Genes encode proteins, some of which in turn regulate other genes. Such interactions make up gene regulatory relationships or (dynamic) gene regulatory networks. With advances in the measurement technology for gene expression and in genome sequencing, it has become possible to measure the expression level of thousands of genes simultaneously in a cell at a series of time points over a specific biological process. Such time-course gene expression data may provide a snapshot of most (if not all) of the interesting genes and may lead to a better understanding gene regulatory relationships and networks. However, inferring either gene regulatory relationships or networks puts a high demand on powerful computational methods that are capable of sufficiently mining the large quantities of time-course gene expression data, while reducing the complexity of the data to make them comprehensible. This dissertation presents several computational methods for inferring gene regulatory relationships and gene regulatory networks from time-course gene expression. These methods are the result of the authors doctoral study. Cluster analysis plays an important role for inferring gene regulatory relationships, for example, uncovering new regulons (sets of co-regulated genes) and their putative cis-regulatory elements. Two dynamic model-based clustering methods, namely the Markov chain model (MCM)-based clustering and the autoregressive model (ARM)-based clustering, are developed for time-course gene expression data. However, gene regulatory relationships based on cluster analysis are static and thus do not describe the dynamic evolution of gene expression over an observation period. The gene regulatory network is believed to be a time-varying system. Consequently, a state-space model for dynamic gene regulatory networks from time-course gene expression data is developed. To account for the complex time-delayed relationships in gene regulatory networks, the state space model is extended to be the one with time delays. Finally, a method based on genetic algorithms is developed to infer the time-delayed relationships in gene regulatory networks. Validations of all these developed methods are based on the experimental data available from well-cited public databases.

Die Arbeit befasst sich mit der effizienten Simulation des funktionellen Verhaltens von Piezoverbundmodulen als Aktor oder Sensor zur Schwingungsbeeinflussung mechanischer Strukturen. Ausgehend von einem FE-Modell werden über den Ansatz energetischer Äquivalenz die effektiven elektro-mechanischen Materialparameter ermittelt. Zur Berücksichtigung im Inneren der Einheitszelle liegender Elektroden werden die elektrischen Randbedingungen der Homogenisierungslastfälle angepasst. Die Homogenisierungslastfälle werden auch genutzt, um Phasenkonzentrationen für die Beanspruchungen der Verbundkomponenten zu ermitteln. Diese Phasenkonzentrationen werden eingesetzt, um aus dem effektiven Gesamtmodell die Beanspruchungen der Komponenten zu extrahieren. Zur dynamischen Modellbildung wird die Zustandsraumbeschreibung verwendet. Die Überführung einer piezo-mechanischen FE-Diskretisierung in ein Zustandsraummodell gelingt mit der Betrachtung der mechanischen Freiheitsgrade als Zustandsvariablen. Zur Abbildung der elektrischen Impedanz im Zustandsraum muss die elektrische Kapazitätsmatrix als Durchgangsmatrix einbezogen werden. Die Reduktion des Zustandsraums basiert auf der modalen Superposition. Die modale Transformationsbasis wird um Moden ergänzt, die die Verformung bei statischer elektrischer Erregung charakterisieren. Die Zustandsraumbeschreibung wird sowohl für eine Potential- als auch für eine Ladungserregung ausgeführt. Das Zustandsraummodell wird unter Verwendung von Filtermatrizen um Ausgangssignale für die mechanischen und elektrischen Beanspruchungsgrößen erweitert. Dies gestattet eine Kopplung der Zustandsraummodelle mit den Beanspruchungsanalysen. Die Anwendung der Berechnungsmethode wird am Beispiel der im SFB/TRR PT-PIESA entwickelten Piezo-Metall-Module demonstriert, die durch direkte Integration von piezokeramischen Basiselementen in Blechstrukturen gekennzeichnet sind. / This thesis deals with the efficient simulation of the functional behaviour of piezo composite modules for applications as actuators or sensors to influence vibrations of machine structures. Based on a FE-discretisation the effective electro-mechanical material parameters of the piezo composite modules are determined with an ansatz of energetic equivalence. To consider electrodes which are located inside the representative volume element the electrical boundary conditions of the load cases for homogenisation are adapted. The load cases for homogenisation are also used to determine the phase concentrations (or fluctuation fields) of stress/strain and electric field/electric displacement field in the composite constituents. These phase concentrations are required to extract stress and strain of the composite components based on the overall model with effective material parameters. For dynamical modelling a state space representation is used. The transformation of a FE-discretisation of the piezo-mechanical system into a state space model is possible by choosing the mechanical degree of freedom as state variables. For consideration of the electrical impedance in the state space model the electrical stiffness respectively capacitance matrix has to incorporate as feedthrough matrix. The dynamical model reduction of the state space model is based on modal superposition. For the correct reproduction of the electrical impedance the modal transformation basis has to be amended by deformation modes which represent the deformation behaviour due to static electrical excitation at the electrodes. The state space representation is built for potential and charge excitation. The state space model is enhanced by filter matrices to incorporate output signals for stress/strain and also for electric field/electric displacement field. This allows the coupling of the state space models with the stress analyses. The application of the simulation method is demonstrated using the example of the piezo-metal-modules developed in the CRC/TR PT-PIESA (German: SFB/TRR PT-PIESA). These piezo-metal-modules are characterised by direct integration of piezoceramic base elements in sheet metal structures.

