Thesis (Ph. D.)--University of Michigan, 1934. / Lithoprinted. "Reprinted from the Annals of Mathematical Statistics, November, 1933."

Thesis (doctoral)--Svenska handelshögskolan, 1986. / Extra t.p. inserted with thesis statement. Includes bibliographical references (p. 210-222).

Thesis (Ph. D.)--Ohio State University, 2005. / Title from first page of PDF file. Document formatted into pages; contains xvii, 321 p.; also includes graphics (some col.). Includes bibliographical references. Available online via OhioLINK's ETD Center

Thesis (M.S)--Ohio University, March, 2005. / Title from PDF t.p. Includes bibliographical references (p. 131-136)

Diss.--Erlangen.

No description available.

- / -

There has been considerable recent interest in models for epidemics on networks describing social contacts. This thesis considers a stochastic SIR (Susceptible - Infective - Removed) model for the spread of an epidemic among a population of individuals, with a random network of social contacts, that is partitioned into households and in which individuals also make casual contacts, i.e. with people chosen uniformly at random from the population. The behaviour of the model as the population tends to infinity is investigated. A threshold parameter that governs whether or not the epidemic with an initial infective can become established is obtained, as is the probability that such an outbreak occurs and, if so, how large it will become. The behaviour of this model is then compared to that of a finite population using Monte Carlo simulations. The effect of the different transmission routes on the final outcome of an epidemic and the effect of introducing social contacts and clustering to the network on the performance of various vaccination strategies are also investigated.

Ca2+ as a universal messenger participates in a great variety of physiological functions and biological events such as cell maturation, chemotaxis or gene expression. These diverse functions are controlled through complex spatio-temporal calcium patterns. To date it is known that these patterns depend on stimuli type and concentration. However, the majority of these observations were from constant or step change stimulation protocols. Under these conditions two leading hypotheses for the stimulus encoding into cytosolic calcium responses were proposed, namely amplitude and frequency modulation. Under physiological conditions, however, cells often experience time dependent stimuli such as transient changes in neurotransmitter or oscillations in hormone concentrations. How cells transduce such dynamic stimuli into an appropriate response is an open question. We exposed HEK293 cells and astrocytes to dynamically varying time courses of carbachol and ATP, respectively, and investigated the corresponding cellular calcium activity. While single cells generally fail to follow the applied stimulation due to their intrinsic stochasticity and heterogeneity, faithful signal reconstruction is observed at the population level. We suggest eight possible population representation measures and using mutual information measure show that the area under the curve and total number of spikes are the most informative ones. Next we provide simple transfer functions that explain how dynamic stimulation is encoded into area under the curve and ensemble calcium spike rates. Cells in a physiological environment often experience diverse stimulation time courses which can be reproduced experimentally. Furthermore, cell populations may differ in the number of cells or exhibit various spatial distributions. In order to understand how these conditions affect population responses, we compute the single cell response to a given dynamic stimulus. Single cell variability and the small number of calcium spikes per cell pose a significant modelling challenge, but we demonstrate that Gaussian processes can successfully describe calcium spike rates in these circumstances and outperform standard tools such as peri-stimulus time histograms and kernel smoothing. Having the single cell response model will allow us to compare responses of various sets of cells to the observed population response and consequently obtain insight into tissue-wide calcium oscillations for heterogeneous cell populations. Finally,in vivo astrocytes respond to a range of hormones and neurotransmitters. Furthermore these agonists can have different characteristics, for example glutamate is a fast excitatory transmitter, while ATP can be an inhibitory transmitter. Despite of this, how (or if at all) astrocytes differentiate between different agonists is still not clear. We hypothesize that astrocytes discriminates between different stimuli by exploiting the spatial-temporal complexity of calcium responses. We show how 2D A Trous wavelet decomposition combined with Bhattacharyya distance measure can be applied to test this hypothesis.

The floral transition is a developmental process through which some plants commit to flowering and stop producing leaves. This is controlled by changes in gene expression in the shoot apical meristem (SAM). Many of the genes involved are known, but their interactions are usually only studied one by one, or in small sets. While it might be necessary to properly ascertain the existence of regulatory interactions from a biological standpoint, it cannot really provide insight in the functioning of the floral-transition process as a whole. For this reason, a modelling approach has been used to integrate knowledge from multiple studies. Several approaches were applied, starting with ordinary differential equation (ODE) models. It revealed in two cases – one on rice and one on Arabidopsis thaliana – that the currently available data were not sufficient to build data-driven ODE models. The main issues were the low temporal resolution of the time series, the low spatial resolution of the sampling methods used on meristematic tissue, and the lack of gene expression measurements in studies of factors affecting the floral transition. These issues made the available gene expression time series of little use to infer the regulatory mechanisms involved. Therefore, another approach based on qualitative data was investigated. It relies on data extracted from published in situ hybridization (ISH) studies, and Boolean modelling. The ISH data clearly showed that shoot apical meristems (SAM) are not homogeneous and contain multiple spatial domains corresponding to coexisting steady-states of the same regulatory network. Using genetic programming, Boolean models with the right steady-states were successfully generated. Finally, the third modelling approach builds upon one of the generated Boolean models and implements its logic into a 3D tissue of SAM. As Boolean models cannot represent quantitative spatio-temporal phenomena such as passive transport, the model had to be translated into ODEs. This model successfully reproduced the patterning of SAM genes in a static tissue structure. The main biological conclusions of this thesis are that the spatial organization of gene expression in the SAM is a crucial part of the floral transition and of the development of inflorescences, and it is mediated by the transport of mobile proteins and hormones. On the modelling front, this work shows that quantitative ODE models, despite their popularity, cannot be applied to all situations. When the data are insufficient, simpler approaches like Boolean models and ODE models with qualitatively selected parameters can provide suitable alternatives and facilitate large-scale explorations of the space of possible models, due to their low computational cost.