PV module using the explicit I–V expression of a PV module under uniform irradiance condition. Further, a new mathematical model of a partially shaded PV array is developed using the proposed explicit expression. Since the explicit I–V expression is used for the estimation of MPP of a DDM PV module under uniform and nonuniform irradiance conditions, the estimation of MPP is simple, accurate, and efficient. The accuracy of the explicit expression is verified considering three different PV modules. A comparison of MPP of a DDM PV module extracted using the proposed method with different existing methods under different environmental conditions (DECs) is presented. The results obtained using the proposed method are validated with the experimental results under DEC. Also, the accuracy of the estimated global MPP of a PV array under partial shading conditions is verified. [ABSTRACT FROM AUTHOR]

We analyze the mathematically rigorous BIBEE (boundary-integral based electrostatics estimation) approximation of the mixed-dielectric continuum model of molecular electrostatics, using the analytically solvable case of a spherical solute containing an arbitrary charge distribution. Our analysis, which builds on Kirkwood's solution using spherical harmonics, clarifies important aspects of the approximation and its relationship to generalized Born models. First, our results suggest a new perspective for analyzing fast electrostatic models: the separation of variables between material properties (the dielectric constants) and geometry (the solute dielectric boundary and charge distribution). Second, we find that the eigenfunctions of the reaction-potential operator are exactly preserved in the BIBEE model for the sphere, which supports the use of this approximation for analyzing charge-charge interactions in molecular binding. Third, a comparison of BIBEE to the recent GB[variant_greek_epsilon] theory suggests a modified BIBEE model capable of predicting electrostatic solvation free energies to within 4% of a full numerical Poisson calculation. This modified model leads to a projection-framework understanding of BIBEE and suggests opportunities for future improvements. [ABSTRACT FROM AUTHOR]

A model for the multiple-pulse laser-induced breakdown behavior of dielectrics is presented. It is based on a critical conduction band (CB) electron density leading to dielectric breakdown. The evolution of the CB electron density during the pulse train is calculated using rate equations involving transitions between band and mid-gap states (native and laser-induced). Using realistic estimations for the trap density and ionization cross-section, the model is able to reproduce the experimentally observed drop in the multiple-pulse damage threshold relative to the single-pulse value, as long as the CB electron density is controlled primarily by avalanche ionization seeded by multiphoton ionization of the traps and the valence band. The model shows that at long pulse duration, the breakdown threshold becomes more sensitive to presence of traps close (within one photon energy) to the CB. The effect of native and laser-induced defects can be distinguished by their saturation behavior. Finally, measurements of the multiple-pulse damage threshold of hafnium oxide films are used to illustrate the application of the model. [ABSTRACT FROM AUTHOR]

A corona model is used in analyzing the Doppler shifted spectroscopy (DSS) data for estimating the ion species mix and beam species fractions in positive ion based neutral beam injectors. In this model the excited neutral atom is assumed to decay solely by a spontaneous radiative process. However, at the beam energies of 20–60 keV/amu, collisional quenching of the excited neutrals affects these estimations when background pressure exceeds 1 mTorr. We present here a modified corona model that takes into account the effects of collisional quenching. We also describe the results of application of the present model to a typical DSS data obtained in the first phase of operation of the SST-1 neutral beam injector. [ABSTRACT FROM AUTHOR]

Increasingly complex particles are pushing the limits of traditional simulation techniques used to study self-assembly. In this work, we test the use of a learning-augmented Monte Carlo method for predicting low energy configurations of patchy particles shaped like “Tetris®” pieces. We extend this method to compare it against Monte Carlo simulations with cluster moves and introduce a new algorithm—bottom-up building block assembly—for quickly generating ordered configurations of particles with a hierarchy of interaction energies. [ABSTRACT FROM AUTHOR]

