Can we have confidence in generic structures?

The system dynamics concept of ‘generic structure’ is dividable into three sub-types. This paper analyses the validity of these three, using both practical and theoretical perspectives. Firstly, a new set of measures is developed for generating validity—‘confidence’—amongst a group using generic structures in a practical modelling situation. It is concluded that different confidence criteria are implicitly employed; there is an argument for trading-off model precision and analytical quality for simplicity and ease of use and future research is needed to combine these ‘process’ and ‘content’ aspects of confidence. From a theoretical stance it is shown that with two of the sub-types a scientific notion of confidence is achievable whereas the third (‘archetypes’) involves merely metaphorical thinking. It is concluded that the theoretical status of archetypes requires further development, whilst ensuring that its benefits are retained.     

Global exponential stability of a delay reduced SIR model for migrant workers’ home residence

The paper is concerned with a reduced SIR model for migrant workers. By using differential inequality technique and a novel argument, we derive a set of conditions to ensure that the endemic equilibrium of the model is globally exponentially stable. The obtained results complement with some existing ones. We also use numerical simulations to demonstrate the theoretical results.     

Global dynamics of an age-structured cholera model with both human-to-human and environment-to-human transmissions and saturation incidence

In this paper, an age-structured cholera model with both human-to-human and environment-to-human transmissions and saturation incidence is proposed. In the model, we consider the infection age of infectious individuals and the biological age of pathogen in the environment. It is verified that the global dynamics of the model is completely determined by the basic reproduction number. Asymptotic smoothness is verified as a necessary argument. By analyzing corresponding characteristic equations, we discuss the local stability of each of feasible steady states. Uniform persistence is shown by using the persistence theory for infinite dimensional dynamical system. The global stability of each of feasible steady states is established by using suitable Lyapunov functionals and LaSalle’s invariance principle. Numerical simulations are carried out to illustrate the theoretical results.     

Bifurcation analysis of a delayed epidemic model

In this paper, Hopf bifurcation for a delayed SIS epidemic model with stage structure and nonlinear incidence rate is investigated. Through theoretical analysis, we show the positive equilibrium stability and the conditions that Hopf bifurcation occurs. Applying the normal form theory and the center manifold argument, we derive the explicit formulas determining the properties of the bifurcating periodic solutions. In addition, we also study the effect of the inhibition effect on the properties of the bifurcating periodic solutions. To illustrate our theoretical analysis, some numerical simulations are also included.     

Bias and variance reduction techniques for bootstrap information criteria

We discuss the problem of constructing information criteria by applying the bootstrap methods. Various bias and variance reduction methods are presented for improving the bootstrap bias correction term in computing the bootstrap information criterion. The properties of these methods are investigated both in theoretical and numerical aspects, for which we use a statistical functional approach. It is shown that the bootstrap method automatically achieves the second-order bias correction if the bias of the first-order bias correction term is properly removed. We also show that the variance associated with bootstrapping can be considerably reduced for various model estimation procedures without any analytical argument. Monte Carlo experiments are conducted to investigate the performance of the bootstrap bias and variance reduction techniques.     

Bayesian cohort models for general cohort table analyses

Summary New Bayesian cohort models designed to resolve the identification problem in cohort analysis are proposed in this paper. At first, the basic cohort model which represents the statistical structure of time-series social survey data in terms of age, period and cohort effects is explained. The logit cohort model for qualitative data from a binomial distribution and the normal-type cohort model for quantitative data from a normal distribution are considered as two special cases of the basic model. In order to overcome the identification problem in cohort analysis, a Bayesian approach is adopted, based on the assumption that the effect parameters change gradually. A Bayesian information criterion ABIC is introduced for the selection of the optimal model. This approach is so flexible that both the logit and the normal-type cohort models can be made applicable, not only to standard cohort tables but also to general cohort tables in which the range of age group is not equal to the interval between periods. The practical utility of the proposed models is demonstrated by analysing two data sets from the literature on cohort analysis. The Institute of Statistical Mathematics     

Well-posedness of a general class of elliptic mixed hemivariational–variational inequalities

In this paper, well-posedness of a general class of elliptic mixed hemivariational–variational inequalities is studied. This general class includes several classes of the previously studied elliptic mixed hemivariational–variational inequalities as special cases. Moreover, our approach of the well-posedness analysis is easily accessible, unlike those in the published papers on elliptic mixed hemivariational–variational inequalities so far. First, prior theoretical results are recalled for a class of elliptic mixed hemivariational–variational inequalities featured by the presence of a potential operator. Then the well-posedness results are extended through a Banach fixed-point argument to the same class of inequalities without the potential operator assumption. The well-posedness results are further extended to a more general class of elliptic mixed hemivariational–variational inequalities through another application of the Banach fixed-point argument. The theoretical results are illustrated in the study of a contact problem. For comparison, the contact problem is studied both as an elliptic mixed hemivariational–variational inequality and as an elliptic variational–hemivariational inequality.     

