The Drosophila larva is a suitable model to study olfaction due to its numerical simplicity. The peripheral olfactory system consists of just 21 pairs of olfactory sensory neurons (OSNs), each expressing one, or at most two classes of olfactory receptors (ORs) that define the receptive range of the OSN. Larvae produce robust behaviours to many odours and are easily genetically manipulated. Unlike audition, relatively little is known regarding olfaction due to its complex nature - most odours exist as multimolecular units that vary in their identity and structure, concentrations and proportions. Until recently, most olfactory research has focused on the processing of simple odours, which does not realistically model real-world odours. Presented here is one of the first in situ investigations of odour mixture processing in the Drosophila melanogaster larva. Processing of odour mixtures was explored using both electrophysiological recordings of the peripheral olfactory system and behavioural assays at the output of the system, and the effects of various factors on responses were also explored. w1118 larvae in which all OSNs were functional, and larvae with only a single class of OSN (using the Gal4-UAS expression system) were studied. At the peripheral level, mixture responses were never entirely transformed from the components, and were always as large as or greater than the response to the strongest component, and therefore the neuron was either 'seeing' just one or more than one of the components, respectively. Mixture responses across all OSNs were always additive, hypoadditive or partially suppressive, and there were no instances of synergistic or fully suppressive responses. Peripheral mixture responses were both OR- and component-dependent, as the same mixture was represented differently across OSNs. At the behavioural level, mixture responses were mostly additive, partially and fully suppressive and therefore not always predictable from the components. Interestingly, responses of larvae with only a single class of OSN were mostly predictable as there was no complexity of processing arising from the combinatorial code. When all OSNs were functional and the combinatorial code appropriately activated, mixture responses were more complex and unpredictable. Associative conditioning experiments revealed that larvae were unable to identify components from within a mixture, providing evidence that, at least at the behavioural level, mixture responses were probably synthetic, and therefore likely that interactions between the components occurred at some point along the processing pathway. Mixtures were often dominated by the component inducing the largest firing rate, and carbon chain length and vapour pressure influenced, to some degree, which component dominated. The nature of mixture responses were affected by concentration which is consistent with a model of receptor competition - at low concentrations mixture responses were additive, whilst at high concentrations responses were reduced compared to an additive response. In contrast, prior experience had little effect on peripheral responses to pure odours and mixtures, although rapid adaptation was observed during exposure. Exposure did have an effect on subsequent behavioural responses to pure odours and mixtures, providing evidence of central effects of adaptation. The data presented here provides evidence that mixture processing is extremely complex, with many factors influencing and affecting the way that the system responds to mixtures. This data reveals an unexpected complexity in a numerically simple system and with such'simple' complex odours, and indicates the likelihood of more complex responses when all OSNs are functional.

Described in this report is stimulated echo pulsed field gradient (STE-PFG) 1H nuclear magnetic resonance (NMR) diffusion on neutral and negatively charged magnetically aligned bicelles incorporating the Pluronic tri-block copolymer F68. Bicelles are model lipid membrane systems composed of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) and 1,2-dihexanoyl-sn-glycero-3-phosphocholine (DHPC). Pluronic F68 incorporated into neutral bicellar mixtures (q= [DMPC]/[DHPC]= 4.5) exhibited resonance intensity decays that are non-exponential and diffusion-time dependent., i.e. non-Gaussian diffusion. In contrast, Pluronic F68 incorporated in negatively charged bicellar mixtures, containing 1 mol% 1,2-dimyristoyl-sn-glycero-3-phosphoglycerol (DMPG), showed the F68 intensity decays that are exponential and diffusion-time independent, viz., Gaussian diffusion. The implication may be that neutral bicellar mixtures incorporating Pluronic F68 consist of extended lamellae composed of meshed ribbon structures, while negatively charged bicellar mixtures incorporating Pluronic F68 consist of perforated lamellae. Pluronic F68 incorporated into the bicelles reports these morphological differences through its diffusion.

