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Modhara, Sunny. "Mathematical modelling of vascular development in zebrafish." Thesis, University of Nottingham, 2015. http://eprints.nottingham.ac.uk/29125/.
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The Notch signalling pathway is pivotal in ensuring that the processes of arterial specification, angiogenic sprouting and haematopoietic stem cell (HSC) specification are correctly carried out in the dorsal aorta (DA), a primary arterial blood vessel in developing vertebrate embryos. Using the zebrafish as a model organism, and additional experimental observations from mouse and cell line models to guide mathematical modelling, this thesis aims to better understand the mechanisms involved in the establishment of a healthy vasculature in the growing embryo. We begin by studying arterial and HSC specification in the zebrafish DA. Mathematical models are used to analyse the dose response of arterial and HSC genes to an input Notch signal. The models determine how distinct levels of Notch signalling may be required to establish arterial and HSC identity. Furthermore, we explore how Delta-Notch coupling, which generates salt-and-pepper patterns, may drive the average gene expression levels higher than their homogeneous levels. The models considered here can qualitatively reproduce experimental observations. Using laboratory experiments, I was able to isolate DA cells from transgenic zebrafish embryos and generate temporal gene expression data using qPCR. We show that it is possible to fit ODE models to such data but more reliable data and a greater number of replicates at each time point is required to make further progress. The same VEGF-Delta-Notch signalling pathway is involved in tip cell selection in angiogenic sprouting. Using an ODE model, we rigourously study the dynamics of a VEGF-Delta-Notch feedback loop which is capable of amplifying differences betwen cells to form period-2 spatial patterns of alternating tip and stalk cells. The analysis predicts that the feeback strengths of Delta ligand and VEGFR-2 production dictate the onset of patterning in the same way, irrespective of the parameter values used. This model is extended to incorporate feedback from filopodia, growing in a gradient of extracellular VEGF, which are capable of facilitating tip cell selection by amplifying the resulting patterns. Lastly, we develop a PDE model which is able to properly account for VEGF receptor distributions in the cell membrane and filopodia. Receptors can diffuse and be advected due to domain growth, defined by a constitutive law, in this model. Our analysis and simulations predict that when receptor diffusivity is large, the ODE model for filopodia growth is an excellent approximation to the PDE model, but that for smaller diffusivity, the PDE model provides valuable insight into the pattern forming potential of the system.
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Cherkaoui, Rbati Mohammed. "Mathematical and physical systems biology : application to pharmacokinetic drug-drug interactions and tumour growth." Thesis, University of Nottingham, 2016. http://eprints.nottingham.ac.uk/33719/.
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In this thesis, a multi-scale approach is provided to a pharmacokinetic and a pharmacodynamic problem. The first part of this research provides a realistic mathematical physiological model of the liver to predict drug drug interactions (DDIs). The model describes the geometry of a lobule (liver unit) and integrates the exchange processes, diffusion and active transport, between the hepatocytes and the blood and possible drug-drug interactions such as; reversible inhibition, mechanistic based inhibition (MBI) and enzyme induction. The liver model is subsequently integrated into a PBPK model with 7 compartments (artery blood, venous blood, gut, liver, kidney, lung, rest of the body). To assess the efficiency of the model to predict DDIs, 77 clinical DDI studies were compared to the model. These 77 clinical studies represent 5 victim drugs (midazolam, simvastatin, triazolam, cerivastatin and nifedipine) and 30 perpetrator drugs. The reversible inhibition, MBI and induction parameters for the majority of the perpetrators were estimated with in vitro experiments and adjusted for the human liver size. The PK parameters, such as clearance and absorption rate, and the physiological parameters were obtained from the literature. The DDIs were measured as the ratio of the AUC (Area Under the Curve of the blood concentration) or the ratio of the maximum concentration Cmax of the victim drug administered with and without the perpetrator drug. The predicted ratios were compared with the clinical observation by calculating the geometric fold error GMFE. The GMFE for AUCratio and Cmax,ratio were calculated to be 1.54 and 1.34, respectively. Moreover, the PBPK model excluding the gut compartment under-predicts both inhibition (lower AUCratio) and induction (higher AUCratio) which strongly suggests that the gut DDI component can not be neglected for accurate clinical prediction. However, the static combined model by Fahmi et al. [1, 2] without the gut component fortuitously predicts the clinical AUCratio better than inclusion with the gut component. To conclude, the model predicts DDIs relatively well as it is in the lower range of errors reported in the literature (1.47-2.00 [1, 2]). Moreover, the model is able to predict the pharmacokinetics of drugs and provides a dynamic description of the DDIs, such as the enzyme level and spatial distribution within a lobule. Furthermore, the perpetrator dose regimen can be changed or the error in the in vitro parameters can be integrated to observe their influences on the AUC ratio. The second part of this research explored the Warburg effect in a avascular tumour growth model incorporating a cell shedding term to account for tumour shrinkage. The tumour model was based on an extension of the Ward and King model [3], where two sub-populations; living cells and dead cells are considered. Three diffusion equations for glucose, lactate and the drug are considered and included into the model for growth rate, natural death rate and a death rate due to the drug. The simulation of the model without a drug shows similar behaviour to the original model by Ward and King despite the presence of the shedding term and predicts an extracellular pH of 6.8. However, when a drug treatment is added, the model is able to simulate the shrinkage of the tumour unlike the original model. Moreover, two scenarios with a basic, neutral and acidic drug were explored, assuming similar efficiency at physiological pH to assess the effect of changes in the extracellular pH. Acidic or weak base drugs seem to be more efficient in low pH environment as the fraction of neutral form is greater and therefore more drug is available to cross the cell membrane to reach its target.
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Handley, Kelly. "Statistical analysis of proteomic mass spectrometry data." Thesis, University of Nottingham, 2007. http://eprints.nottingham.ac.uk/10287/.
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This thesis considers the statistical modelling and analysis of proteomic mass spectrometry data. Proteomics is a relatively new field of study and tried and tested methods of analysis do not yet exist. Mass spectrometry output is high-dimensional and so we firstly develop an algorithm to identify peaks in the spectra in order to reduce the dimensionality of the datasets. We use the results along with a variety of classification methods to examine the classification of new spectra based on a training set. Another method to reduce the complexity of the problem is to fit a parametric model to the data. We model the data as a mixture of Gaussian peaks with parameters representing the peak locations, heights and variances, and apply a Bayesian Markov chain Monte Carlo (MCMC) algorithm to obtain their estimates. These resulting estimates are used to identify m/z values where differences are apparent between groups, where the m/z value of an ion is its mass divided by its charge. A multilevel modelling framework is also considered to incorporate the structure in the data and locations exhibiting differences are again obtained. We consider two mass spectrometry datasets in detail. The first consists of mass spectra from breast cancer cells which either have or have not been treated with the chemotherapeutic agent Taxol. The second consists of mass spectra from melanoma cells classified as stage I or stage IV using the TNM system. Using the MCMC and multilevel techniques described above we show that, in both datasets, small subsets of the available m/z values can be identified which exhibit significant differences in protein expression between groups. Also we see that good classification of new data can also be achieved using a small number of m/z values and that the classification rate does not fall greatly when compared with results from the complete spectra. For both datasets we compare our results with those in the literature which use other techniques on the same data. We conclude by discussing potential areas for further research.
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Young, Gregory D. "Image segmentation and paired shapes asymmetry quantification| An application in a Drosophila wing image set." Thesis, California State University, Long Beach, 2015. http://pqdtopen.proquest.com/#viewpdf?dispub=1589666.
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The current process to identify wing pair shape asymmetry in Drosophila wing images contains multiple layers of potential measurement error. The image segmentation routine is a low-level method performed on a low resolution image set, and is prone to inaccurate edge detection in finding the wing's interior vascular structure and the exterior wing edge. An automated splining procedure on the segmentation result which yields the locations of several landmark points on the wing itself has several erroneous spline control points. The process to correct errors in the data requires both parameter tuning in the algorithm as well as manual correction of the segmentation and splining results. The in-production measures of asymmetry between Drosophila wing pairs are shown to be sensitive to these measurement errors. To reduce error in the segmentation step, several image segmentation methods are analyzed for use in developing a robust, efficient and automated segmentation algorithm for Drosophila wing image sets. Evaluation of the accuracy and efficiency of the methods is discussed, with a focus on the performance of multi-scale methods. A Frangi multi-scale segmentation is shown to more accurately locate the wing's interior vascular network. Additionally, an alternative principal components analysis of the variance structure in the image set is developed to isolate and quantify wing pair shape variation across the data set. This analysis replaces the splining process to identify locations of landmark points. Alternative measures of wing pair shape asymmetry are created from this analysis and an alternative measure of Directional Asymmetry (DA) is shown to reproduce existing benchmark measures of DA.
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Manthey, Seth. "Assessing Current Instructional Practices In General Biology One (Bio1010) And Arguing For A Model-Centered Curriculum." FIU Digital Commons, 2015. http://digitalcommons.fiu.edu/etd/2211.
