The ultimate goal of most prognostic systems is accurate prediction of the remaining useful life (RUL) of individual systems or components based on their use and performance. This class of prognostic algorithms is termed Degradation-Based, or Type III Prognostics. As equipment degrades, measured parameters of the system tend to change; these sensed measurements, or appropriate transformations thereof, may be used to characterize degradation. Traditionally, individual-based prognostic methods use a measure of degradation to make RUL estimates. Degradation measures may include sensed measurements, such as temperature or vibration level, or inferred measurements, such as model residuals or physics-based model predictions. Often, it is beneficial to combine several measures of degradation into a single parameter. Selection of an appropriate parameter is key for making useful individual-based RUL estimates, but methods to aid in this selection are absent in the literature. This dissertation introduces a set of metrics which characterize the suitability of a prognostic parameter. Parameter features such as trendability, monotonicity, and prognosability can be used to compare candidate prognostic parameters to determine which is most useful for individual-based prognosis. Trendability indicates the degree to which the parameters of a population of systems have the same underlying shape. Monotonicity characterizes the underlying positive or negative trend of the parameter. Finally, prognosability gives a measure of the variance in the critical failure value of a population of systems. By quantifying these features for a given parameter, the metrics can be used with any traditional optimization technique, such as Genetic Algorithms, to identify the optimal parameter for a given system. An appropriate parameter may be used with a General Path Model (GPM) approach to make RUL estimates for specific systems or components. A dynamic Bayesian updating methodology is introduced to incorporate prior information in the GPM methodology. The proposed methods are illustrated with two applications: first, to the simulated turbofan engine data provided in the 2008 Prognostics and Health Management Conference Prognostics Challenge and, second, to data collected in a laboratory milling equipment wear experiment. The automated system was shown to identify appropriate parameters in both situations and facilitate Type III prognostic model development.

Biofilms are colonies of bacteria attached to the surface at a solid-fluid interface. Bacteria in biofilm produce exopolysaccharides (EPS) that form a gel-like matrix in which the bacteria are embedded. Biofilms have numerous consequences in industrial and medical settings, both positive (bioreactors, digestion) and negative (blocking, as corrosive damage of materials/devices, food contamination, clinical infection). The use of antibiotics or mechanical clearing can be effective at removing biofilms, but such treatments are not always effective or appropriate in all situations. Recently, non-thermal atmospheric plasma treatments have been proposed as an alternative (or complementary) form of treatment, that can target sites of infection with minimal damage to the surroundings (e.g. host cells in a clinical setting). These plasmas generate a multitude of chemical species, most of which are very short lived, that can infiltrate and diffuse into the biofilm killing the bacteria within. The aim of this thesis is to develop a multi-dimensional mathematical model to investigate the effect of a non- thermal plasma on biofilms in time and space and to identify key factors that determine effectiveness of the treatment. Most of the chemical products of cold plasmas are too short lived, or too reactive, to be effective in killing the biofilms, it is the longer live species, e.g. ozone, hydrogen peroxide, acid species, that penetrated the biofilm and do the most damage. However, the EPS in biofilms is an effective barrier against ozone and hydrogen peroxide. No published biofilm model combines multi-dimensional growth with a detailed description of EPS production, hence a new mathematical model is developed and applied to simulating plasma treatment. The thesis is split broadly into two parts. The first part presents a new biofilm model framework that simulates growth in response to any number of substrates (e.g. nutrient, oxygen). The model combines an Individual based model (IbM) description of bacteria (individuals or clusters) and substrates are described as a continuum. Novel features of the framework are the assumption that EPS forms a continuum over the domain and the explicit consideration of cellular energy (ATP). Simulations of this model demonstrate the contrast between biofilm grown with topical nutrient sources (forming irregular, bumpy biofilm) and basal nutrient source with topical oxygen such as biofilm grown on agar (forming regular spatially uniform biofilms). The former is in broad agreement with experiments whilst the latter, to our knowledge, has been the subject of very little experimental study. The second part extends the modelling framework to consider the effect of the plasma species. The simulations demonstrate that penetration is a key factor in their effectiveness, for which EPS plays a key role in preventing spread within and beyond the plasma treated zone. The simulations provide estimates of the timescale of equilibration of the main plasma species, predict the effect of combining these species and demonstrate how the constituents of the biofilm can change following treatment. A number of recommended suggestions for future theoretical and experimental study are discussed in the conclusions.

