The prediction of a company's financial health is of critical importance to a variety of stakeholders ranging from auditors, creditors, customers, employees, financial institutions and investors through to management. There has been considerable research in this field, ranging from the univariate dichotomous approach of Beaver (1966) to the multivariate multi-state approaches of Lau (1987) and Ward (1994). All of the South African studies namely, Strebel and Andrews (1977), Daya (1977), De La Rey (1981), Clarke et al (1991) and Court et al (1999), and even, Lukhwareni's (2005) four separate models, were dichotomous in nature providing either a "Healthy" or a "Failed" state; or a "Winner" or "Loser" as in the latter case. Notwithstanding, all of these models would be classified as first stage, initial screening models. This study has focused on following a two stage approach to identifying (first stage) and analysing (second stage) the States of Health in a company. It has not adopted the rigid "Healthy" or "Failed" dichotomous methodology. For the first stage, three-state models were developed classifying a company as Healthy, Intermittent or Distressed. Both three year and five year Profit after Tax (PAT) averages for Real Earnings Growth (REG) calculations were used to determine the superior definition for the Intermittent state; with the latter coming out as superior. Models were developed for the current year (Yn), one (Yn-1), two (Yn-2) and three years (Yn-3) forward using a Test sample of twenty companies and their predictive accuracy determined by using a Holdout sample of twenty-two companies and all their data points or years of information. The statistical methods employed were a Naïve model using the simple Shareholder Value Added (SVA) ratio, CHAID and MDA, with the latter providing very disappointing results - for the Yn year (five year average), the Test sample results were 100%, 95% and 95%, respectively; with the Holdout sample results being 81.3%, 83.8% and 52.5%, respectively. The Yn-1 to Yn-3 models produced very good results for the Test sample but somewhat disappointing Holdout sample results. The best two Yn models namely, the Naïve and the CHAID models, were modified so as to enable a comparison with the notable, dichotomous De La Rey (1981) model. As such, three different approaches were adopted and in all cases, both the modified Naïve (100%, 81.3%, 100%) and the modified CHAID (100%, 85.9%, 98%) produced superior results to the De La Rey model (84.8%, 62.6%, 75.3%). For the second stage, a Financial Risk Analysis Model (FRAM) using ratios in the categories of Growth, Performance Analysis, Investment Analysis and Financial Status were used to provide underlying information or clues, independent of the first stage model, so as to enable the stakeholder to establish a more meaningful picture of the company. This would pave the way for the appropriate strategy and course of action to be followed, to take the company to the next level; whether it be taking the company out of a Distressed State (D) or further improving on its Healthy status (H). / Business Management / D. BL.

Die vorliegende Arbeit befasst sich mit dem Einfluss von nicht-weißem oder nicht-Gauß’schem synaptischen Rauschen auf die Informationsübertragung in stochastischen Neuronenmodellen. Ziel ist es, zu verstehen, wie eine Nervenzelle ein Signal in ihrer Pulsaktivität kodiert. Synaptisches Rauschen beschreibt hier den Einfluss anderer Nervenzellen, die nicht das interessierende Signal tragen, aber seine Übertragung durch ihre synaptische Wirkung auf die betrachtete Zelle beeinflussen. In stochastischen Neuronenmodellen wird diese Hintergrundaktivität durch einen stochastischen Prozess mit geeigneter Statistik beschrieben. Ist die Rate, mit der präsynaptische Pulse auftreten, hoch und zeitlich konstant, die Wirkung einzelner Pulse aber verschwindend gering, so wird das synaptische Rauschen durch einen Gauß’schen Prozess beschrieben. Oft wird zudem angenommen, dass das Rauschen unkorreliert (weiß) ist. In dieser Arbeit wird neuronale Signalübertragung in dem Fall untersucht, dass eine solche Näherung nicht mehr gerechtfertigt ist, d.h. wenn der synaptische Hintergrund durch einen stochastischen Prozess beschrieben werden muss, der nicht weiß, nicht Gauß’sch, oder weder weiß noch Gauß’sch ist. Mittels Simulationen und analytischer Rechnungen werden drei Szenarien behandelt: Zunächst betrachten wir eine Zelle, die nicht ein, sondern zwei Signale empfängt, welche zusätzlich durch synaptische Kurzzeitplastizität gefiltert werden. In diesem Fall muss der Hintergrund durch ein farbiges Rauschen beschrieben werden. Im zweiten Szenario betrachten wir den Fall, dass der Effekt einzelner Pulse nicht mehr als schwach angenommen werden kann. Das Rauschen ist dann nicht mehr Gauß’sch, sondern ein Schrotrauschen. Schließlich untersuchen wir den Einfluss einer präsynaptischen Population, deren Feuerrate nicht zeitlich konstant ist, sondern zwischen Phasen hoher und niedriger Aktivität, sogenannten up und down states, springt. In diesem Fall ist das Rauschen weder weiß noch Gauß’sch. / This thesis is concerned with the effect of non-white or non-Gaussian synaptic noise on the information transmission properties of single neurons. Synaptic noise subsumes the massive input that a cell receives from thousands of other neurons. In the framework of stochastic neuron models, this input is described by a stochastic process with suitably chosen statistics. If the overall arrival rate of presynaptic action potentials is high and constant in time and if each individual incoming spike has only a small effect on the dynamics of the cell, the massive synaptic input can be modeled as a Gaussian process. For mathematical tractability, one often assumes that furthermore, the input is devoid of temporal structure, i.e. that it is well described by a Gaussian white noise. This is the so-called diffusion approximation (DA). The present thesis explores neuronal signal transmission when the conditions that underlie the DA are no longer met, i.e. when one must describe the synaptic background activity by a stochastic process that is not white, not Gaussian, or neither. We explore three distinct scenarios by means of simulations and analytical calculations: First, we study a cell that receives not one but two signals, additionally filtered by synaptic short-term plasticity (STP), so that the background has to be described by a colored noise. The second scenario deals with synaptic weights that cannot be considered small; here, the effective noise is no longer Gaussian and the shot-noise nature of the input has to be taken into account. Finally, we study the effect of a presynaptic population that does not fire at a rate which is constant in time but instead undergoes transitions between states of high and low activity, so-called up and down states.