Described in this report is stimulated echo pulsed field gradient (STE-PFG) 1H nuclear magnetic resonance (NMR) diffusion on neutral and negatively charged magnetically aligned bicelles incorporating the Pluronic tri-block copolymer F68. Bicelles are model lipid membrane systems composed of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) and 1,2-dihexanoyl-sn-glycero-3-phosphocholine (DHPC). Pluronic F68 incorporated into neutral bicellar mixtures (q= [DMPC]/[DHPC]= 4.5) exhibited resonance intensity decays that are non-exponential and diffusion-time dependent., i.e. non-Gaussian diffusion. In contrast, Pluronic F68 incorporated in negatively charged bicellar mixtures, containing 1 mol% 1,2-dimyristoyl-sn-glycero-3-phosphoglycerol (DMPG), showed the F68 intensity decays that are exponential and diffusion-time independent, viz., Gaussian diffusion. The implication may be that neutral bicellar mixtures incorporating Pluronic F68 consist of extended lamellae composed of meshed ribbon structures, while negatively charged bicellar mixtures incorporating Pluronic F68 consist of perforated lamellae. Pluronic F68 incorporated into the bicelles reports these morphological differences through its diffusion.

Previous studies exposing fish to xenoestrogens have demonstrated vitellogenin (VTG) induction, delayed gametogenesis, altered sex distribution, and decreased reproductive performance, with a majority of those studies focusing on exposure to single chemicals. The objective of this study was to determine the effects of binary mixtures of a weak estrogen receptor agonist, nonylphenol (NP) and a potent estrogen receptor agonist, 17α-ethinylestradiol (EE) on sex distribution, gametogenesis, VTG induction, heat shock protein 70 (HSP70) expression and reproductive capacity in zebrafish (Danio rerio). Fish were exposed from 2 to 60 days post-hatch (dph) to nominal concentrations of 10 or 100 µg/l NP (NP10 or NP100, respectively), 1 or 10 ng/l EE (EE1 or EE10, respectively), 1 ng/l EE + 10 or 100 µg/l NP (EE1+NP10 or EE1+NP100, respectively), 10 ng/l EE + 10 or 100 µg/l NP (EE10+NP10 or EE10+NP100, respectively) or solvent control (0.01% acetone v/v) in a static-renewal system with replacement every 48h. At 60 dph, fish from each treatment were euthanized for histological examination of gonads, and whole body VTG and HSP70 levels. Remaining fish were reared in clean water until adulthood (240 dph) for breeding studies. In all EE10 exposure groups (EE10, EE10+NP10 and EE10+NP100), increasing NP concentration acted less than additively to the action of EE in terms of VTG induction at 60 dph. Similarly, a less than additivity of effect was observed with egg production, where EE1+NP100 exposure resulted in significantly more eggs produced per breeding trial than EE1 alone. Histological staging of oogenesis revealed suppressed gametogenesis in females at 60 dph. There were no differences among treatment groups in whole body HSP70 expression in 60 dph fish or in gonadal HSP70 expression in adult fish. Although there was no statistical evidence of non-additivity, breeding trials in adults revealed significant reductions in egg viability, egg hatchability and/or F1 swim-up success, suggesting that developmental exposures to xenoestrogens may cause irreversible effects on egg quality and progeny even after depuration. In conclusion, these results suggest that environmentally relevant mixtures of NP and EE can produce additive or non-additive effects depending on the particular response being determined and the respective exposure concentrations of each chemical. Thus, it is recommended that caution be exercised in ecological risk assessments when assuming additivity in piscine responses to xenoestrogen mixtures.