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This collected papers dissertation focused on the argument for the need to adapt and develop a model-centered General Biology I course through the analyses of current instructional practices at a large, public, Hispanic-serving university. This dissertation included a comparison of General Biology I course sections taught in two differing formats, one is a traditional lecture with face-to-face meetings and the other is an online instruction setting. The comparison of these sections was accomplished through the use of a conceptual inventory, student attitude survey, drop-fail-withdraw (DFW) rates, and Social Network Analysis. This comparison found that there was no detectible significant difference between course type for both the conceptual understanding and formation of student-to-student networks. It was also found that there was a significant difference between course type when looking at students’ attitudes towards Biology and success in the two course types.
Additionally in a second study the project used a phenomoenographic analysis of student interviews that explored the students’ use of scientific models when asked about plant cells and animal cells. It was found that during the analysis of students’ ideas that students predominantly used a single model function. The cell types of focus in the second study were two models that were identified, in a third study, through a coded analysis of faculty interviews and textbook analysis. These models are viewed as essential for students to possess an understanding of upon completion of General Biology I.
The model-based course that this study argued for is based on a curricular framework initially developed for use in introductory physics courses. University Modeling Instruction courses in physics (UMI-P) have been linked to improved student conceptual understanding positive attitudinal shifts, and decreased DFW rates. UMI, however, has not been expanded for implementation within the other science disciplines. Drawing from the success of UMI within physics this dissertation focused on the argument for the need for the adaptation and development of UMI for introductory biology.
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Huntley, Miriam. "Quantitative Methods for Analyzing Structure in Genomes, Self-Assembly, and Random Matrices." Thesis, Harvard University, 2016. http://nrs.harvard.edu/urn-3:HUL.InstRepos:33493360.
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This dissertation presents my graduate work analyzing biological structure. My research spans three different areas, which I discuss in turn. First I present my work studying how the genome folds. The three-dimensional structure of the genome inside of the nucleus is a matter of great biological importance, yet there are many questions about just how the genetic material is folded up. To probe this, we performed Hi-C experiments to create the highest resolution dataset (to date) of genome-wide contacts in the nucleus. Analysis of this data uncovered an array of fundamental structures in the folded genome. We discovered approximately 10,000 loops in the human genome, which each bring a pair of loci far apart along the DNA strand (up to millions of basepairs away) into close proximity. We found that contiguous stretches of DNA are segregated into self-associating contact domains. These domains are associated with distinct patterns of histone marks and segregate into six nuclear subcompartments. We found that these spatial structures are deeply connected to the regulation of the genome and cell function, suggesting that understanding and characterizing the 3D structure of the genome is crucial for a complete description of biology. Second, I present my work on self-assembly. Many biological structures are formed via `bottom-up' assembly, wherein a collection of subunits assemble into a complex arrangement. In this work we developed a theory which predicts the fundamental complexity limits for these types of systems. Using an information theory framework, we calculated the capacity, the maximum amount of information that can be encoded and decoded in systems of specific interactions, giving possible future directions for improvements in experimental realizations of self-assembly. Lastly, I present work examining the statistical structure of noisy data. Experimental datasets are a combination of signal and randomness, and data analysis algorithms, such as Principal Component Analysis (PCA), all seek to extract the signal. We used random matrix theory to demonstrate that even in situations where the dataset contains too much noise for PCA to be successful, the signal can be still be recovered with the use of prior information.Engineering and Applied Sciences - Applied Math
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Kondrashov, Dmitry A. "Protein control of a ligand: Modeling nitric oxide release in nitrophorin 4." Diss., The University of Arizona, 2005. http://hdl.handle.net/10150/280770.
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The nitric oxide (NO) transport protein nitrophorin 4 (Np4) is able to modulate NO release rates by two orders of magnitude in response to pH change, and the rates are much slower than in the classic transport protein myoglobin. Experiments have shown that a large conformational change in two loops near the heme binding site from a closed state at pH 5 to an open pocket at pH 7 is apparently responsible for controlling NO release. The mechanism of protein control of ligand escape was investigated using atomic-resolution X-ray crystallography, molecular dynamics simulations, and stochastic modeling. Crystal structures at pH 5 and pH 7 with and without NO revealed that the loops exhibit a mixture of conformations under all the conditions, suggesting they are not a static barrier to NO escape. Molecular dynamics simulations at both pH 5 and pH 7 were performed to observe NO migration as a function of protein conformation. The simulations agree closely with the X-ray structures, and show the loops opening and NO escaping at pH 7, while at pH 5 the loops remain closed and NO never leaves the binding pocket. A stochastic model was based on these observations, modeling the loops as a gate fluctuating between open and closed states and NO as a diffusing particle inside the protein, where it can rebind to the heme or escape out of the protein. An analytical solution of NO escape rates as a function of loop opening and closing rates demonstrates that in the appropriate regime the escape rate is determined by the probability of ligand rebinding to the heme. This indicates the reason for the difference in off rates between Np4 and Mb: Np4 encourages rebinding, while Mb provides internal space for ligand migration. Similarly, pH dependence of Np4 off rates is attributed to a greater rebinding fraction in the closed state at pH 5. However, the source of multiple rates in the experimental kinetics remains unclear, and the model will need to be extended to capture this complexity.
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Yates, Christian. "Comparing stochastic discrete and deterministic continuum models of cell migration." Thesis, University of Oxford, 2011. http://ora.ox.ac.uk/objects/uuid:6f9cb70e-937c-441f-83c3-50e37e1cb420.
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Multiscale mathematical modelling is one of the major driving forces behind the systems biology revolution. The inherently interdisciplinary nature of its study and the multiple spatial and temporal scales which characterise its dynamics make cell migration an ideal candidate for a systems biology approach. Due to its ease of analysis and its compatibility with the type of data available, phenomenological continuum modelling has long been the default framework adopted by the cell migration modelling community. However, in recent years, with increased computational power, complex, discrete, cell-level models, able to capture the detailed dynamics of experimental systems, have become more prevalent. These two modelling paradigms have complementary advantages and disadvantages. The challenge now is to combine these two seemingly disparate modelling regimes in order to exploit the benefits offered by each in a comprehensive, multiscale equivalence framework for modelling cell migration. The main aim of this thesis is to begin with an on-lattice, individual-based model and derive a continuum, population-based model which is equivalent to it in certain limits. For simple models this is relatively easy to achieve: beginning with a one-dimensional, discrete model of cell migration on a regular lattice we derive a partial differential equation for the evolution of cell density on the same domain. We are also able to simply incorporate various signal sensing dynamics into our fledgling equivalence framework. However, as we begin to incorporate more complex model attributes such as cell proliferation/death, signalling dynamics and domain growth we find that deriving an equivalent continuum model requires some innovative mathematics. The same is true when considering a non-uniform domain discretisation in the one-dimensional model and when determining appropriate domain discretisations in higher dimensions. Higher-dimensional simulations of individual-based models bring with them their own computational challenges. Increased lattice sites in order to maintain spatial resolution and increased cell numbers in order to maintain consistent densities lead to dramatic reductions in simulation speeds. We consider a variety of methods to increase the efficiency of our simulations and derive novel acceleration techniques which can be applied to general reaction systems but are especially useful for our spatially extended cell migration algorithms. The incorporation of domain growth in higher dimensions is the final hurdle we clear on our way to constructing a complex discrete-continuum modelling framework capable of representing signal-mediated cell migration on growing (possibly non-standard) domains in multiple dimensions.
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Ortiz, Lugo Alvaro A. Sr. "Qualitative Analysis of Pathogen Dynamics within Cyclic and Time-Varying Water Networks." University of Cincinnati / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1563872208710325.
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Gjini, Erida. "Bridging between parasite genomic data and population processes : trypanosome dynamics and the antigenic archive." Thesis, University of Glasgow, 2012. http://theses.gla.ac.uk/3375/.