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In this study we look at the problem of analysing survival data in the presence of longitudinally collected covariates. New methodology for analysing such data has been developed through the use of hidden Markov modeling. Special attention has been given to the case of large information volume, where a preliminary data reduction is necessary. Novel graphical diagnostics have been proposed to assess goodness of fit and significance of covariates. The methodology developed has been applied to the data collected on behaviors of Mexican fruit flies, which were monitored throughout their lives. It has been found that certain patterns in eating behavior may serve as an aging marker. In particular it has been established that the frequency of eating is positively correlated with survival times. / Thesis (Ph.D, Mathematics & Statistics) -- Queen's University, 2010-04-26 18:34:01.131

Evidence for a human contribution to climatic changes during the past century is accumulating rapidly. Given the strength of the evidence, it seems natural to ask whether forcing projections can be used to forecast climate change. A Bayesian method for post-processing forced climate model simulations that produces probabilistic hindcasts of inter-decadal temperature changes on large spatial scales is proposed. Hindcasts produced for the last two decades of the 20th century are shown to be skillful. The suggestion that skillful decadal forecasts can be produced on large regional scales by exploiting the response to anthropogenic forcing provides additional evidence that anthropogenic change in the composition of the atmosphere has influenced our climate. In the absence of large negative volcanic forcing on the climate system (which cannot presently be forecast), the global mean temperature for the decade 2000-2009 is predicted to lie above the 1970-1999 normal with probability 0.94. The global mean temperature anomaly for this decade relative to 1970-1999 is predicted to be 0.35C (5-95% confidence range: 0.21C-0.48C). Reconstruction of temperature variability of the past centuries using climate proxy data can also provide important information on the role of anthropogenic forcing in the observed 20th century warming. A state-space model approach that allows incorporation of additional non-temperature information, such as the estimated response to external forcing, to reconstruct historical temperature is proposed. An advantage of this approach is that it permits simultaneous reconstruction and detection analysis as well as future projection. A difficulty in using this approach is that estimation of several unknown state-space model parameters is required. To take advantage of the data structure in the reconstruction problem, the existing parameter estimation approach is modified, resulting in two new estimation approaches. The competing estimation approaches are compared based on theoretical grounds and through simulation studies. The two new estimation approaches generally perform better than the existing approach. A number of studies have attempted to reconstruct hemispheric mean temperature for the past millennium from proxy climate indicators. Different statistical methods are used in these studies and it therefore seems natural to ask which method is more reliable. An empirical comparison between the different reconstruction methods is considered using both climate model data and real-world paleoclimate proxy data. The proposed state-space model approach and the RegEM method generally perform better than their competitors when reconstructing interannual variations in Northern Hemispheric mean surface air temperature. On the other hand, a variety of methods are seen to perform well when reconstructing decadal temperature variability. The similarity in performance provides evidence that the difference between many real-world reconstructions is more likely to be due to the choice of the proxy series, or the use of difference target seasons or latitudes, than to the choice of statistical method.

