Compositional Model Repositories via Dynamic Constraint Satisfaction with Order-of-Magnitude Preferences

The predominant knowledge-based approach to automated model construction, compositional modelling, employs a set of models of particular functional components. Its inference mechanism takes a scenario describing the constituent interacting components of a system and translates it into a useful mathematical model. This paper presents a novel compositional modelling approach aimed at building model repositories. It furthers the field in two respects. Firstly, it expands the application domain of compositional modelling to systems that can not be easily described in terms of interacting functional components, such as ecological systems. Secondly, it enables the incorporation of user preferences into the model selection process. These features are achieved by casting the compositional modelling problem as an activity-based dynamic preference constraint satisfaction problem, where the dynamic constraints describe the restrictions imposed over the composition of partial models and the preferences correspond to those of the user of the automated modeller. In addition, the preference levels are represented through the use of symbolic values that differ in orders of magnitude

Modeling the Structure and Complexity of Engineering Routine Design Problems

This paper proposes a model to structure routine design problems as well as a model of its design complexity. The idea is that having a proper model of the structure of such problems enables understanding its complexity, and likewise, a proper understanding of its complexity enables the development of systematic approaches to solve them. The end goal is to develop computer systems capable of taking over routine design tasks based on generic and systematic solving approaches. It is proposed to structure routine design in three main states: problem class, problem instance, and problem solution. Design complexity is related to the degree of uncertainty in knowing how to move a design problem from one state to another. Axiomatic Design Theory is used as reference for understanding complexity in routine design

Causes of Ineradicable Spurious Predictions in Qualitative Simulation

It was recently proved that a sound and complete qualitative simulator does not exist, that is, as long as the input-output vocabulary of the state-of-the-art QSIM algorithm is used, there will always be input models which cause any simulator with a coverage guarantee to make spurious predictions in its output. In this paper, we examine whether a meaningfully expressive restriction of this vocabulary is possible so that one can build a simulator with both the soundness and completeness properties. We prove several negative results: All sound qualitative simulators, employing subsets of the QSIM representation which retain the operating region transition feature, and support at least the addition and constancy constraints, are shown to be inherently incomplete. Even when the simulations are restricted to run in a single operating region, a constraint vocabulary containing just the addition, constancy, derivative, and multiplication relations makes the construction of sound and complete qualitative simulators impossible

Nonparametric Bayesian methods for one-dimensional diffusion models

In this paper we review recently developed methods for nonparametric Bayesian inference for one-dimensional diffusion models. We discuss different possible prior distributions, computational issues, and asymptotic results

Lorenz, G\"{o}del and Penrose: New perspectives on determinism and causality in fundamental physics

Despite being known for his pioneering work on chaotic unpredictability, the key discovery at the core of meteorologist Ed Lorenz's work is the link between space-time calculus and state-space fractal geometry. Indeed, properties of Lorenz's fractal invariant set relate space-time calculus to deep areas of mathematics such as G\"{o}del's Incompleteness Theorem. These properties, combined with some recent developments in theoretical and observational cosmology, motivate what is referred to as the `cosmological invariant set postulate': that the universe $U$ can be considered a deterministic dynamical system evolving on a causal measure-zero fractal invariant set $I_U$ in its state space. Symbolic representations of $I_U$ are constructed explicitly based on permutation representations of quaternions. The resulting `invariant set theory' provides some new perspectives on determinism and causality in fundamental physics. For example, whilst the cosmological invariant set appears to have a rich enough structure to allow a description of quantum probability, its measure-zero character ensures it is sparse enough to prevent invariant set theory being constrained by the Bell inequality (consistent with a partial violation of the so-called measurement independence postulate). The primacy of geometry as embodied in the proposed theory extends the principles underpinning general relativity. As a result, the physical basis for contemporary programmes which apply standard field quantisation to some putative gravitational lagrangian is questioned. Consistent with Penrose's suggestion of a deterministic but non-computable theory of fundamental physics, a `gravitational theory of the quantum' is proposed based on the geometry of $I_U$, with potential observational consequences for the dark universe.Comment: This manuscript has been accepted for publication in Contemporary Physics and is based on the author's 9th Dennis Sciama Lecture, given in Oxford and Triest

A COMPLETE CHARACTERIZATION OF THE LINEAR, LOG-LINEAR, AND SEMI-LOG INCOMPLETE DEMAND SYSTEM MODELS

This study extends LaFranceÂ’'s (1985, 1986, 1990) previous research by deriving the necessary parameter restrictions for two additional classes of incomplete demand system models to be integrable. In contrast to LaFrance'Â’s earlier work, this analysis considers models that treat expenditures and expenditure shares as the dependent variables in the specified incomplete demand systems. With environmental economists increasingly turning to demand system approaches to value changes in environmental quality, these new results significantly expand the menu of empirical specifications which can be used to fit a given data set. Moreover, the alternative specifications considered in this study, in combination with LaFrance'Â’s original work, represent a complete characterization of the linear, log-linear, and semi-log incomplete demand system models.Research Methods/ Statistical Methods,

On the methodology of management research

Epistemology, methodology or philosophy of science, i.e., the foundations and validity of knowledge, have never been very popular subjects as applied to management research. Lately, though, the need for better theories and the methodological discussion underlying the creation of such theories appears to be receiving more attention. In this paper, I will review some basic underlying issues in the area by taking a look at to some of the classical authors. I will first analyze Hayek's view of methodological problems in economics and then apply his analysis to the development of management theory. Then, I'll elaborate on Elster's distinction between causal, functional and intentional explanations. Naïve methodological attitudes will be discussed in this context. I will use agency theory as an example of what should and should not be done. Finally, I'll examine the falsification criterion in management theory and discuss the role of mathematics in the development of theory.epistemology; philosophy of science; methodology; management theory; foundations of management;