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Antigenic variation processes play a central role in parasite invasion and chronic infectious disease, and are likely to respond to host immune mechanisms and epidemiological characteristics. Whether changes in antigenic variation strategies lead to net positive or negative effects for parasite fitness is unclear. To improve our understanding of pathogen evolution, it is important to investigate the mechanisms by which pathogens regulate antigenic variant expression. This involves consideration of the complex interactions that occur between parasites and their hosts, and top-down and bottom-up factors that might drive changes in the genetic architecture of their antigenic archives. Increasing availability of pathogen genomic data offers new opportunities to understand the fundamental mechanisms of immune evasion and pathogen population dynamics during chronic infection. Motivated by the growing knowledge on the antigenic variation system of the sleeping sickness parasite, the African trypanosome, in this thesis, we present different models that analyze antigenic variation of this parasite at different biological scales, ranging from the within-host level, to between-host transmission, and finally the parasite genetics level. First, we describe mechanistically how the structure of the antigenic archive impacts the parasite population dynamics within a single host, and how it interplays with other within-host processes, such as parasite density-dependent differentiation into transmission life-stages and specific host immune responses. Our analysis focuses first on a single parasitaemia peak and then on the dynamics of multiple peaks that rely on stochastic switching between groups of parasite variants. We show that the interplay between the two types of parasite control within the host: specific and general, depends on the modular structure of the parasite antigenic archive. Our modelling reveals that the degree of synchronization in stochastic variant emergence (antigenic block size) determines the relative dominance of general over specific control within a single peak, and can divide infection scenarios into stationary and oscillatory regimes. A requirement for multiple-peak dynamics is a critical switch rate between blocks of antigenic variants, which depends on host characteristics, such as the immune delay, and implies constraints on variant surface glycoprotein (VSG) archive genetic diversification. Secondly, we study the interactions between the structure and function of the antigenic archive at the transmission level. By using nested modelling, we show that the genetic architecture of the archive has important consequences for pathogen fitness within and between hosts. We find host-dependent optimality criteria for the antigenic archive that arise as a result of typical trade-offs between parasite transmission and virulence. Our analysis suggests that different traits of the host population can select for different aspects of the antigenic archive, reinforcing the importance of host heterogeneity in the evolutionary dynamics of parasites. Variant-specific host immune competence is likely to select for larger antigenic block sizes. Parasite tolerance and host life-span are likely to select for whole archive expansion as more archive blocks provide the parasite with a fitness advantage. Within-host carrying capacity, resulting from density-dependent parasite regulation, is likely to impact the evolution of between-block switch rates in the antigenic archive. Our study illustrates the importance of quantifying the links between parasite genetics and within-host dynamics, and suggests that host body size might play a significant role in the evolution of trypanosomes. In Chapters 4 and 5 we consider the genetics behind trypanosome antigenic variation. Antigen switch rates are thought to depend on a range of genetic features, among which, the genetic identity between the switch-off and switch-on gene. The subfamily structure of the VSG archive is important in providing the conditions for this type of switching to occur. We develop a hidden Markov model to describe and estimate evolutionary processes generating clustered patterns of genetic identity between closely related gene sequences. Analysis of alignment data from high-identity VSG genes in the silent antigen gene archive of the African trypanosome identifies two scales of subfamily diversification: local clustering of sequence mismatches, a putative indicator of gene conversion events with other lower-identity donor genes in the archive, and the sparse scale of isolated mismatches, likely to arise from independent point mutations. In addition to quantifying the respective rates of these two processes, our method yields estimates for the gene conversion tract length distribution and the average diversity contributed locally by conversion events. Model fitting is conducted for a range of models using a Bayesian framework. We find that gene conversion events with lower-identity partners are at least 5 times less common than point mutations for VSG pairs, and the average imported conversion tract is short. However, due to the high frequency of mismatches in converted segments, the two processes have almost equal impact on the rate of sequence diversification between VSG sub-family members. We are able to disentangle the most likely locations of point mutations vs. conversions on each aligned gene pair. Finally we model VSG archive diversification at the global scale, as a result of opposing evolutionary forces: point mutation, which induces diversification, and gene conversion, which promotes global homogenization. By adopting stochastic simulation and theoretical approaches such as population genetics and the diffusion approximation, we find how the stationary identity configuration of the archive depends on mutation and conversion parameters. By fitting the theoretical form of the distribution to the current VSG archive configuration, we estimate the global rates of gene conversion and point mutation. The relative dominance of mutation as an evolutionary force quantifies the high divergence propensity of VSG genes in response to host immune pressures. The success of our models in describing realistic infection patterns and making predictions about the fitness consequences of the parasite antigenic archive illustrates the advantage of using integrative approaches that bridge between different biological scales. Even though quantifying the genetic signatures of antigenic variation remains a challenging task, cross-disciplinary analyses and mechanistic modelling of parasite genomic data can help in this direction, to better understand parasite evolution.
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Allehiany, Faiza Mohammad. "Frequency and time domain analysis of networks of interacting processes : what can be achieved from records of short duration." Thesis, University of Glasgow, 2012. http://theses.gla.ac.uk/3741/.
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Abstract Recently, there has been increasing interest in investigating the interrelationships among the component stochastic processes of a dynamical system. The applications of these studies are to be found in various fields such as Economics, Neuroscience, Engineering and Neurobiology. Also the determination of the direction of the information flow is one of the important subjects studied widely. These investigations have usually been implemented in the time and frequency domains. Consequently, several mathematical and statistical procedures have been developed to facilitate these analyses. The aim of this thesis is to discuss the relationships between stochastic processes of a relatively short time duration. Specifically, the research concerns the analysis of the electrical activity of the dysfunctional brain, where the available data belong to a right-handed focal epileptic patient. EEG signals are recorded directly from the scalp using numbered electrodes according to the International 10/20 system introduced by Jasper [1958]. The analysis is only performed for processes of the left hemisphere as they represent the dominant hemisphere. Moreover, since each region of the brain is responsible for a special function, we have chosen five processes to represent the five main lobes of the brain; the frontal lobe, the central region, the parietal lobe, the occipital lobe and the temporal lobe. The analyses of these signals are carried out using four spectral density estimation procedures, namely the multivariate autoregressive model of order 2; the average of periodograms of adjacent segments of the single record; the smoothed periodogram approach for the entire record; and the multi-taper method. Thereafter comparisons among the results of these methods are made. The strength of the correlation between signals is measured by coherence and partial coherence functions. Also, the Granger causality concept is implemented for these data in the form of determining the direction of the information flow between these signals using the partial directed coherence (PDC) proposed by Baccala and Sameshima [2001] using the statistical level of significance suggested by Schelter et al.[2005]. The structure of the causal influences produced by the PDC shows that there are statistically significant reciprocal causal effects between processes representing the brain's region, the frontal lobe, the central area, the parietal lobe and the temporal lobe. However, there are two uni-directed causal influence relations, one is between the central area and the occipital lobe and the second one is between the occipital and temporal lobes. The indirect causal influences are detected between these processes throughout the process representing the temporal lobe. Generally, the values of the PDC in the anterior-posterior direction are larger than the values of the PDC in the opposite direction. Also, the causal influences of each process on the temporal lobe process is larger than the causal influences in the opposite direction. The spectral analyses show that the estimated power spectra and coherences of these signals are approximately peak in the delta wave band of frequency [1, 4) Hz. The significant non-zero estimated coherences are captured between the brain's lobes except for the occipital lobe which is uncorrelated with any of the other lobes. The depth of non-zero significant estimated coherences is given by partial coherence, which measures the strength of the estimated coherence between any two processes after removing the linear influence of one or more other processes. For the current data, we found that the depth of correlations depends on the spectral estimation method adopted. For example, the depth of correlation is of order 2 for the method of averaging across periodograms of adjacent segments of the single record and the method of smoothed periodogram of the entire single record and is of order one for the multi-taper method. However, the depth of correlations is unknown for the multivariate autoregressive model of order 2. The comparisons made between the results of the four spectral estimation methods mentioned previously, indicated that MVAR is not sensitive to rapid changes occurring in the signal such as the effect of the notch filter at 60Hz and a calibration signal at 47Hz, while the other three methods exhibited good sensitivity to these changes with different strengths of responses. Furthermore, the smoothed periodogram and the multi-taper methods persistently detect the notch filter effect at 60Hz in the ordinary estimated coherence curves, while the method of averaging across periodograms of adjacent segments of the single record does not.
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Jones, Ryan C. "Hopper Bands: Locust Aggregation." Scholarship @ Claremont, 2016. https://scholarship.claremont.edu/hmc_theses/81.
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Locust swarms cause famine and hunger in parts of Sub-Saharan Africa as they travel across croplands and eat vegetation. Current models start with biological properties of locusts and analyze the macroscopic behavior of the system. These models exhibit the desired migratory behavior, but do so with too many parameters. To account for this, a new model, the Alignment and Intermittent Motion (AIM) model, is derived with minimal assumptions. AIM is constructed with regards to locust biology, allowing it to elicit biologically correct locust behavior: the most noteworthy being the fingering of hopper bands. A Particle-in-Cell method is used to optimize simulations, allowing for trials of up to 106 particles over reasonable timescales. We analyze the shapes of these swarms, note the similarities between simulations of large and small swarms, and propose possible methods for analyzing simulation metrics.
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Mazzag, Barbara Cathrine. "Mathematical models in biology /." For electronic version search Digital dissertations database. Restricted to UC campuses. Access is free to UC campus dissertations, 2002. http://uclibs.org/PID/11984.
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Li, Yifei. "Nonlinear diffusion in mathematical biology." Thesis, Queensland University of Technology, 2022. https://eprints.qut.edu.au/234381/1/Yifei_Li_Thesis.pdf.
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Reaction-diffusion models with nonlinear diffusion are widely used for studying population dynamics in biology and ecology. Yet, the relationship between nonlinear diffusion mechanisms in populations and the behaviours of individuals is hard to be intuitively interpreted in classical models. To address this problem, we develop a discrete-continuum modelling framework, where the movement of individuals influenced by crowding effects is connected to the nonlinear diffusivity functions in a well-defined continuum limit. Using this framework, we explore the influence of nonlinear diffusion on population extinction, and analyse the existence and stability of travelling waves in continuous equations which model the invasion process.
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Bozic, Ivana. "Mathematical Models of Cancer." Thesis, Harvard University, 2012. http://dissertations.umi.com/gsas.harvard:10220.
