69, A16 leaves : illustrations

Model reduction is motivated by the fact that complex process models may pre- vent the application of model-based process control. While extensive research on model reduction has been done in the past few decades, model reduction of systems exhibiting two-time scale behavior as well as parametric uncertainty has received little attention to date. This work addresses these types of problems in detail. Systems with two-time scale behavior can be described by differential-algebraic equations (DAEs). A new technique based on projections and system identification is presented for reducing this type of system. This method reduces the order of the differential equations as well as the number and complexity of the algebraic equations. Additionally, the algebraic equations of the resulting system can be replaced by an explicit expression for the algebraic variables such as a feed-forward neural network or partial least squares. This last property is important insofar as the reduced model does not require a DAE solver for its solution, but system trajectories can instead be computed with regular ordinary differential equation (ODE) solvers. For systems with uncertain parameters, two types of problems are investigated, including parameter reduction and parameter dependent model reduction. The pa- rameter reduction problem is motivated by the fact that a large number of parameters exist in process models while some of them contribute little to a system's input-output behavior. This portion of the work presents three novel methodologies which include (1) parameter reduction where the contribution is measured by Hankel singular val- ues, (2) reduction of the parameter space via singular value decomposition, and (3) a combination of these two techniques. Parameter dependent model reduction investigates how to incorporate the influ- ence of parameters in the procedure of conventional model reductions. An approach augmenting the input vector to include the parameters are developed to solve this problem. Finally, a nonlinear model predictive control scheme is developed in which the reduced models are used for the controller. Examples are investigated to illustrate these techniques. The results show that excellent performance can be obtained for the reduced models.

The main goal of this thesis is to suggest an appropriate approach to interest rate risk modeling in the Czech financial market environment in various situations. Three distinct periods are analyzed. These periods, which are the period before the global financial crisis, period during the financial crisis and in the aftermath of the global financial crisis and calming subsequent debt crisis in the eurozone, are characterized by different evaluation of liquidity and credit risk, different relationship between financial variables and market participants and different degree of market regulations. Within this goal, an application of the BGM model in the Czech financial market environment is crucial. Use of the BGM model for the purpose of predicting a dynamics of a yield curve is not very common. This is firstly due to the fact that primary use of this model is a valuation of interest rate derivatives while ensuring the absence of arbitrage and secondly its application is relatively difficult. Nevertheless, I apply the BGM model to obtain predictions of the probability distributions of interest rates in the Czech and eurozone market environment, because its complexity, direct modeling of a yield curve based on market rates and especially a possibility of parameter estimation based on current swaptions volatilities quotations may lead to a significant improvement of predictions. This improvement was also confirmed in this thesis. Use of swaptions volatilities market quotations is especially useful in the period of unprecedented mone- tary easing and increased number of central banks and other regulators interventions into financial markets that occur after the financial crisis, because it reflects current market expectations which also include future interventions. As a consequence of underdevelopment of the Czech financial market there are no market quotations of Czech koruna denominated swaptions volatilities. I suggest their approximations based on quotations of euro denominated swaptions volatilities and also using volatilities of koruna and euro forward rates. Use of this approach ensures that predictions of the Czech yield curve dynamics contain current market expectations. To my knowledge, any other author has not presented similar application of the BGM model in the Czech financial market environment. In this thesis I further predict a Czech and Euro area money market yield curve dynamics using the CIR and the GP models as representatives of various types of interest rates models to compare these predictions with BGM predictions. I suggest a comprehensive system of three criteria, based on comparison of predicti- ons with reality, to describe a predictive power of selected models and an appropria- teness of their use in the Czech market environment during different situations in the market. This analysis shows that predictions of the Czech money market yield curve dynamics based on the BGM model demonstrate high predictive power and the best 8 quality in comparison with other models. GP model also produces relatively good qua- lity predictions. Conversely, predictions based on the CIR model as a representative of short rate model family completely failed when describing reality. In a situation when the economy allows negative rates and there is simultaneously a significant likelihood of their implementation, I recommend to obtain predictions of Czech money market yield curve dynamics using GP model which allows existence of negative interest rates. This analysis also contains a statistical test for validating the predictive power of each model and information on other tests. Berkowitz test rejects a hypothesis of accurate predictions for each model. However, this fact is common in real data testing even when using relatively good model. This fact is especially caused by difficult fulfilment of test conditions in real world. To my knowledge, such an analysis of the predictive power of selected interest rate models moreover in the Czech financial market environment has not been published yet. The last goal of this thesis is to suggest an appropriate approach to obtaining pre- dictions of Czech government bonds risk premium dynamics. I define this risk premium as a difference between government bond yields and fixed rate of CZK IRS with the same length. I apply the GP model to describe the dynamics of this indicator of the Czech Republic credit risk. In order to obtain a time series of the risk premium which are necessary for estimation of GP model parameters I firstly estimate yield curves of Czech government bonds using Svensson model for each trading day since 2005. Resulting si- mulations of risk premium show that the GP model predicts the real development of risk premiums of all maturities relatively well. Hence, the proposed approach is suitable for modeling of Czech Republic credit risk based on the use of information extracted from financial markets. I have not registered proposed approach to risk premium modeling moreover in the Czech financial market environment in other publications.

