Oxidative stability of phytosterols in food models and foods

An important safety aspect to be considered when foods are enriched with phytosterols and phytostanols is the oxidative stability of these lipid compounds, i.e. their resistance to oxidation and thus to the formation of oxidation products. This study concentrated on producing scientific data to support this safety evaluation process. In the absence of an official method for analyzing of phytosterol/stanol oxidation products, we first developed a new gas chromatographic - mass spectrometric (GC-MS) method. We then investigated factors affecting these compounds' oxidative stability in lipid-based food models in order to identify critical conditions under which significant oxidation reactions may occur. Finally, the oxidative stability of phytosterols and stanols in enriched foods during processing and storage was evaluated. Enriched foods covered a range of commercially available phytosterol/stanol ingredients, different heat treatments during food processing, and different multiphase food structures. The GC-MS method was a powerful tool for measuring the oxidative stability. Data obtained in food model studies revealed that the critical factors for the formation and distribution of the main secondary oxidation products were sterol structure, reaction temperature, reaction time, and lipid matrix composition. Under all conditions studied, phytostanols as saturated compounds were more stable than unsaturated phytosterols. In addition, esterification made phytosterols more reactive than free sterols at low temperatures, while at high temperatures the situation was the reverse. Generally, oxidation reactions were more significant at temperatures above 100°C. At lower temperatures, the significance of these reactions increased with increasing reaction time. The effect of lipid matrix composition was dependent on temperature; at temperatures above 140°C, phytosterols were more stable in an unsaturated lipid matrix, whereas below 140°C they were more stable in a saturated lipid matrix. At 140°C, phytosterols oxidized at the same rate in both matrices. Regardless of temperature, phytostanols oxidized more in an unsaturated lipid matrix. Generally, the distribution of oxidation products seemed to be associated with the phase of overall oxidation. 7-ketophytosterols accumulated when oxidation had not yet reached the dynamic state. Once this state was attained, the major products were 5,6-epoxyphytosterols and 7-hydroxyphytosterols. The changes observed in phytostanol oxidation products were not as informative since all stanol oxides quantified represented hydroxyl compounds. The formation of these secondary oxidation products did not account for all of the phytosterol/stanol losses observed during the heating experiments, indicating the presence of dimeric, oligomeric or other oxidation products, especially when free phytosterols and stanols were heated at high temperatures. Commercially available phytosterol/stanol ingredients were stable during such food processes as spray-drying and ultra high temperature (UHT)-type heating and subsequent long-term storage. Pan-frying, however, induced phytosterol oxidation and was classified as a rather deteriorative process. Overall, the findings indicated that although phytosterols and stanols are stable in normal food processing conditions, attention should be paid to their use in frying. Complex interactions between other food constituents also suggested that when new phytosterol-enriched foods are developed their oxidative stability must first be established. The results presented here will assist in choosing safe conditions for phytosterol/stanol enrichment.

Topological stability through tame retractions

A smooth map is said to be stable if small perturbations of the map only differ from the original one by a smooth change of coordinates. Smoothly stable maps are generic among the proper maps between given source and target manifolds when the source and target dimensions belong to the so-called nice dimensions, but outside this range of dimensions, smooth maps cannot generally be approximated by stable maps. This leads to the definition of topologically stable maps, where the smooth coordinate changes are replaced with homeomorphisms. The topologically stable maps are generic among proper maps for any dimensions of source and target. The purpose of this thesis is to investigate methods for proving topological stability by constructing extremely tame (E-tame) retractions onto the map in question from one of its smoothly stable unfoldings. In particular, we investigate how to use E-tame retractions from stable unfoldings to find topologically ministable unfoldings for certain weighted homogeneous maps or germs. Our first results are concerned with the construction of E-tame retractions and their relation to topological stability. We study how to construct the E-tame retractions from partial or local information, and these results form our toolbox for the main constructions. In the next chapter we study the group of right-left equivalences leaving a given multigerm f invariant, and show that when the multigerm is finitely determined, the group has a maximal compact subgroup and that the corresponding quotient is contractible. This means, essentially, that the group can be replaced with a compact Lie group of symmetries without much loss of information. We also show how to split the group into a product whose components only depend on the monogerm components of f. In the final chapter we investigate representatives of the E- and Z-series of singularities, discuss their instability and use our tools to construct E-tame retractions for some of them. The construction is based on describing the geometry of the set of points where the map is not smoothly stable, discovering that by using induction and our constructional tools, we already know how to construct local E-tame retractions along the set. The local solutions can then be glued together using our knowledge about the symmetry group of the local germs. We also discuss how to generalize our method to the whole E- and Z- series.