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Major efforts to sequence cancer genomes are now occurring throughout the world. Though the emerging data from these studies are illuminating, their reconciliation with epidemiologic and clinical observations poses a major challenge. Here we present mathematical models that begin to address this challenge. First we present a model of accumulation of driver and passenger mutations during tumor progression and derive a formula for the number of driver mutations as a function of the total number of mutations in a tumor. Fitting this formula to recent experimental data, we were able to calculate the selective advantage provided by a typical driver mutation. Second, we performed a quantitative analysis of pancreatic cancer metastasis genetic data. The results of this analysis define a broad time window for detection of pancreatic cancer before metastatic dissemination. Finally, we model the evolution of resistance to targeted cancer therapy. We apply our model to experimental data on the response to panitumumab, targeted therapy against colorectal cancer. Our modeling suggested that cells resistant to therapy were likely present in patients’ tumors prior to the start of therapy.Mathematics
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Abdelfattah, Derhham. "General Relativity and penrose process." Master's thesis, University of Cape Town, 2016. http://hdl.handle.net/11427/28961.
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Murphy, Ryan John. "Mechanochemical and experimental models in mathematical biology." Thesis, Queensland University of Technology, 2022. https://eprints.qut.edu.au/228428/1/Ryan%20John_Murphy_Thesis.pdf.
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Experiments that probe epithelial tissue dynamics, cell competition, and tumour growth are fundamental to understand processes in developmental biology, cancer progression and treatment. However, interpreting complex biological experiments is challenging. To address this challenge, we develop and use a range of mathematical models. First, we focus on epithelial tissue dynamics. Second, we use real-time cell cycle imaging to reveal the structure of growing tumour spheroids. We then revisit the seminal Greenspan tumour growth model and use statistical analysis to quantitatively connect it to experimental data for the first time to reveal experimental design choices that lead to reliable biological insight.
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Mashoof, Said. "The mathematical modelling of concrete constitutive relationships." Thesis, City University London, 1989. http://openaccess.city.ac.uk/7952/.
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The available experimental evidence demonstrates the extreme nonlinear material behaviour of reinforced concrete structures. These nonlinear effects are attributed to the collective behaviour of the constituent materials in addition to factors such as cracking, crushing, aggregate interlock, creep, shrinkage, bond slip and rate of loading. Analytical methods have been improved in the past two decades as a result of the availibility of more powerful computers. It is, therefore, feasible to model these nonlinear features in order to conduct an analysis of the behaviour of reinforced concrete structures. The present research is concerned with some of these nonlinear effects. These include the formulation of a constitutive model for the three-dimensional stress-strain relationships of concrete and the mathematical modelling of cracked and crushed concrete. The proposed models have been implemented into a finite element system for the analysis of reinforced and pre-stressed concrete structures. Chapter One is a general introduction to structural nonlinearities and the finite element method. The structure of the thesis is also outlined. Chapter Two reviews available theoretical approaches used for the formulation of the concrete behaviour and assesses their relative advantages. The theory of plasticity is discussed in greater depth as it forms the foundation of the work in Chapter Three. A three-dimensional concrete yield surface is developed in Chapter Three. This yield surface is used in the theory of hardening plasticity to establish the incremental constitutive relationships for concrete. Furthermore, this model is extended to represent the strain-softening effect in concrete. The hardening and softening rule which has been developed is based on experimental results obtained from the literature. The results of the proposed model are compared with these experimental data. The cracking and crushing of concrete have been studied in Chapter Four. A rough crack model is developed for concrete and crack stress-displacement relationships due to aggregate interlock are formulated. A mathematical model is proposed for the effect of dowel forces in cracked reinforced concrete structures. The effect of bond stress between a steel bar and concrete has been introduced by a tension-stiffening factor and suitable formulations has been proposed. The results from the crack related models have also been compared with experimental data from the literature. Finally, stiffness matrices for cracked plain and reinforced concrete have been developed using a smeared crack approach. The concrete constitutive model and the crack model developed in Chapters Three and Four have been implemented into a finite element program for the numerical analyses given in Chapter Five. This implementation has been carried out for plane stress and axisymmetric solid stress problems. A reinforced concrete beam and a prestressed concrete reactor vessel have been analysed and the results compared with experimental data. Finally Chapter Six presents the overall conclusions and recommendations for further research.
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Jones, Jennifer Grace. "A mathematical model of emphysema." Thesis, University of Bristol, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.269229.
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Murphy, Stephen D. "Mathematical model of the sprint relay race." Thesis, University of Ottawa (Canada), 1992. http://hdl.handle.net/10393/7745.
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The purpose of this investigation was to develop and validate mathematical models of the sprint relay race. Two approaches, a classical exponential approach and a "new" polynomial approach, were chosen for implementation. Archival film of a 100 m sprint was used to gather displacement data for the first 60 m of the race. Filming had been performed with a single highspeed 16 mm cine camera (LOCAM) at 50 fps. The coordinates were digitized, scaled and filtered using a low pass, critically damped, 4$\sp{\rm th}$ order, zero-lag Butterworth digital filter with a 1 Hz cutoff frequency. Linear velocities were calculated using finite differences. A sprinter was modelled in two ways. The first was an Exponential Model which required as input a personal best time for the 100 m race and the sprinter's maximum constant velocity. The second was a Polynomial Model which required as input the parameters mentioned in the Exponential Model and, additionally, the displacement coefficients for the first 60 m of the 100 m sprint. Relay software was developed to piece the sprint relay together using the corresponding exponential or polynomial approach. The results indicated that the relay software reasonably simulated the kinematic and temporal quantities of a 4 x 100 m relay and can be used by coaches to gain insight into the sprint relay without risking injury to their athletes. Furthermore, the Exponential Model, using less information, described the sprinter's kinematics better than the Polynomial Model.
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Anderson, Kerri-Ann. "A Mathematical Model of Cytokinetic Morphogenesis." The Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1429607984.
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Hendawy, Zeinab Mohamed. "Mathematical algorithms for optimisation of large scale systems." Thesis, City University London, 1989. http://openaccess.city.ac.uk/8248/.
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This research is concerned with the problem of optimisation of steady state large scale systems using mathematical models. Algorithms for on-line optimisation of interconnected industrial processes are investigated. The research is concerned with two different kinds of algorithms which are based on the structure of the model used and the way of incorporating the real process information in order to compensate for model-reality differences. The first class of algorithms are developed from the price method with global feedback information which is mainly based on the normal Lagrangian function. Two existing algorithms are examined: The double iterative price correction mechanism and the augmented interaction balance method. Both methods use a double iterative coordination strategy and global feedback measurements from the real process. They are based respectively on the normal and the augmented Lagrangian functions. Hence, the first algorithm can only be recommended for application to convex problems. An algorithm, namely the augmented price correction mechanism, has been developed to extend the applicability of the previous price correction mechanism to non-convex problems. It is also applicable to convex problems with the advantage of reducing the number of times that information is required from the real process. The second class of algorithms is known as integrated system optimisation and parameter estimation (ISOPE) • The model used contains uncertain parameters and the algorithm solves the optimisation and parameter estimation tasks repeatedly until no furthur improvement is obtained. Developed ISOPE algorithms are involved in this research to cover the problems with output dependent constraints. Simulation results show superiority of the double iterative algorithm over that of single loop method in considerably reducing the number of times that information is required from the real process and hence saving on-line computing time. It is hoped that this work will provide useful information for implementing and furthur developing on-line steady state optimisation techniques.
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Cole, D. J. "Stochastic branching processes in biology." Thesis, University of Kent, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.270684.
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Ferrara, Joseph. "A Study of Nonlinear Dynamics in Mathematical Biology." UNF Digital Commons, 2013. http://digitalcommons.unf.edu/etd/448.
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We first discuss some fundamental results such as equilibria, linearization, and stability of nonlinear dynamical systems arising in mathematical modeling. Next we study the dynamics in planar systems such as limit cycles, the Poincaré-Bendixson theorem, and some of its useful consequences. We then study the interaction between two and three different cell populations, and perform stability and bifurcation analysis on the systems. We also analyze the impact of immunotherapy on the tumor cell population numerically.
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Hunt, Gordon S. "Mathematical modelling of pattern formation in developmental biology." Thesis, Heriot-Watt University, 2013. http://hdl.handle.net/10399/2706.
