Noisy random Boolean formulae:a statistical physics perspective

Properties of computing Boolean circuits composed of noisy logical gates are studied using the statistical physics methodology. A formula-growth model that gives rise to random Boolean functions is mapped onto a spin system, which facilitates the study of their typical behavior in the presence of noise. Bounds on their performance, derived in the information theory literature for specific gates, are straightforwardly retrieved, generalized and identified as the corresponding macroscopic phase transitions. The framework is employed for deriving results on error-rates at various function-depths and function sensitivity, and their dependence on the gate-type and noise model used. These are difficult to obtain via the traditional methods used in this field.

On the robustness of random Boolean formulae

Random Boolean formulae, generated by a growth process of noisy logical gates are analyzed using the generating functional methodology of statistical physics. We study the type of functions generated for different input distributions, their robustness for a given level of gate error and its dependence on the formulae depth and complexity and the gates used. Bounds on their performance, derived in the information theory literature for specific gates, are straightforwardly retrieved, generalized and identified as the corresponding typical-case phase transitions. Results for error-rates, function-depth and sensitivity of the generated functions are obtained for various gate-type and noise models. © 2010 IOP Publishing Ltd.

The influence of marketing factors and substance characteristics on pharmaceutical sales in a state-controlled prescriptions pharmaceuticals market

The present dissertation investigates the influence of brand as well as substance-related marketing attributes on prescription pharmaceutical sales within a state-controlled market. For this purpose, a systematic literature review was conducted in the first instance, during which knowledge about the most relevant research within this field was gathered. Consequently, over 538 publications were reviewed and indicated as being potentially relevant, leading to an eventual count of 98 core publications. However, most of these studies had been conducted in the mainly unrestricted US market. These findings were then summarised and statistically evaluated. In a second step, based on the literature review, a qualitative study, containing focus and Delphi groups, was then performed. The participants in these studies were involved in pharmaceutical marketing within a state-controlled prescriptions pharmaceuticals market. Consequently, the findings were slightly different to those derived by the systematic literature review. Based on this second step, seven hypotheses were proposed. In the third step, these hypotheses were tested, using collected data and a secondary market dataset provided by a market research institute. A statistical analysis was then performed, applying descriptive as well as multiple regression analytical methods. The evaluation of the results resulted in a conceptual model of physician targeting, leading to several theoretical, methodological and managerial implications.