| This dissertation explores two different topics. In Part I we present data analysis and modeling studies characterizing how simple cell receptive fields in the mammalian primary visual cortex collectively represent visual information. We build on standard models which treat simple cell responses as the outputs of linear spatio-temporal filters. We characterize a widely assumed but previously unquantified linear trend relating simple cell preferred spatial frequencies and spatial frequency bandwidths. In contrast with popular assumptions, we discover that receptive field shapes are not scale invariant on average, but evolve systematically with preferred spatial frequency. We present a new parametric model for simple cell space-time receptive fields, and a new index for directional-tuning strength. Examination of this new index suggests that strongly directionally-selective simple cells are more common than previously believed. Finally, we present theoretical arguments to account for the way in which simple cell populations represent time-varying imagery. These arguments predict a novel constraint between a receptive field's temporal bandwidth and its preferred spatial and temporal frequencies and spatial frequency bandwidth. We find this constraint is obeyed by cat simple cell receptive fields.; In Part II we present an information theoretic analysis of pattern recognition. Biological and machine pattern recognition systems face a common challenge: Given sensory data about an unknown object, classify the object by comparing the sensory data with a library of internal representations stored in memory. In real-world environments, the number of possible objects to be recognized and the richness of the raw sensory data often force recognition systems to internally represent memory and sensory information in a compressed format. However, these representations must preserve information in the original data with some minimum level of fidelity to support reliable pattern recognition. Thus, there is an intrinsic tradeoff between the amount of resources devoted to data representation and the complexity of the environment in which a recognition system may reliably operate. We propose a general mathematical model for pattern recognition problems subject to resource constraints, and prove single-letter information theoretic bounds governing the aforementioned tradeoff. We apply our theoretical results to the example of recognizing sequences of binary symbols. |