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The transformation from a single cell to the adult form is one of the remarkable wonders of nature. However, the fundamental mechanisms and interactions involved in this metamorphic change still remain elusive. Due to the complexity of the process, researchers have attempted to exploit simpler systems and, in particular, have focussed on the emergence of varied and spectacular patterns in nature. A number of mathematical models have been proposed to study this problem with one of the most well studied and prominent being the novel concept provided by A.M. Turing in 1952. Turing's simple yet elegant idea consisted of a system of interacting chemicals that reacted and di used such that, under certain conditions, spatial patterns can arise from near homogeneity. However, the implicit assumption that cells respond to respective chemical levels, di erentiating accordingly, is an oversimpli cation and may not capture the true extent of the biology. Here, we propose mathematical models that explicitly introduce cell dynamics into pattern formation mechanisms. The models presented are formulated based on Turing's classical mechanism and are used to gain insight into the signi cance and impact that cells may have in biological phenomena. The rst part of this work considers cell di erentiation and incorporates two conceptually di erent cell commitment processes: asymmetric precursor di erentiation and precursor speci cation. A variety of possible feedback mechanisms are considered with the results of direct activator upregulation suggesting a relaxation of the two species Turing Instability requirement of long range inhibition, short range activation. Moreover, the results also suggest that the type of feedback mechanism should be considered to explain observed biological results. In a separate model, cell signalling is investigated using a discrete mathematical model that is derived from Turing's classical continuous framework. Within this, two types of cell signalling are considered, namely autocrine and juxtacrine signalling, with both showing the attainability of a variety of wavelength patterns that are illustrated and explainable through individual cell activity levels of receptor, ligand and inhibitor. Together with the full system, a reduced two species system is investigated that permits a direct comparison to the classical activator-inhibitor model and the results produce pattern formation in systems considering both one and two di usible species together with an autocrine and/or juxtacrine signalling mechanism. Formulating the model in this way shows a greater applicability to biology with fundamental cell signalling and the interactions involved in Turing type patterning described using clear and concise variables.
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Yang, Xige. "MATHEMATICAL MODELS OF PATTERN FORMATION IN CELL BIOLOGY." The Ohio State University, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=osu1542236214346341.
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Xu, Yiyang. "Topics in population genetics and mathematical evolutionary biology." Thesis, University of Bristol, 2015. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.682366.
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Part A studies the optimal strategies of seed germination problems where the population has a class structure under a fluctuating environment . In particular, a multidimensional age-class model is studied using a dynamical programming method. Numerical results about the so-called optimal stochastic strategy which consists of information about previous environmental states are computed. Comparing the optimal stochastic strategy with the optimal population-based strategy shows that the optimal stochastic strategy is highly effective in genera.l. A potentially useful diffusion approximation for the seed germination problem is also derived with numerical results. For part B, a multi-dimensional Moran model is studied using a diffusion approximation approach. The scaling limit and corresponding governing stochastic partial differential equations (SDEs) are derived. An expansion method is used to approximate the stationary distribution of the SDEs. An approximation formula for the effective migration rate is then derived.
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Piper, David. "A mathematical model of frost heave in granular materials." Thesis, University of Nottingham, 1987. http://eprints.nottingham.ac.uk/28821/.
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An initial review of the various theories of frost heave indicated that Miller's theory of secondary heave was the most convincing. The crucial area in this is the representation of the behaviour in the partially frozen region, known as the frozen fringe, which exists below the lowest ice lens. However, the computational difficulties of the associated mathematical model were likely to limit its application. A simpler quasi-static approach for a semi-infinite region had therefore been initiated, for a restricted range of conditions, by Holden. The work described in this thesis traces the development of the quasi-static approach and its application to the unidirectional freezing of a finite soil column. The resulting generalised model successfully predicts the freezing behaviour under a wide range of conditions. In particular, it is applicable to all overburden pressures, including zero. At low overburdens the frozen fringe disappears, but the final phase is nevertheless modelled to its ultimate equilibrium state. The predictions of the model agree with published experimental data from a number of investigators, and thus support the validity of Miller's theory. Parametric studies with the model have highlighted the importance of the hydraulic conductivity and the relationship between suction, temperature and ice content in the frozen fringe. Simulations are relatively insensitive to variations in thermal conductivity. The model has proved to be robust and stable and should form a sound basis for further studies. However, its full application will depend on the development of experimental techniques to determine the hydraulic conductivity in the frozen fringe.
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Campanelli, Mark Benjamin. "Multicellular mathematical models of somitogenesis." Thesis, Montana State University, 2009. http://etd.lib.montana.edu/etd/2009/campanelli/CampanelliM0809.pdf.
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Somitogenesis is an important pattern formation process in the developmental biology of vertebrates. The phenomenon has received wide attention from experimental, theoretical, and computational biologists. Numerous mathematical models of the process have been proposed, with the clock and wavefront mechanism rising to prominence over the last ten years. This work presents two multicellular mathematical models of somitogenesis. The first is a phenomenological phase oscillator model that reproduces both the clock and wavefront aspects of somitogenesis, but lacks a biological basis. The second is a biologically informed delay differential equation model of the clock-wave that is produced by coordinated oscillatory gene expression across many cells. Careful and efficient model construction, parameter estimation, and model validation identify important nonlinear mechanisms in the genetic control circuit of the somitogenesis clock. In particular, a graded control protein combined with differential decay of clock protein monomers and dimers is found to be a key mechanism for slowing oscillations and generating experimentally observed waves of gene expression. This represents a mode of combinatorial control that has not been previously examined in somitogenesis, and warrants further experimental and theoretical investigation.
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Sandells, Jamie Ian. "Mathematical modelling of planar solid oxide fuel cells." Thesis, University of Birmingham, 2014. http://etheses.bham.ac.uk//id/eprint/4908/.
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In this thesis we construct a series of mathematical models from first principles to examine the advection, diffusion and reactions of species within a planar Solid Oxide Fuel Cell (SOFC). We reduce the complexity of an SOFC to flow and reaction across a flat, impermeable plate and begin by establishing a simplistic model for the incompressible, isothermal flow and reaction of hydrogen. Throughout the thesis we seek to extend this initial model by adding appropriate levels of complexity such as alternative fuels, compressibility and thermal effects. In establishing solutions to these models we use a series of analytical techniques. We adopt the concept of boundary-layer flow and self similarity to simplify the model equations into a form where we can obtain analytical and efficient numerical solutions. We also utilise asymptotics to examine and validate the model around regions of singularities within the flow. Within each model we have examined the electrical performance of the cell and in some cases we have validated these results with existing experimental data.
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Gironi, Fabio. "Naturalising Badiou : mathematical ontology and structural realism." Thesis, Cardiff University, 2013. http://orca.cf.ac.uk/56408/.
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This thesis offers a naturalist revision of Alain Badiou’s philosophy. This goal is pursued through an encounter of Badiou’s mathematical ontology and theory of truth with contemporary trends in philosophy of mathematics (mathematical structuralism) and philosophy of science (ontic structural realism). I take issue with Badiou’s inability to elucidate the link between the empirical and the ontological, and his residual reliance on a Heideggerian project of fundamental ontology, which undermines his own immanentist principles. I will argue for both a bottom-up naturalisation of Badiou’s philosophical approach to mathematics (insisting on an account mindful of the socio-biological roots of our mathematical abilities and concepts – brains to universe) and a top-down naturalisation (arguing that our best physical theories seem to indicate a collapse of the distinction between the mathematical and the non-mathematical – universe to brains). Articulating my particular understanding of what realism and naturalism should commit us to, I propose a creative fusion of Badiou’s attention to metamathematical results with a structural-informational metaphysics, proposing a ‘matherialism’ uniting the more daring speculative insights of the former with the naturalist and empiricist commitments motivating the latter.
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Rado, Anita 1967. "Mathematical models of ionic diffusion in olfactory glomeruli." Diss., The University of Arizona, 1998. http://hdl.handle.net/10150/282741.
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Many vertebrate and invertebrate olfactory systems are similar in the organization of their synaptic neuropil into glomeruli, structures surrounded by an incomplete layer of glial processes. Within glomeruli, the axons of olfactory receptor neurons synapse with the dendrites of their target brain neurons. Glomeruli are likely to be odor specific in that each glomerulus processes information from a subset of axons about a particular chemical feature of odorant molecules. Therefore, a large proportion of the neurons within a glomerulus may be excited simultaneously in response to a particular odor. The resulting release of potassium ions from neurons may be sufficient to cause a substantial increase in the extracellular concentration of potassium ions and thus affect the excitability of neighboring neurons. The goal of this study is to develop theoretical models for the diffusion of potassium ions in the extracellular space, and to predict how the glial border affects the spread of potassium ions following the activation of olfactory sensory neurons. Observations of the morphology of the interior and border of the glomerulus were used to estimate the porosity and effective diffusivity of these regions, and the size of the "mouth" region where there is no glial covering. Potassium was assumed to be released into the extracellular space during an initial 0.5 seconds. The time-dependent diffusion equation was solved in spherical coordinates using a finite-difference method. The results indicated that the glial envelope forms a partial barrier to the diffusion of potassium ions, and greatly reduces the spread of potassium ions to neighboring glomeruli following release. According to the model, the decline in potassium concentration within the glomerulus due to the leakage from the mouth and glial boundaries is relatively slow, taking more than 10 seconds to approach its resting level. These findings support the hypothesis that the characteristic distribution of glial cells around glomeruli could play a significant role in olfactory information processing.
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Urquiza, García José María Uriel. "Mathematical model in absolute units for the Arabidopsis circadian oscillator." Thesis, University of Edinburgh, 2018. http://hdl.handle.net/1842/31132.