In the archaeological literature, mountains are often portrayed as the boundaries between inhabited spaces. Yet occupying high elevations may have been an adaptive choice for ancient peoples, as rapidly changing elevations also offer variation in climate and resources over a relatively small area. So what happens, instead, if we put mountain landscapes at the center of our analyses of prehistoric seasonal rounds and ecological adaptation? This Ph.D. argues that, in order to understand any landscape that includes mountains, from the Alps to the Andes, one must include the ecology and archaeology of the highest elevations. Specifically, I base my findings on new fieldwork and lithic collections from the Absaroka and Beartooth Mountains in the Greater Yellowstone Ecosystem (GYE) of the Rocky Mountains, which was a vital crossroads of prehistoric cultures for more than 11,000 years. I include five interlocking analyses. First, I consider the impacts of anthropogenic climate change on high elevation cultural resources, focusing on the diminishing resiliency of ancient high elevation ice patches and the loss of the organic artifacts and paleobiological materials they contain. Second, I create a dichotomous key for chronologically typing projectile points, suggesting a methodological improvement for typological dating in the GYE and for surface archaeology more broadly. Third, I use obsidian source data to consider whether mountain people were a single, unified group or were represented by a variety of peoples with different zones of land tenure. Fourth, I consider high elevation occupation in both mountain ranges as part of the seasonal round, using indices of diversity in tool types and raw material to study how the duration of those occupations changed through time. And, finally, I test the common contention that ancient people primarily used mountains as refugia from extreme climatic pressure at lower elevations. Ultimately, I find that, in both mountain ranges, increased high elevation activity is most highly correlated with increased population, not with hot, dry climatic conditions. In other words, the mountains were more than simply refugia for plains or basin people to occupy when pressured by climatic hardship. In addition, between the Absarokas and the Beartooths the evidence suggests two different patterns of occupation, not a monolithic pan-mountain adaptation. These results demonstrate the potential contributions of surface archaeology to our understanding of prehistory, and have important implications for the way we think about mountain landscapes as peopled spaces in relation to adjacent lower-elevation areas.

The prediction of a company's financial health is of critical importance to a variety of stakeholders ranging from auditors, creditors, customers, employees, financial institutions and investors through to management. There has been considerable research in this field, ranging from the univariate dichotomous approach of Beaver (1966) to the multivariate multi-state approaches of Lau (1987) and Ward (1994). All of the South African studies namely, Strebel and Andrews (1977), Daya (1977), De La Rey (1981), Clarke et al (1991) and Court et al (1999), and even, Lukhwareni's (2005) four separate models, were dichotomous in nature providing either a "Healthy" or a "Failed" state; or a "Winner" or "Loser" as in the latter case. Notwithstanding, all of these models would be classified as first stage, initial screening models. This study has focused on following a two stage approach to identifying (first stage) and analysing (second stage) the States of Health in a company. It has not adopted the rigid "Healthy" or "Failed" dichotomous methodology. For the first stage, three-state models were developed classifying a company as Healthy, Intermittent or Distressed. Both three year and five year Profit after Tax (PAT) averages for Real Earnings Growth (REG) calculations were used to determine the superior definition for the Intermittent state; with the latter coming out as superior. Models were developed for the current year (Yn), one (Yn-1), two (Yn-2) and three years (Yn-3) forward using a Test sample of twenty companies and their predictive accuracy determined by using a Holdout sample of twenty-two companies and all their data points or years of information. The statistical methods employed were a Naïve model using the simple Shareholder Value Added (SVA) ratio, CHAID and MDA, with the latter providing very disappointing results - for the Yn year (five year average), the Test sample results were 100%, 95% and 95%, respectively; with the Holdout sample results being 81.3%, 83.8% and 52.5%, respectively. The Yn-1 to Yn-3 models produced very good results for the Test sample but somewhat disappointing Holdout sample results. The best two Yn models namely, the Naïve and the CHAID models, were modified so as to enable a comparison with the notable, dichotomous De La Rey (1981) model. As such, three different approaches were adopted and in all cases, both the modified Naïve (100%, 81.3%, 100%) and the modified CHAID (100%, 85.9%, 98%) produced superior results to the De La Rey model (84.8%, 62.6%, 75.3%). For the second stage, a Financial Risk Analysis Model (FRAM) using ratios in the categories of Growth, Performance Analysis, Investment Analysis and Financial Status were used to provide underlying information or clues, independent of the first stage model, so as to enable the stakeholder to establish a more meaningful picture of the company. This would pave the way for the appropriate strategy and course of action to be followed, to take the company to the next level; whether it be taking the company out of a Distressed State (D) or further improving on its Healthy status (H). / Business Management / D. BL.