A mixture-fraction-based thermodynamic equilibrium approach for modeling gas-phase combustion was adapted and used in FIRETEC, a wildfire computational fluid dynamics model. The motivation behind this work was the desire to incorporate the features of complex chemistry calculations from the thermodynamic equilibrium model into FIRETEC without significantly increasing the computational burden of the program. In order to implement the mixture-fraction-based thermodynamic equilibrium approach, a sub-grid pocket model was developed to simulate the local mixture fraction of sub-grid flame sheets. Numerical simulations of wildfires were performed using FIRETEC with the new sub-grid, mixture-fraction-based pocket model to model gas-phase combustion. The thermodynamic equilibrium model was used to calculate flame temperatures and combustion products, including CO2 and CO, for sub-grid, gas-phase combustion in FIRETEC simulations. Fire spread rates from simulations using the new sub-grid combustion model were 25-100% higher than fire spread rates from previous FIRETEC simulations, but the successes of modeling propagating fire lines and calculating detailed equilibrium combustion products from simulated sub-grid flame sheets demonstrated the feasibility of this new approach. Future work into the fine-tuning of pocket model parameters and modifying the conservation equation for energy in FIRETEC was recommended.

Asset pricing models are well established and have been used extensively by practitioners both for pricing options as well as for hedging them. Though Black-Scholes is the original and most commonly communicated asset pricing model, alternative asset pricing models which incorporate additional features have since been developed. We present three asset pricing models here - the Black-Scholes model, the Heston model and the Merton (1976) model. For each asset pricing model we test the hedge effectiveness of delta hedging, minimum variance hedging and static hedging, where appropriate. The options hedged under the aforementioned techniques and asset pricing models are down-and-out call options, lookback options and cliquet options. The hedges are performed over three strikes, which represent At-the-money, Out-the-money and In-the-money options. Stock prices are simulated under the stochastic-volatility double jump diffusion (SVJJ) model, which incorporates stochastic volatility as well as jumps in the stock and volatility process. Simulation is performed under two ’Worlds’. World 1 is set under normal market conditions, whereas World 2 represents stressed market conditions. Calibrating each asset pricing model to observed option prices is performed via the use of a least squares optimisation routine. We find that there is not an asset pricing model which consistently provides a better hedge in World 1. In World 2, however, the Heston model marginally outperforms the Black-Scholes model overall. This can be explained through the higher volatility under World 2, which the Heston model can more accurately describe given the stochastic volatility component. Calibration difficulties are experienced with the Merton model. These difficulties lead to larger errors when minimum variance hedging and alternative calibration techniques should be considered for future users of the optimiser.

This research has been undertaken to further our knowledge of decade-to-century timescale braided, gravel-bed river delta growth dynamics. The study included: a review of available literature; field studies; the development of microscale models for two study deltas; and the development of a simple numerical model incorporating movement of braided river channels across a delta topset (varying the location of sediment delivery to the delta). Results from the microscale modelling showed that successful physical modelling requires well-defined fixed boundaries and, ideally, good historical aerial photography for the estimation of the model time scale. A complex braided gravel-bed river delta system composed of two merging deltas entering a deep, low-energy receiving basins was able to be successfully modelled to provide valuable information on delta growth dynamics. However, a microscale model of a delta prograding into shallow receiving basins, with a large supply of fine sediment, was more difficult to calibrate and assess (partly due to limited field data), and was considered less reliable. The simple rule-based numerical model ‘DELGROW’, developed to simulate a braided river system entering a deep, low-energy body of water, requires a known sediment supply rate, as well as information on the braided river topography, submerged delta foreset, and lakebed bathymetry. Unlike simple 1-d width-averaged geometric models, DELGROW takes into consideration barriers (e.g. islands) as well as relatively complex converging braided river delta configurations. By changing the sediment supply, or modifying the river system, the response of the river system to various scenarios can also be assessed. Microscale models and DELGROW appear to realistically simulate decade-to-century timescale growth of braided gravel-bed river deltas entering a deep, low-energy, receiving basin. Both of these modelling methods initially use the supplied sediment to try and eliminate any riverbed irregularities (e.g. low areas), before continuing to advance and deposit sediment in a more evenly-distributed manner, whilst taking into consideration irregularities due to barriers, and asymmetric sediment sources such as merging deltas. Neither model can reliably predict locations of bank erosion, or channel avulsions that divert flow and sediment outside of the fixed model boundaries.