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The Earth’s oblique rotation results in changes in light and temperature across the day and time of year. Living organisms evolved rhythmic behaviours to anticipate these changes and execute appropriate responses at particular times. The current paradigm for the biological clocks in several branches of life is an underlying biochemical oscillator mainly composed by a network of repressive transcription factors. The slow decay in their activity is fundamental for generating anticipatory dynamics. Interestingly, these dynamics can be well appreciated when the biological system is left under constant environmental conditions, where oscillation of several physiological readouts persists with a period close to 24 hours, hence the term “circadian clocks”, circa=around dian=day. In plants the model species Arabidopsis thaliana has served as an invaluable tool for analysing the genetics, biochemical, developmental, and physiological effects of the oscillator. Many of these experimental results have been integrated in mechanistic and mathematical theories for the circadian oscillator. These models predict the timing of gene expression and protein presence in several genetic backgrounds and photoperiodic conditions. The aim of this work is the introduction of a correct mass scale for both the RNA transcript and protein variables of the clock models. The new mass scale is first introduced using published RNA data in absolute units, from qRT-PCR. This required reinterpreting several assumptions of an established clock model (P2011), resulting in an updated version named U2017. I evaluate the performance of the U2017 model in using data in absolute mass units, for the first time for this clock system. Introducing absolute units for the protein variables takes place by generating hypothetical protein data from the existing qRT-PCR data and comparing a data-driven model with western blot data from the literature. I explore the consequences of these predicted protein numbers for the model’s dynamics. The process required a meta-analysis of plant parameter values and genomic information, to interpret the biological relevance of the updated protein parameters. The predicted protein amounts justify, for example, the revised treatment of the Evening Complex in the U2017 model, compared to P2011. The difficulties of introducing absolute units for the protein components are discussed and components for experimental quantification are proposed. Validating the protein predictions required a new methodology for absolute quantification. The methodology is based on translational fusions with a luciferase reporter than has been little used in plants, NanoLUC. Firstly, the characterisation of NanoLUC as a new circadian reporter was explored using the clock gene BOA. The results show that this new system is a robust, sensitive and automatable approach for addressing quantitative biology questions. I selected five clock proteins CCA1, LHY, PRR7, TOC1 and LUX for absolute quantification using the new NanoLUC methodology. Functionality of translation fusions with NanoLUC was assessed by complementation experiments. The closest complementing line for each gene was selected to generate protein time series data. Absolute protein quantities were determined by generation of calibration curves using a recombinant NanoLUC standard. The developed methodology allows absolute quantification comparable to the calibrated qRT-PCR data. These experimental results test the predicted protein amounts and represent a technical resource to understand protein dynamics of Arabidopsis’ circadian oscillator quantitatively. The new experimental, meta-analysis and modelling results in absolute units allows future researchers to incorporate further, quantitative biochemical data.
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Stavrinides, Alexander James. "Isothermal microwave biology : catalysis and fermentation." Thesis, Liverpool John Moores University, 2012. http://researchonline.ljmu.ac.uk/6110/.
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This thesis looks directly into the controversial subject of the microwave field effect by the production of a versatile prototype isothermal microwave reactor for the investigation of enzymatic and microbiological reactions. The observed results from the prototype reactor and experiments conducted conclude that there is a nonthermal, nonlinear response between the exposure microwave power and rate and yield of cellulose saccharification. The nature of the nonthermal response is controversial and may be dependent on the definition of "nonthermal,' leading to ambiguity of exact mechanism. Enzymatic and microbial conversion of cellulosic material to ethanol is a highly desirable industrial process. Whether the demand is for the mitigation of climate change, political obligations or energy independence, the use of arable land for energy crops limits the available glucose carbon sources for conversion to bioproducts. To prevent this limitation, cellulose (~-l,4-linked glucose polymers) are touted as the "silver bullet" to prevent carbon exhaustion or impinging on food crops. The technical constraint for the industrialization of cellulose based processing is the rate limitation in the cellulase enzymatic action on cellulose. The enzyme rate is limited by feedback cycles and limited mechanical freedom, therefore a relatively high enzyme concentration is required to speed up the process. To date, the associated enzyme production costs and infrastructure prevents bulk volume exploitation. Biomolecular advances (amino acid substitutions, recombination of expression vectors etc) have gone some way to increase either enzymatic rate or enzyme concentration. The work presented in this thesis differs by increasing the rate of the enzyme without molecular modification. Using a microwave field, the work presented shows that by separating the system into its base units, irradiation of the enzyme/substrate complex in an aqueous environment can increase both the initial enzyme rate and the saccharification yield without alteration of the temperature set point. This study shows that the rate increase is not proportional to the microwave field power. An optimal power in each study is either found or suggested. The results cited show that in the three systems (Endoglucanase and cellobiohydrolase with cellulose, endoglucanase and cellobiohydrolase and ~- glucosidase with cellulose, and ~-glucosidase with cellobiose) the initial rates can be increased by 201 %, 65.5% and 69% respectively. In the total hydrolytic process (endoglucanase and cellobiohydrolase and ~-glucosidase on a cellulose substrate) the final glucose yield was increased by 43% in comparison to the conventional thermal control reaction. This is shown in Figure 1. 10.000 1 9.000 1 8.000 j 7.000 6.000 o 20 40 60 80 100 120 140 160 180 I I 1 I U 5.000 r:: o u 4.000 3.000 2.000 j i t t , f 1.000 0.000 Time (hours) =->=OOOW Glucose' °012W Glucose ?p025W Glucose ~050W Glucose ·075W Glucose Figure 1. Microwave irradiated "cellulase" enzymes with cellulose substrate I For development into an industrial system and looking towards simultaneous saccharification and fermentation (SSF), the yeast Saccharomyces cerevisiae was subjected to irradiated microwave fermentations on a glucose substrate. Although inconclusive in terms of rate increase, cell density 1 was comparable across the power range showing that the irradiation does not have a derogatory effect. ! The natural evolution of the conclusions drawn would be development of the system into a SSF or SSCF configuration for bio-product formation is possible with irradiation up to SOW. ii The novelty of the experiments conducted is twofold. Firstly, the reactor has been designed to ensure that the microwave irradiation is independent of the bulk temperature therefore allowing the exploration of the microwave field effect independently to the thermal effect. Secondly, the microwave source is a continuous microwave irradiation (none pulse irradiation) ensuring that the reaction is subjected to the microwave field for the entire reaction.
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Katshunga, Dominique. "Identifying outliers and influential observations in general linear regression models." Thesis, University of Cape Town, 2004. http://hdl.handle.net/11427/6772.
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Includes bibliographical references (leaves 140-149).Identifying outliers and/or influential observations is a fundamental step in any statistical analysis, since their presence is likely to lead to erroneous results. Numerous measures have been proposed for detecting outliers and assessing the influence of observations on least squares regression results. Since outliers can arise in different ways, the above mentioned measures are based on motivational arguments and they are designed to measure the influence of observations on different aspects of various regression results. In what follows, we investigate how one can combine different test statistics based on residuals and diagnostic plots to identify outliers and influential observations (both in the single and multiple case) in general linear regression models.
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Camacho, Diogo Mayo. "In silico cell biology and biochemistry: a systems biology approach." Diss., Virginia Tech, 2007. http://hdl.handle.net/10919/27960.
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In the post-"omic" era the analysis of high-throughput data is regarded as one of the major challenges faced by researchers. One focus of this data analysis is uncovering biological network topologies and dynamics. It is believed that this kind of research will allow the development of new mathematical models of biological systems as well as aid in the improvement of already existing ones. The work that is presented in this dissertation addresses the problem of the analysis of highly complex data sets with the aim of developing a methodology that will enable the reconstruction of a biological network from time series data through an iterative process.
The first part of this dissertation relates to the analysis of existing methodologies that aim at inferring network structures from experimental data. This spans the use of statistical tools such as correlations analysis (presented in Chapter 2) to more complex mathematical frameworks (presented in Chapter 3). A novel methodology that focuses on the inference of biological networks from time series data by least squares fitting will then be introduced. Using a set of carefully designed inference rules one can gain important information about the system which can aid in the inference process. The application of the method to a data set from the response of the yeast Saccharomyces cerevisiae to cumene hydroperoxide is explored in Chapter 5. The results show that this method can be used to generate a coarse-level mathematical model of the biological system at hand. Possible developments of this method are discussed in Chapter 6.Ph. D.
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Buckalew, Richard L. "Mathematical Models in Cell Cycle Biology and Pulmonary Immunity." Ohio University / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1395242276.
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Warne, David James. "Computational inference in mathematical biology: Methodological developments and applications." Thesis, Queensland University of Technology, 2020. https://eprints.qut.edu.au/202835/1/David_Warne_Thesis.pdf.
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Complexity in living organisms occurs on multiple spatial and temporal scales. The function of tissues depends on interactions of cells, and in turn, cell dynamics depends on intercellular and intracellular biochemical networks. A diverse range of mathematical modelling frameworks are applied in quantitative biology. Effective application of models in practice depends upon reliable statistical inference methods for experimental design, model calibration and model selection. In this thesis, new results are obtained for quantification of contact inhibition and cell motility mechanisms in prostate cancer cells, and novel computationally efficient inference algorithms suited for the study of biochemical systems are developed.
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Chisholm, Christopher. "The development of mathematical resilience in KS4 learners." Thesis, University of Warwick, 2017. http://wrap.warwick.ac.uk/88601/.