Mixture models provide a natural framework for unobserved heterogeneity in a population. They are widely applied in astronomy, biology, engineering, finance, genetics, medicine, social sciences, and other areas. An important first step for using mixture models is the test of homogeneity. Before one tries to fit a mixture model, it might be of value to know whether the data arise from a homogeneous or heterogeneous population. If the data are homogeneous, it is not even necessary to go into mixture modeling. The rejection of the homogeneous model may also have scientific implications. For example, in classical statistical genetics, it is often suspected that only a subgroup of patients have a disease gene which is linked to the marker. Detecting the existence of this subgroup amounts to the rejection of a homogeneous null model in favour of a two-component mixture model. This problem has attracted intensive research recently. This thesis makes substantial contributions in this area of research. Due to partial loss of identifiability, classic inference methods such as the likelihood ratio test (LRT) lose their usual elegant statistical properties. The limiting distribution of the LRT often involves complex Gaussian processes, which can be hard to implement in data analysis. The modified likelihood ratio test (MLRT) is found to be a nice alternative of the LRT. It restores the identifiability by introducing a penalty to the log-likelihood function. Under some mild conditions, the limiting distribution of the MLRT is 1/2\chi^2_0+1/2\chi^2_1, where \chi^2_{0} is a point mass at 0. This limiting distribution is convenient to use in real data analysis. The choice of the penalty functions in the MLRT is very flexible. A good choice of the penalty enhances the power of the MLRT. In this thesis, we first introduce a new class of penalty functions, with which the MLRT enjoys a significantly improved power for testing homogeneity. The main contribution of this thesis is to propose a new class of methods for testing homogeneity. Most existing methods in the literature for testing of homogeneity, explicitly or implicitly, are derived under the condition of finite Fisher information and a compactness assumption on the space of the mixing parameters. The finite Fisher information condition can prevent their usage to many important mixture models, such as the mixture of geometric distributions, the mixture of exponential distributions and more generally mixture models in scale distribution families. The compactness assumption often forces applicants to set artificial bounds for the parameters of interest and makes the resulting limiting distribution dependent on these bounds. Consequently, developing a method without such restrictions is a dream of many researchers. As it will be seen, the proposed EM-test in this thesis is free of these shortcomings. The EM-test combines the merits of the classic LRT and score test. The properties of the EM-test are particularly easy to investigate under single parameter mixture models. It has a simple limiting distribution 0.5\chi^2_0+0.5\chi^2_1, the same as the MLRT. This result is applicable to mixture models without requiring the restrictive regularity conditions described earlier. The normal mixture model is a very popular model in applications. However it does not satisfy the strong identifiability condition, which imposes substantial technical difficulties in the study of the asymptotic properties. Most existing methods do not directly apply to the normal mixture models, so the asymptotic properties have to be developed separately. We investigate the use of the EM-test to normal mixture models and its limiting distributions are derived. For the homogeneity test in the presence of the structural parameter, the limiting distribution is a simple function of the 0.5\chi^2_0+0.5\chi^2_1 and \chi^2_1 distributions. The test with this limiting distribution is still very convenient to implement. For normal mixtures in both mean and variance parameters, the limiting distribution of the EM-test is found be to \chi^2_2. Mixture models are also widely used in the analysis of the directional data. The von Mises distribution is often regarded as the circular normal model. Interestingly, it satisfies the strong identifiability condition and the parameter space of the mean direction is compact. However the theoretical results in the single parameter mixture models can not directly apply to the von Mises mixture models. Because of this, we also study the application of the EM-test to von Mises mixture models in the presence of the structural parameter. The limiting distribution of the EM-test is also found to be 0.5\chi^2_0+0.5\chi^2_1. Extensive simulation results are obtained to examine the precision of the approximation of the limiting distributions to the finite sample distributions of the EM-test. The type I errors with the critical values determined by the limiting distributions are found to be close to nominal values. In particular, we also propose several precision enhancing methods, which are found to work well. Real data examples are used to illustrate the use of the EM-test.