Stochastic Filtering

The stochastic filtering has been in general an estimation of indirectly observed states given observed data. This means that one is discussing conditional expected values as being one of the most accurate estimation, given the observations in the context of probability space. In my thesis, I have presented the theory of filtering using two different kind of observation process: the first one is a diffusion process which is discussed in the first chapter, while the third chapter introduces the latter which is a counting process. The majority of the fundamental results of the stochastic filtering is stated in form of interesting equations, such the unnormalized Zakai equation that leads to the Kushner-Stratonovich equation. The latter one which is known also by the normalized Zakai equation or equally by Fujisaki-Kallianpur-Kunita (FKK) equation, shows the divergence between the estimate using a diffusion process and a counting process. I have also introduced an example for the linear gaussian case, which is mainly the concept to build the so-called Kalman-Bucy filter. As the unnormalized and the normalized Zakai equations are in terms of the conditional distribution, a density of these distributions will be developed through these equations and stated by Kushner Theorem. However, Kushner Theorem has a form of a stochastic partial differential equation that needs to be verify in the sense of the existence and uniqueness of its solution, which is covered in the second chapter.

Computing the Stochastic Complexity of Simple Probabilistic Graphical Models

Minimum Description Length (MDL) is an information-theoretic principle that can be used for model selection and other statistical inference tasks. There are various ways to use the principle in practice. One theoretically valid way is to use the normalized maximum likelihood (NML) criterion. Due to computational difficulties, this approach has not been used very often. This thesis presents efficient floating-point algorithms that make it possible to compute the NML for multinomial, Naive Bayes and Bayesian forest models. None of the presented algorithms rely on asymptotic analysis and with the first two model classes we also discuss how to compute exact rational number solutions.

Ecological communities in variable environments : dynamics and diversity under coloured environmental stochasticity

While environmental variation is an ubiquitous phenomenon in the natural world which has for long been appreciated by the scientific community recent changes in global climatic conditions have begun to raise consciousness about the economical, political and sociological ramifications of global climate change. Climate warming has already resulted in documented changes in ecosystem functioning, with direct repercussions on ecosystem services. While predicting the influence of ecosystem changes on vital ecosystem services can be extremely difficult, knowledge of the organisation of ecological interactions within natural communities can help us better understand climate driven changes in ecosystems. The role of environmental variation as an agent mediating population extinctions is likely to become increasingly important in the future. In previous studies population extinction risk in stochastic environmental conditions has been tied to an interaction between population density dependence and the temporal autocorrelation of environmental fluctuations. When populations interact with each other, forming ecological communities, the response of such species assemblages to environmental stochasticity can depend, e.g., on trophic structure in the food web and the similarity in species-specific responses to environmental conditions. The results presented in this thesis indicate that variation in the correlation structure between species-specific environmental responses (environmental correlation) can have important qualitative and quantitative effects on community persistence and biomass stability in autocorrelated (coloured) environments. In addition, reddened environmental stochasticity and ecological drift processes (such as demographic stochasticity and dispersal limitation) have important implications for patterns in species relative abundances and community dynamics over time and space. Our understanding of patterns in biodiversity at local and global scale can be enhanced by considering the relevance of different drift processes for community organisation and dynamics. Although the results laid out in this thesis are based on mathematical simulation models, they can be valuable in planning effective empirical studies as well as in interpreting existing empirical results. Most of the metrics considered here are directly applicable to empirical data.