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This action research project focussed on the key components of the construct mathematical resilience and how mathematical resilience can be developed in learners who are working towards their GCSE in mathematics. Split-screen lesson objectives, one related to a mathematical skill and the other related to a learning skill, were used to focus the learner’s attention onto each skill. These learning skills were chosen to encourage a particular group of learners to gain the confidence, persistence and perseverance to allow them to work inside the Growth Zone. The overall aim of this action research project was to improve the attainment of learners in their GCSE mathematics examination.
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Vorwerk, Michael Conrad. "A mathematical study of mimicry and opportunism." Thesis, Georgia Institute of Technology, 1989. http://hdl.handle.net/1853/28944.
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Durney, Clinton H. "A Two-Component Model For Bacterial Chemotaxis." The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1366312981.
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Apostu, Raluca. "Mathematical model of GAL regulon dynamics in «Saccharomyces cerevisiae»." Thesis, McGill University, 2012. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=107676.
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Genetic switches are prevalent in nature, and provide cells with a strategy to adapt to changing environmental conditions. This thesis focuses on an intriguing example which is not understood in complete detail: the GAL switch. The GAL switch allows organisms to metabolize the sugar galactose, and controls whether the machinery responsible for the galactose metabolism is turned ON or OFF. Currently, it is not known exactly how the galactose signal is sensed by the transcriptional machinery. Moreover, there are two contradictory hypotheses concerning the regulatory mechanism at GAL promoters in galactose induced cells: the dissociation and non-dissociation models. This work uses quantitative tools to understand the Saccharomyces cerevisiae cell response to galactose challenge, and to analyze the plausible molecular mechanisms underlying its operation. The thesis proposes a novel dynamic mathematical model which is based on the interplay of the key regulatory proteins Gal4p, Gal80p, and Gal3p, in a cell population. To my knowledge, the deterministic model presented here is the first to reproduce qualitatively the bistable GAL network behavior found experimentally. Given the current understanding of the GAL circuit induction (Wightman et al., 2008; Jiang et al., 2009), this work proposes that the most likely in vivo mechanism leading to the transcriptional activation of the GAL genes is the physical interaction between galactose-activated Gal3p and Gal80p, with the complex Gal3p-Gal80p remaining bound at the GAL promoters. The mathematical model is in agreement with the flow cytometry profiles of wild type, gal3∆ and gal80∆ mutant strains from Acar et al. (2005), and involves a fraction of actively transcribing cells with the same qualitative features as in the data set collected by Acar et al. (2010). Furthermore, the computational modelling provides an explanation for the contradictory results obtained by independent laboratories when tackling experimentally the issue of binary versus graded GAL response to galactose induction.Les signaux génétiques binaires sont répandues dans la nature, et fournissent aux cellules une stratégie pour s'adapter à des environnements variables. Cette thése cherche a comprendre un example intéressant qui n'est pas compris complètement: le commutateur GAL. Le commutateur GAL en est un exemple fascinant qui n'est pas pas compris dans tous ses détails. Le commutateur GAL permet aux organismes de métaboliser du galactose, et contrôle si les mécanismes responsables du métabolisme du galactose sont en marche ou non. Actuellement, on ne connaît pas exactement comment le signal galactose est senti par les mécanismes de transcription. En fait, il y a deux hypothèses qui s'opposent à propos du mécanisme régulatoire au site du promoteur de GAL dans les cellules qui étaient induites avec galactose: le modèle de dissociation et le modèle de non-dissociation. Ce travail utilise des outils quantitatifs pour comprendre la réponse de la cellule S. cerevisiae au stimuli de galactose et pour analyser les mécanismes moléculaires possibles à la base de son fonctionnement. Cette thèse propose un modèle dynamique à l'échelle de population de cellules basé sur l'interaction des protéines régulatrices clées Gal4p, Gal80p et Gal3p. À notre connaissance, le modèle présenté ici est le premier à reproduire qualitativement le comportement bistable du réseau observé expérimentalement. Étant donné la compréhension actuelle du circuit d'induction GAL (Wightman et al., 2008; Jiang et al., 2009), ce travail propose que le mécanisme in vivo le plus probable menant à l'activation de la transcription des gènes GAL soit l'interaction physique entre la protéine galactose-activé Gal3p et la protéine Gal80p, avec le complexe Gal3p-Gal80p attaché aux promoteurs des gènes GAL. Notre modèle mathématique est en accord avec les profils de cytométrie en flux des souches sauvages, des souches mutées gal3∆ et gal80∆ d'Acar et al. (2005), et implique une fraction de cellules qui transcrit activement avec les mêmes caractéristiques qualitatives que dans le jeu de données rassemblées par Acar et al. (2010). En outre, les simulations informatiques du modèle fournissent une explication des résultats contradictoires obtenus par des laboratoires indépendants qui abordent expérimentalement la question de la réponse binaire ou graduelle à l'induction de galactose.
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Carden, Steven James. "A mathematical framework for a general purpose constraint management system." Thesis, University of Leeds, 1998. http://etheses.whiterose.ac.uk/1272/.
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The use of constraints in engineering for designing complex models is very popular. Current constraint solvers are divided into two broad classes: general and domain specific. Those that are general can handle very general constraint problems but are typically slow; while those that are domain specific can handle only a specific type of problem but are typically fast. For example, numerical algorithms are slow but general, whilst local propagation techniques are fast but limited to simple problems. It is generally acknowledged that there is a close coupling between engineering constraints and geometric constraints in the design process and so the solution of constraint problems consisting of engineering and geometric constraints is an important research issue. Some authors attempt to overcome the expressive limitations of domain specific solvers by using hybrid systems which try to find a balance between the speed of domain specific solvers and the generality of general solvers. Previous research at the University of Leeds has led to the development of a number of domain specific solvers that are capable of solving geometric and engineering constraint problems separately. In particular, the Leeds solvers are incremental and can find solutions when a new constraint is added very quickly. This thesis investigates the use of a hybrid of the various Leeds solvers with an aim to interactively solving constraint problems in engineering design, This Hybrid would have the speed advantages of the domain specific solvers and the expressiveness of a more general solver. In order for the hybrid to be constructed, commonalties of existing engineering constraints solvers must be identified. A characterisation of existing constraint solvers leads to the identification of a number of issues that need to be addressed before the hybrid can be built. In order to examine these issues, a framework for the constraint satisfaction process is presented that allows abstractions of constraint definition, constraint representation and constraint satisfaction. Using the constraint satisfaction framework, it is possible to study the quality of solution of constraint solvers. This leads to the identification of important problems in current constraint solvers. The constraint process framework leads to a study of the use of various paradigms of collaboration within the hybrid, such as sequential, parallel and concurrent. The study of the quality of solution allows concrete statements to be made about the hybrid collaborations. A new incremental constraint solver is presented that uses the hybrid collaboration paradigms and provides a first step towards a powerful engineering constraint solver.
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Jones, Rhys Gareth. "The mathematical modelling of gearbox vibration under applied lateral misalignment." Thesis, University of Warwick, 2012. http://wrap.warwick.ac.uk/54939/.
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In the mathematical modelling of gear vibrations it is found that there is a gap between the transient models developed in academia and the steady state models frequently used in industry. It is seen that the academic models are adept at modelling the nonlinear phenomena seen during gear contact for system with only a few degrees-of-freedom, whereas the industrial models are capable of solving the linear steady state response of more complex transmission systems. The work presented in this thesis attempts to bridge the gap between the two models, through the development of a transient nonlinear model of a gear pair with increased degrees-of-freedom. An understanding of the gear contact is achieved through the use of advanced static finite element analysis with nonlinear gear contact. Through FEA the effects of gear misalignment on these contact conditions is also investigated. The findings from the FEA are then used in a mathematical model of a single stage spur gear transmission, which is developed as part of the thesis, to determine the system accelerations. The mathematical model includes the time varying mesh stiffness and the time varying and nonlinear bearing stiffness's and frictional forces. The effects of lateral misalignment seen in the FEA results are also included into the model to investigate their effects. The model parameters are then varied to determine their effects and the simulated accelerations are compared against experimental results. It is found from this comparison that although some similarities between the simulated and experimental results are achieved for the aligned case, insufficient corroboration is found for the axially and radially misaligned results to confirm the validity of the mathematical model for modelling misalignment. From this, further experimental results were requested to gain a better con- fidence in the effects of lateral misalignment.
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Buck, Alec. "Mathematical modelling of welded pipes and plates using Cosserat theory." Thesis, University of Southampton, 1998. https://eprints.soton.ac.uk/50643/.
Full textAbstract:
Creep deformation in welded pipes and plates is of particular importance in the power industries. Most failures of welded pipes occur in the type IV region at the boundary with the parent material, which is relatively much harder. This thesis extends the work of Nicol (1985), Hawkes (1989) and Newman (1993) on the Cosserat theory of plates and shells, and has two major aims. The first is to develop the work of Hawkes to model successfully the strain rates in four-zone, thickwalled welded pipes. It is possible to determine the effects that the thickness of the pipe wall, the radius of the pipe and the creep index, n, in Norton's law have on the strain-rate distribution throughout the pipe. Using Continuum Damage Mechanics and this Cosserat model, the position and time to rupture in welded pipes is then calculated. The second aim of this thesis is to develop further the initial modelling work of Nicol (1985) and Hawkes (1989) by obtaining some simple perturbation models for both welded pipes and plates. The results obtained with the perturbation solutions are then compared with the numerical solutions of Newman (1993) for a plate and the numerical solutions derived in this thesis for a pipe.
