• signals
• probability
• neuroscience
• information transmission
• Cox processes
• spike trains

Neurons transmit information with each other through spike trains, that are sequences of action potentials, mathematically described as Cox processes. We study a neural population encoding a Gaussian signal received as an input. We estimate the amounts of information transmitted about the signal, when such population is subject to independent noise sources, and we see that noise actually may have a beneficial role in information transmission. With this aim, we introduce some concepts of neuroscience, which are useful for a first approach to the subject. We describe the main concepts about the theory of point processes and random measures, focusing on the Cox processes. Then, an overview of the analysis of random signals is provided, which is necessary to quantify the amounts of information encoded by a neural population.
We then show two models, studied in "Shifting Spike Times or Adding and Deleting Spikes" (S. Voronenko, W. Stannat, B. Lindner, 2015) and replay their numerical experiments. The models describe two different ways in which the noise shapes the population response to the stimulus, increasing the amounts of information transmitted in both cases. Finally, we present several new models combining the previous models and their respective numerical results.