We have studied the microscopic structure and thermodynamic properties of isotropic three-dimensional core-softened model fluid by using extensive grand canonical Monte Carlo computer simulations and Ornstein–Zernike integral equations with hypernetted chain and Rogers–Young closures. Applied simulation tools permit to obtain insights into the properties of the model in addition to available molecular dynamics data of other authors. We discuss equation of state in the density–chemical potential projection and explore the temperature dependence of the chemical potential along different isochores. The limits of the region of anomalous behavior of the structural and thermodynamic properties are established by investigating derivatives resulting from the equation of state, pair contribution to excess entropy, and translational order parameter. Besides, we evaluate the dependence of the heat capacity on temperature and density. The microscopic structure is discussed in terms of the pair distribution functions and corresponding structure factors. We have established that the hypernetted chain approximation is not successful to capture the region of anomalies in contrast to Rogers–Young approximation, but is very accurate for high fluid densities. Thus we have studied the onset for crystallization transition within this theoretical framework. Moreover, using the replicated Ornstein–Zernike integral equations with hypernetted chain closure, we explore the possibility of glass transition and described it in terms of transition density and chemical potential. [ABSTRACT FROM AUTHOR]

An isobaric-isothermal Gibbs ensemble Monte Carlo simulation has been carried out to study the adsorption of a model surfactant/solvent mixture in slit nanopores. The adsorption isotherms, the density distributions, and the configuration snapshots were simulated to illustrate the adsorption and self-assembly behaviors of the surfactant in the confined pores. The adsorption isotherms are stepwise: a two-step curve for the smaller (30 Å) pore and a three-step one for the larger (50 Å) pore. The adsorption isotherms and the interfacial aggregate structure of the surfactants in the pores with various sizes show a qualitatively consistent performance with the previous experimental observation. The micelle size distributions of the adsorbed surfactant aggregates have been analyzed in order to understand the adsorption mechanism, which suggests that the step rise in the surfactant adsorption is associated with the considerable formation of the micelle aggregates in the confined pores. The effect of the interaction between the pore surface and the surfactant on the adsorption behavior has also been investigated. The simulation results indicate that a change in the interaction can modify the shape of adsorption isotherms. A nonlinear mathematical model was used to represent the multistep adsorption isotherms. A good agreement between the model fitting and the simulation data was obtained for both the amount of adsorption and the jump point concentration. [ABSTRACT FROM AUTHOR]

We have performed lattice Monte Carlo simulations to study the self-assembled morphology of symmetric diblock copolymers in nanopores. The pore diameter and surface preference are systematically varied to examine their effects on the chain conformations, structures of various morphologies, and their phase transition. Various ensemble-averaged profiles and quantities are used to provide detailed information about the system. The simulation results are also compared with the predictions of a strong-stretching theory commonly used in the literature. Such comparisons reveal the deficiencies of this theory in describing the morphologies under cylindrical confinement, and call for further theoretical studies using more accurate formalisms. [ABSTRACT FROM AUTHOR]

We present a modification of the gauge cell Monte Carlo simulation method [A. V. Neimark and A. Vishnyakov, Phys. Rev. E 62, 4611 (2000)] designed for chemical potential calculations in small confined inhomogeneous systems. To measure the chemical potential, the system under study is set in chemical equilibrium with the gauge cell, which represents a finite volume reservoir of ideal particles. The system and the gauge cell are immersed into the thermal bath of a given temperature. The size of the gauge cell controls the level of density fluctuations in the system. The chemical potential is rigorously calculated from the equilibrium distribution of particles between the system cell and the gauge cell and does not depend on the gauge cell size. This scheme, which we call a mesoscopic canonical ensemble, bridges the gap between the canonical and the grand canonical ensembles, which are known to be inconsistent for small systems. The ideal gas gauge cell method is illustrated with Monte Carlo simulations of Lennard-Jones fluid confined to spherical pores of different sizes. Special attention is paid to the case of extreme confinement of several molecular diameters in cross section where the inconsistency between the canonical ensemble and the grand canonical ensemble is most pronounced. For sufficiently large systems, the chemical potential can be reliably determined from the mean density in the gauge cell as it was implied in the original gauge cell method. The method is applied to study the transition from supercritical adsorption to subcritical capillary condensation, which is observed in nanoporous materials as the pore size increases. [ABSTRACT FROM AUTHOR]

