Immunological synapse: a mathematical model of the bond formation process:mathematical modelling of the immature synapse

The cell:cell bond between an immune cell and an antigen presenting cell is a necessary event in the activation of the adaptive immune response. At the juncture between the cells, cell surface molecules on the opposing cells form non-covalent bonds and a distinct patterning is observed that is termed the immunological synapse. An important binding molecule in the synapse is the T-cell receptor (TCR), that is responsible for antigen recognition through its binding with a major-histocompatibility complex with bound peptide (pMHC). This bond leads to intracellular signalling events that culminate in the activation of the T-cell, and ultimately leads to the expression of the immune eector function. The temporal analysis of the TCR bonds during the formation of the immunological synapse presents a problem to biologists, due to the spatio-temporal scales (nanometers and picoseconds) that compare with experimental uncertainty limits. In this study, a linear stochastic model, derived from a nonlinear model of the synapse, is used to analyse the temporal dynamics of the bond attachments for the TCR. Mathematical analysis and numerical methods are employed to analyse the qualitative dynamics of the nonequilibrium membrane dynamics, with the specic aim of calculating the average persistence time for the TCR:pMHC bond. A single-threshold method, that has been previously used to successfully calculate the TCR:pMHC contact path sizes in the synapse, is applied to produce results for the average contact times of the TCR:pMHC bonds. This method is extended through the development of a two-threshold method, that produces results suggesting the average time persistence for the TCR:pMHC bond is in the order of 2-4 seconds, values that agree with experimental evidence for TCR signalling. The study reveals two distinct scaling regimes in the time persistent survival probability density prole of these bonds, one dominated by thermal uctuations and the other associated with the TCR signalling. Analysis of the thermal fluctuation regime reveals a minimal contribution to the average time persistence calculation, that has an important biological implication when comparing the probabilistic models to experimental evidence. In cases where only a few statistics can be gathered from experimental conditions, the results are unlikely to match the probabilistic predictions. The results also identify a rescaling relationship between the thermal noise and the bond length, suggesting a recalibration of the experimental conditions, to adhere to this scaling relationship, will enable biologists to identify the start of the signalling regime for previously unobserved receptor:ligand bonds. Also, the regime associated with TCR signalling exhibits a universal decay rate for the persistence probability, that is independent of the bond length.

The order selection and lot sizing problem in the make-to-order environment

This research is motivated by the need for considering lot sizing while accepting customer orders in a make-to-order (MTO) environment, in which each customer order must be delivered by its due date. Job shop is the typical operation model used in an MTO operation, where the production planner must make three concurrent decisions; they are order selection, lot size, and job schedule. These decisions are usually treated separately in the literature and are mostly led to heuristic solutions. The first phase of the study is focused on a formal definition of the problem. Mathematical programming techniques are applied to modeling this problem in terms of its objective, decision variables, and constraints. A commercial solver, CPLEX is applied to solve the resulting mixed-integer linear programming model with small instances to validate the mathematical formulation. The computational result shows it is not practical for solving problems of industrial size, using a commercial solver. The second phase of this study is focused on development of an effective solution approach to this problem of large scale. The proposed solution approach is an iterative process involving three sequential decision steps of order selection, lot sizing, and lot scheduling. A range of simple sequencing rules are identified for each of the three subproblems. Using computer simulation as the tool, an experiment is designed to evaluate their performance against a set of system parameters. For order selection, the proposed weighted most profit rule performs the best. The shifting bottleneck and the earliest operation finish time both are the best scheduling rules. For lot sizing, the proposed minimum cost increase heuristic, based on the Dixon-Silver method performs the best, when the demand-to-capacity ratio at the bottleneck machine is high. The proposed minimum cost heuristic, based on the Wagner-Whitin algorithm is the best lot-sizing heuristic for shops of a low demand-to-capacity ratio. The proposed heuristic is applied to an industrial case to further evaluate its performance. The result shows it can improve an average of total profit by 16.62%. This research contributes to the production planning research community with a complete mathematical definition of the problem and an effective solution approach to solving the problem of industry scale.