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Dyson, Louise. "Mathematical models of cranial neural crest cell migration." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:66955fb9-691f-4d27-ad26-39bb2b089c64.
Full textAbstract:
From the developing embryo to the evacuation of football stadiums, the migration and movement of populations of individuals is a vital part of human life. Such movement often occurs in crowded conditions, where the space occupied by each individual impacts on the freedom of others. This thesis aims to analyse and understand the effects of occupied volume (volume exclusion) on the movement of the individual and the population. We consider, as a motivating system, the rearrangement of individuals required to turn a clump of cells into a functioning embryo. Specifically, we consider the migration of cranial neural crest cells in the developing chick embryo. Working closely with experimental collaborators we construct a hybrid model of the system, consisting of a continuum chemoattractant and individual-based cell description and find that multiple cell phenotypes are required for successful migration. In the crowded environment of the migratory system, volume exclusion is highly important and significantly enhances the speed of cell migration in our model, whilst reducing the numbers of individuals that can enter the domain. The developed model is used to make experimental predictions, that are tested in vivo, using cycles of modelling and experimental work to give greater insight into the biological system. Our formulated model is computational, and is thus difficult to analyse whilst considering different parameter regimes. The second part of the thesis is driven by the wish to systematically analyse our model. As such, it concentrates on developing new techniques to derive continuum equations from diffusive and chemotactic individual-based and hybrid models in one and two spatial dimensions with the incorporation of volume exclusion. We demonstrate the accuracy of our techniques under different parameter regimes and using different mechanisms of movement. In particular, we show that our derived continuum equations almost always compare better to data averaged over multiple simulations than the equivalent equations without volume exclusion. Thus we establish that volume exclusion has a substantial effect on the evolution of a migrating population.
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Kumbhari, Adarsh. "Mathematical models of cellular dysfunction." Thesis, University of Sydney, 2020. https://hdl.handle.net/2123/23711.
Full textAbstract:
Mathematical models provide a framework to confirm or reject hypotheses via the generation of quantitative predictions and offer rich insights into the processes that drive complex biological phenomena. In this thesis, we develop mathematical models that integrate experimental data and use these models to explore cellular dysfunction at different scales. The core of this thesis focuses on the selection of high-avidity T cells in cancer vaccines. High-avidity T cells, unlike low-avidity T cells, are adept at killing cancer cells and are essential for durable anti-tumour immunity. Using an ordinary differential equation (ODE) model, we show that we can optimise dosages to elicit high-avidity T cells. We find that increased numbers of immune cells known as immature dendritic cells, can also promote high-avidity T cells. We then reduce the complexity of our model and perform a thorough sensitivity analysis. We then study how immune cells regulate PD-L1 in the tumour niche. PD-L1 is an immunosuppressive molecule that tumours upregulate. Intriguingly, PD-L1 expression does not always correlate with tumour progression. To understand why we develop an ODE model that we calibrate to in vitro data. Using this model, we show that PD-L1 expression equilibrates in response to changes in immune activity via a feedforward circuit. This finding explains why some patients may respond to therapies targeting PD-L1 despite being PD-L1 negative. The last part of this thesis tests whether the spatial arrangement of cardiac mitochondria affects bioenergetics, as speculated by scholars. To test this, we develop an agent-based model of mitochondrial structure linked to a validated model of energy production and show that cardiac bioenergetics are robust to changes in fission and fusion over a physiological range. This thesis contains several foundational models. We expect the findings from this thesis to be a starting point for further interdisciplinary modelling and experimental work.
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Thomas, Angeli Elizabeth. "Mathematical modelling of evaporation mechanisms and instabilities in cryogenic liquids." Thesis, University of Southampton, 1999. https://eprints.soton.ac.uk/50640/.
Full textAbstract:
In this thesis we propose a model for laminar natural convection within a mixture of two cryogenic fluids with preferential evaporation. This full model was developed after a number of smaller models of the behaviour of the surface of the fluid had been examined. Throughout we make careful comparison between our analytical and computational work and existing experimental and theoretical results. The coupled differential equations for the main model were solved using an explicit upwind scheme for the vorticity-transport, temperature and concentration equations and the multigrid method for the Poisson equation. From plots of the evolution of the system, it is found that convection becomes stronger when preferential evaporation is included. This new model demonstrates how to include preferential evaporation, and can be applied to other fluid systems.
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Garnier, Celine. "Performance measurement and mathematical modelling of integrated solar water heaters." Thesis, Edinburgh Napier University, 2009. http://researchrepository.napier.ac.uk/Output/2593.
Full textAbstract:
In a period of rapidly growing deployment of sustainable energy sources the exploitation of solar energy systems is imperative. Colder climates like those experienced in Scotland show a good potential in addressing the thermal energy requirement of buildings; particularly for hot water derived from solar energy. The result of many years of global research on solar water heating systems has outlined the promising approach of integrated collector storage solar water heaters (ICS-SWH) in cold climates. This calls for a need to estimate the potential of ICS-SWH for the Scottish climate. This research project aims to study and analyse the performance of a newly developed ICS-SWH for Scottish weather conditions, optimise its performance, model its laboratory and field performance together with its environmental impacts and analyse its integration into buildings and benefits of such a heating system, for the primary purpose of proposing a feasible ICS-SWH prototype. Laboratory and field experiments were performed to investigate the performance of the newly developed ICS-SWH and the parameters affecting it which were fundamental to modelling its performance. This was followed by developing a thermal macro-model able to compare the temperature variation in different ICS-SWH designs; including internal temperature and external weather conditions for a given aspect ratio and to evaluate the performance of this ICS-SWH for laboratory and field conditions. This was followed by a three-dimensional Computational Fluid Dynamic (CFD) analysis of the ICS-SWH in order to optimise the fin spacing as a means of improving its performance. A Life Cycle Assessment (LCA) and monetary analysis considering the whole life energy of the different ICS-SWH designs were carried out using a previously developed thermal model in order to establish the most viable ICS-SWH with the smallest carbon footprint. Finally, a study to show how the ICS-SWH could be integrated into buildings and its potential benefits to builders and households was undertaken. Through this work, important parameters for modelling laboratory and field performance of ICS-SWH are established. The innovative modelling tool developed can predict the bulk water temperature of the ICS-SWH for any orientation and location in the world with good accuracy. Improvements of the ICS-SWH fin design were suggested through the CFD analysis while keeping the costs to a minimum. The ICS-SWH prototype showed a high commercial potential due to its environmental and monetary benefits as well as its potential for integration into commonly used solar water heating installations and modern methods of construction such as roof panels which could result in a viable commercialisation of the prototype.
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Chapman, Lloyd A. C. "Mathematical modelling of cell growth in tissue engineering bioreactors." Thesis, University of Oxford, 2015. https://ora.ox.ac.uk/objects/uuid:7c9ee131-7d9b-4e5d-8534-04a059fbd039.
Full textAbstract:
Expanding cell populations extracted from patients or animals is essential to the process of tissue engineering and is commonly performed in laboratory incubation devices known as bioreactors. Bioreactors provide a means of controlling the chemical and mechanical environment experienced by cells to ensure growth of a functional population. However, maximising this growth requires detailed knowledge of how cell proliferation is affected by bioreactor operating conditions, such as the flow rate of culture medium into the bioreactor, and by the initial cell seeding distribution in the bioreactor. Mathematical modelling can provide insight into the effects of these factors on cell expansion by describing the chemical and physical processes that affect growth and how they interact over different length- and time-scales. In this thesis we develop models to investigate how cell expansion in bioreactors is affected by fluid flow, solute transport and cell seeding. For this purpose, a perfused single-fibre hollow fibre bioreactor is used as a model system. We start by developing a model of the growth of a homogeneous cell layer on the outer surface of the hollow fibre in response to local nutrient and waste product concentrations and fluid shear stress. We use the model to simulate the cell layer growth with different flow configurations and operating conditions for cell types with different nutrient demands and responses to fluid shear stress. We then develop a 2D continuum model to investigate the influence of oxygen delivery, fluid shear stress and cell seeding on cell aggregate growth along the outer surface of the fibre. Using the model we predict operating conditions and initial aggregate distributions that maximise the rate of growth to confluence over the fibre surface for different cell types. A potential limitation of these models is that they do not explicitly consider individual cell interaction, movement and growth. To address this, we conclude the thesis by assessing the suitability of a hybrid framework for modelling bioreactor cell aggregate growth, with a discrete cell model coupled to a continuum nutrient transport model. We consider a simple set-up with a 1D cell aggregate growing along the base of a 2D nutrient bath. Motivated by trying to reduce the high computational cost of simulating large numbers of cells with a cell-based model, and to assess the validity of our previous continuum description of cell aggregate growth, we derive a continuum approximation of the discrete model in the large cell number limit and determine whether it agrees with the discrete model via numerical simulations.