Ultraproducts and Higher Order Models

<p>The programme of work for this thesis began with the somewhat genenal intention of parallelling in the context of higher order models the ultraproduct construction and its consequences as developed in the literature for first order models. Something of this was, of course, already available in the ultrapower construction of W.A.J. Luxemburg used in Non Standand Analysis. It may have been considered that such a genenal intention was not likely to yield anything of significance oven and above what was already available from viewing the higher order situation as a 'many sorted' first order one and interpreting the first order theory accordingly. In the event, however, I believe this has proved not to be so. In particular the substructure concepts developed in Chapter II of this thesis together with the various embedding theorems and their applications are not immediately available fnom the first order theory and seem to be of sufficient worth to warrant developing the higher order theory in its own terms. This, anyway, is the basic justification for the approach and content of the thesis.</p>

DESIGNING SHIP COURSE MOVEMENT USING PSEUDOINVERSE MATRICES FOR MEASURING STATE VECTOR OF CONTROLLED OBJECT

To configure the control systems of the ship movement along the trajectory, it is necessary to be concerned with the parameters of its controllability. There has been proposed building a matrix model based on measurements of the state vector of a controlled object. The construction of the model is considered on the example of the problem of ship course control. An algorithm for determining the matrix coefficients of the selected model is proposed. The operation of the considered algorithm has been checked for square matrices by finding their inverse matrices, as well as for rectangular matrices for which the pseudo inverse matrix was found. The illustration of the proposed approach is carried out using the example of a simple 1-order linear Nomoto model. The considered approach is quite universal and can be applied to higher order models, including nonlinear ones.

Higher-Order Models for Resonant Viscosity and Mass-Density Sensors

Advanced fluid models relating viscosity and density to resonance frequency and quality factor of vibrating structures immersed in fluids are presented. The numerous established models which are ultimately all based on the same approximation are refined, such that the measurement range for viscosity can be extended. Based on the simple case of a vibrating cylinder and dimensional analysis, general models for arbitrary order of approximation are derived. Furthermore, methods for model parameter calibration and the inversion of the models to determine viscosity and/or density from measured resonance parameters are shown. One of the two presented fluid models is a viscosity-only model, where the parameters of it can be calibrated without knowledge of the fluid density. The models are demonstrated for a tuning fork-based commercial instrument, where maximum deviations between measured and reference viscosities of approximately ±0.5% in the viscosity range from 1.3 to 243 mPas could be achieved. It is demonstrated that these results show a clear improvement over the existing models.

Lattice Nomenclature Survey from LGA to Modern LBM

Lattice configuration is a core parameter in Lattice-Boltzmann (LB) methods, both from theoretical and implementation standpoints. As LB methods have progressed over the past decades, a variety of lattice configurations have been proposed and referred to according to a plurality of lattice nomenclature systems that usually include the Euclidean space dimensionality, the lattice velocity count and, in fewer instances, the discretization order in their format. This work surveys lattice nomenclature systems, or lattice naming schemes, along the history of LB methods, starting from their Lattice Gas Automata (LGA) predecessor method, up to the present time. Findings include multiple lattice categories, competing naming standards, ambiguous names particularly in higher-order models, naming systems of varying model parameter scopes, and lack of unambiguous naming schemes even for space-filling, Bravais lattice types.

Higher-order Markov models for metagenomic sequence classification

Motivation Alignment-free, stochastic models derived from k-mer distributions representing reference genome sequences have a rich history in the classification of DNA sequences. In particular, the variants of Markov models have previously been used extensively. Higher-order Markov models have been used with caution, perhaps sparingly, primarily because of the lack of enough training data and computational power. Advances in sequencing technology and computation have enabled exploitation of the predictive power of higher-order models. We, therefore, revisited higher-order Markov models and assessed their performance in classifying metagenomic sequences. Results Comparative assessment of higher-order models (HOMs, 9th order or higher) with interpolated Markov model, interpolated context model and lower-order models (8th order or lower) was performed on metagenomic datasets constructed using sequenced prokaryotic genomes. Our results show that HOMs outperform other models in classifying metagenomic fragments as short as 100 nt at all taxonomic ranks, and at lower ranks when the fragment size was increased to 250 nt. HOMs were also found to be significantly more accurate than local alignment which is widely relied upon for taxonomic classification of metagenomic sequences. A novel software implementation written in C++ performs classification faster than the existing Markovian metagenomic classifiers and can therefore be used as a standalone classifier or in conjunction with existing taxonomic classifiers for more robust classification of metagenomic sequences. Availability and implementation The software has been made available at https://github.com/djburks/SMM. Contact [email protected] Supplementary information Supplementary data are available at Bioinformatics online.

On top or underneath: where does the general factor of psychopathology fit within a dimensional model of psychopathology?

Background Dimensional models of psychopathology are increasingly common and there is evidence for the existence of a general dimension of psychopathology (‘p’). The existing literature presents two ways to model p: as a bifactor or as a higher-order dimension. Bifactor models typically fit sample data better than higher-order models, and are often selected as better fitting alternatives but there are reasons to be cautious of such an approach to model selection. In this study the bifactor and higher-order models of p were compared in relation to associations with established risk variables for mental illness. Methods A trauma exposed community sample from the United Kingdom (N = 1051) completed self-report measures of 49 symptoms of psychopathology. Results A higher-order model with four first-order dimensions (Fear, Distress, Externalising and Thought Disorder) and a higher-order p dimension provided satisfactory model fit, and a bifactor representation provided superior model fit. Bifactor p and higher-order p were highly correlated (r = 0.97) indicating that both parametrisations produce near equivalent general dimensions of psychopathology. Latent variable models including predictor variables showed that the risk variables explained more variance in higher-order p than bifactor p. The higher-order model produced more interpretable associations for the first-order/specific dimensions compared to the bifactor model. Conclusions The higher-order representation of p, as described in the Hierarchical Taxonomy of Psychopathology, appears to be a more appropriate way to conceptualise the general dimension of psychopathology than the bifactor approach. The research and clinical implications of these discrepant ways of modelling p are discussed.