Non-equilibrium pattern selection in particle sedimentation

In this paper, we explain some well known experimental observations in fluid solid interaction from a thermodynamic perspective. In particular we use the extremum of the rate of entropy production to establish the stability of specific patterns observed in single and multiparticle sedimentation in an infinite fluid and the sedimentation of spheres in the presence of walls. While these phenomena have been explained numerically, there is no known rigorous theoretical argument to establish the stability of the observed configurations. We provide a very convincing theoretical basis using entropy based arguments that are considered by several scientists as the underlying theme of nature, life and evolution. In the absence of many rigorous examples for the entropy production principle, our paper advances this argument and lends it much credibility. In addition to looking at the rate of entropy production, we also put forth a very plausible heuristic argument based on the thermal gradients in the systems being studied, which could be the underlying causal principle for many known patterns in nature.     

Probabilistic qualification of attack in abstract argumentation

An argument graph is a graph where each node denotes an argument, and each arc denotes an attack by one argument on another. It offers a valuable starting point for theoretical analysis of argumentation following the proposals by Dung. However, the definition of an argument graph does not take into account the belief in the attacks. In particular, when constructing an argument graph from informal arguments, where each argument is described in free text, it is often evident that there is uncertainty about whether some of the attacks hold. This might be because there is some expressed doubt that an attack holds or because there is some imprecision in the language used in the arguments. In this paper, we use the set of spanning subgraphs of an argument graph as a sample space. A spanning subgraph contains all the arguments, and a subset of the attacks, of the argument graph. We assign a probability value to each spanning subgraph such that the sum of the assignments is 1. This means we can reflect the uncertainty over which is the actual subgraph using this probability distribution. Using the probability distribution over subgraphs, we can then determine the probability that a set of arguments is admissible or an extension. We can also obtain the probability of an attack relationship in the original argument graph as a marginal distribution (i.e. it is the sum of the probability assigned to each subgraph containing that attack relationship). We investigate some of the features of this proposal, and we consider the utility of our framework for capturing some practical argumentation scenarios.     

The effects of asset specificity on maintenance financial performance: An empirical application of Transaction Cost Theory to the medical device maintenance field

This study uses multivariate regression analysis to examine the effects of asset specificity on the financial performance of both external and internal governance structures for medical device maintenance, and investigates how the financial performance of external governance structures differs depending on whether a hospital is private or public. The hypotheses were tested using information on 764 medical devices and 62 maintenance service providers, resulting in 1403 maintenance transactions. As such, our data sample is significantly larger than those used in previous studies in this area. The results empirically support our core theoretical argument that governance financial performance is influenced by assets specificity.     

Sufficient statistic likelihood construction for age- and time-dependent multi-state joint recapture and recovery data

Two closed-form likelihoods for multi-state joint recapture and recovery data were proposed in King and Brooks (2003); the first incorporated dependence on time and cohort whilst the second included dependence on age and cohort. However, when multi-state joint recapture and recovery data are modelled, it is likely that dependence on age and time will both be potentially of interest and therefore the most useful model formulation will incorporate both of these parameter structures. Within this article the likelihood function required for such a model is derived in terms of a set of sufficient statistics.     

Nonlinear scheme with high accuracy for nonlinear coupled parabolic-hyperbolic system

A nonlinear finite difference scheme with high accuracy is studied for a class of two-dimensional nonlinear coupled parabolic-hyperbolic system. Rigorous theoretical analysis is made for the stability and convergence properties of the scheme, which shows it is unconditionally stable and convergent with second order rate for both spatial and temporal variables. In the argument of theoretical results, difficulties arising from the nonlinearity and coupling between parabolic and hyperbolic equations are overcome, by an ingenious use of the method of energy estimation and inductive hypothesis reasoning. The reasoning method here differs from those used for linear implicit schemes, and can be widely applied to the studies of stability and convergence for a variety of nonlinear schemes for nonlinear PDE problems. Numerical tests verify the results of the theoretical analysis. Particularly it is shown that the scheme is more accurate and faster than a previous two-level nonlinear scheme with first order temporal accuracy.     

Dynamics of a rod undergoing a longitudinal impact by a body

A longitudinal elastic impact caused by a body on a thin rod is considered. The results of theoretical, finite element, and experimental approaches to solving the problem are compared. The theoretical approach takes into account both the propagation of longitudinal waves in the rod and the local deformations described in the Hertz model. This approach leads to a differential equation with a delayed argument. The three-dimensional dynamic problem is considered in terms of the finite element approach in which the wave propagation and local deformation are automatically taken into account. A benchmark test of these two approaches showed a complete qualitative and satisfactory quantitative agreement of the results concerning the contact force and the impact time. In the experiments, only the impact time was determined. The comparison of the measured impact time with the theoretical and finite element method’s results was satisfactory. Owing to the fact that the tested rod was relatively short, the approximate model with two degrees of freedom was also developed to calculate the force and the impact time. The problem of excitation of transverse oscillation after the rebound of the impactor off the rod is solved. For the parametric resonance, the motion has a character of beats at which the energy of longitudinal oscillation is transferred into the energy of transverse oscillation and vice versa. The estimate for the maximum possible amplitude of transverse oscillation is obtained.     

