Exploring Neural Network Models with Hierarchical Memories and Their Use in Modeling Biological Systems

Energy landscapes are often used as metaphors for phenomena in biology, social sciences and finance. Different methods have been implemented in the past for the construction of energy landscapes. Neural network models based on spin glass physics provide an excellent mathematical framework for the construction of energy landscapes. This framework uses a minimal number of parameters and constructs the landscape using data from the actual phenomena. In the past neural network models were used to mimic the storage and retrieval process of memories (patterns) in the brain. With advances in the field now, these models are being used in machine learning, deep learning and modeling of complex phenomena.;Most of the past literature focuses on increasing the storage capacity and stability of stored patterns in the network but does not study these models from a modeling perspective or an energy landscape perspective. This dissertation focuses on neural network models both from a modeling perspective and from an energy landscape perspective. I firstly show how the cellular interconversion phenomenon can be modeled as a transition between attractor states on an epigenetic landscape constructed using neural network models. The model allows the identification of a reaction coordinate of cellular interconversion by analyzing experimental and simulation time course data. Monte Carlo simulations of the model show that the initial phase of cellular interconversion is a Poisson process and the later phase of cellular interconversion is a deterministic process.;Secondly, I explore the static features of landscapes generated using neural network models, such as sizes of basins of attraction and densities of metastable states. The simulation results show that the static landscape features are strongly dependent on the correlation strength and correlation structure between patterns. Using different hierarchical structures of the correlation between patterns affects the landscape features. These results show how the static landscape features can be controlled by adjusting the correlations between patterns.;Finally, I explore the dynamical features of landscapes generated using neural network models such as the stability of minima and the transition rates between minima. The results from this project show that the stability depends on the correlations between patterns. It is also found that the transition rates between minima strongly depend on the type of bias applied and the correlation between patterns. The results from this part of the dissertation can be useful in engineering an energy landscape without even having the complete information about the associated minima of the landscape.