Mortality and climatic/environmental correlates of Widdringtonia cedargensis trees in the Cederberg, South Africa

Background: Conifer populations appear disproportionately threatened by global change. Most examples are, however, drawn from the northern hemisphere and long-term rates of population decline are not well documented as historical data are often lacking. We use a large and long-term (1931-2013) repeat photography dataset together with environmental data and fire records to account for the decline of the critically endangered Widdringtonia cedarbergensis. Eighty-seven historical and repeat photo-pairs were analysed to establish 20th century changes in W. cedarbergensis demography. A generalized linear mixed-effects model was fitted to determine the relative importance of environmental factors and fire-return interval on mortality for the species. Results: From an initial total of 1313 live trees in historical photographs, 74% had died and only 44 (3.4%) had recruited in the repeat photographs, leaving 387 live individuals. Juveniles (mature adults) had decreased (increased) from 27% (73%) to 8% (92%) over the intervening period. Our model demonstrates that mortality is related to greater fire frequency, higher temperatures, lower elevations, less rocky habitats and aspect (i.e. east-facing slopes had the least mortality). Conclusions: Our results show that W. cedarbergensis populations have declined significantly over the recorded period, with a pronounced decline in the last 30 years. Individuals that established in open habitats at lower, hotter elevations and experienced a greater fire frequency appear to be more vulnerable to mortality than individuals growing within protected, rocky environments at higher, cooler locations with less frequent fires. Climate models predict increasing temperatures for our study area (and likely increases in wildfires). If these predictions are realised, further declines in the species can be expected. Urgent management interventions, including seedling out-planting in fire-protected high elevation sites, reducing fire frequency in higher elevation populations, and assisted migration, should be considered.

Model reduction for nonlinear aeroelasticity using the Discrete Empirical Interpolation Method

A novel surrogate model is proposed in lieu of computational fluid dynamic (CFD) code for fast nonlinear aerodynamic modeling. First, a nonlinear function is identified on selected interpolation points defined by discrete empirical interpolation method (DEIM). The flow field is then reconstructed by a least square approximation of flow modes extracted by proper orthogonal decomposition (POD). The proposed model is applied in the prediction of limit cycle oscillation for a plunge/pitch airfoil and a delta wing with linear structural model, results are validate against a time accurate CFD-FEM code. The results show the model is able to replicate the aerodynamic forces and flow fields with sufficient accuracy while requiring a fraction of CFD cost.

Schedulazione delle rotte marittime nel settore ortofrutticolo. Modelli e Metodi

Il trasporto marittimo è una delle modalità più utilizzate soprattutto per la movimentazione di grandi volumi di prodotti tra i continenti in quanto è a basso costo, sicuro e meno inquinante rispetto ad altri mezzi di movimentazione. Ai giorni nostri è responsabile di circa l’80% del commercio globale (in volume di carichi trasportati). Il settore del trasporto marittimo ha avuto una lunga tradizione di pianificazione manuale effettuata da progettisti esperti.
 L’obiettivo principale di questa trattazione è stato quello di implementare un modello matematico lineare (MILP, Mixed-Integer Linear Programming Model) per l’ottimizzazione delle rotte marittime nell’ambito del mercato orto-frutticolo che si sviluppa nel bacino del Mediterraneo (problema di Ship-Scheduling). Il modello fornito in questa trattazione è un valido strumento di supporto alle decisioni che può utilizzare uno spedizioniere nell’ambito della pianificazione delle rotte marittime della flotta di navi in suo possesso. Consente di determinare l’insieme delle rotte ottimali che devono essere svolte da un insieme di vettori al fine di massimizzare il profitto complessivo dello spedizioniere, generato nell’arco di tempo considerato. Inoltre, permette di ottenere, per ogni nave considerata, la ripartizione ottimale della merce (carico ottimale).

