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This thesis presents a study of the visual change detection mechanism. This mechanism is thought to be responsible for the detection of sudden and unexpected changes in our visual environment. As the brain is a capacity limited system and has to deal with a continuous stream of information from its surroundings only a part of the vast amount of information can be completely processed and be brought to conscious awareness. This information, which passes through attentional filters, is used for goal-directed behaviour. Therefore, the change detection mechanism is a very useful aid to cope with important information which is outside the focus of our attention. rnIt is thought that a neural memory trace of repetitive visual information is stored. Each new information input is compared to this existing memory trace by a so-called change or mismatch detection system. Following a sudden change, the comparison process leads to a mismatch and the detection system elicits a warning signal, to which an orienting response can follow. This involves a change in the focus of attention towards this sudden environmental change which can then be evaluated for potential danger and allows for a behavioural adaptation to the new situation. rnTo this purpose a paradigm was developed combining a 2-choice response time task with in the background a mismatch detection task of which the subjects were not aware. This paradigm was implemented in an ERP and an fMRI study and was used to study the the change detection mechanism and its relationship with impulsivity.rnIn previous studies a change detection system for auditory information had already been established. As the brain is a very efficient system it was thought to be unlikely that this change detection system is only available for the processing of auditory information. rnIndeed, a modality specific mismatch response at the sensory specific occipital cortex and a more general response at the frontocentral midline, both resembling the components shown in auditory research, were found in the ERP study.rnAdditionally, magnetic resonance imaging revealed a possible functional network of regions, which responded specifically to the processing of a deviant. These regions included the occipital gyrus, premotor cortex, inferior frontal cortex, thalamas, insula, and parts of the cingular cortex. rnThe relationship between impulsivity measures and visual change detection was established in an additional study. More impulsive subjects showed less detection of deviant stimuli, which was most likely due to too fast and imprecise information processing.rnIn summary it can be said, that the work presented in this thesis demonstrates that visual mismatch negativity was established, a number of regions could be associated with change detection and additionally the relevance of change detection in information processing was shown.rn
The thesis studies the question how universal behavior is inherited by the Hadamard product. The type of universality that is considered here is universality by overconvergence; a definition will be given in chapter five. The situation can be described as follows: Let f be a universal function, and let g be a given function. Is the Hadamard product of f and g universal again? This question will be studied in chapter six. Starting with the Hadamard product for power series, a definition for a more general context must be provided. For plane open sets both containing the origin this has already been done. But in order to answer the above question, it becomes necessary to have a Hadamard product for functions that are not holomorphic at the origin. The elaboration of such a Hadamard product and its properties are the second central part of this thesis; chapter three will be concerned with them. The idea of the definition of such a Hadamard product will follow the case already known: The Hadamard product will be defined by a parameter integral. Crucial for this definition is the choice of appropriate integration curves; these will be introduced in chapter two. By means of the Hadamard product- properties it is possible to prove the Hadamard multiplication theorem and the Borel-Okada theorem. A generalization of these theorems will be presented in chapter four.