Nonlinear encoding of sounds in the auditory cortex

The relation between sensory input and neural activity is often complex. In peripheral neurons, such as photoreceptors, it can be relatively straightforward to describe the way in which a stimulus causes the generation of action potentials. Activity of neurons that are more deeply embedded in sensory networks tends to be harder to understand. Experimental efforts to uncover their stimulus-response relationship consists of two general approaches. First, one may present simple, easy to parameterise stimuli, such as pure tones, and describe in detail the evoked neural responses in each of the limited number of stimulus conditions. Alternatively, one might mimic the complexity of the natural environment and present a set of complex, often time-varying, stimuli, and construct a statistical description — usually called a neural encoding model — of the stimulus-response function. A statistical approach is now necessary because one cannot tabulate the response properties for each stimulus condition separately, as there are too many (possibly an infinite number). Here, we report on advances made on this problem, with focus on the encoding of sounds in the primary auditory cortex. Neurons in the auditory cortex respond in complex and nonlinear ways to sounds, and efforts to describe their stimulus-response functions have met with limited success. Here we make use of multilinear, or tensor, mathematics, in order to formulate highly nonlinear, yet compact and easy to estimate, neural encoding models. These models can capture nonlinear phenomena such as cross-frequency suppression, and short term stimulus-specific adaptation. Besides yielding a richer description of neuronal function, the models are more predictive than traditional models. We also present a range of tools and extensions for multilinear models. Finally, in the last two chapters, we describe two applications of the methods to the auditory cortex, in order to answer specific biological questions. The work presented in this thesis sheds light on the processing that takes place in the auditory cortex, as well as providing a range of new statistical tools for analysing neural data