This paper describes a new Monte Carlo method based on a novel stochastic potential switching algorithm. This algorithm enables the equilibrium properties of a system with potential V to be computed using a Monte Carlo simulation for a system with a possibly less complex stochastically altered potential V. By proper choices of the stochastic switching and transition probabilities, it is shown that detailed balance can be strictly maintained with respect to the original potential V. The validity of the method is illustrated with a simple one-dimensional example. The method is then generalized to multidimensional systems with any additive potential, providing a framework for the design of more efficient algorithms to simulate complex systems. A near-critical Lennard-Jones fluid with more than 20 000 particles is used to illustrate the method. The new algorithm produced a much smaller dynamic scaling exponent compared to the Metropolis method and improved sampling efficiency by over an order of magnitude. [ABSTRACT FROM AUTHOR]

Electron transfer (ET) across molecular chains including an impurity is studied based on a recently improved real-time path-integral Monte Carlo (PIMC) approach [L. Mühlbacher, J. Ankerhold, and C. Escher, J. Chem. Phys. 121 12696 (2004)]. The reduced electronic dynamics is studied for various bridge lengths and defect site energies. By determining intersite hopping rates from PIMC simulations up to moderate times, the relaxation process in the extreme long-time limit is captured within a sequential transfer model. The total transfer rate is extracted and shown to be enhanced for certain defect site energies. Superexchange turns out to be relevant for extreme gap energies only and then gives rise to different dynamical signatures for high- and low-lying defects. Further, it is revealed that the entire bridge compound approaches a steady state on a much shorter time scale than that related to the total transfer. This allows for a simplified description of ET along donor-bridge-acceptor systems in the long-time range. [ABSTRACT FROM AUTHOR]

Using a coarse-grained model we perform a Monte Carlo simulation of the state behavior of an individual semiflexible macromolecule. Chains consisting of N=256 and 512 monomer units have been investigated. A recently proposed enhanced sampling Monte Carlo technique for the bond fluctuation model in an expanded ensemble in four-dimensional coordinate space was applied. The algorithm allows one to accelerate the sampling of statistically independent three-dimensional conformations in a dense globular state. We found that the temperature of the intraglobular liquid–solid transition decreases with increasing chain stiffness. We have investigated the possible intraglobular orientationally ordered (i.e., liquid-crystalline) structures and obtained a diagram of states for chains consisting of N=256 monomer units. This diagram contains regions of stability of coil, two spherical globules (liquid and solid), and rod-like globule conformations. Transitions between the globular states are rounded first-order ones since the states of liquid, solid, and cylinder-like globules do have different internal symmetry. [ABSTRACT FROM AUTHOR]

The structure and the statistical fluctuations of interfaces between coexisting phases in the Asakura–Oosawa model [J. Chem. Phys. 22, 1255 (1954)] for a colloid-polymer mixture are analyzed by extensive Monte Carlo simulations. We make use of a recently developed grand canonical cluster move with an additional constraint stabilizing the existence of two interfaces in the (rectangular) box that is simulated. Choosing very large systems, of size L×L×D with L=60 and D=120, measured in units of the colloid radius, the spectrum of capillary wave-type interfacial excitations is analyzed in detail. The local position of the interface is defined in terms of a (local) Gibbs surface concept. For small wave vectors capillary wave theory is verified quantitatively, while for larger wave vectors pronounced deviations show up. When one analyzes the data in terms of the concept of a wave vector–dependent interfacial tension, a monotonous decrease of this quantity with increasing wave vector is found. Limitations of our analysis are critically discussed. [ABSTRACT FROM AUTHOR]

