Mechanistic population Models in Biology: Model Derivation and Application

In general, models of ecological systems can be broadly categorized as ’top-down’ or ’bottom-up’ models, based on the hierarchical level that the model processes are formulated on. The structure of a top-down, also known as phenomenological, population model can be interpreted in terms of population characteristics, but it typically lacks an interpretation on a more basic level. In contrast, bottom-up, also known as mechanistic, population models are derived from assumptions and processes on a more basic level, which allows interpretation of the model parameters in terms of individual behavior. Both approaches, phenomenological and mechanistic modelling, can have their advantages and disadvantages in different situations. However, mechanistically derived models might be better at capturing the properties of the system at hand, and thus give more accurate predictions. In particular, when models are used for evolutionary studies, mechanistic models are more appropriate, since natural selection takes place on the individual level, and in mechanistic models the direct connection between model parameters and individual properties has already been established. The purpose of this thesis is twofold. Firstly, a systematical way to derive mechanistic discrete-time population models is presented. The derivation is based on combining explicitly modelled, continuous processes on the individual level within a reproductive period with a discrete-time maturation process between reproductive periods. Secondly, as an example of how evolutionary studies can be carried out in mechanistic models, the evolution of the timing of reproduction is investigated. Thus, these two lines of research, derivation of mechanistic population models and evolutionary studies, are complementary to each other.

Inversion and assimilation methods with applications in geophysical remote sensing

Stratospheric ozone can be measured accurately using a limb scatter remote sensing technique at the UV-visible spectral region of solar light. The advantages of this technique includes a good vertical resolution and a good daytime coverage of the measurements. In addition to ozone, UV-visible limb scatter measurements contain information about NO2, NO3, OClO, BrO and aerosols. There are currently several satellite instruments continuously scanning the atmosphere and measuring the UVvisible region of the spectrum, e.g., the Optical Spectrograph and Infrared Imager System (OSIRIS) launched on the Odin satellite in February 2001, and the Scanning Imaging Absorption SpectroMeter for Atmospheric CartograpHY (SCIAMACHY) launched on Envisat in March 2002. Envisat also carries the Global Ozone Monitoring by Occultation of Stars (GOMOS) instrument, which also measures limb-scattered sunlight under bright limb occultation conditions. These conditions occur during daytime occultation measurements. The global coverage of the satellite measurements is far better than any other ozone measurement technique, but still the measurements are sparse in the spatial domain. Measurements are also repeated relatively rarely over a certain area, and the composition of the Earth’s atmosphere changes dynamically. Assimilation methods are therefore needed in order to combine the information of the measurements with the atmospheric model. In recent years, the focus of assimilation algorithm research has turned towards filtering methods. The traditional Extended Kalman filter (EKF) method takes into account not only the uncertainty of the measurements, but also the uncertainty of the evolution model of the system. However, the computational cost of full blown EKF increases rapidly as the number of the model parameters increases. Therefore the EKF method cannot be applied directly to the stratospheric ozone assimilation problem. The work in this thesis is devoted to the development of inversion methods for satellite instruments and the development of assimilation methods used with atmospheric models.

Validation of a 3D model for oxygen combustion in a circulating fluidized bed

In this thesis, a model called CFB3D is validated for oxygen combustion in circulating fluidized bed boiler. The first part of the work consists of literature review in which circulating fluidized bed and oxygen combustion technologies are studied. In addition, the modeling of circulating fluidized bed furnaces is discussed and currently available industrial scale three-dimensional furnace models are presented. The main features of CFB3D model are presented along with the theories and equations related to the model parameters used in this work. The second part of this work consists of the actual research and modeling work including measurements, model setup, and modeling results. The objectives of this thesis is to study how well CFB3D model works with oxygen combustion compared to air combustion in circulating fluidized bed boiler and what model parameters need to be adjusted when changing from air to oxygen combustion. The study is performed by modeling two air combustion cases and two oxygen combustion cases with comparable boiler loads. The cases are measured at Ciuden 30 MWth Flexi-Burn demonstration plant in April 2012. The modeled furnace temperatures match with the measurements as well in oxygen combustion cases as in air combustion cases but the modeled gas concentrations differ from the measurements clearly more in oxygen combustion cases. However, the same model parameters are optimal for both air and oxygen combustion cases. When the boiler load is changed, some combustion and heat transfer related model parameters need to be adjusted. To improve the accuracy of modeling results, better flow dynamics model should be developed in the CFB3D model. Additionally, more measurements are needed from the lower furnace to find the best model parameters for each case. The validation work needs to be continued in order to improve the modeling results and model predictability.

