On Markovian decision models with a finite skeleton

We present a class of countable state space Markovian decision models that can be investigated by means of an associated finite-state, finite-action reduced model which we call the skeleton. In particular, we obtain a turnpike theorem for the original model (Theorem 2 in Section 5) from a known turnpike theorem for the reduced finite model. For illustration, we present in detail an application of this approach to an inventory model (re-establishing a known turnpike result) and sketch analogous results for a cash-balance model and a growth model.

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Zusammenfassung Wir führen eine Klasse von Markovschen Entscheidungsmodellen mit abzählbarem Zustandsraum ein, die mittels eines verbundenen, reduzierten Modells mit endlichem Zustands- und Aktionsraum, welches wir das Skelett nennen, untersucht werden können. Insbesondere erhalten wir ein Turnpike Theorem für das ursprüngliche Modell (Theorem 2 im Abschnitt 5) von einem bekannten Turnpike Theorem für das reduzierte endliche Modell. Zur Erläuterung stellen wir im einzelnen eine Anwendung dieses Ansatzes für ein Lagerhaltungsmodell (Wiederherleitung eines bekannten Turnpike Ergebnisses) dar, und wir skizzieren analoge Ergebnisse für ein Kassenhaltungsmodell und ein Wachstumsmodell.

     

On stability in finite models

We search for a set-up in which results from the theory of infinite models hold for finite models. As an example we prove results from stability theory. Received: 23 February 1998     

Vehicle dynamics simulations with coupled multibody and finite element models

With the advent of multibody system simulations (MSS) programs, it has become common practice to use computer modeling to evaluate vehicle dynamics performance. This approach has proved to be very effective for predicting the handling performance of vehicles; however, it has proved less successful for predicting the vehicle response at frequencies that are of interest in ride harshness and durability applications. The lack of correlation between theory and experiment can be partially traced back to tire models that are inadequate for rough road simulation. This paper presents a comprehensive vehicle dynamics model for simulating the dynamic response of ground vehicles on rough surfaces. This approach uses a MSS program to simulate the vehicle and a nonlinear FE program for the tires. Parallel processing of the tire models improves the efficiency of the overall simulation. Applications for this technology include vehicle ride and harshness analysis and durability loads simulation. This paper describes the MSS vehicle model, the tire FE model, and the interface which transfers data between the two simulations. Simulation and experiment results for a single tire without a vehicle encountering an obstacle and for a vehicle with four tires driving across a pot hole are presented. Conclusions and opportunities for further research end the paper.     

Theories with only a finite number of existentially complete models

We construct, in particular, a countable universal theory with JEP which has exactly 2 non-isomorphic countable existentially complete models, and these two models can be either elementarily equivalent or inequivalent.     

Arithmetic of divisibility in finite models

We prove that the finite‐model version of arithmetic with the divisibility relation is undecidable (more precisely, it has Π⁰₁‐complete set of theorems). Additionally we prove FM‐representability theorem for this class of finite models. This means that a relation R on natural numbers can be described correctly on each input on almost all finite divisibility models if and only if R is of degree ≤ 0 ′. We obtain these results by interpreting addition and multiplication on initial segments of finite models with divisibility only. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Substandard models of finite set theory

A survey of the isomorphic submodels of V_ω, the set of hereditarily finite sets. In the usual language of set theory, V_ω has 2^?0 isomorphic submodels. But other set‐theoretic languages give different systems of submodels. For example, the language of adjunction allows only countably many isomorphic submodels of V_ω (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Networks of interacting stochastic fluid models with infinite and finite buffers

Queueing Systems - Stochastic fluid models have been widely used to model the level of a resource that changes over time, where the rate of variation depends on the state of some continuous-time...     