A molecular approach to heterogeneous nucleation has been developed. The expressions for the equilibrium cluster distribution, the reversible work of the cluster formation, and the nucleation rate have been derived. Two separate statements for the work of formation were formulated. If the equilibrium cluster distribution is normalized on the monomer concentration near the substrate surface, the reversible work of formation is expressed by ΔGhetI=(Fnhet-Fnhom)-(F1het-F1hom)+ΔGhom where Fnhet and Fnhom are the Helmholtz free energies of a cluster interacting with a substrate and a cluster not interacting with the substrate, respectively. If the equilibrium cluster distribution is normalized on the monomer concentration far from the substrate surface, the work of cluster formation is given by ΔGhetII=(Fnhet-Fnhom)+ΔGhom. The former expression corresponds to the approach of the classical heterogeneous nucleation theory. The cluster partition function appears to be dependent on the location of a virtual plane, which separates the volume, where the interaction of the clusters with the substrate is effective from the one where interaction is negligible. Our Monte Carlo simulations have shown that the dependence is rather weak and thus the location of the plane is not very important. According to the simulations the variation of the plane position in the range from 20 to 50 Å does not lead to a considerable change of the heterogeneous nucleation rate. [ABSTRACT FROM AUTHOR]

We report coefficients of the h-bond expansion of the bridge function of the hard-sphere system up to order ρ4 (where ρ is the density in units of the hard-sphere diameter), which in the highest-order term includes 88 cluster diagrams with bonds representing the total correlation function h(r). Calculations are performed using the recently introduced Mayer-sampling method for evaluation of cluster integrals, and an iterative scheme is applied in which the h(r) used in the cluster integrals is determined by solution of the Ornstein–Zernike equation with a closure given by the calculated clusters. Calculations are performed for reduced densities from 0.1 to 0.9 in increments of 0.1. Comparison with molecular simulation data shows that the convergence is very slow for the density expansion of the bridge function calculated this way. [ABSTRACT FROM AUTHOR]

The effect of solvent quality on dilute and semidilute regimes of polymers in solution is studied by means of Monte Carlo simulations. The equation of state, adsorption near a hard wall, wall–polymer surface tension, and effective depletion potential are all calculated as a function of concentration and solvent quality. We find important differences between polymers in good and θ solvents. In the dilute regime, the physical properties for polymers in a θ solvent closely resemble those of ideal polymers. In the semidilute regime, however, significant differences are found. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We consider estimating the mode of a response given an error‐prone covariate. It is shown that ignoring measurement error typically leads to inconsistent inference for the conditional mode of the response given the true covariate, as well as misleading inference for regression coefficients in the conditional mode model. To account for measurement error, we first employ the Monte Carlo corrected score method (Novick & Stefanski, 2002) to obtain an unbiased score function based on which the regression coefficients can be estimated consistently. To relax the normality assumption on measurement error this method requires, we propose another method where deconvoluting kernels are used to construct an objective function that is maximized to obtain consistent estimators of the regression coefficients. Besides rigorous investigation on asymptotic properties of the new estimators, we study their finite sample performance via extensive simulation experiments, and find that the proposed methods substantially outperform a naive inference method that ignores measurement error. The Canadian Journal of Statistics 47: 262–280; 2019 © 2019 Statistical Society of Canada [ABSTRACT FROM AUTHOR]

We propose a consistent and locally efficient method of estimating the model parameters of a logistic mixed effect model with random slopes. Our approach relaxes two typical assumptions: the random effects being normally distributed, and the covariates and random effects being independent of each other. Adhering to these assumptions is particularly difficult in health studies where, in many cases, we have limited resources to design experiments and gather data in long‐term studies, while new findings from other fields might emerge, suggesting the violation of such assumptions. So it is crucial to have an estimator that is robust to such violations; then we could make better use of current data harvested using various valuable resources. Our method generalizes the framework presented in Garcia & Ma (2016) which also deals with a logistic mixed effect model but only considers a random intercept. A simulation study reveals that our proposed estimator remains consistent even when the independence and normality assumptions are violated. This contrasts favourably with the traditional maximum likelihood estimator which is likely to be inconsistent when there is dependence between the covariates and random effects. Application of this work to a study of Huntington's disease reveals that disease diagnosis can be enhanced using assessments of cognitive performance. The Canadian Journal of Statistics 47: 140–156; 2019 © 2019 Statistical Society of Canada [ABSTRACT FROM AUTHOR]