Globalexponential stability of an epidemic model with saturated and periodic incidence rate

This paper is concerned with a SIR model with saturated and periodic incidence rate and saturated treatment function. By using differential inequality technique, we employ a novel argument to show that the disease‐free equilibrium is globally exponentially stable. The obtained results improve and supplement existing ones. We also use numerical simulations to demonstrate our theoretical results. Copyright © 2015 John Wiley & Sons, Ltd.     

Legendre–Gauss–Lobatto spectral collocation method for nonlinear delay differential equations

A Legendre–Gauss–Lobatto spectral collocation method is introduced for the numerical solutions of a class of nonlinear delay differential equations. An efficient algorithm is designed for the single‐step scheme and applied to the multiple‐domain case. As a theoretical result, we obtain a general convergence theorem for the single‐step case. Numerical results show that the suggested algorithm enjoys high‐order accuracy both in time and in the delayed argument and can be implemented in a robust and efficient manner. Copyright © 2013 John Wiley & Sons, Ltd.     

Maximum Level and Hitting Probabilities in Stochastic Fluid Flows Using Matrix Differential Riccati Equations

In this work, we expose a clear methodology to analyze maximum level and hitting probabilities in a Markov driven fluid queue for various initial condition scenarios and in both cases of infinite and finite buffers. Step by step we build up our argument that finally leads to matrix differential Riccati equations for which there exists a unique solution. The power of the methodology resides in the simple probabilistic argument used that permits to obtain analytic solutions of these differential equations. We illustrate our results by a comprehensive fluid model that we exactly solve.     

The Argument from Silence

The argument from silence is a pattern of reasoning in which the failure of a known source to mention a particular fact or event is used as the ground of an inference, usually to the conclusion that the supposed fact is untrue or the supposed event did not actually happen. Such arguments are widely used in historical work, but they are also widely contested. This paper surveys some inadequate attempts to model this sort of argument, offers a new analysis using a Bayesian probabilistic framework that isolates the most problematic step in such arguments, illustrates a key problem besetting many uses of the argument, diagnoses the attraction of the argument in terms of a known human cognitive bias affecting the critical step, and suggests a standard that must be met in order for any argument from silence to have more than a very weak influence on historical reasoning.     

On a limiting system of the triangular SKT competition model with large cross-diffusion and random-diffusion

This paper mainly focus on the limiting system which arises from the study of SKT competition model when both the cross-diffusion rate and the random-diffusion rate tend to infinity. For multi-dimensional domains, the existence of positive steady states bifurcating from a double eigenvalue can be proved by applying the bifurcation argument with some special transformation when the birth rate of one species is near some critical value. Further by virtue of the spectral perturbation argument based on the Lyapunov–Schmidt decomposition method, we prove the spectral instability of such nontrivial positive steady states for the limiting system.     

How persuaded are you? A typology of responses

Several recent studies have suggested that there are two different ways in which a person can proceed when assessing the persuasiveness of a mathematical argument: by evaluating whether it is personally convincing, or by evaluating whether it is publicly acceptable. In this paper, using Toulmin's (1958) argumentation scheme, we produce a more detailed theoretical classification of the ways in which participants can interpret a request to assess the persuasiveness of an argument. We suggest that there are (at least) five ways in which such a question can be interpreted. The classification is illustrated with data from a study that asked undergraduate students and research-active mathematicians to rate how persuasive they found a given argument. We conclude by arguing that researchers interested in mathematical conviction and proof validation need to be aware of the different ways in which participants can interpret questions about the persuasiveness of arguments, and that they must carefully control for these variations during their studies.     

Robust Simulation-Based Estimation of ARMA Models

This article proposes a new approach to the robust estimation of a mixed autoregressive and moving average (ARMA) model. It is based on the indirect inference method that originally was proposed for models with an intractable likelihood function. The estimation algorithm proposed is based on an auxiliary autoregressive representation whose parameters are first estimated on the observed time series and then on data simulated from the ARMA model. To simulate data the parameters of the ARMA model have to be set. By varying these we can minimize a distance between the simulation-based and the observation-based auxiliary estimate. The argument of the minimum yields then an estimator for the parameterization of the ARMA model. This simulation-based estimation procedure inherits the properties of the auxiliary model estimator. For instance, robustness is achieved with GM estimators. An essential feature of the introduced estimator, compared to existing robust estimators for ARMA models, is its theoretical tractability that allows us to show consistency and asymptotic normality. Moreover, it is possible to characterize the influence function and the breakdown point of the estimator. In a small sample Monte Carlo study it is found that the new estimator performs fairly well when compared with existing procedures. Furthermore, with two real examples, we also compare the proposed inferential method with two different approaches based on outliers detection.