Homogeneous model theory of metric structures

This thesis studies homogeneous classes of complete metric spaces. Over the past few decades model theory has been extended to cover a variety of nonelementary frameworks. Shelah introduced the abstact elementary classes (AEC) in the 1980s as a common framework for the study of nonelementary classes. Another direction of extension has been the development of model theory for metric structures. This thesis takes a step in the direction of combining these two by introducing an AEC-like setting for studying metric structures. To find balance between generality and the possibility to develop stability theoretic tools, we work in a homogeneous context, thus extending the usual compact approach. The homogeneous context enables the application of stability theoretic tools developed in discrete homogeneous model theory. Using these we prove categoricity transfer theorems for homogeneous metric structures with respect to isometric isomorphisms. We also show how generalized isomorphisms can be added to the class, giving a model theoretic approach to, e.g., Banach space isomorphisms or operator approximations. The novelty is the built-in treatment of these generalized isomorphisms making, e.g., stability up to perturbation the natural stability notion. With respect to these generalized isomorphisms we develop a notion of independence. It behaves well already for structures which are omega-stable up to perturbation and coincides with the one from classical homogeneous model theory over saturated enough models. We also introduce a notion of isolation and prove dominance for it.

Graphoids and separoids in model theory

We treat graphoid and separoid structures within the mathematical framework of model theory, specially suited for representing and analysing axiomatic systems with multiple semantics. We represent the graphoid axiom set in model theory, and translate algebraic separoid structures to another axiom set over the same symbols as graphoids. This brings both structures to a common, sound theoretical ground where they can be fairly compared. Our contribution further serves as a bridge between the most recent developments in formal logic research, and the well-known graphoid applications in probabilistic graphical modelling.

Mechanisms influencing levitation and the scaling laws in nanopores: Oscillator model theory

We provide here a detailed theoretical explanation of the floating molecule or levitation effect, for molecules diffusing through nanopores, using the oscillator model theory (Phys. Rev. Lett. 2003, 91, 126102) recently developed in this laboratory. It is shown that on reduction of pore size the effect occurs due to decrease in frequency of wall collision of diffusing particles at a critical pore size. This effect is, however, absent at high temperatures where the ratio of kinetic energy to the solid-fluid interaction strength is sufficiently large. It is shown that the transport diffusivities scale with this ratio. Scaling of transport diffusivities with respect to mass is also observed, even in the presence of interactions.

A new model construction by making a detour via intuitionistic theories I: Operational set theory without choice is Π1-equivalent to KP

We introduce a version of operational set theory, OST−, without a choice operation, which has a machinery for Δ0Δ0 separation based on truth functions and the separation operator, and a new kind of applicative set theory, so-called weak explicit set theory WEST, based on Gödel operations. We show that both the theories and Kripke–Platek set theory KPKP with infinity are pairwise Π1Π1 equivalent. We also show analogous assertions for subtheories with ∈-induction restricted in various ways and for supertheories extended by powerset, beta, limit and Mahlo operations. Whereas the upper bound is given by a refinement of inductive definition in KPKP, the lower bound is by a combination, in a specific way, of realisability, (intuitionistic) forcing and negative interpretations. Thus, despite interpretability between classical theories, we make “a detour via intuitionistic theories”. The combined interpretation, seen as a model construction in the sense of Visser's miniature model theory, is a new way of construction for classical theories and could be said the third kind of model construction ever used which is non-trivial on the logical connective level, after generic extension à la Cohen and Krivine's classical realisability model.

Deeper model endgame analysis

A reference model of Fallible Endgame Play has been implemented and exercised with the chess-engine WILHELM. Past experiments have demonstrated the value of the model and the robustness of decisions based on it: experiments agree well with a Markov Model theory. Here, the reference model is exercised on the well-known endgame KBBKN.

Coupling ensemble weather predictions based on TIGGE database with Grid-Xinanjiang model for flood forecast

The incorporation of numerical weather predictions (NWP) into a flood forecasting system can increase forecast lead times from a few hours to a few days. A single NWP forecast from a single forecast centre, however, is insufficient as it involves considerable non-predictable uncertainties and lead to a high number of false alarms. The availability of global ensemble numerical weather prediction systems through the THORPEX Interactive Grand Global Ensemble' (TIGGE) offers a new opportunity for flood forecast. The Grid-Xinanjiang distributed hydrological model, which is based on the Xinanjiang model theory and the topographical information of each grid cell extracted from the Digital Elevation Model (DEM), is coupled with ensemble weather predictions based on the TIGGE database (CMC, CMA, ECWMF, UKMO, NCEP) for flood forecast. This paper presents a case study using the coupled flood forecasting model on the Xixian catchment (a drainage area of 8826 km2) located in Henan province, China. A probabilistic discharge is provided as the end product of flood forecast. Results show that the association of the Grid-Xinanjiang model and the TIGGE database gives a promising tool for an early warning of flood events several days ahead.