This paper is devoted to the analysis of the estimation of the proportion of a sensitive variable. The use of a randomized response (rr) procedure gives confidence to the interviewed that his privacy is protected. We consider that a simple random sampling with replacement design is used for selecting a sample. The behavior of the rr procedure, when ranked set sampling is the design used, is developed under three different ranking criteria. The usual gain in accuracy associated with the use of ranked set sampling is exhibited only by one of the designs. The behavior of the models is illustrated using data provided by a study of samples of persons infected with AIDS. [ABSTRACT FROM AUTHOR]

Control charts are commonly evaluated in terms of their average run length (ARL). However, since run length distributions are typically strongly skewed, the ARL gives a very limited impression about the actual run length performance. In this study, it is proposed to evaluate a control chart's performance using risk metrics, specifically the value at risk and the tail conditional expectation. When a control chart is evaluated for an in‐control performance, the risk is an early occurrence of a false alarm, whereas in an out‐of‐control state, there is a risk of a delayed detection. For these situations, risk metric computations are derived and exemplified for diverse types of control charts. It is demonstrated that the use of such risk metrics leads to important new insights into a control chart's performance. In addition to the cases of known process parameters for control chart design, these risk metrics are further used to analyze the estimation uncertainty in evaluating a control chart's performance if the design parameters rely on a phase 1 analysis. Benefits of the risk‐based metrics are discussed thoroughly, and these are recommended as supplements to the traditional ARL metric. [ABSTRACT FROM AUTHOR]

A smoothed bootstrap method is presented for the purpose of bandwidth selection in nonparametric hazard rate estimation for iid data. In this context, two new bootstrap bandwidth selectors are established based on the exact expression of the bootstrap version of the mean integrated squared error of some approximations of the kernel hazard rate estimator. This is very useful since Monte Carlo approximation is no longer needed for the implementation of the two bootstrap selectors. A simulation study is carried out in order to show the empirical performance of the new bootstrap bandwidths and to compare them with other existing selectors. The methods are illustrated by applying them to a diabetes data set. [ABSTRACT FROM AUTHOR]

Abstract We study the regularity of solutions of elliptic fractional systems of order 2 s , s ∈ (0 , 1) , where the right hand side f depends on a nonlocal gradient and has the same scaling properties as the nonlocal operator. Under some structural conditions on the system we prove interior Hölder estimates in the spirit of [1]. Our results are stable in s allowing us to recover the classic results for elliptic systems due to S. Hildebrandt and K. Widman [11] and M. Wiegner [19]. [ABSTRACT FROM AUTHOR]

Water waves are well-known to be dispersive at the linearization level. Considering the fully nonlinear systems, we prove for reasonably smooth solutions the optimal Strichartz estimates for pure gravity waves and the semiclassical Strichartz estimates for gravity-capillary waves for both 2D and 3D waves. Here, by optimal we mean the gains of regularity (over the Sobolev embedding from Sobolev spaces to Hölder spaces) obtained for the linearized systems. Our proofs combine the paradifferential reductions of Alazard-Burq-Zuily with a dispersive estimate using a localized wave package type parametrix of Koch-Tataru. [ABSTRACT FROM AUTHOR]

