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Full-Text Articles in Computational Neuroscience
Energy As A Limiting Factor In Neuronal Seizure Control: A Mathematical Model, Sophia E. Epstein
Energy As A Limiting Factor In Neuronal Seizure Control: A Mathematical Model, Sophia E. Epstein
CMC Senior Theses
The majority of seizures are self-limiting. Within a few minutes, the observed neuronal synchrony and deviant dynamics of a tonic-clonic or generalized seizure often terminate. However, a small epilesia partialis continua can occur for years. The mechanisms that regulate subcortical activity of neuronal firing and seizure control are poorly understood. Published studies, however, through PET scans, ketogenic treatments, and in vivo mouse experiments, observe hypermetabolism followed by metabolic suppression. These observations indicate that energy can play a key role in mediating seizure dynamics. In this research, I seek to explore this hypothesis and propose a mathematical framework to model how …
Extending Power Series Methods For The Hodgkin-Huxley Equations, Including Sensitive Dependence, James S. Sochacki
Extending Power Series Methods For The Hodgkin-Huxley Equations, Including Sensitive Dependence, James S. Sochacki
CODEE Journal
A neural cell or neuron is the basic building block of the brain and transmits information to other neurons. This paper demonstrates the complicated dynamics of the neuron through a numerical study of the Hodgkin-Huxley differential equations that model the ionic mechanisms of the neuron: slight changes in parameter values and inputted electrical impulses can lead to very different (unexpected) results. The methods and ideas developed for the ordinary differential equations are extended to partial differential equations for Hodgkin-Huxley networks of neurons in one, two and three dimensions.
Toric Ideals, Polytopes, And Convex Neural Codes, Caitlin Lienkaemper
Toric Ideals, Polytopes, And Convex Neural Codes, Caitlin Lienkaemper
HMC Senior Theses
How does the brain encode the spatial structure of the external world?
A partial answer comes through place cells, hippocampal neurons which
become associated to approximately convex regions of the world known
as their place fields. When an organism is in the place field of some place
cell, that cell will fire at an increased rate. A neural code describes the set
of firing patterns observed in a set of neurons in terms of which subsets
fire together and which do not. If the neurons the code describes are place
cells, then the neural code gives some information about the …