A Detailed Look at Scale and Translation Invariance in a Hierarchical Neural Model of Visual Object Recognition

The HMAX model has recently been proposed by Riesenhuber & Poggio as a hierarchical model of position- and size-invariant object recognition in visual cortex. It has also turned out to model successfully a number of other properties of the ventral visual stream (the visual pathway thought to be crucial for object recognition in cortex), and particularly of (view-tuned) neurons in macaque inferotemporal cortex, the brain area at the top of the ventral stream. The original modeling study only used ``paperclip'' stimuli, as in the corresponding physiology experiment, and did not explore systematically how model units' invariance properties depended on model parameters. In this study, we aimed at a deeper understanding of the inner workings of HMAX and its performance for various parameter settings and ``natural'' stimulus classes. We examined HMAX responses for different stimulus sizes and positions systematically and found a dependence of model units' responses on stimulus position for which a quantitative description is offered. Interestingly, we find that scale invariance properties of hierarchical neural models are not independent of stimulus class, as opposed to translation invariance, even though both are affine transformations within the image plane.

A Multi-scale Model for Copper Dishing in Chemical-Mechanical Polishing

The present success in the manufacture of multi-layer interconnects in ultra-large-scale integration is largely due to the acceptable planarization capabilities of the chemical-mechanical polishing (CMP) process. In the past decade, copper has emerged as the preferred interconnect material. The greatest challenge in Cu CMP at present is the control of wafer surface non-uniformity at various scales. As the size of a wafer has increased to 300 mm, the wafer-level non-uniformity has assumed critical importance. Moreover, the pattern geometry in each die has become quite complex due to a wide range of feature sizes and multi-level structures. Therefore, it is important to develop a non-uniformity model that integrates wafer-, die- and feature-level variations into a unified, multi-scale dielectric erosion and Cu dishing model. In this paper, a systematic way of characterizing and modeling dishing in the single-step Cu CMP process is presented. The possible causes of dishing at each scale are identified in terms of several geometric and process parameters. The feature-scale pressure calculation based on the step-height at each polishing stage is introduced. The dishing model is based on pad elastic deformation and the evolving pattern geometry, and is integrated with the wafer- and die-level variations. Experimental and analytical means of determining the model parameters are outlined and the model is validated by polishing experiments on patterned wafers. Finally, practical approaches for minimizing Cu dishing are suggested.

A Multi-scale Model for Copper Dishing in Chemical-Mechanical Polishing

The present success in the manufacture of multi-layer interconnects in ultra-large-scale integration is largely due to the acceptable planarization capabilities of the chemical-mechanical polishing (CMP) process. In the past decade, copper has emerged as the preferred interconnect material. The greatest challenge in Cu CMP at present is the control of wafer surface non-uniformity at various scales. As the size of a wafer has increased to 300 mm, the wafer-level non-uniformity has assumed critical importance. Moreover, the pattern geometry in each die has become quite complex due to a wide range of feature sizes and multi-level structures. Therefore, it is important to develop a non-uniformity model that integrates wafer-, die- and feature-level variations into a unified, multi-scale dielectric erosion and Cu dishing model. In this paper, a systematic way of characterizing and modeling dishing in the single-step Cu CMP process is presented. The possible causes of dishing at each scale are identified in terms of several geometric and process parameters. The feature-scale pressure calculation based on the step-height at each polishing stage is introduced. The dishing model is based on pad elastic deformation and the evolving pattern geometry, and is integrated with the wafer- and die-level variations. Experimental and analytical means of determining the model parameters are outlined and the model is validated by polishing experiments on patterned wafers. Finally, practical approaches for minimizing Cu dishing are suggested.

Data assimilation for a coastal area morphodynamic model: Morecambe Bay

This paper investigates the use of data assimilation in coastal area morphodynamic modelling using Morecambe Bay as a study site. A simple model of the bay has been enhanced with a data assimilation scheme to better predict large-scale changes in bathymetry observed in the bay over a 3-year period. The 2DH decoupled morphodynamic model developed for the work is described, as is the optimal interpolation scheme used to assimilate waterline observations into the model run. Each waterline was acquired from a SAR satellite image and is essentially a contour of the bathymetry at some level within the inter-tidal zone of the bay. For model parameters calibrated against validation observations, model performance is good, even without data assimilation. However the use of data assimilation successfully compensates for a particular failing of the model, and helps to keep the model bathymetry on track. It also improves the ability of the model to predict future bathymetry. Although the benefits of data assimilation are demonstrated using waterline observations, any observations of morphology could potentially be used. These results suggest that data assimilation should be considered for use in future coastal area morphodynamic models.

