Unit:
Κατεύθυνση Εφαρμοσμένα ΜαθηματικάLibrary of the School of Science
Supervisors info:
Ι.Στρατής, Καθηγητής, Τμήμα Μαθηματικών, Ε.Κ.Π.Α. (Επιβλέπων)
Δ.Χελιώτης, Αναπληρωτής Καθηγητής, Τμήμα Μαθηματικών, Ε.Κ.Π.Α.
Δ.Πινότσης, Research Scientist, Department of Brain and Cognitive Sciences, M.I.T.
Original Title:
Probabilistic Approaches for describing Neural Population Density
Translated title:
Probabilistic Approaches for describing Neural Population Density
Summary:
Probabilistic approaches model neural population density
directly and bypass direct simulations of individual neurons. In this
Dissertation, we will review Fokker-Planck equations that describe
population density dynamics and summarize the flow and dispersion of states.
These can be derived by grouping together single units into statistically
similar populations. A statistical description of each population is given
by a probability density function that expresses the distribution of
neuronal states (i.e., membrane potential) over the population. In general,
neurons with the same state V(t) at a given time t have a different
history because of random fluctuations in the input current I(t). Starting from a spiking model that describe the activity of individual cells, we first derive the time evolution of the population density. Depending on our assumptions, we derive a different equation. In chapter 2, where we have made the assumption that the arrival times of synaptic inputs are Poisson distributed, we derive the Fokker-Planck equation. In chapter 3 , we introduce more assupmtions and derive different equations. We then use this equation to introduce mean field models that describe ensemble responses and discuss their application in describing neuronal interactions at the mesoscopic scale.
Main subject category:
Science
Keywords:
Ornstein-Uhlenbeck, Fokker-Planck, Mean Field Models, Neurons, Stochastic
