Modeling the coverage probability of a confidence interval on the among-group variance component in the unbalanced random one-way model

The coverage probability of an approximate confidence interval on the among-group variance component, σ _α ² , in a one-way random model is modeled using generalized linear models techniques. The purpose of the proposed modeling is to derive an empirical relationship between the coverage probability on one hand, andk, n., ?, and the model’s variance components on the other hand, wherek is the number of groups, n. is the total number of observations, and ? is a measure of imbalance for the design used. The latter quantities serve as control variables in the derived model, and the coverage probability is treated as the response variable. Contour plots generated from this model can be easily used to depict the effects of the control variables on the coverage probability. In particular, the plots are utilized to compare four methods for constructing approximate confidence intervals on σ _α ² . Additional advantages of the derived model include prediction of the coverage probability for a given method using only specified values of the control variables, and the determination of operating conditions that result in improved coverage probability within the region of interest.     

D-Optimal Designs for Trigonometric Regression Models on a Partial Circle

In the common trigonometric regression model we investigate the D-optimal design problem, where the design space is a partial circle. It is demonstrated that the structure of the optimal design depends only on the length of the design space and that the support points (and weights) are analytic functions of this parameter. By means of a Taylor expansion we provide a recursive algorithm such that the D-optimal designs for Fourier regression models on a partial circle can be determined in all cases. In the linear and quadratic case the D-optimal design can be determined explicitly.     

Multiphysics finite element model for the computation of the electro-mechanical dynamics of a hybrid reluctance actuator

ABSTRACT

In hybrid reluctance actuators, the achievable closed-loop system bandwidth is affected by the eddy currents and hysteresis in the ferromagnetic components and the mechanical resonance modes. Such effects must be accurately predicted to achieve high performance via feedback control. Therefore, a multiphysics electro-mechanical finite element model is proposed in this paper to compute the dynamics of a 2-DoF hybrid reluctance actuator. An electromagnetic simulation is adopted to compute the electromagnetic dynamics and the actuation torque, which is employed as input for a structural dynamic simulation computing the electro-mechanical frequency response function. For model validation, the simulated and measured frequency response plots are compared for two actuators with solid and laminated outer yoke, respectively. In both cases, the model accurately predicts the measurement results, with a maximum relative phase error of 1.7% between the first resonance frequency and 1 kHz and a relative error of 1.5% for the second resonance frequency..     

Local Unit Roots and Global Stationarity of TARMA Models

In this paper the (strict and weak) stationarity of threshold autoregressive moving average models is discussed. After examining the strict stationarity, mainly based on the random coefficient autoregressive representation of the model, we provide sufficient conditions for its weak stationarity that allow to obtain a wider stationarity region with respect to some previous results given in the literature. These conditions are discussed to distinguish between global and local stationarity, whose relation has been considered in detail. The threshold process has been further evaluated to face the problem related to the so called existence of a threshold structure in the data generating process that is strictly related to the stationarity and has significant relevance when the parameters of the model have to be estimated.     

Improving estimated sufficient summary plots in dimension reduction using minimization criteria based on initial estimates

In this paper we show that estimated sufficient summary plots can be greatly improved when the dimension reduction estimates are adjusted according to minimization of an objective function. The dimension reduction methods primarily considered are ordinary least squares, sliced inverse regression, sliced average variance Estimates and principal Hessian directions. Some consideration to minimum average variance estimation is also given. Simulations support the usefulness of the approach and three data sets are considered with an emphasis on two- and three-dimensional estimated sufficient summary plots.     