The aim of this study is to get some approach which can help in improving the predictions of daily temperature of Umeå. Weather forecasts are available through various sources nowadays. There are various software and methods available for time series forecasting. Our aim is to investigate the daily maximum temperatures of Umeå, and compare the performance of some methods in forecasting these temperatures. Here we analyse the data of daily maximum temperatures and find the predictions for some local period using methods of autoregressive integrated moving average (ARIMA), exponential smoothing (ETS), and cubic splines.  The forecast package in R is used for this purpose and automatic forecasting methods available in the package are applied for modelling with ARIMA, ETS, and cubic splines. The thesis begins with some initial modelling on univariate time series of daily maximum temperatures. The data of daily maximum temperatures of Umeå from 2008 to 2013 are used to compare the methods using various lengths of training period. On the basis of accuracy measures we try to choose the best method. Keeping in mind the fact that there are various factors which can cause the variability in daily temperature, we try to improve the forecasts in the next part of thesis by using multivariate time series forecasting method on the time series of maximum temperatures together with some other variables. Vector auto regressive (VAR) model from the vars package in R is used to analyse the multivariate time series. Results: ARIMA is selected as the best method in comparison with ETS and cubic smoothing splines to forecast one-step-ahead daily maximum temperature of Umeå, with the training period of one year. It is observed that ARIMA also provides better forecasts of daily temperatures for the next two or three days. On the basis of this study, VAR (for multivariate time series) does not help to improve the forecasts significantly. The proposed ARIMA with one year training period is compatible with the forecasts of daily maximum temperature of Umeå obtained from Swedish Meteorological and Hydrological Institute (SMHI).

Bayesian inference for stochastic volatility models using MCMC methods highly depends on actual parameter values in terms of sampling efficiency. While draws from the posterior utilizing the standard centered parameterization break down when the volatility of volatility parameter in the latent state equation is small, non-centered versions of the model show deficiencies for highly persistent latent variable series. The novel approach of ancillarity-sufficiency interweaving has recently been shown to aid in overcoming these issues for a broad class of multilevel models. In this paper, we demonstrate how such an interweaving strategy can be applied to stochastic volatility models in order to greatly improve sampling efficiency for all parameters and throughout the entire parameter range. Moreover, this method of "combining best of different worlds" allows for inference for parameter constellations that have previously been infeasible to estimate without the need to select a particular parameterization beforehand. / Series: Research Report Series / Department of Statistics and Mathematics

Cette thèse porte sur l'estimation bayésienne d'état dans les séries temporelles modélisées à l'aide des variables latentes hybrides, c'est-à-dire dont la densité admet une composante discrète-finie et une composante continue. Des algorithmes généraux d'estimation des variables d'états dans les modèles de Markov partiellement observés à états hybrides sont proposés et comparés avec les méthodes de Monte-Carlo séquentielles sur un plan théorique et appliqué. Le résultat principal est que ces algorithmes permettent de réduire significativement le coût de calcul par rapport aux méthodes de Monte-Carlo séquentielles classiques / This thesis addresses the Bayesian estimation of hybrid-valued state variables in time series. The probability density function of a hybrid-valued random variable has a finite-discrete component and a continuous component. Diverse general algorithms for state estimation in partially observable Markov processesare introduced. These algorithms are compared with the sequential Monte-Carlo methods from a theoretical and a practical viewpoint. The main result is that the proposed methods require less processing time compared to the classic Monte-Carlo methods

The thesis introduces an overview of techniques for filtering of unobserved variables using a state-space representation of a model and state inequality constraints. It is mainly aimed at a derivation of the linear Kalman filter, its extension into a form of a non-linear filter and imposing state constraints. The state uniform model with noise bounds and the sequential importance sampling, as a method of particle filters using Monte Carlo simulations, are described as alternative methods. These three methods are applied on a simple semi-structural model for a monetary policy analysis. The filtration is based on Czech macroeconomic data and reflects an imposed non-negative state constraint on the interest rate. Results of the algorithms are compared and discussed.

This thesis aims to investigate the possibility of using a mathematical model to detect several common faults in a hydraulic rock drill. To this end, a parameterized state space model of the hydraulic drill, which simulate its behavior, is created. The model parameters are divided into two categories where different estimation methods are used to determine their values. The first category consists mainly of the parameters that are assumed to be invariant and independent of the various operating conditions. Experimental data are used to estimate these parameters. The other category is the variables that change depending on the machine’s current condition and operating settings. These include the response from the rock and internal leakages in the hydraulic drill. These parameters are estimated by integrating the impact piston position measurements in the simulation algorithm. The model is simulated for different fault modes, and the resulting estimated parameters are studied. It is shown that the resulting distributions for some of the estimated parameters differ between the fault modes, which makes fault detection possible. Furthermore, a condition monitoring system based on the estimated parameters provided by the model is designed and evaluated. It is shown that the performance and the robustness of the monitoring system depend on the machine’s operating settings and condition, where the system performs best for an operating pressure of 220 bar and the internal cylinder leakages.