Variational data assimilation for parameter estimation: application to a simple morphodynamic model

Data assimilation is a sophisticated mathematical technique for combining observational data with model predictions to produce state and parameter estimates that most accurately approximate the current and future states of the true system. The technique is commonly used in atmospheric and oceanic modelling, combining empirical observations with model predictions to produce more accurate and well-calibrated forecasts. Here, we consider a novel application within a coastal environment and describe how the method can also be used to deliver improved estimates of uncertain morphodynamic model parameters. This is achieved using a technique known as state augmentation. Earlier applications of state augmentation have typically employed the 4D-Var, Kalman filter or ensemble Kalman filter assimilation schemes. Our new method is based on a computationally inexpensive 3D-Var scheme, where the specification of the error covariance matrices is crucial for success. A simple 1D model of bed-form propagation is used to demonstrate the method. The scheme is capable of recovering near-perfect parameter values and, therefore, improves the capability of our model to predict future bathymetry. Such positive results suggest the potential for application to more complex morphodynamic models.

Uncertainty assessment of a process-based integrated catchment model of phosphorus

Despite the many models developed for phosphorus concentration prediction at differing spatial and temporal scales, there has been little effort to quantify uncertainty in their predictions. Model prediction uncertainty quantification is desirable, for informed decision-making in river-systems management. An uncertainty analysis of the process-based model, integrated catchment model of phosphorus (INCA-P), within the generalised likelihood uncertainty estimation (GLUE) framework is presented. The framework is applied to the Lugg catchment (1,077 km2), a River Wye tributary, on the England–Wales border. Daily discharge and monthly phosphorus (total reactive and total), for a limited number of reaches, are used to initially assess uncertainty and sensitivity of 44 model parameters, identified as being most important for discharge and phosphorus predictions. This study demonstrates that parameter homogeneity assumptions (spatial heterogeneity is treated as land use type fractional areas) can achieve higher model fits, than a previous expertly calibrated parameter set. The model is capable of reproducing the hydrology, but a threshold Nash-Sutcliffe co-efficient of determination (E or R 2) of 0.3 is not achieved when simulating observed total phosphorus (TP) data in the upland reaches or total reactive phosphorus (TRP) in any reach. Despite this, the model reproduces the general dynamics of TP and TRP, in point source dominated lower reaches. This paper discusses why this application of INCA-P fails to find any parameter sets, which simultaneously describe all observed data acceptably. The discussion focuses on uncertainty of readily available input data, and whether such process-based models should be used when there isn’t sufficient data to support the many parameters.

The radiative effect of a fir canopy on a snowpack

Models of snow processes in areas of possible large-scale change need to be site independent and physically based. Here, the accumulation and ablation of the seasonal snow cover beneath a fir canopy has been simulated with a new physically based snow-soil vegetation-atmosphere transfer scheme (Snow-SVAT) called SNOWCAN. The model was formulated by coupling a canopy optical and thermal radiation model to a physically based multilayer snow model. Simple representations of other forest effects were included. These include the reduction of wind speed and hence turbulent transfer beneath the canopy, sublimation of intercepted snow, and deposition of debris on the surface. This paper tests this new modeling approach fully at a fir site within Reynolds Creek Experimental Watershed, Idaho. Model parameters were determined at an open site and subsequently applied to the fir site. SNOWCAN was evaluated using measurements of snow depth, subcanopy solar and thermal radiation, and snowpack profiles of temperature, density, and grain size. Simulations showed good agreement with observations (e.g., fir site snow depth was estimated over the season with r(2) = 0.96), generally to within measurement error. However, the simulated temperature profiles were less accurate after a melt-freeze event, when the temperature discrepancy resulted from underestimation of the rate of liquid water flow and/or the rate of refreeze. This indicates both that the general modeling approach is applicable and that a still more complete representation of liquid water in the snowpack will be important.