A TWO‐STAGE INFORMATION‐THEORETIC APPROACH TO MODELING LANDSCAPE‐LEVEL ATTRIBUTES AND MAXIMUM RECRUITMENT OF CHINOOK SALMON IN THE COLUMBIA RIVER BASIN

ABSTRACT. Many anadromous salmonid stocks in the Pacific Northwest are at their lowest recorded levels, which has raised questions regarding their long‐term persistence under current conditions. There are a number of factors, such as freshwater spawning and rearing habitat, that could potentially influence their numbers. Therefore, we used the latest advances in information‐theoretic methods in a two‐stage modeling process to investigate relationships between landscape‐level habitat attributes and maximum recruitment of 25 index stocks of chinook salmon (Onocorhynchus tshawy‐tscha) in the Columbia River basin. Our first‐stage model selection results indicated that the Ricker‐type, stock recruitment model with a constant Ricker a, i.e., recruits‐per‐spawner at low numbers of fish) across stocks was the only plausible one given these data, which contrasted with previous unpublished findings. Our second‐stage results revealed that maximum recruitment of chinook salmon had a strongly negative relationship with percentage of surrounding subwatersheds categorized as predominantly containing U.S. Forest Service and private moderate‐high impact managed forest. That is, our model predicted that average maximum recruitment of chinook salmon would decrease by at least 247 fish for every increase of 33% in surrounding subwatersheds categorized as predominantly containing U.S. Forest Service and privately managed forest. Conversely, mean annual air temperature had a positive relationship with salmon maximum recruitment, with an average increase of at least 179 fish for every increase in 2°C mean annual air temperature.     

微生物批式流加发酵脉冲系统的参数辨识及稳定性

针对微生物批式流加发酵生产1,3-丙二醇的非线性脉冲系统,建立敏感参数的优化辨识模型(PDP),论述了模型解的性质、解与参量的关系以及辨识问题最优解的存在性.通过构造算法求得辨识问题最优解,并讨论了新参数下脉冲系统解的稳定性.     

Extending Mosaic Displays: Marginal,Conditional, and Partial Views of Categorical Data

Abstract

This article first illustrates the use of mosaic displays for the analysis of multiway contingency tables. We then introduce several extensions of mosaic displays designed to integrate graphical methods for categorical data with those used for quantitative data. The scatterplot matrix shows all pairwise (bivariate marginal) views of a set of variables in a coherent display. One analog for categorical data is a matrix of mosaic displays showing some aspect of the bivariate relation between all pairs of variables. The simplest case shows the bivariate marginal relation for each pair of variables. Another case shows the conditional relation between each pair, with all other variables partialled out. For quantitative data this represents (a) a visualization of the conditional independence relations studied by graphical models, and (b) a generalization of partial residual plots. The conditioning plot, or coplot shows a collection of partial views of several quantitative variables, conditioned by the values of one or more other variables. A direct analog of the coplot for categorical data is an array of mosaic plots of the dependence among two or more variables, stratified by the values of one or more given variables. Each such panel then shows the partial associations among the foreground variables; the collection of such plots shows how these associations change as the given variables vary.     

Static-parameter estimation in piecewise deterministic processes using particle Gibbs samplers

We develop particle Gibbs samplers for static-parameter estimation in discretely observed piecewise deterministic process (PDPs). PDPs are stochastic processes that jump randomly at a countable number of stopping times but otherwise evolve deterministically in continuous time. A sequential Monte Carlo (SMC) sampler for filtering in PDPs has recently been proposed. We first provide new insight into the consequences of an approximation inherent within that algorithm. We then derive a new representation of the algorithm. It simplifies ensuring that the importance weights exist and also allows the use of variance-reduction techniques known as backward and ancestor sampling. Finally, we propose a novel Gibbs step that improves mixing in particle Gibbs samplers whose SMC algorithms make use of large collections of auxiliary variables, such as many instances of SMC samplers. We provide a comparison between the two particle Gibbs samplers for PDPs developed in this paper. Simulation results indicate that they can outperform reversible-jump MCMC approaches.     

Average Impulse Control of Piecewise Deterministic Processes

In this paper, we consider the average impulse control of piecewisedeterministic Markov processes (PDPs). In the first part ofthe paper, we present a policy-iteration technique which consistsof solving a sequence of optimal stopping problems that allowonly a finite number of jumps. In the second part, we presenta discretization of the state space which, along with the techniquementioned above, reduces the average impulse control of PDPsto a sequence of one-dimensional minimizations. A numericalexample is presented.     

