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Dynamical Systems of the BCM Learning Rule: Emergent Properties and Application to Clustering

Udeigwe, Lawrence (2014) Dynamical Systems of the BCM Learning Rule: Emergent Properties and Application to Clustering. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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The BCM learning rule has been used extensively to model how neurons in the brain cortex respond to stimulus. One reason for the popularity of the BCM learning rule is that, unlike its predecessors which use static thresholds to modulate neuronal activity, the BCM learning rule incorporates a dynamic threshold that serves as a homeostasis mechanism, thereby providing a larger regime of stability.
This dissertation explores the properties of the BCM learning rule – as a dynamical system– in different time-scale parametric regimes. The main observation is that, under certain stimulus conditions, when homeostasis is at least as fast as synapse, the dynamical system undergoes bifurcations and may trade stability for oscillations, torus dynamics, and chaos. Analytically, it is shown that the conditions for stability are a function of the homeostasis time-scale parameter and the angle between the stimuli coming into the neuron.
When the learning rule achieves stability, the BCM neuron becomes selective. This means that it exhibits high-response activities to certain stimuli and very low-response activities to others. With data points as stimuli, this dissertation shows how this property of the BCM learning rule can be used to perform data clustering analysis. The advantages and limitations of this approach are discussed, in comparison to a few other clustering algorithms.


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Item Type: University of Pittsburgh ETD
Status: Unpublished
CreatorsEmailPitt UsernameORCID
Udeigwe, Lawrencelcu2@pitt.eduLCU2
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairMunro, Paulpwm@pitt.eduPWM
Committee CoChairErmentrout, Bardbard@pitt.eduBARD
Committee MemberHirtle, Stephen C.hirtle@pitt.eduHIRTLE
Committee MemberKarimi, Hassan A.hkarimi@pitt.eduHKARIMI
Committee MemberRubin, Jonathanjonrubin@pitt.eduJONRUBIN
Date: 4 September 2014
Date Type: Publication
Defense Date: 18 July 2014
Approval Date: 4 September 2014
Submission Date: 8 August 2014
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Number of Pages: 112
Institution: University of Pittsburgh
Schools and Programs: School of Information Sciences > Information Science
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: oscillation, information science, applied mathematics, neurosciences
Date Deposited: 04 Sep 2014 14:39
Last Modified: 15 Nov 2016 14:23


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