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4th Annual Student Workshop: Abstracts
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Phase resetting curves, noise, and synchrony
In this talk, I will discuss recent work with the Nathan Urban lab and the role of noise in the synchronization of neural oscillations. I will use phase resetting curves to analyze the rate of synchronization and the degree of synchrony that correlated noise induces in uncoupled oscillators. I will also explore the relationship of the phase resetting curve to other aspects of neural firing such as the spike triggered average, the peri-stimulus time histogram, and if time permits, the spike triggered covariance. This is joint work with Roberto Galan, Sashi Marella, Aushra Abouzeid, and Nathan Urban.
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Reading the Thoughts of a Mollusk: The Neural Origins of Seashell Structure and Pattern
We explain how the simple neurosecretory system of aquatic mollusks is able to generate the diverse array of structures and pigmentation patterns found among their shells. By constructing a mathematical representation of this biological system, we first explain how it gives rise to many distinct shell shapes. Then we shift our focus to the pigmentation control system. We demonstrate how our mathematical model also faithfully reproduces many of the even more diverse pigmentation patterns. The anatomical and physiological basis of this model sets it apart from other mathematical representations of shape and pattern. In addition to explaining the shell construction and patterns, we also predict patterns of shell repair in response to environmentally induced disruptions. The model makes additional predictions about the potential evolutionary relationships between shells with different patterns. This is joint work with Alistair Boettiger and George Oster.
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A coupla ducks: slow currents, canards, clustering, and weak coupling
A recent interneuron model by Erisir et al (J. neurophys, 1999) introduces a slow potassium current which at low currents has the effect of producing mixed mode oscillations (MMO). When such neurons are coupled via gap junctions they form clustered states. We analyze this by considering the phase resetting curves of these neurons when in the MMO state and show that complex phase interactions are a natural consequence. We perform an analysis of the local dynamics to show the existence of a folded canard structure which gives restrictions on the parameters for this to occur.
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Not having a swell time: mathematics of inflammation
In this survey talk, I describe some recent work of our group on the interactions between the innate immune system, pathogens, and injury. These simple models shed insight into the roles of pro- and anti-inflammatory cytokines. I will speculate about some possible mechanisms for periodic and recurrent inflammatory pathologies such as Familial Mediterranean Fever and TNF receptor associated periodic fever syndrome (TRAPS).
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The excited cortex: phosphenes, trails, and other visual confections
The cortex sits at a balanced state and thus it is very easy to tip this balance.In this talk, I will discuss some thoughts on epilepsy, flicker phosphenes (flicker induced hallucinations), LSD trails, and up and down states in terms of simple firing rate models.
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