Mean-field backward stochastic differential equations driven by G-Brownian motion and related partial differential equations

In this paper, we study mean-field backward stochastic differential equations driven by G-Brownian motion (G-BSDEs). We first obtain the existence and uniqueness theorem of these equations. In fact, we can obtain local solutions by constructing Picard contraction mapping for Y term on small interval, and the global solution can be obtained through backward iteration of local solutions. Then, a comparison theorem for this type of mean-field G-BSDE is derived. Furthermore, we establish the connection of this mean-field G-BSDE and a nonlocal partial differential equation. Finally, we give an application of mean-field G-BSDE in stochastic differential utility model.     

A model for stochastic hybrid systems with application to communication networks

We propose a model for stochastic hybrid systems (SHSs) where transitions between discrete modes are triggered by stochastic events much like transitions between states of a continuous-time Markov chains. However, the rate at which transitions occur is allowed to depend both on the continuous and the discrete states of the SHS. Based on results available for piecewise-deterministic Markov process (PDPs), we provide a formula for the extended generator of the SHS, which can be used to compute expectations and the overall distribution of the state.As an application, we construct a stochastic model for on-off TCP flows that considers both the congestion-avoidance and slow-start modes and takes directly into account the distribution of the number of bytes transmitted. Using the tools derived for SHSs, we model the dynamics of the moments of the sending rate by an infinite system of ODEs, which can be truncated to obtain an approximate finite-dimensional model. This model shows that, for transfer-size distributions reported in the literature, the standard deviation of the sending rate is much larger than its average. Moreover, the later seems to vary little with the probability of packet drop. This has significant implications for the design of congestion control mechanisms.     

Statistical estimation in partial linear models with covariate data missing at random

In this paper, we consider the partial linear model with the covariables missing at random. A model calibration approach and a weighting approach are developed to define the estimators of the parametric and nonparametric parts in the partial linear model, respectively. It is shown that the estimators for the parametric part are asymptotically normal and the estimators of g(·) converge to g(·) with an optimal convergent rate. Also, a comparison between the proposed estimators and the complete case estimator is made. A simulation study is conducted to compare the finite sample behaviors of these estimators based on bias and standard error.     

Inventory control with an order-time constraint: optimality,uniqueness and significance

This paper analyzes a stochastic inventory problem with an order-time constraint that restricts the times at which a manufacturer places new orders to a supplier. This constraint stems from the limited upstream capacity in a supply chain, such as production capacity at a supplier or transportation capacity between a supplier and a manufacturer. Consideration of limited upstream capacity extends the classical inventory literature that unrealistically assumes infinite supplier/transporter capacity. But this consideration increases the complexity of the problem. We study the constraint under a Poisson demand process and allow for a fixed ordering cost. In presence of the constraint, we establish the optimality of an (s,S) policy under both the discounted and average cost objectives. Under the average cost objective, we show the uniqueness of the order-up-to level S. We numerically compare our model with the classical unconstrained model. We report significant savings in costs that can be achieved by using our model when the order time is constrained.     

A Graphical Method of Exploring the Mean Structure in Longitudinal Data Analysis

Abstract

In a longitudinal study, individuals are observed over some period of time. The investigator wishes to model the responses over this time as a function of various covariates measured on these individuals. The times of measurement may be sparse and not coincident across individuals. When the covariate values are not extensively replicated, it is very difficult to propose a parametric model linking the response to the covariates because plots of the raw data are of little help. Although the response curve may only be observed at a few points, we consider the underlying curve y(t). We fit a regression model y(t) = x ^Tβ(t) + ε(t) and use the coefficient functions β(t) to suggest a suitable parametric form. Estimates of y(t) are constructed by simple interpolation, and appropriate weighting is used in the regression. We demonstrate the method on simulated data to show its ability to recover the true structure and illustrate its application to some longitudinal data from the Panel Study of Income Dynamics.     