Mixture models provide a natural framework for unobserved heterogeneity in a population. They are widely applied in astronomy, biology, engineering, finance, genetics, medicine, social sciences, and other areas. An important first step for using mixture models is the test of homogeneity. Before one tries to fit a mixture model, it might be of value to know whether the data arise from a homogeneous or heterogeneous population. If the data are homogeneous, it is not even necessary to go into mixture modeling. The rejection of the homogeneous model may also have scientific implications. For example, in classical statistical genetics, it is often suspected that only a subgroup of patients have a disease gene which is linked to the marker. Detecting the existence of this subgroup amounts to the rejection of a homogeneous null model in favour of a two-component mixture model. This problem has attracted intensive research recently. This thesis makes substantial contributions in this area of research. Due to partial loss of identifiability, classic inference methods such as the likelihood ratio test (LRT) lose their usual elegant statistical properties. The limiting distribution of the LRT often involves complex Gaussian processes, which can be hard to implement in data analysis. The modified likelihood ratio test (MLRT) is found to be a nice alternative of the LRT. It restores the identifiability by introducing a penalty to the log-likelihood function. Under some mild conditions, the limiting distribution of the MLRT is 1/2\chi^2_0+1/2\chi^2_1, where \chi^2_{0} is a point mass at 0. This limiting distribution is convenient to use in real data analysis. The choice of the penalty functions in the MLRT is very flexible. A good choice of the penalty enhances the power of the MLRT. In this thesis, we first introduce a new class of penalty functions, with which the MLRT enjoys a significantly improved power for testing homogeneity. The main contribution of this thesis is to propose a new class of methods for testing homogeneity. Most existing methods in the literature for testing of homogeneity, explicitly or implicitly, are derived under the condition of finite Fisher information and a compactness assumption on the space of the mixing parameters. The finite Fisher information condition can prevent their usage to many important mixture models, such as the mixture of geometric distributions, the mixture of exponential distributions and more generally mixture models in scale distribution families. The compactness assumption often forces applicants to set artificial bounds for the parameters of interest and makes the resulting limiting distribution dependent on these bounds. Consequently, developing a method without such restrictions is a dream of many researchers. As it will be seen, the proposed EM-test in this thesis is free of these shortcomings. The EM-test combines the merits of the classic LRT and score test. The properties of the EM-test are particularly easy to investigate under single parameter mixture models. It has a simple limiting distribution 0.5\chi^2_0+0.5\chi^2_1, the same as the MLRT. This result is applicable to mixture models without requiring the restrictive regularity conditions described earlier. The normal mixture model is a very popular model in applications. However it does not satisfy the strong identifiability condition, which imposes substantial technical difficulties in the study of the asymptotic properties. Most existing methods do not directly apply to the normal mixture models, so the asymptotic properties have to be developed separately. We investigate the use of the EM-test to normal mixture models and its limiting distributions are derived. For the homogeneity test in the presence of the structural parameter, the limiting distribution is a simple function of the 0.5\chi^2_0+0.5\chi^2_1 and \chi^2_1 distributions. The test with this limiting distribution is still very convenient to implement. For normal mixtures in both mean and variance parameters, the limiting distribution of the EM-test is found be to \chi^2_2. Mixture models are also widely used in the analysis of the directional data. The von Mises distribution is often regarded as the circular normal model. Interestingly, it satisfies the strong identifiability condition and the parameter space of the mean direction is compact. However the theoretical results in the single parameter mixture models can not directly apply to the von Mises mixture models. Because of this, we also study the application of the EM-test to von Mises mixture models in the presence of the structural parameter. The limiting distribution of the EM-test is also found to be 0.5\chi^2_0+0.5\chi^2_1. Extensive simulation results are obtained to examine the precision of the approximation of the limiting distributions to the finite sample distributions of the EM-test. The type I errors with the critical values determined by the limiting distributions are found to be close to nominal values. In particular, we also propose several precision enhancing methods, which are found to work well. Real data examples are used to illustrate the use of the EM-test.

