i'am currently reading  theoretical neuroscience by dayan abbott and it says  If we ignore the brief duration of an action potential (about1 ms), an action potential sequence can be characterized simply by a listof the times when spikes occurred. For n spikes, we denote these timesby $ti$ with i = 1, 2,... , n. The trial during which the spikes are recordedis taken to start at time zero and end at time T, so 0  $ti$  T for all i. Thespike sequence can also be represented as a sum of infinitesimally narrow,idealized spikes in the form of Dirac  functions . then it says we average  (t) s that we get during the trials . We use angle brackets, <> , to denote averages over trials that usethe same stimulus, so that  for any quantity z is the sum of the valuesof z obtained from many trials involving the same stimulus, divided bythe number of trials. The trial-averaged neural response function is thusdenoted by <(t)> how can we average (t) . it consists of many infinity long spikes . so summing them and then dividing them by number of trials . is just like summing them . and does not give us the sense of average spikes .the book further explains : In any integral expression, the neural response function generates a contribution whenever a spike occurs. If instead, we use the trial-average response function this generates contributions proportional to the fraction of trials on which a spike occurred. the materials I'm referring to are from pages 7 and 8 .
what is the trial-averaged neural response function?
theoretical neuroscience;computational modeling