Amalgamation properties and finite models in Ln-theories

 Djordjević [Dj 1] proved that under natural technical assumptions, if a complete L ⁿ -theory is stable and has amalgamation over sets, then it has arbitrarily large finite models. We extend his study and prove the existence of arbitrarily large finite models for classes of models of L ⁿ -theories (maybe omitting types) under weaker amalgamation properties. In particular our analysis covers the case of vector spaces. Received: 24 July 2000 / Published online: 20 December 2001     

Clustering via finite nonparametric ICA mixture models

We propose a novel extension of nonparametric multivariate finite mixture models by dropping the standard conditional independence assumption and incorporating the independent component analysis (ICA) structure instead. This innovation extends nonparametric mixture model estimation methods to situations in which conditional independence, a necessary assumption for the unique identifiability of the parameters in such models, is clearly violated. We formulate an objective function in terms of penalized smoothed Kullback–Leibler distance and introduce the nonlinear smoothed majorization-minimization independent component analysis algorithm for optimizing this function and estimating the model parameters. Our algorithm does not require any labeled observations a priori; it may be used for fully unsupervised clustering problems in a multivariate setting. We have implemented a practical version of this algorithm, which utilizes the FastICA algorithm, in the R package icamix. We illustrate this new methodology using several applications in unsupervised learning and image processing.

     

A unsplitting finite volume method for models with stiff relaxation source terms

We developed an unsplitting finite volume scheme to account the delicate nonlinear balance between numerical approximations of the hyperbolic flux function and the source linked to balance laws. The method is Riemann-solver-free and no upwinding technique is used. By means of this new approach, we conducted an analysis for two new models of balance laws linked to compositional and thermal flow in porous media problems, under and without a thermodynamic equilibrium hypothesis. For concreteness, we adopt the nitrogen and steam injection models in a porous media. To this model we found an interesting behavior linked to the relaxation term, which is the existence of a non-monotonic traveling wave. We applied this numerical technique to others well-known differential models with relaxation terms available in the literature. Qualitatively we were able to reproduce the expected results.     

Sensitivity analysis with finite changes: An application to modified EOQ models

In this work, we introduce a new method for the sensitivity analysis of model output in the presence of finite changes in one or more of the exogenous variables. We define sensitivity measures that do not rest on differentiability. We relate the sensitivity measures to classical differential and comparative statics indicators. We prove a result that allows us to obtain the sensitivity measures at the same cost of one-variable-at-a-time methods, thus making their estimation feasible also for computationally intensive models. We discuss in detail the derivation of managerial insights formulating a procedure based on the concept of “Settings”. The method is applied to the sensitivity analysis of a discrete change in optimal order quantity following a jump in the exogenous variables of a non-linear programming inventory model.     

A numerical method for nonlinear age-structured population models with finite maximum age

We propose a new numerical method for the approximation of solutions to a non-autonomous form of the classical Gurtin-MacCamy population model with a mortality rate that is the sum of an intrinsic age-dependent rate that becomes unbounded as the age approaches its maximum value, plus a non-local, non-autonomous, bounded rate that depends on some weighted population size. We prove that our new quadrature based method converges to second-order and we show the results of several numerical simulations.     

Uniqueness of certain Fourier-Jacobi models over finite fields

In this paper, we prove the uniqueness of certain Fourier-Jacobi models for the split exceptional group ${\mathrm{G}}_2$ over finite fields with odd characteristic. Similar results are also proved for ${\mathrm{Sp}}_4$ and ${\mathrm{U}}_4$.     

Robust variable selection for finite mixture regression models

Finite mixture regression (FMR) models are frequently used in statistical modeling, often with many covariates with low significance. Variable selection techniques can be employed to identify the covariates with little influence on the response. The problem of variable selection in FMR models is studied here. Penalized likelihood-based approaches are sensitive to data contamination, and their efficiency may be significantly reduced when the model is slightly misspecified. We propose a new robust variable selection procedure for FMR models. The proposed method is based on minimum-distance techniques, which seem to have some automatic robustness to model misspecification. We show that the proposed estimator has the variable selection consistency and oracle property. The finite-sample breakdown point of the estimator is established to demonstrate its robustness. We examine small-sample and robustness properties of the estimator using a Monte Carlo study. We also analyze a real data set.