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Reduced representation of neural networks
Title
Reduced representation of neural networks.
Creator
Stefanescu, Roxana A., Charles E. Schmidt College of Science, Department of Physics
Abstract/Description
Experimental and computational investigations addressing how various neural functions are achieved in the brain converged in recent years to a unified idea that the neural activity underlying most of the cognitive functions is distributed over large scale networks comprising various cortical and subcortical areas. Modeling approaches represent these areas and their connections using diverse models of neurocomputational units engaged in graph-like or neural field-like structures. Regardless of...
Show moreExperimental and computational investigations addressing how various neural functions are achieved in the brain converged in recent years to a unified idea that the neural activity underlying most of the cognitive functions is distributed over large scale networks comprising various cortical and subcortical areas. Modeling approaches represent these areas and their connections using diverse models of neurocomputational units engaged in graph-like or neural field-like structures. Regardless of the manner of network implementation, simulations of large scale networks have encountered significant difficulties mainly due to the time delay introduced by the long range connections. To decrease the computational effort, it is common to assume severe approximations to simplify the descriptions of the neural dynamics associated with the system's units. In this dissertation we propose an alternative framework allowing the prevention of such strong assumptions while efficiently representing th e dynamics of a complex neural network. First, we consider the dynamics of small scale networks of globally coupled non-identical excitatory and inhibitory neurons, which could realistically instantiate a neurocomputational unit. We identify the most significant dynamical features the neural population exhibits in different parametric configuration, including multi-cluster dynamics, multi-scale synchronization and oscillator death. Then, using mode decomposition techniques, we construct analytically low dimensional representations of the network dynamics and show that these reduced systems capture the dynamical features of the entire neural population. The cases of linear and synaptic coupling are discussed in detail. In chapter 5, we extend this approach for spatially extended neural networks., We consider the dynamical behavior of a neural field-like network, which incorporates many biologically realistic characteristics such as heterogeneous local and global connectivity as well as dispersion in the neural membrane excitability. We show that in this case as well, we can construct a reduced representation, which may capture well the dynamical features of the full system. The method outlined in this dissertation provides a consistent way to represent complex dynamical features of various neural networks in a computationally efficient manner.
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Date Issued
2009
PURL
http://purl.flvc.org/FAU/369387
Subject Headings
Molecular neurobiology, Neural networks (Neurobiology), Brain, Mathematical models, Cognitive neuroscience, Recognition (Psychology)
Format
Document (PDF)
Investigation of Mathematical Modeling for the general treatment of Glioblastoma
Title
Investigation of Mathematical Modeling for the general treatment of Glioblastoma.
Creator
Khatiwada, Dharma Raj, Kalantzis, Georgios, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Physics
Abstract/Description
The purpose of this research is to validate various forms of mathematical modeling of glioblastoma multiforme (GBM) expressed as differential equations, numerically. The first work was involved in the numerical solution of the reaction-convection model, efficacy of which is expressed in terms of survival time. It was calculated using simple numerical scheme for the standard-of-care treatment in clinics which includes surgery followed by the radiation and chemotherapy. Survival time using all...
Show moreThe purpose of this research is to validate various forms of mathematical modeling of glioblastoma multiforme (GBM) expressed as differential equations, numerically. The first work was involved in the numerical solution of the reaction-convection model, efficacy of which is expressed in terms of survival time. It was calculated using simple numerical scheme for the standard-of-care treatment in clinics which includes surgery followed by the radiation and chemotherapy. Survival time using all treatment options increased significantly to 57 weeks compared to that of surgery close to 14 weeks. It was also observed that survival time increased significantly to 90 weeks if tumor is totally resected. In reaction-diffusion model using simple numerical scheme, tumor cell density patterns due to variation in patient specific tumor parameters such as net proliferation rate and diffusion coefficient were computed. Significant differences were observed in the patterns while using dominant diffusion and proliferation rate separately. Numerical solution of the tumor growth model under the anti-angiogenic therapy revealed some impacts in optimum tumor growth control however it was not significant.
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Date Issued
2016
PURL
http://purl.flvc.org/fau/fd/FA00004703
Subject Headings
Antineoplastic agents, Brain -- Cancer -- Treatment, Cancer -- Research, Cytology, Glioblastoma multiforme -- Treatment, Immune system -- Mathematical models, Systems biology
Format
Document (PDF)