Abstract
This chapter explores some of the most relevant mathematical structures used by brain researchers to unravel brain’s structure, function and dynamics. It starts by looking into the concept of brain state. The concept of the state of a system is key in engineering and physics, but maybe it is a not a very well understood concept in other relevant fields of brain science like cognitive psychology. Scientific models and theories of the brain are empirically tested against signal measurements of brain activity. Undoubtedly, the methodology and technology used constrain the possible interpretations of the models. For example, single cell recording typically consists on time series of voltage values that represents spikes or action potentials. Spikes are characterised by two parameters: amplitude and duration. Recording a population of neurons, on the other hand, is far from trivial. The recorded signal is not a point process, rather it represents a summation of several events in the neighborhood of the electrode. Neuroscience constitutes a challenging and promising testing ground for developing our understanding of how the macroscopic level emerges from the interaction of large numbers of interacting components. The functioning of the brain at the high level of mental processing is, of course, expected to be the result of the co-operate action of a very large number of neurons.
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Notes
- 1.
Theta oscillation can be used with two different interpretations. In rats and mice, theta oscillation is a specific type of regular oscillation seen in the hippocampus and several other brain regions connected to it. Thus in rats we say “hippocampal theta oscillation”. The original sense of theta is used in human experimentation meaning: EEG waves falling into a frequency range of 4–7 Hz, regardless of where in the brain they occur or what their functional significance. Therefore “theta oscillation” and “hippocampal theta rhythm” are different because in the first case the EEG waves are obtained through electrodes glued to the scalp measuring several areas of the cortex, while in the latter case is implicitly assumed that the EEG wave comes from the hippocampus, using invasive techniques in rodents.
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Gómez-Ramirez, J. (2014). State of the Art: Mathematical Approaches in Brain Science. In: A New Foundation for Representation in Cognitive and Brain Science. Springer Series in Cognitive and Neural Systems, vol 7. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7738-5_2
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