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SUMMARY:Spatio-temporal canards & bifurcation delay in neural reaction-dif
fusion systems
DTSTART;VALUE=DATE-TIME:20180710T020000Z
DTEND;VALUE=DATE-TIME:20180710T023000Z
DTSTAMP;VALUE=DATE-TIME:20211026T144140Z
UID:indico-contribution-54-158@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Theodore Vo (Florida State University)\nNeural spiki
ng and bursting rhythms in space-clamped (i.e.\, ODE) models are typically
driven by either canard dynamics or slow passage through Hopf bifurcation
s. In both cases\, solutions which are attracted to quasi-stationary state
s (QSS) sufficiently before a fold or Hopf bifurcation remain near the QSS
for long times after the states have become repelling\, resulting in a si
gnificant delay in the loss of stability and hence in the onset of oscilla
tions. In this work\, we present the spatio-temporal analogues of these de
layed bifurcation phenomena in multi-time-scale reaction-diffusion equatio
ns. We show the existence of canard-induced bursting rhythms in a spatiall
y extended model of the electrical activity in pituitary cells. We then de
rive asymptotic formulas for the space-time boundaries that act as buffers
beyond which solutions cannot remain near the repelling QSS (and hence at
which the delayed onset of oscillations must occur) for slow passage thro
ugh Hopf bifurcations in reaction-diffusion equations.\n\nThis is joint wo
rk with Tasso J. Kaper (Boston University).\n\nhttps://conferences.maths.u
nsw.edu.au/event/2/contributions/158/
LOCATION:University of Sydney New Law School/--026
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/158/
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SUMMARY:Low- and high-waking modes in the corticothalamic system
DTSTART;VALUE=DATE-TIME:20180710T010000Z
DTEND;VALUE=DATE-TIME:20180710T013000Z
DTSTAMP;VALUE=DATE-TIME:20211026T144140Z
UID:indico-contribution-54-182@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Paula Sanz-Leon (University of Sydney)\nIn this talk
presented at the Mathematical Neuroscience Subgroup Minisymposium I will
discuss a numerical analysis of the steady-state solutions of a neural fie
ld model of the corticothalamic system. The independent synaptic connectio
ns of the corticothalamic model define an eight-dimensional parameter spac
e\, while specific combinations of these connections parameterize intracor
tical\, corticothalamic\, and intrathalamic loops. \n\nThe first part of t
he analysis consists of a systematic identification of multistable regions
for physiological parameter ranges representing normal arousal waking sta
tes in adult humans. Parameter values have been derived from human electro
encephalographic recordings (EEG). The key results are the confirmation of
the existence of up to five steady-state solutions\, up to three of which
are linearly stable. The presence of multiple stable steady-state solutio
ns implies that the system has enough degrees of freedom to capture multip
le operating points (e.g.\, mutiple global brain states). Indeed\, two out
of the three linearly stable steady-state equilibria represent two waking
modes for adult human physiology while resting with the eyes closed. Thes
e two modes are termed the low- and high- waking modes. \n\nWhile the low-
waking mode has been previously identified with normal brain activity duri
ng quiet wakefulness\, the high-waking mode has not been fully characteriz
ed. The second part of the analysis focus on (i) the spectral features of
high-waking mode states\; (ii) the nonlinear attractors between the two wa
king modes\; and\, (iii) the switching dynamics between the low- and high-
waking modes using small amplitude and bandlimited random perturbations.\n
\nWe argue that the high-waking mode may represent hyperarousal waking sta
tes. This result opens up the possibility to predict and identify subtypes
of primary insomnia in which cortical hyperarousal is the main hallmark f
rom human neuroimaging data.\n\nhttps://conferences.maths.unsw.edu.au/even
t/2/contributions/182/
LOCATION:University of Sydney New Law School/--026
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/182/
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SUMMARY:Volume transmission and neurotransmitter homeostasis
DTSTART;VALUE=DATE-TIME:20180710T003000Z
DTEND;VALUE=DATE-TIME:20180710T010000Z
DTSTAMP;VALUE=DATE-TIME:20211026T144140Z
UID:indico-contribution-54-181@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Janet Best (The Ohio State University)\nIn volume tr
ansmission\, neurons in one brain nucleus send their axons to a second nuc
leus where neurotransmitter is released into the extracellular space. In [
1] we showed how to calculate the average amount of neurotransmitter at di
fferent parts of the extracellular space\, depending on neural properties
and the geometry of the projections and extracellular space. We showed how
to formulate questions as boundaries value problems for the heat equation
with stochastically switching boundary conditions\, and we derived result
s in one space dimension. \n\nHere we discuss the two- and three-dimension
al problems\, along with mechanistic models of neurotransmitter homeostasi
s.\n\n[1] Lawley\, Best\, Reed 2016\n\nhttps://conferences.maths.unsw.edu.
au/event/2/contributions/181/
LOCATION:University of Sydney New Law School/--026
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/181/
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SUMMARY:Temperature sensitivity of PO/AH neurons
DTSTART;VALUE=DATE-TIME:20180710T013000Z
DTEND;VALUE=DATE-TIME:20180710T020000Z
DTSTAMP;VALUE=DATE-TIME:20211026T144140Z
UID:indico-contribution-54-174@conferences.maths.unsw.edu.au
DESCRIPTION:Speakers: Martin Wechselberger (University of Sydney)\nThermor
egulatory responses are partially controlled by the preoptic area and ante
rior hypothalamus (PO/AH)\, which contains a mixed population of temperatu
re-sensitive and insensitive neurons. In [1] based on physiological data\,
a Hodgkin-Huxley-like conductance based model was constructed. This model
suggests that most PO/AH neurons have the same types of ionic channels\,
but different levels of channel expression can explain the inherent proper
ties of the various types of temperature-sensitive and insensitive neurons
which is encoded in their frequency sensitivity relative to temperature.\
n\nHere we present a detailed bifurcation analysis of this model to confir
m these observations. We focus on three main physiological bifurcation par
ameters\, the temperature T and the maximum conductances of two specific b
ackground potassium leak channels\, $g_{task}$ and $g_{trek}$\, that are k
nown to be expressed in these PO/AH neurons. These three bifurcation param
eters are sufficient to explain the dynamics of PO/AH neurons observed in
experiments. \n\nIf time permits\, we also discuss the multiple timescales
inherent in this model and explain the creation of action potentials base
d on a geometric singular perturbation analysis.\n\n[1] Wechselberger *et
al.*\, 2006\n\nhttps://conferences.maths.unsw.edu.au/event/2/contributions
/174/
LOCATION:University of Sydney New Law School/--026
URL:https://conferences.maths.unsw.edu.au/event/2/contributions/174/
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