A Richardson-type iterative approach for identification of delamination boundaries

A direct problem of applied mathematical modelling is to determine the response of a system given the governing partial differential equations, the geometry of interest, the complete boundary and initial conditions, and material properties. When one or more of the conditions for the solution of the direct problem are unknown, an inverse problem can be formulated. One of the methods frequently used for the solution of inverse problems involves finding the values of the unknowns in a mathematical formulation such that the behavior calculated with the model matches the measured response to a degree evaluated in terms of the classical L ₂ norm. Considered in this sense, the inverse problem is equivalent to an ill-posed optimization problem for the estimation of parameters whose solution in the majority of cases is a real mathematical challenge. In this contribution, we report a novel approach that avoids the mathematical difficulties inspired by the ill-posed character of the model. Our method is devoted to the computation of inverse problems furnished by second-order elliptical systems of partial differential equations and falls in the same conceptual line with the method initiated by Kozlov et al. and further extended and algorithmized by Weikl et al. We construct and employ a weak version of the algorithm found by Weikl et al. Proofs for the convergence and regularity of this version are given for the case of a single layer. The computational realization of the algorithm (called briefly AICRA) is applied and numerical results are obtained. Comparison with experiments demonstrates a good significance and representativeness. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 4, pp. 209–230, 2006.     

Singularity of Lotka‐Volterra models under unfoldings

In this paper, we classify the singularity of a Lotka‐Volterra competitive model with a Gaussian competition function and non‐Gaussian carrying capacity functions. These functions need not be completely different to affect adaptive dynamics of the model. For instance, it will be seen how ostensibly similar models can actually give rise to quite different behaviors due to their properties under unfolding. The use of Gaussian‐like carrying capacity functions can also show the sensitivity of the model to assumptions on the carrying capacity function's shapes. The classification is achieved using singularity theory of fitness functions under dimorphism equivalence. We also investigate the effect of the presence of unfolding and bifurcation parameters on the evolution of the system near its singular points. Particularly, we study the adaptive dynamics of the system near the singularity by focusing on ESS and CvSS types, and dimorphisms. Mutual invasibility plots are used to show regions of coexistence.     

Delay and partial system contents for a discrete-time G-D-c queue

We consider a discrete-time multiserver queueing system with infinite buffer size, constant service times of multiple slots and a first-come-first-served queueing discipline. A relationship between the probability distributions of the partial system contents and the packet delay is established. The relationship is general in the sense that it doesn’t require knowledge of the exact nature of the arrival process. By means of the relationship, results for the distribution of the partial system contents for a wide variety of discrete-time queueing models can be transformed into corresponding results for the delay distribution. As a result, a separate full analysis of the packet delay becomes unnecessary.      

A Relation Between the Weighted Logarithmic Norm of a Matrix and the Lyapunov Equation

In this note, we define a weighted logarithmic norm for any matrix. In the case when a stable matrix A is considered, we obtain the relationship between the maximal eigenvalue of a symmetric positive definite matrix H which is a solution of the Lyapunov equation and the weight H logarithmic norm of A. It can be seen that the weighted logarithmic norm of A is always a negative value in this case. Several examples illustrate the relationship.     

Finding Hamiltonian paths in cocomparability graphs using the bump number algorithm

Hamiltonian Path/Cycle are well known NP-complete problems on general graphs, but their complexity status for permutation graphs has been an open question in algorithmic graph theory for many years. In this paper, we prove that theHamiltonian Path problem is solvable in polynomial time even for the larger class of cocomparability graphs. Our result is based on a nice relationship between Hamiltonian paths and the bump number of partial orders. As another consequence we get a new interpretation of the bump number in terms of path partitions, leading to polynomial time solutions of theHamiltonian Path/Cycle Completion problems in cocomparability graphs.This research was supported in part by ONR for third author and by NSERC under grant number A1798 for fourth author.