Sparse model identification using orthogonal forward regression with basis pursuit and D-optimality

An efficient model identification algorithm for a large class of linear-in-the-parameters models is introduced that simultaneously optimises the model approximation ability, sparsity and robustness. The derived model parameters in each forward regression step are initially estimated via the orthogonal least squares (OLS), followed by being tuned with a new gradient-descent learning algorithm based on the basis pursuit that minimises the l(1) norm of the parameter estimate vector. The model subset selection cost function includes a D-optimality design criterion that maximises the determinant of the design matrix of the subset to ensure model robustness and to enable the model selection procedure to automatically terminate at a sparse model. The proposed approach is based on the forward OLS algorithm using the modified Gram-Schmidt procedure. Both the parameter tuning procedure, based on basis pursuit, and the model selection criterion, based on the D-optimality that is effective in ensuring model robustness, are integrated with the forward regression. As a consequence the inherent computational efficiency associated with the conventional forward OLS approach is maintained in the proposed algorithm. Examples demonstrate the effectiveness of the new approach.

Meson properties in an extended nonlocal NJL model

A nonlocal version of the NJL model is investigated. It is based on a separable quark-quark interaction, as suggested by the instanton liquid picture of the QCD vacuum. The interaction is extended to include terms that bind vector and axial-vector mesons. The nonlocality means that no further regulator is required. Moreover the model is able to confine the quarks by generating a quark propagator without poles at real energies. Features of the continuation of amplitudes from Euclidean space to Minkowski energies are discussed. These features lead to restrictions on the model parameters as well as on the range of applicability of the model. Conserved currents are constructed, and their consistency with various Ward identities is demonstrated. In particular, the Gell-Mann-Oakes-Renner relation is derived both in the ladder approximation and at meson loop level. The importance of maintaining chiral symmetry in the calculations is stressed throughout. Calculations with the model are performed to all orders in momentum. Meson masses are determined, along with their strong and electromagnetic decay amplitudes. Also calculated are the electromagnetic form factor of the pion and form factors associated with the processes gamma gamma* --> pi0 and omega --> pi0 gamma*. The results are found to lead to a satisfactory phenomenology and demonstrate a possible dynamical origin for vector-meson dominance. In addition, the results produced at meson loop level validate the use of 1/Nc as an expansion parameter and indicate that a light and broad scalar state is inherent in models of the NJL type.

Nonlinear model structure design and construction using orthogonal least squares and D-optimality design

A very efficient learning algorithm for model subset selection is introduced based on a new composite cost function that simultaneously optimizes the model approximation ability and model robustness and adequacy. The derived model parameters are estimated via forward orthogonal least squares, but the model subset selection cost function includes a D-optimality design criterion that maximizes the determinant of the design matrix of the subset to ensure the model robustness, adequacy, and parsimony of the final model. The proposed approach is based on the forward orthogonal least square (OLS) algorithm, such that new D-optimality-based cost function is constructed based on the orthogonalization process to gain computational advantages and hence to maintain the inherent advantage of computational efficiency associated with the conventional forward OLS approach. Illustrative examples are included to demonstrate the effectiveness of the new approach.

Neurofuzzy design and model construction of nonlinear dynamical processes from data

A common problem in many data based modelling algorithms such as associative memory networks is the problem of the curse of dimensionality. In this paper, a new two-stage neurofuzzy system design and construction algorithm (NeuDeC) for nonlinear dynamical processes is introduced to effectively tackle this problem. A new simple preprocessing method is initially derived and applied to reduce the rule base, followed by a fine model detection process based on the reduced rule set by using forward orthogonal least squares model structure detection. In both stages, new A-optimality experimental design-based criteria we used. In the preprocessing stage, a lower bound of the A-optimality design criterion is derived and applied as a subset selection metric, but in the later stage, the A-optimality design criterion is incorporated into a new composite cost function that minimises model prediction error as well as penalises the model parameter variance. The utilisation of NeuDeC leads to unbiased model parameters with low parameter variance and the additional benefit of a parsimonious model structure. Numerical examples are included to demonstrate the effectiveness of this new modelling approach for high dimensional inputs.

Nonlinear model structure detection using optimum experimental design and orthogonal least squares

A very efficient learning algorithm for model subset selection is introduced based on a new composite cost function that simultaneously optimizes the model approximation ability and model adequacy. The derived model parameters are estimated via forward orthogonal least squares, but the subset selection cost function includes an A-optimality design criterion to minimize the variance of the parameter estimates that ensures the adequacy and parsimony of the final model. An illustrative example is included to demonstrate the effectiveness of the new approach.