Stepped Wedge Design for Multiple Interventions

Thesis (Master's)--University of Washington, 2016-08

Air Pollution and High Density Lipoprotein Structure and Function

Thesis (Ph.D.)--University of Washington, 2016-06

Adiponectin and insulin in grey seals during suckling and fasting: relationship with nutritional state and body mass during nursing in mothers and pups

Animals that fast during breeding and/or development, such as phocids, must regulate energy balance carefully to maximize reproductive fitness and survival probability. Adiponectin, produced by adipose tissue, contributes to metabolic regulation by modulating sensitivity to insulin, increasing fatty acid oxidation by liver and muscle, and promoting adipogenesis and lipid storage in fat tissue. We tested the hypotheses that (1) circulating adiponectin, insulin, or relative adiponectin gene expression is related to nutritional state, body mass, and mass gain in wild gray seal pups; (2) plasma adiponectin or insulin is related to maternal lactation duration, body mass, percentage milk fat, or free fatty acid (FFA) concentration; and (3) plasma adiponectin and insulin are correlated with circulating FFA in females and pups. In pups, plasma adiponectin decreased during suckling (linear mixed-effects model [LME]: T = 4.49; P < 0.001) and the early postweaning fast (LME: T = 3.39; P = 0.004). In contrast, their blubber adiponectin gene expression was higher during the early postweaning fast than early in suckling (LME: T = 2.11; P = 0.046). Insulin levels were significantly higher in early (LME: T = 3.52; P = 0.004) and late (LME: T = 6.99; P < 0.001) suckling than in fasting and, given the effect of nutritional state, were also positively related to body mass (LME: T = 3.58; P = 0.004). Adiponectin and insulin levels did not change during lactation and were unrelated to milk FFA or percentage milk fat in adult females. Our data suggest that adiponectin, in conjunction with insulin, may facilitate fat storage in seals and is likely to be particularly important in the development of blubber reserves in pups.

Critère de validation croisée pour le choix des modèles des petits domaines au niveau des unités

Ce mémoire s’intéresse à l’étude du critère de validation croisée pour le choix des modèles relatifs aux petits domaines. L’étude est limitée aux modèles de petits domaines au niveau des unités. Le modèle de base des petits domaines est introduit par Battese, Harter et Fuller en 1988. C’est un modèle de régression linéaire mixte avec une ordonnée à l’origine aléatoire. Il se compose d’un certain nombre de paramètres : le paramètre β de la partie fixe, la composante aléatoire et les variances relatives à l’erreur résiduelle. Le modèle de Battese et al. est utilisé pour prédire, lors d’une enquête, la moyenne d’une variable d’intérêt y dans chaque petit domaine en utilisant une variable auxiliaire administrative x connue sur toute la population. La méthode d’estimation consiste à utiliser une distribution normale, pour modéliser la composante résiduelle du modèle. La considération d’une dépendance résiduelle générale, c’est-à-dire autre que la loi normale donne une méthodologie plus flexible. Cette généralisation conduit à une nouvelle classe de modèles échangeables. En effet, la généralisation se situe au niveau de la modélisation de la dépendance résiduelle qui peut être soit normale (c’est le cas du modèle de Battese et al.) ou non-normale. L’objectif est de déterminer les paramètres propres aux petits domaines avec le plus de précision possible. Cet enjeu est lié au choix de la bonne dépendance résiduelle à utiliser dans le modèle. Le critère de validation croisée sera étudié à cet effet.

Wind Farm Facilities in Germany Kill Noctule Bats from Near and Far

Over recent years, it became widely accepted that alternative, renewable energy may come at some risk for wildlife, for example, when wind turbines cause large numbers of bat fatalities. To better assess likely populations effects of wind turbine related wildlife fatalities, we studied the geographical origin of the most common bat species found dead below German wind turbines, the noctule bat (Nyctalus noctula). We measured stable isotope ratios of non-exchangeable hydrogen in fur keratin to separate migrants from local individuals, used a linear mixed-effects model to identify temporal, spatial and biological factors explaining the variance in measured stable isotope ratios and determined the geographical breeding provenance of killed migrants using isoscape origin models. We found that 72% of noctule bat casualties (n = 136) were of local origin, while 28% were long-distance migrants. These findings highlight that bat fatalities at German wind turbines may affect both local and distant populations. Our results indicated a sex and age-specific vulnerability of bats towards lethal accidents at turbines, i.e. a relatively high proportion of killed females were recorded among migratory individuals, whereas more juveniles than adults were recorded among killed bats of local origin. Migratory noctule bats were found to originate from distant populations in the Northeastern parts of Europe. The large catchment areas of German wind turbines and high vulnerability of female and juvenile noctule bats call for immediate action to reduce the negative cross-boundary effects of bat fatalities at wind turbines on local and distant populations. Further, our study highlights the importance of implementing effective mitigation measures and developing species and scale-specific conservation approaches on both national and international levels to protect source populations of bats. The efficacy of local compensatory measures appears doubtful, at least for migrant noctule bats, considering the large geographical catchment areas of German wind turbines for this species.