Considering the problem of risk-sensitive parameter estimation, we propose a fairly wide family of lower bounds on the exponential moments of the quadratic error, both in the Bayesian and the non-Bayesian regime. This family of bounds, which is based on a change of measures, offers considerable freedom in the choice of the reference measure, and our efforts are devoted to explore this freedom to a certain extent. Our focus is mostly on signal models that are relevant to communication problems, namely, models of a parameter-dependent signal (modulated signal) corrupted by additive white Gaussian noise, but the methodology proposed is also applicable to other types of parametric families, such as models of linear systems driven by random input signals (white noise, in most cases), and others. In addition to the well-known motivations of the risk-sensitive cost function (i.e., the exponential quadratic cost function), which is most notably, the robustness to model uncertainty, we also view this cost function as a tool for studying fundamental limits concerning the tail behavior of the estimation error. Another interesting aspect that we demonstrate in a certain parametric model is that the risk-sensitive cost function may be subjected to phase transitions, owing to some analogies with statistical mechanics. [ABSTRACT FROM AUTHOR]

In view of the impossibility theorem of Azriel et al., the Maximum Tolerated Dose (MTD), as currently defined in Phase I and Phase I/II trials, cannot be consistently estimated without making some very strong parametric assumptions. Experimentation carried out at a single dose will fail to provide a consistent estimator of the MTD. We require that information be obtained on a subset of the doses which we describe as the ‘minimal set’. We provide a definition of this set and study its role in semiparametric inference concerning the MTD. Focusing inference on the minimal set, and only indirectly on the MTD, has important consequences. Among these is consistency of estimators for both the minimal set and the MTD, in completely general conditions. Even when the goal is only to estimate the MTD, we do no worse, and often better than other methods and without making any sacrifice in terms of safety for the patient. [ABSTRACT FROM AUTHOR]

In many applications involving large dataset or online learning, stochastic gradient descent (SGD) is a scalable algorithm to compute parameter estimates and has gained increasing popularity due to its numerical convenience and memory efficiency. While the asymptotic properties of SGD-based estimators have been well established, statistical inference such as interval estimation remains much unexplored. The classical bootstrap is not directly applicable if the data are not stored in memory. The plug-in method is not applicable when there is no explicit formula for the covariance matrix of the estimator. In this paper, we propose an online bootstrap procedure for the estimation of confidence intervals, which, upon the arrival of each observation, updates the SGD estimate as well as a number of randomly perturbed SGD estimates. The proposed method is easy to implement in practice. We establish its theoretical properties for a general class of models that includes linear regressions, generalized linear models, M-estimators and quantile regressions as special cases. The finite-sample performance and numerical utility is evaluated by simulation studies and real data applications. [ABSTRACT FROM AUTHOR]

We study maximum selection and sorting of n numbers using imperfect pairwise comparators. The imperfect comparator returns the larger of the two inputs if the inputs are more than a given threshold apart and an adversarially-chosen input otherwise. We consider two adversarial models: a non-adaptive adversary that decides on the outcomes in advance and an adaptive adversary that decides on the outcome of each comparison depending on the previous comparisons and outcomes. Against the non-adaptive adversary, we derive a maximum-selection algorithm that uses at most 2n comparisons in expectation and a sorting algorithm that uses at most 2n ln n comparisons in expectation. In the presence of the adaptive adversary, the proposed maximum-selection algorithm uses ϴ(n log(1/ϵ)) comparisons to output a correct answer with probability at least 1- ϵ, resolving an open problem in Ajtai et al. (2015). Our study is motivated by a density-estimation problem. Given samples from an unknown distribution, we would like to find a distribution among a known class of n candidate distributions that is close to the underlying distribution in l1 distance. Scheffe's algorithm, for example, in Devroye and Lugosi (2001) outputs a distribution at an l1 distance at most 9 times the minimum and runs in time ϴ(n2 log n). Using our algorithm, the runtime reduces to ϴ(n log n). [ABSTRACT FROM AUTHOR]

