The “weight” of models and complexity

This article introduces a way of measuring the intrinsic complexity of models. Unlike complication, complexity is an irreducible indication of the innate characteristics of models. Instead of a reductionist paradigm, complexity should be measured in a holistic way. This article redefines the relationship between models and data, and proposes the concept of the “weight” of models, that is, how “heavy” a model is. Based on this concept, this article further defines the complexity of a model to be its ability to distort the space configuration. Three complexity indices are proposed to quantify the extent to which the input space is distorted by a model. It is recognized that there is a lack of widely accepted definition or measure of model complexity. The answer provided by this article is an attempt to move the inquiry a step closer to that goal. © 2014 Wiley Periodicals, Inc. Complexity 21: 21–35, 2016     

Mathematical models of suspension bridges

In this work we try to explain various mathematical models describing the dynamical behaviour of suspension bridges such as the Tacoma Narrows bridge. Our attention is concentrated on the derivation of these models, an interpretation of particular parameters and on a discussion of their advantages and disadvantages. Our work should be a starting point for a qualitative study of dynamical structures of this type and that is why we have a closer look at the models, which have not been studied in literature yet. We are also trying to find particular conditions for unique solutions of some models.     

Chebyshev model arithmetic for factorable functions

This article presents an arithmetic for the computation of Chebyshev models for factorable functions and an analysis of their convergence properties. Similar to Taylor models, Chebyshev models consist of a pair of a multivariate polynomial approximating the factorable function and an interval remainder term bounding the actual gap with this polynomial approximant. Propagation rules and local convergence bounds are established for the addition, multiplication and composition operations with Chebyshev models. The global convergence of this arithmetic as the polynomial expansion order increases is also discussed. A generic implementation of Chebyshev model arithmetic is available in the library MC++. It is shown through several numerical case studies that Chebyshev models provide tighter bounds than their Taylor model counterparts, but this comes at the price of extra computational burden.     

Identification of graphical models for nonignorable nonresponse of binary outcomes in longitudinal studies

In this paper, we use directed acyclic graphs (DAGs) with temporal structure to describe models of nonignorable nonresponse mechanisms for binary outcomes in longitudinal studies, and we discuss identification of these models under an assumption that the sequence of variables has the first-order Markov dependence, that is, the future variables are independent of the past variables conditional on the present variables. We give a stepwise approach for checking identifiability of DAG models. For an unidentifiable model, we propose adding completely observed variables such that this model becomes identifiable.     

Towards an Ontology of Scientific Models

Scientific models occupy centre stage in scientific practice. Correspondingly, in recent literature in the philosophy of science, scientific models have been a focus of research. However, little attention has been paid so far to the ontology of scientific models. In this essay, I attempt to clarify the issues involved in formulating an informatively rich ontology of scientific models. Although no full-blown theory—containing all ontological issues involved—is provided, I make several distinctions and point to several characteristic properties exhibited by scientific models that are relevant for individuating scientific models.     

A unified treatment of single component replacement models

In this paper we discuss a general framework for single component replacement models. This framework is based on the regenerative structure of these models and by using results from renewal theory a unified presentation of the discounted and average finite and infinite horizon cost models is given. Finally, some well-known replacement models are discussed, and making use of the previous results an easy derivation of their cost functions is presented.     

Counterexamples in theory of fractal dimension for fractal structures

Fractal dimension constitutes the main tool to test for fractal patterns in Euclidean contexts. For this purpose, it is always used the box dimension, since it is easy to calculate, though the Hausdorff dimension, which is the oldest and also the most accurate fractal dimension, presents the best analytical properties. Additionally, fractal structures provide an appropriate topological context where new models of fractal dimension for a fractal structure could be developed in order to generalize the classical models of fractal dimension. In this survey, we gather different definitions and counterexamples regarding these new models of fractal dimension in order to show the reader how they behave mathematically with respect to the classical models, and also to point out which features of such models can be exploited to powerful effect in applications.     