Previous studies exposing fish to xenoestrogens have demonstrated vitellogenin (VTG) induction, delayed gametogenesis, altered sex distribution, and decreased reproductive performance, with a majority of those studies focusing on exposure to single chemicals. The objective of this study was to determine the effects of binary mixtures of a weak estrogen receptor agonist, nonylphenol (NP) and a potent estrogen receptor agonist, 17α-ethinylestradiol (EE) on sex distribution, gametogenesis, VTG induction, heat shock protein 70 (HSP70) expression and reproductive capacity in zebrafish (Danio rerio). Fish were exposed from 2 to 60 days post-hatch (dph) to nominal concentrations of 10 or 100 µg/l NP (NP10 or NP100, respectively), 1 or 10 ng/l EE (EE1 or EE10, respectively), 1 ng/l EE + 10 or 100 µg/l NP (EE1+NP10 or EE1+NP100, respectively), 10 ng/l EE + 10 or 100 µg/l NP (EE10+NP10 or EE10+NP100, respectively) or solvent control (0.01% acetone v/v) in a static-renewal system with replacement every 48h. At 60 dph, fish from each treatment were euthanized for histological examination of gonads, and whole body VTG and HSP70 levels. Remaining fish were reared in clean water until adulthood (240 dph) for breeding studies. In all EE10 exposure groups (EE10, EE10+NP10 and EE10+NP100), increasing NP concentration acted less than additively to the action of EE in terms of VTG induction at 60 dph. Similarly, a less than additivity of effect was observed with egg production, where EE1+NP100 exposure resulted in significantly more eggs produced per breeding trial than EE1 alone. Histological staging of oogenesis revealed suppressed gametogenesis in females at 60 dph. There were no differences among treatment groups in whole body HSP70 expression in 60 dph fish or in gonadal HSP70 expression in adult fish. Although there was no statistical evidence of non-additivity, breeding trials in adults revealed significant reductions in egg viability, egg hatchability and/or F1 swim-up success, suggesting that developmental exposures to xenoestrogens may cause irreversible effects on egg quality and progeny even after depuration. In conclusion, these results suggest that environmentally relevant mixtures of NP and EE can produce additive or non-additive effects depending on the particular response being determined and the respective exposure concentrations of each chemical. Thus, it is recommended that caution be exercised in ecological risk assessments when assuming additivity in piscine responses to xenoestrogen mixtures.

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Asphalt oxidation causes major changes to binder properties and is hypothesized to be a major contributor to age-related pavement failure such as fatigue cracking. Extensive laboratory aging research has been done to assess the effects of oxidation on binder properties. Previous work shows binder oxidation makes the binder stiffer and more brittle, leading to higher binder stresses under a given deformation. Failure occurs when these stresses exceed the strength of the binder. However, binder oxidation in pavements has not been studied in the same detail as laboratory aging of neat binders. The impact of binder oxidation on long-term pavement performance has been either underestimated or ignored. This research includes studies of binder oxidation in Texas pavements to compare the field aging with laboratory neat binder aging, the impact of binder oxidation on HMAC mixture aging and HMAC mixture fatigue performance, and fundamental rheological property changes of the binder and the mixture. Binder oxidation is studied in fifteen pavements from locations across Texas. Results indicate that unmodified binders in pavements typically oxidize and harden to a degree that exceeds generally accepted pavement aging assumptions. This hardening may also extend much deeper into the pavement than has been previously assumed or documented. Data suggest that pavements can oxidize at rates surprisingly uniform with depth once early oxidation occurs, and that these rates continue for an extended time. Laboratory-aged HMAC mixtures and binders were tested and analyzed for fatigue resistance and their rheological properties. Mixture aging shows the same aging mechanisms as neat binder aging. Both binder and mixture have a higher modulus with aging and a good rheological correlation. The decline in mixture fatigue life (determined using the calibrated mechanistic fatigue analysis approach with surface energy measurement) due to oxidation is significant. Pavement service life is dependent on the mixture, but can be estimated by a cumulative damage approach that considers binder oxidation and pavement loading rate simultaneously. The differences in expected pavement life arise from differences in the rate of binder stiffening due to oxidation and the impact of this stiffening on the decline of fatigue life.

The discovery of proteomic information through the use of mass spectrometry (MS) has been an active area of research in the diagnosis and prognosis of many types of cancer. This process involves feature selection through peak detection but is often complicated by many forms of non-biologicalbias. The need to extract biologically relevant peak information from MS data has resulted in the development of statistical techniques to aid in spectra pre-processing. Baseline estimation and normalization are important pre-processing steps because the subsequent quantification of peak heights depends on this baseline estimate. This dissertation introduces a mixture model to estimate the baseline and peak heights simultaneously through the expectation-maximization (EM) algorithm and a penalized likelihood approach. Our model-based pre-processing performs well in the presence of raw, unnormalized data, with few subjective inputs. We also propose a model-based normalization solution for use in subsequent classification procedures, where misclassification results compare favorably with existing methods of normalization. The performance of our pre-processing method is evaluated using popular matrix-assisted laser desorption and ionization (MALDI) and surface-enhanced laser desorption and ionization (SELDI) datasets as well as through simulation.