title: A set probability technique for detecting relative time order across multiple neurons.
abstract: With the development of multielectrode recording techniques, it is possible to measure the cell firing patterns of multiple neurons simultaneously, generating a large quantity of data. Identification of the firing patterns within these large groups of cells is an important and a challenging problem in data analysis. Here, we consider the problem of measuring the significance of a repeat in the cell firing sequence across arbitrary numbers of cells. In particular, we consider the question, given a ranked order of cells numbered 1 to N, what is the probability that another sequence of length n contains j consecutive increasing elements? Assuming each element of the sequence is drawn with replacement from the numbers 1 through N, we derive a recursive formula for the probability of the sequence of length j or more. For n<2j, a closed-form solution is derived. For n>or=2j, we obtain upper and lower bounds for these probabilities for various combinations of parameter values. These can be computed very quickly. For a typical case with small N (<10) and large n (<3000), sequences of 7 and 8 are statistically very unlikely. A potential application of this technique is in the detection of repeats in hippocampal place cell order during sleep. Unlike most previous articles on increasing runs in random lists, we use a probability approach based on sets of overlapping sequences.
authors.affiliation: Department of Anesthesiology and Pain Medicine, University of California at Davis, Davis, CA 95616, USA. annesmith@ucdavis.edu
authors.forename: Anne C
authors.initials: AC
authors.lastname: Smith
authors.forename: Peter
authors.initials: P
authors.lastname: Smith
mesh_terms: D000200:Action Potentials / Q000502:physiology*; D000465:Algorithms; D000818:Animals; D002490:Central Nervous System / Q000502:physiology*; D006624:Hippocampus / Q000502:physiology; D006801:Humans; D008959:Models, Neurological; D015233:Models, Statistical; D009415:Nerve Net / Q000502:physiology*; D009434:Neural Pathways / Q000502:physiology*; D009474:Neurons / Q000502:physiology*; D011336:Probability; D012815:Signal Processing, Computer-Assisted; D012890:Sleep / Q000502:physiology; D013028:Space Perception / Q000502:physiology; D009435:Synaptic Transmission / Q000502:physiology; D013997:Time Factors