Nonparametric Evaluation of Quantitative Traits in Population-Based Association Studies when the Genetic Model is Unknown

Statistical association between a single nucleotide polymorphism (SNP) genotype and a quantitative trait in genome-wide association studies is usually assessed using a linear regression model, or, in the case of non-normally distributed trait values, using the Kruskal-Wallis test. While linear regression models assume an additive mode of inheritance via equi-distant genotype scores, Kruskal-Wallis test merely tests global differences in trait values associated with the three genotype groups. Both approaches thus exhibit suboptimal power when the underlying inheritance mode is dominant or recessive. Furthermore, these tests do not perform well in the common situations when only a few trait values are available in a rare genotype category (disbalance), or when the values associated with the three genotype categories exhibit unequal variance (variance heterogeneity). We propose a maximum test based on Marcus-type multiple contrast test for relative effect sizes. This test allows model-specific testing of either dominant, additive or recessive mode of inheritance, and it is robust against variance heterogeneity. We show how to obtain mode-specific simultaneous confidence intervals for the relative effect sizes to aid in interpreting the biological relevance of the results. Further, we discuss the use of a related all-pairwise comparisons contrast test with range preserving confidence intervals as an alternative to Kruskal-Wallis heterogeneity test. We applied the proposed maximum test to the Bogalusa Heart Study dataset, and gained a remarkable increase in the power to detect association, particularly for rare genotypes. Our simulation study also demonstrated that the proposed non-parametric tests control family-wise error rate in the presence of non-normality and variance heterogeneity contrary to the standard parametric approaches. We provide a publicly available R library nparcomp that can be used to estimate simultaneous confidence intervals or compatible multiplicity-adjusted p-values associated with the proposed maximum test.

A Triple-Isotope Approach to Predict the Breeding Origins of European Bats

Despite a commitment by the European Union to protect its migratory bat populations, conservation efforts are hindered by a poor understanding of bat migratory strategies and connectivity between breeding and wintering grounds. Traditional methods like mark-recapture are ineffective to study broad-scale bat migratory patterns. Stable hydrogen isotopes (delta D) have been proven useful in establishing spatial migratory connectivity of animal populations. Before applying this tool, the method was calibrated using bat samples of known origin. Here we established the potential of delta D as a robust geographical tracer of breeding origins of European bats by measuring delta D in hair of five sedentary bat species from 45 locations throughout Europe. The delta D of bat hair strongly correlated with well-established spatial isotopic patterns in mean annual precipitation in Europe, and therefore was highly correlated with latitude. We calculated a linear mixed-effects model, with species as random effect, linking delta D of bat hair to precipitation delta D of the areas of hair growth. This model can be used to predict breeding origins of European migrating bats. We used delta C-13 and delta N-15 to discriminate among potential origins of bats, and found that these isotopes can be used as variables to further refine origin predictions. A triple-isotope approach could thereby pinpoint populations or subpopulations that have distinct origins. Our results further corroborated stable isotope analysis as a powerful method to delineate animal migrations in Europe.

