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This thesis is designed to be a self-contained exposition of the neurobiological and mathematical aspects of sensory perception, memory, and learning with a bias towards olfaction. The final chapters introduce a new approach to modeling focusing more on the geometry of the system as opposed to element wise dynamics. Additionally, we construct an organism independent model for olfactory processing: something which is currently missing from the literature.
The receptive fields of simple cells in the visual cortex can be understood as linear filters. These filters can be modelled by Gabor functions, or by Gaussian derivatives. Gabor functions can also be combined in an `energy model of the complex cell
This paper proposes a novel topological learning framework that can integrate brain networks of different sizes and topology through persistent homology. This is possible through the introduction of a new topological loss function that enables such c
Neural population activity is theorized to reflect an underlying dynamical structure. This structure can be accurately captured using state space models with explicit dynamics, such as those based on recurrent neural networks (RNNs). However, using r
The Reward Prediction Error hypothesis proposes that phasic activity in the midbrain dopaminergic system reflects prediction errors needed for learning in reinforcement learning. Besides the well-documented association between dopamine and reward pro
Most of mathematic forgetting curve models fit well with the forgetting data under the learning condition of one time rather than repeated. In the paper, a convolution model of forgetting curve is proposed to simulate the memory process during learni