In today’s schools students enter classrooms with different experiences and knowledge level. In order to promote the development and learning of all pupils, teaching should be adapted to each pupil’s circumstances and needs. According to the Swedish school curriculum (Lgr 11) and the Education Act (2010:800) there is an emphasis to have all students reach the same academic goals and standards. However past research indicates that individual adaption tailored for the individual needs of students in English teaching is considered somewhat average. Based on Vinterek’s (2006) individualization types the aim of this study has been to examine whether and if so, in what way teachers individualize English teaching based on the varying circumstances and needs of pupils. This study also aims to identify what factors teachers’ claim affect their work with individual adaption in teaching, based on Lundgren’s (1972) and Stensmo’s (2008) frame factor theory. Based on a qualitative method with both observations and interviews, two questions have been answered: 1. In what way do three teachers work with individualize English teaching, based on the varying circumstances and needs of each pupil? 2. What factors do teachers consider affects their work with individualization in English teaching? From the outcomes of the observations and interviews the results show that the teachers do work with an individual based education tailored for the individual needs of the pupil’s. The result from this study also shows that the teachers face several difficulties with individualization in English teaching. All of the teachers claim that time and the size of the class are factors that most affect the teaching process with individualization in the classroom.

Individual-based models have been applied to study a broad spectrum of problems across multiple disciplines, such as the spread of epidemics or the outcome of social dilemma. They are used to investigate the macroscopic effects that arise from the microscopic dynamics of interacting individuals. Fixation describes the taking over of the population by a single type of individual or species. It is a prominent feature in the field of population genetics, which interprets many biological scenarios of evolution. Equilibration describes the process of reaching a heterogeneous steady state. In this thesis we analyse these macroscopic features through techniques derived from statistical physics and the theory of stochastic processes. Birth-death processes are used to describe the interaction of two types of individual in a population, such as competing strains of bacteria. These interactions are often specified using the framework of evolutionary game theory. The environment in which the population evolves can have a crucial impact on selection. In systems where the environment switches between multiple states we develop a general theory to calculate the fixation time statistics of a mutant individual in a population of wild-types, as well as the stationary distributions when mutations are present in the dynamics. In some birth--death processes, and in particular those described by evolutionary game theory, the mean fixation time contains only limited information. By diagonalising the master equation that describes the process, we are able to obtain closed-form expressions for the complete fixation time distributions. Individual-based models can also be used to describe the accumulation of mutations in a cell. This has important consequences for the initiation and progression of cancer. We find that such systems exhibit metastable states in the dynamics, and we can exploit the separation of timescales between relaxing to the quasi-stationary state and reaching fixation to characterise these phenomena. In this scenario we employ the WKB method to describe the population-level dynamics. Although this method has been used to describe numerous stochastic processes, a clear and coherent description is lacking in the literature. Through the use of multiple examples, including the aforementioned cancer initiation model, we carefully explain the multitude of constructs and equations that result from the application of this methodThe analytical characterisation of the evolutionary dynamics that are observed in these stochastic processes has resulted in a greater understanding of fixation and equilibration. This thesis promotes the benefits of analytical, or even semi-analytical methods, and on a more general level contributes toward a more complete understanding of evolutionary processes.

Utility companies and regulatory agencies are interested in understanding juvenile salmon swimming patterns as they approach hydropower dams because it can allow them to assess fish bypass efficiency and conduct fish survival studies. A model capable of predicting juvenile salmon swim paths can assist in the design of fish bypasses and diversion structures. This thesis presents a mechanistic model tailored to simulate swimming patterns of juvenile salmon swimming in forebays, tailraces, and free-flowing rivers. The model integrates information on juvenile salmon behavior at both field and laboratory scale and literature on juvenile salmon swimming capabilities. Simulated fish swim paths are determined by solving Newton's Second Law. Most of the model parameters are represented by probability distributions. Behavioral responses are triggered for the most part by the flow acceleration and pressure. The model uses conditional probability distributions of thrust magnitude and direction, given flow acceleration. Simulated fish select a swimming direction referenced to the flow velocity vector. To consider juvenile salmon's tendency to coast with the flow, the model intersperses periods of active swimming and gliding. Chinook salmon measured swim paths were analyzed. The flow variables at the fish locations were obtained from CFD simulations. Juvenile salmon mean thrust was determined from solving Newton's Second Law at every measured location. Results show that as flow acceleration increases, the juvenile salmon average thrust increases and the probability of gliding decreases. Chinook salmon tend to migrate tail-first as flow acceleration increases. For the flow accelerations of 5x10-4 m/s2 and 1x10-2 m/s2, approximately 85% and 95% of the analyzed fish migrated tail-first, respectively. The model capacity to predict fish migration route selection, fish-like trajectories, and residence times was tested at two hydropower dams. On average, migration routes were predicted with 17 percent of relative error. Model predictions for fish average residence times were within 10 percent of measured values.