The number of longitudinal studies has increased steadily in various social science disciplines over the last decade. Growth Mixture Modeling (GMM) has emerged among the new approaches for analyzing longitudinal data. It can be viewed as a combination of Hierarchical Linear Modeling, Latent Growth Curve Modeling and Finite Mixture Modeling. The combination of both continuous and categorical latent variables makes GMM a flexible analysis procedure. However, when researchers analyze their data using GMM, some may assume that the units are independent of each other even though it may not always be the case. The purpose of this dissertation was to examine the impact of ignoring a higher nesting structure in Multilevel Growth Mixture Modeling on the accuracy of classification of individuals and the accuracy on tests of significance (i.e., Type I error rate and statistical power) of the parameter estimates for the model in each subpopulation. Two simulation studies were conducted. In the first study, the impact of misspecifying the multilevel mixture model is investigated by ignoring a level of nesting structure in cross-sectional data. In the second study, longitudinal clustered data (e.g., repeated measures nested within units and units nested within clusters) are analyzed correctly and with a misspecification ignoring the highest level of the nesting structure. Results indicate that ignoring a higher level nesting structure results in lower classification accuracy, less accurate fixed effect estimates, inflation of lower-level variance estimates, and less accurate standard error estimates, the latter result which in turn affects the accuracy of tests of significance for the fixed effects. The magnitude of the intra-class correlation (ICC) coefficient has a substantial impact when a higher level nesting structure is ignored; the higher the ICC, the more variance at the highest level is ignored, and the worse the performance of the model. The implication for applied researchers is that it is important to model the multilevel data structure in (growth) mixture modeling. In addition, researchers should be cautious in interpreting their results if ignoring a higher level nesting structure is inevitable. Limitations concerning appropriate use of latent class analysis in growth modeling include unknown effects of incorrect estimation of the number of latent classes, non-normal distribution effects, and different growth patterns within-group and between-group.

Abstract This study is based on the theory of biology and economy to establish the open access model, dynamic optimization model and static optimization of fishery mathematical models, to discuss the problem of fishery management. To be aimed at getting the equilibrium of resource stock and effort, research data are mainly analyzed by comparative statues. In so doing, the amount of grey mullet, collect and analyze the estimation of exogenous variable. Then, we can use Mathematica program to calculate the equilibrium value resource stock and the effort, and do the sensitivity analysis by standing on the change of estimation of exogenous variable. The result of analysis is as follow: These three fishery mathematical models¡¦ resource stock and effort are consistency. In another view of CPUE, it is not obvious of the economic effect of open access model. We must strengthen the management in policy of fishing for grey mullet, to let the fisherman earn the highest economic benefits. Keyword: open access model static optimization model. dynamic optimization model.

On the subject of what affect voters¡¦ vote choice, political scientists for a long time emphasize three answers: party identification, candidate orientation, and issue orientation. About issue orientation, Rational Choice Theory assumes that human are rational pursuing maximizing self- interests. When voters are making their vote decisions, they would observe the issues positions of competing parties or candidates, comparing with their own positions, and then vote the party or the candidate who can represent their own positions best. Spatial Theory, from Rational Choice Theory, takes those abstract issue positions into some issue space. Both the issue positions of voters and parties could be presented by some points in the space, and the length and direction between the points can represent the differences between issue positions. There are several different models in Spatial Theory, and different models advocate different ways about how voters use the points in issue space to form their evaluations to competing parties or candidates. In this paper, we take the viewpoints of Spatial Theory to research the issue voting behavior of Taiwanese voters. First, we try to know the spatial distribution of voters¡¦ issue positions. Then we inspect the association between voters¡¦ social back- ground elements and issue position. Finally, we test three models of Spatial Theory, proximity model, directional model, and RM mixed model, to know how Taiwanese voters use issue positions to form their party-evaluation.

The fishery of the shrimp Acetes intermedius in the southwestern coast of Taiwan has long history , and it is the food of many species of fishes and large-scale shrimps . Shrimp Acetes has not only fallen on dead ears , but also been ignored its importantce of ecologyical status in the southwestern coast by the academia because of less harvest and output value in the past . It then comes into operation the management of catch , leading the price going up and output value increasing rapidly when the establishment of TungKang producer organization of the shrimp Acetes intrmedius in 1994 , and it also becomes the important seasonal fishery . According to as was mentioned above , the study is based on the theory of biology and economy to put out the open access model , static optimization model and dynamic optimization of fishery mathematical models , and further discuss the problem of fishery management. In connection with getting the equilibrium of resource stock and effort , research data from the substitution of real data are mainly analyzed by compareative statues on exogenous variable .By means of understanding the sensitivity of variation on endogenous variable depending on exogenous variable , we can provide the member of TungKang producer organization of the shrimp Acetes intrmedius with the control on harvest and preservation of stock . The study can get the fact that the management of TungKang producer organization of the shrimp Acetes intrmedius has the notion of sustainable administration by the deriveation of theoretical model and the simulate analysis of historyical data. I hope the management of TungKang producer organization of the shrimp Acetes intrmedius can be popularized.