The mast cell as a regulator of atherosclerotic plaque stability

Atherosclerosis is an inflammatory disease progressing over years via the accumulation of cholesterol in arterial intima with subsequent formation of atherosclerotic plaques. The stability of a plaque is determined by the size of its cholesterol-rich necrotic lipid core and the thickness of the fibrous cap covering it. The strength and thickness of the cap are maintained by smooth muscle cells and the extracellular matrix produced by them. A plaque with a large lipid core and a thin cap is vulnerable to rupture that may lead to acute atherothrombotic events, such as myocardial infarction and stroke. In addition, endothelial erosion, possibly induced by apoptosis of endothelial cells, may lead to such clinical events. One of the major causes of plaque destabilization is inflammation induced by accumulated and modified lipoproteins, and exacerbated by local aberrant shear stress conditions. Macrophages, T-lymphocytes and mast cells infiltrate particularly into the plaque’s shoulder regions prone to atherothrombotic events, and they are present at the actual sites of plaque rupture and erosion. Two major mechanisms of plaque destabilization induced by inflammation are extracellular matrix remodeling and apoptosis. Mast cells are bone marrow-derived inflammatory cells that as progenitors upon chemotactic stimuli infiltrate the target tissues, such as the arterial wall, differentiate in the target tissues and mediate their effects via the release of various mediators, typically in a process called degranulation. The released preformed mast cell granules contain proteases such as tryptase, chymase and cathepsin G bound to heparin and chondroitin sulfate proteoglycans. In addition, various soluble mediators such as histamine and TNF-alpha are released. Mast cells also synthesize many mediators such as cytokines and lipid mediators upon activation. Mast cells are capable of increasing the level of LDL cholesterol in the arterial intima by increasing accumulation and retention of LDL and by decreasing removal of cholesterol by HDL in vitro. In addition, by secreting proinflammatory mediators and proteases, mast cells may induce plaque destabilization by inducing apoptosis of smooth muscle and endothelial cells. Also in vivo data from apoE-/- and ldlr-/- mice suggest a role for mast cells in the progression of atherosclerosis. Furthermore, mast cell-deficient mice have become powerful tools to study the effects of mast cells in vivo. In this study, evidence suggesting a role for mast cells in the regulation of plaque stability is presented. In a mouse model genetically susceptible to atherosclerosis, mast cell deficiency (ldlr-/-/KitW-sh/W-sh mice) was associated with a less atherogenic lipid profile, a decreased level of lipid accumulation in the aortic arterial wall and a decreased level of vascular inflammation as compared to mast-cell competent littermates. In vitro, mast cell chymase-induced smooth muscle cell apoptosis was mediated by inhibition of NF-kappaB activity, followed by downregulation of bcl-2, release of cytochrome c, and activation of caspase-8, -9 and -3. Mast cell-induced endothelial cell apoptosis was mediated by chymase and TNF-alpha, and involved chymase-mediated degradation of fibronectin and vitronectin, and inactivation of FAK- and Akt-mediated survival signaling. Subsequently, mast cells induced inhibition of NF-kappaB activity and activation of caspase-8 and -9. In addition, possible mast cell protease-mediated mechanisms of endothelial erosion may include degradation of fibronectin and VE-cadherin. Thus, the present results suggest a role for mast cells in destabilization of atherosclerotic plaques.

Generalizations and Models in Ecology : Lawlikeness, Invariance, Stability, and Robustness

The question at issue in this dissertation is the epistemic role played by ecological generalizations and models. I investigate and analyze such properties of generalizations as lawlikeness, invariance, and stability, and I ask which of these properties are relevant in the context of scientific explanations. I will claim that there are generalizable and reliable causal explanations in ecology by generalizations, which are invariant and stable. An invariant generalization continues to hold or be valid under a special change called an intervention that changes the value of its variables. Whether a generalization remains invariant during its interventions is the criterion that determines whether it is explanatory. A generalization can be invariant and explanatory regardless of its lawlike status. Stability deals with a generality that has to do with holding of a generalization in possible background conditions. The more stable a generalization, the less dependent it is on background conditions to remain true. Although it is invariance rather than stability of generalizations that furnishes us with explanatory generalizations, there is an important function that stability has in this context of explanations, namely, stability furnishes us with extrapolability and reliability of scientific explanations. I also discuss non-empirical investigations of models that I call robustness and sensitivity analyses. I call sensitivity analyses investigations in which one model is studied with regard to its stability conditions by making changes and variations to the values of the model s parameters. As a general definition of robustness analyses I propose investigations of variations in modeling assumptions of different models of the same phenomenon in which the focus is on whether they produce similar or convergent results or not. Robustness and sensitivity analyses are powerful tools for studying the conditions and assumptions where models break down and they are especially powerful in pointing out reasons as to why they do this. They show which conditions or assumptions the results of models depend on. Key words: ecology, generalizations, invariance, lawlikeness, philosophy of science, robustness, explanation, models, stability