<p>The school is responsible to make sure that each students´ individual needs are met as well as that the lessons are suitable for all students´ ability. As this is the case it is very interesting to evaluate how this is done in reality. The purpose with the study has been to shed light upon what different methods teachers in various schools use in order to individualize their teach­ings. Are their obvious differences in the way teachers work with individualization and how does this affect the students? The teachers in the different schools provided me with informa­tion on how they work in order to teach, stimulate and motivate well achievers as well as stu­dents who find school more difficult. I also asked if, and to what degree they apply different learning techniques as well as if, and how often they consider various learning styles.</p><p>The phenomenological study is qualitative. Methods used are interviews with the different teachers as well as observations in all four classrooms. The classes were each observed for a full day and after time spent in the classroom teachers involved that particular day was inter­viewed.</p><p>The results showed that the teachers work in many different ways in order to individualize their teaching. It was also clear that there were differences on the classrooms physical shape as well as material and books. There were also differences in class sizes and the amount of teachers in the classrooms – which surely affected the situations. A conclusion of the study is that two main methods of individualization were noted. One method used by one group of teachers was to let all students work on the same problems but to their own ability. The other group of teachers used and offered, to a larger extent, different and various materials to their students in order to meet the child at its level of scholastic development and ability.</p>

Population replenishment through recruitment is an essential process for the long term viability of corals and their associated communities, particularly under increasing stresses that threaten their vitality. Although many researchers have identified specific factors that influence individual processes in the early life cycle of corals, few studies to date have attempted to determine the cumulative success of a cohort's progression through these stages in natural reef settings. Specifically, there is a paucity of knowledge regarding appropriate and realistic techniques to forecast the success of recruitment in natural settings, while taking into account both the individual and environmental factors that regulate these recruitment dynamics at local scales. Because of this need, the overall goals of this dissertation research were to (1) assess key life stage processes leading to recruitment - specifically, settlement and early post-settlement processes - for which previous knowledge was limited or absent; and (2) using this knowledge, develop a local-scale recruitment model that assessed the cumulative success of a cohort's progression through all the early life stages and identified those processes that had a strong relative influence on regulating recruitment dynamics. Focusing on the common western Atlantic brooding coral, Porites astreoides, this dissertation research was divided into three main sections to address the overall objectives: (1) identification and quantification of recruitment patterns in natural reef settings, in order to guide the development and testing of the recruitment model (Chapter 2); (2) assessment of the focal species' behaviors, survivorship rates, and factors affecting those rates during its progression through the primary early life stage processes (i.e., basic habitat preferences during the settlement stage, Chapter 3; early post-settlement survivorship, Chapters 4 and 5); and (3) development of a local recruitment model that accounted for the full complement of early life stage processes in a spatially-explicit simulation framework (Chapter 6). While unique study-specific insights were gained from each of the individual chapters, a few general insights emerged with respect to the overarching study objectives from this dissertation research. First, larval supply is a key driver for recruitment, where a high degree of larval loss, either through direct larval mortality or export from the reef, occurs prior to settlement on the substrate. Rates of loss were 96-99% in the model analyses, and as such represent the first major population bottleneck for this species and others with similar life histories. Compounding this larval loss is a second population bottleneck during the early post-settlement stage, where mortality was typically greater than 75% within the first week after settlement. Such high rates of loss have important implications for future population dynamics, as relatively minor changes to these rates of loss can have relatively strong influences on future dynamics. Second, habitat influences on recruitment were found to be relatively minimal when compared to high rates of mortality in both the larval supply and early post-settlement stages. Although the relative influence of habitat may be strong under unique situations where substantial space preemption limits settlement (e.g., high macroalgal cover, sedimentation, or adult coral cover), these effects may not be reflective of average systems. However, the influence of habitat may still be crucial for ensuring that the few individuals who survive the larval supply and the early post-settlement bottlenecks recruit into the future adult population, and these influences may interact with other density-dependent processes as adult cover increases. Overall, this research presents valuable and novel insights on a number of the under-studied early life stage processes. By identifying the key processes which regulate recruitment, this work highlights those stages whose responses to environmental change will have strong impacts on recruitment and subsequent population dynamics. In addition to the process-based insights gained on these dynamics, this work provides informative criteria for managers on the stages most responsive to conservation efforts aimed at promoting resilience and recovery.

