Hey, I am a mathematician, but working with all these experimentalist, you gaotta call it a lab.
- Julia Arciera (CBSG)
- Stefanos Folias (CBSG)
- Cheng Ly (NSF)
- Stephanie Hoogendoorn
- Aushra Abouzeid
- Angela Reynolds
- Sergio Verduzco
- Sashi Marella
- Alex Urban
I also frequently work with undergraduates and I am always willing to
supervise them on various projects of interest.
This is a brief summary of some of the work that we do here. There are
always tons of other projects!
Noisy oscillators How does noise interact with
rhythmic phenomena in the nervous system and other areas of biology?
We use small noise expansion and the phase resetting curve of
oscillators to understand how correlated inputs can affect the
synchrony or both coupled and uncoupled oscillators. We also
characterize what types of oscillators are optimal fro transmitting
correlated inputs to correlated outputs. This work is with the Urban
lab as well as with students Aushra Abouzeid & Sashi Marella and
postdoc Cheng Ly.
Dynamics and phase resetting The phase resetting
curve (PRC) tells us how the timing of inputs shift the timing of
oscillators. The shapse of these curves are important both in coupled
and in forced systems and play a critical role in synchronization. In
neurons, there are many currents which are subject to modulation and
these currents can have a strong affect on the shape and sensitivity
of the PRC. Uncorrelated noise and coupling to other oscillators also
alter the shape of the PRC. We use nonlinear dynamics and simulations
to study how these curves are changed. This work is with postdoc
TaeWook Ko, former student, Boris Gutkin, and in collaboration with several experimentalists
including Nathan Urban (CMU), Charlie Wilson (UTSA), and Theoden
Pattern formation in neural systems This is fun
stuff. I continue a long held interest in hallucinations and
phosphenes as well as various types of pattern sensitive and reflex
epilepsies. I am interested in mechanisms through which flickering
light can induce geometric hallucinations as well as seizures in
susceptible populations. This work is with Mark Bodner and Sergio
Verduzco. With George Oster and Alistair Boettiger, we have
revisited early work on the pigmentation and shell construction of
Waves and persistent states in neural systems Due to
the massive recurrent interactions between neurons, networks are able
to sustain various types of persistent activity. By persistent, I mean
activity that remains after a stimulus is removed. Working memory is
believed to be such a state - a localized region of cortex remains
active until the memory task is completed. We have several types of
models involving combinations of multi-region interactions,
multi-layer interactions and facilitation. This work is with Stephanie
Hoogendoorn, Mark Bodner, and Sergio Verduzco.
Another type of persistent activity comes in the form of propagating
waves. These are observed in brain slices, cell cultures, and in
vivo. We use spatial networks of neurons and singular perturbation
theory to study propagation of activity in one- and
two-dimensions. This work is with Jian-young Wu (Georgetown), Sashi
marella, and Julie Goulet.
Modeling the inflammatory response Pathogens, damage,
and other insults to the body can result in inflammation which can
sometimes be worse than the original insult. We work closely with
several people at UPMC (Gilles Clermont, Yoram Vodovotz) developing
models for the signalling pathways and responses of the innate immune
system. We have applied these models to influenza, malaria, lung
inflammation, necrotizing enterocolitis, and multiple organ
dysfunction syndrome. This is work with David Swigon, Jon Rubin, and
students, Angela Reynolds and Ian Price.