73 research outputs found
On Inverse Scattering at a Fixed Energy for Potentials with a Regular Behaviour at Infinity
We study the inverse scattering problem for electric potentials and magnetic
fields in \ere^d, d\geq 3, that are asymptotic sums of homogeneous terms at
infinity. The main result is that all these terms can be uniquely reconstructed
from the singularities in the forward direction of the scattering amplitude at
some positive energy.Comment: This is a slightly edited version of the previous pape
Assessment of the left ventricular function in normotensive prediabetics: a tissue Doppler echocardiography study
Biophysical Basis for Three Distinct Dynamical Mechanisms of Action Potential Initiation
Transduction of graded synaptic input into trains of all-or-none action
potentials (spikes) is a crucial step in neural coding. Hodgkin identified three
classes of neurons with qualitatively different analog-to-digital transduction
properties. Despite widespread use of this classification scheme, a
generalizable explanation of its biophysical basis has not been described. We
recorded from spinal sensory neurons representing each class and reproduced
their transduction properties in a minimal model. With phase plane and
bifurcation analysis, each class of excitability was shown to derive from
distinct spike initiating dynamics. Excitability could be converted between all
three classes by varying single parameters; moreover, several parameters, when
varied one at a time, had functionally equivalent effects on excitability. From
this, we conclude that the spike-initiating dynamics associated with each of
Hodgkin's classes represent different outcomes in a nonlinear
competition between oppositely directed, kinetically mismatched currents. Class
1 excitability occurs through a saddle node on invariant circle bifurcation when
net current at perithreshold potentials is inward (depolarizing) at steady
state. Class 2 excitability occurs through a Hopf bifurcation when, despite net
current being outward (hyperpolarizing) at steady state, spike initiation occurs
because inward current activates faster than outward current. Class 3
excitability occurs through a quasi-separatrix crossing when fast-activating
inward current overpowers slow-activating outward current during a stimulus
transient, although slow-activating outward current dominates during constant
stimulation. Experiments confirmed that different classes of spinal lamina I
neurons express the subthreshold currents predicted by our simulations and,
further, that those currents are necessary for the excitability in each cell
class. Thus, our results demonstrate that all three classes of excitability
arise from a continuum in the direction and magnitude of subthreshold currents.
Through detailed analysis of the spike-initiating process, we have explained a
fundamental link between biophysical properties and qualitative differences in
how neurons encode sensory input
Asymptotic formulas with sharp remainder estimates for bound states of Schrödinger operators, I
Solvability of the general boundary-value problem for the linearized nonstationary system of Navier-Stokes equations
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