The school is responsible to make sure that each students´ individual needs are met as well as that the lessons are suitable for all students´ ability. As this is the case it is very interesting to evaluate how this is done in reality. The purpose with the study has been to shed light upon what different methods teachers in various schools use in order to individualize their teach­ings. Are their obvious differences in the way teachers work with individualization and how does this affect the students? The teachers in the different schools provided me with informa­tion on how they work in order to teach, stimulate and motivate well achievers as well as stu­dents who find school more difficult. I also asked if, and to what degree they apply different learning techniques as well as if, and how often they consider various learning styles. The phenomenological study is qualitative. Methods used are interviews with the different teachers as well as observations in all four classrooms. The classes were each observed for a full day and after time spent in the classroom teachers involved that particular day was inter­viewed. The results showed that the teachers work in many different ways in order to individualize their teaching. It was also clear that there were differences on the classrooms physical shape as well as material and books. There were also differences in class sizes and the amount of teachers in the classrooms – which surely affected the situations. A conclusion of the study is that two main methods of individualization were noted. One method used by one group of teachers was to let all students work on the same problems but to their own ability. The other group of teachers used and offered, to a larger extent, different and various materials to their students in order to meet the child at its level of scholastic development and ability.

White-tailed deer (Odocoileus virginianus) are important game mammals and potential reservoirs of diseases of domestic livestock, so diseases of deer are of great concern to wildlife managers. In many situations, models can be useful for integrating existing data, understanding disease transmission patterns, and predicting effects on host populations. Individual-based modeling (IBM) has become more commonplace in ecology as a tool to link individual behavior to population dynamics and community interactions, especially for gauging the effects of management actions. Spatially explicit IBMs are especially useful when ecological processes, such as disease transmission, are affected by the spatial composition of the environment. I developed a spatially explicit IBM, DeerLandscapeDisease (DLD), to simulate direct and indirect disease transmission in white-tailed deer. Using data from GPS-collared deer in southern Illinois, I developed methods to identify habitats and times of high contact probability. I parameterized movement models, for use in DLD, using field data from GPS-collared deer in both southern and east-central Illinois. I then used DLD to simulate deer movements and epizootiology in two different landscapes: a predominantly agricultural landscape with fragmented forest patches in east-central Illinois and a landscape dominated by forest in southern Illinois. Behavioral and demographic parameters that could not be estimated from the field data were estimated using published literature of deer ecology. I assumed that bioavailability of infectious pathogens deposited in the environment decreased exponentially. Transmission probabilities were estimated by fitting to published trends in infection prevalence, assuming that infection probability during an encounter was equal for all age classes, so infection prevalence varied with sex- and age-specific behavior. DLD simulations of chronic wasting disease epizootiology demonstrated significant effects of landscape structure, social behavior, and mode of transmission on prevalence, emphasizing the importance of spatial, temporal and behavioral heterogeneity in disease modeling. These results demonstrate the utility of IBMs in incorporating spatio-temporal variables as well as animal behavior when predicting and modeling disease spread.

abstract: The spread of invasive species may be greatly affected by human responses to prior species spread, but models and estimation methods seldom explicitly consider human responses. I investigate the effects of management responses on estimates of invasive species spread rates. To do this, I create an agent-based simulation model of an insect invasion across a county-level citrus landscape. My model provides an approximation of a complex spatial environment while allowing the "truth" to be known. The modeled environment consists of citrus orchards with insect pests dispersing among them. Insects move across the simulation environment infesting orchards, while orchard managers respond by administering insecticide according to analyst-selected behavior profiles and management responses may depend on prior invasion states. Dispersal data is generated in each simulation and used to calculate spread rate via a set of estimators selected for their predominance in the empirical literature. Spread rate is a mechanistic, emergent phenomenon measured at the population level caused by a suite of latent biological, environmental, and anthropogenic. I test the effectiveness of orchard behavior profiles on invasion suppression and evaluate the robustness of the estimators given orchard responses. I find that allowing growers to use future expectations of spread in management decisions leads to reduced spread rates. Acting in a preventative manner by applying insecticide before insects are actually present, orchards are able to lower spread rates more than by reactive behavior alone. Spread rates are highly sensitive to spatial configuration. Spatial configuration is hardly a random process, consisting of many latent factors often not accounted for in spread rate estimation. Not considering these factors may lead to an omitted variables bias and skew estimation results. The ability of spread rate estimators to predict future spread varies considerably between estimators, and with spatial configuration, invader biological parameters, and orchard behavior profile. The model suggests that understanding the latent factors inherent to dispersal is important for selecting phenomenological models of spread and interpreting estimation results. This indicates a need for caution when evaluating spread. Although standard practice, current empirical estimators may both over- and underestimate spread rate in the simulation. / Dissertation/Thesis / M.S. Biology 2012