The Robustness of Multi-echelon Service Models under Autocorrelated Demands

A common assumption underlying the development of multi-echelon service models is that successive demands are independent. In this paper we study the robustness of two models, developed for a two-echelon serial inventory network, when the demand process is autocorrelated. Both stockpoints operate a periodic review order-up-to-S echelon inventory policy. Using an analytic approach, we extend the original models so that they apply exactly for any autocorrelated period demand process and explore the behaviour of the extended models under different scenarios. In order to study the effects of different autocorrelation characteristics, an MA(1) and an AR(1) process are analysed in detail. Our results demonstrate that, depending on the overall system parameters setting, models which ignore the effects of autocorrelation may provide very unsatisfactory estimates of the system performance. Hence, extreme caution is required when deciding the use of multi-echelon service models in practice.     

Cutting optimization of structural tubes to build agricultural light aircrafts

In this study we deal with the one-dimensional cutting of metallic structural tubes used in the manufacturing of agricultural light aircrafts. The problem is modeled by mixed integer linear formulations aiming to minimize material trim losses and considering the possibility of generating remainders (leftovers) with enough size to reuse. To validate the application of the models in practice, we carried out experiments with real data of order lists from Ipanema, an agricultural airplane produced by a Brazilian aeronautical company. The models were solved using a modeling language and an optimization software. The computational results show that the models are useful in supporting decisions in this cutting process.     

Dynamics and Coarsening of Interfaces for the Viscous Cahn—Hilliard Equation in One Spatial Dimension

In one spatial dimension, the metastable dynamics and coarsening process of an n -layer pattern of internal layers is studied for the Cahn–Hilliard equation, the viscous Cahn–Hilliard equation, and the constrained Allen–Cahn equation. These models from the continuum theory of phase transitions provide a caricature of the physical process of the phase separation of a binary alloy. A homotopy parameter is used to encapsulate these three phase separation models into one parameter-dependent model. By studying a differential-algebraic system of ordinary differential equations describing the locations of the internal layers for a metastable pattern for this parameter-dependent model, we are able to provide detailed comparisons between the internal layer dynamics for the three models. Layer collapse events are studied in detail, and the analytical theory is supplemented by numerical results showing the different behaviors for the different models. Finally, an asymptotic-numerical algorithm, based on our asymptotic information of layer collapse events and the conservation of mass condition, is devised to characterize the entire coarsening process for each of these models. Numerical realizations of this algorithm are shown.     

Reservoir operations optimization via fuzzy criterion decision processes

In this paper, we propose the treatment of complex reservoir operation problems via our newly developed tool of fuzzy criterion decision processes. This novel approach has been shown to be a more flexible and useful analysis tool especially when it is desirable to incorporate an expert’s knowledge into the decision models. Additionally, it has been demonstrated that this form of decision models will usually result in an optimal solution, which guarantees the highest satisfactory degree. We provide a practical exemplification procedure for the models presented as well as an application example.     

非线性再生散度模型的Bayes估计

非线性再生散度模型是指数族非线性模型、广义线性模型和正态非线性回归模型的推广和发展,唐年胜等人研究了该模型参数的极大似然估计及其统计诊断。本文基于Gibbs抽样和MH抽样算法讨论非线性再生散度模型参数的Bayes估计。模拟研究和实例分析被用来说明该方法的有效性。     

Two-phase flow modeling for low concentration spherical particle motion through a Newtonian fluid

Models that are used for the simulation of two-phase flows in coastal dynamics make extensive use of empirical data. The main focus of this investigation is to develop models for specific aspects of two-phase flows that are based on physical principles in order to reduce the use of such data. In this study several existing empirically based drag force models are discussed. The motion of spherical or near-spherical solid particles through a Newtonian fluid is investigated and a new method for closure of the drag force, using a Representative Unit Cell is discussed and compared to the existing models as well as to experimental data. The various drag models were also evaluated by numerical simulations, using an in-house developed program based on an adaptation of the SIMPLE procedure.     