This article investigates the performance of the shrinkage estimator (SE) of the parameters of a simple linear regression model under the LINEX loss criterion. The risk function of the estimator under the asymmetric LINEX loss is derived and analyzed. The moment-generating functions and the first two moments of the estimators are also obtained. The risks of the SE have been compared numerically with that of pre-test and least-square estimators (LSEs) under the LINEX loss criterion. The numerical comparison reveals that under certain conditions the LSE is inadmissible, and the SE is the best among the three estimators. [ABSTRACT FROM AUTHOR]

In this paper, the risk model with constant interest based on an entrance process is investigated. Under the assumptions that the entrance process is a renewal process and the claim sizes satisfy a certain dependency, which belong to the different heavy-tailed distribution classes, the finite-time and infinite-time asymptotic estimates of the risk model with constant interest force are obtained. [ABSTRACT FROM AUTHOR]

In this note we introduce a new class of boundary kernels for distribution function estimation which shows itself to be especially performing when the classical kernel distribution function estimator suffers from severe boundary problems. [ABSTRACT FROM AUTHOR]

We propose a method to estimate the essential matrix using two affine correspondences for a pair of calibrated perspective cameras. Two novel, linear constraints are derived between the essential matrix and a local affine transformation. The proposed method is also applicable to the over-determined case. We extend the normalization technique of Hartley to local affinities and show how the intrinsic camera matrices modify them. Even though perspective cameras are assumed, the constraints can straightforwardly be generalized to arbitrary camera models since they describe the relationship between local affinities and epipolar lines (or curves). Benefiting from the low number of exploited points, it can be used in robust estimators, e.g. RANSAC, as an engine, thus leading to significantly less iterations than the traditional point-based methods. The algorithm is validated both on synthetic and publicly available data sets and compared with the state-of-the-art. Its applicability is demonstrated on two-view multi-motion fitting, i.e., finding multiple fundamental matrices simultaneously, and outlier rejection. [ABSTRACT FROM AUTHOR]

Estimation of common location parameter of two exponential populations is considered when the scale parameters are ordered using type-II censored samples. A general inadmissibility result is proved which helps in deriving improved estimators. Further, a class of estimators dominating the MLE has been derived by an application of integrated expression of risk difference (IERD) approach of Kubokawa. A discussion regarding extending the results to a general k( ⩾ 2) populations has been done. Finally, all the proposed estimators are compared through simulation. [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]

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]

Brazil is the major coffee producer in the world, with 2 million hectares cropped, with 75% of this area with Coffea arabica and 25% with Coffea canephora. Coffee leaf rust (CLR) is one of the main diseases that cause yield losses by reducing healthy leaf area. As CLR is highly influenced by weather conditions, this study aimed to determine the best linearization model to estimate the CLR apparent infection rate, to correlate CLR infection rates with weather variables, and to develop and assess the performance of weather-based infection rate models to be used as a disease warning system. The CLR epidemic was analyzed for 88 site-seasons, while progress curves were assessed by linear, monomolecular, logistic, Gompertz, and exponential linearization models for apparent infection rate determination. Correlations between CLR infection rates and weather variables were conducted at different periods. From these correlations, multiple linear regressions were developed to estimate CLR infection rates, using the most weather-correlated variables. The Gompertz growth model had the best fit with CLR progress curves. Minimum temperature and relative humidity were the weather variables most correlated to infection rate and, therefore, chosen to compose a CLR forecast system. Among the models developed, the one for the condition of high coffee yield at a narrow row spacing was the best, with only 9.4% of false negative occurrences for all the months assessed. [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]

For an entire function f ( z ) = ∑ k = 0 ∞ a k z k , a k > 0 , we show that f belongs to the Laguerre–Pólya class if the quotients a n − 1 2 / a n − 2 a n are decreasing in n , and b : = lim n → ∞ ⁡ a n − 1 2 / a n − 2 a n such that b ≥ q ∞ ( q ∞ ≈ 3 . 2336 ) . This estimation is sharp. [ABSTRACT FROM AUTHOR]