Modeling height-diameter relationship in pinus pinaster ait. in the forest intervention zone of Lomba, NE-Portugal

In this work, the relationship between diameter at breast height (d) and total height (h) of individual-tree was modeled with the aim to establish provisory height-diameter (h-d) equations for maritime pine (Pinus pinaster Ait.) stands in the Lomba ZIF, Northeast Portugal. Using data collected locally, several local and generalized h-d equations from the literature were tested and adaptations were also considered. Model fitting was conducted by using usual nonlinear least squares (nls) methods. The best local and generalized models selected, were also tested as mixed models applying a first-order conditional expectation (FOCE) approximation procedure and maximum likelihood methods to estimate fixed and random effects. For the calibration of the mixed models and in order to be consistent with the fitting procedure, the FOCE method was also used to test different sampling designs. The results showed that the local h-d equations with two parameters performed better than the analogous models with three parameters. However a unique set of parameter values for the local model can not be used to all maritime pine stands in Lomba ZIF and thus, a generalized model including covariates from the stand, in addition to d, was necessary to obtain an adequate predictive performance. No evident superiority of the generalized mixed model in comparison to the generalized model with nonlinear least squares parameters estimates was observed. On the other hand, in the case of the local model, the predictive performance greatly improved when random effects were included. The results showed that the mixed model based in the local h-d equation selected is a viable alternative for estimating h if variables from the stand are not available. Moreover, it was observed that it is possible to obtain an adequate calibrated response using only 2 to 5 additional h-d measurements in quantile (or random) trees from the distribution of d in the plot (stand). Balancing sampling effort, accuracy and straightforwardness in practical applications, the generalized model from nls fit is recommended. Examples of applications of the selected generalized equation to the forest management are presented, namely how to use it to complete missing information from forest inventory and also showing how such an equation can be incorporated in a stand-level decision support system that aims to optimize the forest management for the maximization of wood volume production in Lomba ZIF maritime pine stands.

Explaining dinophysis cf. acuminata abundance in Antifer (Normandy, France) using dynamic linear regression

Classical regression analysis can be used to model time series. However, the assumption that model parameters are constant over time is not necessarily adapted to the data. In phytoplankton ecology, the relevance of time-varying parameter values has been shown using a dynamic linear regression model (DLRM). DLRMs, belonging to the class of Bayesian dynamic models, assume the existence of a non-observable time series of model parameters, which are estimated on-line, i.e. after each observation. The aim of this paper was to show how DLRM results could be used to explain variation of a time series of phytoplankton abundance. We applied DLRM to daily concentrations of Dinophysis cf. acuminata, determined in Antifer harbour (French coast of the English Channel), along with physical and chemical covariates (e.g. wind velocity, nutrient concentrations). A single model was built using 1989 and 1990 data, and then applied separately to each year. Equivalent static regression models were investigated for the purpose of comparison. Results showed that most of the Dinophysis cf. acuminata concentration variability was explained by the configuration of the sampling site, the wind regime and tide residual flow. Moreover, the relationships of these factors with the concentration of the microalga varied with time, a fact that could not be detected with static regression. Application of dynamic models to phytoplankton time series, especially in a monitoring context, is discussed.

Mode locking in a spatially extended neuron model: active soma and compartmental tree

Understanding the mode-locked response of excitable systems to periodic forcing has important applications in neuroscience. For example it is known that spatially extended place cells in the hippocampus are driven by the theta rhythm to generate a code conveying information about spatial location. Thus it is important to explore the role of neuronal dendrites in generating the response to periodic current injection. In this paper we pursue this using a compartmental model, with linear dynamics for each compartment, coupled to an active soma model that generates action potentials. By working with the piece-wise linear McKean model for the soma we show how the response of the whole neuron model (soma and dendrites) can be written in closed form. We exploit this to construct a stroboscopic map describing the response of the spatially extended model to periodic forcing. A linear stability analysis of this map, together with a careful treatment of the non-differentiability of the soma model, allows us to construct the Arnol'd tongue structure for 1:q states (one action potential for q cycles of forcing). Importantly we show how the presence of quasi-active membrane in the dendrites can influence the shape of tongues. Direct numerical simulations confirm our theory and further indicate that resonant dendritic membrane can enlarge the windows in parameter space for chaotic behavior. These simulations also show that the spatially extended neuron model responds differently to global as opposed to point forcing. In the former case spatio-temporal patterns of activity within an Arnol'd tongue are standing waves, whilst in the latter they are traveling waves.