Consequences of long-range temporal dependence in neural spiking activity for theories of processing and coding

Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Biomedical and Chemical Engineering


Laurel H. Carney


Long-range temporal dependence, Neural spiking, Cortical neurons

Subject Categories

Biomedical Engineering and Bioengineering | Engineering | Life Sciences | Neuroscience and Neurobiology


In the last decade-and-a-half, a number of unexpected statistical properties have been found in the pulsatile activity of neurons in many sensory systems. These properties have been variously called "fractal behavior", "self-similarity", "1/f fluctuations", and "long-duration correlation". In this dissertation, we develop a cohesive and robust theory of long-range dependence in point processes that subsumes these statistical properties and connects them to the much broader mathematical and scientific literature on long-range dependence in general stochastic processes. As this theory is developed, we examine ways in which the presence of long-range dependence can be used to discriminate between potential models of neural processing and analyze ways in which it can undermine standard statistical analyses of neural activity.

We first study integrate-and-fire models of cortical processing that were designed to explain the high variability of the activity in cortical neurons to see if they can also produce long-range dependence. Since a large number of these models produce renewal-process outputs, we prove analytically that such models cannot simultaneously possess long-range dependence and physiologically realistic variability. We then consider integrate-and-fire models with renewal point process inputs. By analyzing the outputs of simulations, we show that these models can possess long-range dependence and realistic variability if the interval distribution of their inputs has infinite variance. Since this latter requirement contradicts empirical results, we suggest a new integrate-and-fire model with long-range dependent inputs having finite interval-variance. Through the use of simulations, we show that this model is able to produce both long-range dependence and realistic variability.

We also explore the impact that long-range dependence has on empirical estimates of the mean, standard deviation, and variance of spike counts in neural activity. We derive mathematical formulae for the actual mean and variance and for the statistical behavior of sample mean and sample variance estimators for a model neuron. Using these formulae and simulations of the model, we show that long-range dependence significantly increases the variability of the sample mean and causes the sample standard deviation and sample variance to be negatively biased. The significance of these results for existing empirical measurements is demonstrated.


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