New physics from warped compact extra dimensions: from model building to colliders signals

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A model of factors determining levels of public support for health care policy in the United States

Public preferences for policy are formed in a little-understood process that is not adequately described by traditional economic theory of choice. In this paper I suggest that U.S. aggregate support for health reform can be modeled as tradeoffs among a small number of behavioral values and the stage of policy development. The theory underlying the model is based on Samuelson, et al.'s (1986) work and Wilke's (1991) elaboration of it as the Greed/Efficiency/Fairness (GEF) hypothesis of motivation in the management of resource dilemmas, and behavioral economics informed by Kahneman and Thaler's prospect theory. ^ The model developed in this paper employs ordered probit econometric techniques applied to data derived from U.S. polls taken from 1990 to mid-2003 that measured support for health reform proposals. Outcome data are four-tiered Likert counts; independent variables are dummies representing the presence or absence of operationalizations of each behavioral variable, along with an integer representing policy process stage. Marginal effects of each independent variable predict how support levels change on triggering that variable. Model estimation results indicate a vanishingly small likelihood that all coefficients are zero and all variables have signs expected from model theory. ^ Three hypotheses were tested: support will drain from health reform policy as it becomes increasingly well-articulated and approaches enactment; reforms appealing to fairness through universal health coverage will enjoy a higher degree of support than those targeted more narrowly; health reforms calling for government operation of the health finance system will achieve lower support than those that do not. Model results support the first and last hypotheses. Contrary to expectations, universal health care proposals did not provide incremental support beyond those targeted to “deserving” populations—children, elderly, working families. In addition, loss of autonomy (e.g. restrictions on choice of care giver) is found to be the “third rail” of health reform with significantly-reduced support. When applied to a hypothetical health reform in which an employer-mandated Medical Savings Account policy is the centerpiece, the model predicts support that may be insufficient to enactment. These results indicate that the method developed in the paper may prove valuable to health policy designers. ^

A useful method for model-building /

AD 266 222.

Simulation methods and model design

Most of the pages of the photocopy, which are in double columns, represent two pages of the original.

Seeing is understanding : the effect of visualisation in understanding programming concepts

How and why visualisations support learning was the subject of this qualitative instrumental collective case study. Five computer programming languages (PHP, Visual Basic, Alice, GameMaker, and RoboLab) supporting differing degrees of visualisation were used as cases to explore the effectiveness of software visualisation to develop fundamental computer programming concepts (sequence, iteration, selection, and modularity). Cognitive theories of visual and auditory processing, cognitive load, and mental models provided a framework in which student cognitive development was tracked and measured by thirty-one 15-17 year old students drawn from a Queensland metropolitan secondary private girls’ school, as active participants in the research. Seventeen findings in three sections increase our understanding of the effects of visualisation on the learning process. The study extended the use of mental model theory to track the learning process, and demonstrated application of student research based metacognitive analysis on individual and peer cognitive development as a means to support research and as an approach to teaching. The findings also forward an explanation for failures in previous software visualisation studies, in particular the study has demonstrated that for the cases examined, where complex concepts are being developed, the mixing of auditory (or text) and visual elements can result in excessive cognitive load and impede learning. This finding provides a framework for selecting the most appropriate instructional programming language based on the cognitive complexity of the concepts under study.

Logic as the Universal Science : Bertrand Russell's Early Conception of Logic and Its Philosophical Context

Bertrand Russell (1872 1970) introduced the English-speaking philosophical world to modern, mathematical logic and foundational study of mathematics. The present study concerns the conception of logic that underlies his early logicist philosophy of mathematics, formulated in The Principles of Mathematics (1903). In 1967, Jean van Heijenoort published a paper, Logic as Language and Logic as Calculus, in which he argued that the early development of modern logic (roughly the period 1879 1930) can be understood, when considered in the light of a distinction between two essentially different perspectives on logic. According to the view of logic as language, logic constitutes the general framework for all rational discourse, or meaningful use of language, whereas the conception of logic as calculus regards logic more as a symbolism which is subject to reinterpretation. The calculus-view paves the way for systematic metatheory, where logic itself becomes a subject of mathematical study (model-theory). Several scholars have interpreted Russell s views on logic with the help of the interpretative tool introduced by van Heijenoort,. They have commonly argued that Russell s is a clear-cut case of the view of logic as language. In the present study a detailed reconstruction of the view and its implications is provided, and it is argued that the interpretation is seriously misleading as to what he really thought about logic. I argue that Russell s conception is best understood by setting it in its proper philosophical context. This is constituted by Immanuel Kant s theory of mathematics. Kant had argued that purely conceptual thought basically, the logical forms recognised in Aristotelian logic cannot capture the content of mathematical judgments and reasonings. Mathematical cognition is not grounded in logic but in space and time as the pure forms of intuition. As against this view, Russell argued that once logic is developed into a proper tool which can be applied to mathematical theories, Kant s views turn out to be completely wrong. In the present work the view is defended that Russell s logicist philosophy of mathematics, or the view that mathematics is really only logic, is based on what I term the Bolzanian account of logic . According to this conception, (i) the distinction between form and content is not explanatory in logic; (ii) the propositions of logic have genuine content; (iii) this content is conferred upon them by special entities, logical constants . The Bolzanian account, it is argued, is both historically important and throws genuine light on Russell s conception of logic.