Optimal adjustment of manpower-requirement forecasts: A case study of Iran

The manpower forecasting models are frequently used in development planning. The usual approach in these models is to correlate the manpower requirement with the level of economic activities and to declare the forecasted figures as the educational targets of the development plan. In this paper we show that because of uncertainties involved in these forecasts, and due to the lack of a cost consideration mechanism in the above models, the implementation of such an educational plan causes an inefficiency in the society's allocation of resources. We then derive an adjustment rule which modifies the manpower-requirement forecasts based on balancing the trade-offs between the cost of educational and the degree of target realization.For demonstration purposes, we apply the above rule to the case of Iran and, through this application, we introduce a methodology for analyzing the sensitivity of results to different types of errors contained in the manpower-requirement forecasts.     

A comparison of strategies to develop a customer default scoring model

Behavioural scoring models are generally used to estimate the probability that a customer of a financial institution who owns a credit product will default on this product in a fixed time horizon. However, one single customer usually purchases many credit products from an institution while behavioural scoring models generally treat each of these products independently. In order to make credit risk management easier and more efficient, it is interesting to develop customer default scoring models. These models estimate the probability that a customer of a certain financial institution will have credit issues with at least one product in a fixed time horizon. In this study, three strategies to develop customer default scoring models are described. One of the strategies is regularly utilized by financial institutions and the other two will be proposed herein. The performance of these strategies is compared by means of an actual data bank supplied by a financial institution and a Monte Carlo simulation study.     

A new algorithm for decomposition of graphical models

In this paper, we combine Leimer’s algorithm with MCS-M algorithm to decompose graphical models into marginal models on prime blocks. It is shown by experiments that our method has an easier and faster implementation than Leimer’s algorithm.     

Parsimonious modelling and forecasting of seasonal time series

Some seasonal time series models are considered which are appropriate for the univariate modelling and forecasting of many time series. The equivalent ARIMA forms of these models provide the basis for a critical examination of the Box-Jenkins approach to seasonal model-building. It is concluded that this approach is unsatisfactory and in particular can often result in over-differencing and the adoption of an inappropriate model. Two main reasons for this are discussed: (a) the inadequate class of models considered which rests on a restricted view of parsimony, and (b) the shortcomings of the basic approach to model identification.     

Linear mixed models and penalized least squares

Linear mixed-effects models are an important class of statistical models that are used directly in many fields of applications and also are used as iterative steps in fitting other types of mixed-effects models, such as generalized linear mixed models. The parameters in these models are typically estimated by maximum likelihood or restricted maximum likelihood. In general, there is no closed-form solution for these estimates and they must be determined by iterative algorithms such as EM iterations or general nonlinear optimization. Many of the intermediate calculations for such iterations have been expressed as generalized least squares problems. We show that an alternative representation as a penalized least squares problem has many advantageous computational properties including the ability to evaluate explicitly a profiled log-likelihood or log-restricted likelihood, the gradient and Hessian of this profiled objective, and an ECME update to refine this objective.     

A hierarchy of approximate models for the Maxwell equations

Summary. In this paper we perform an asymptotic study of the Maxwell equations with respect to the small parameter where is the characteristic velocity associated with the physical problem and is the speed of light. This enables us to derive the quasistatic and Darwin models as respectively first and second order approximations of the Maxwell equations. Moreover, an interpretation of the obtained variational formulations gives us the appropriate boundary conditions for these models. Received May 18, 1995     

带有缺失数据的结构方程模型中的模型选择问题

结构方程模型在社会学、教育学、医学、市场营销学和行为学中有很广泛的应用。在这些领域中,缺失数据比较常见,很多学者提出了带有缺失数据的结构方程模型,并对此模型进行过很多研究。在这一类模型的应用中,模型选择非常重要,本文将一个基于贝叶斯准则的统计量,称为L_v测度,应用到此类模型中进行模型选择。最后,本文通过一个模拟研究及实例分析来说明L_v测度的有效性及应用,并在实例分析中给出了根据贝叶斯因子进行模型选择的结果,以此来进一步说明该测度的有效性。