188 research outputs found
Computing the local field potential (LFP) from integrate-and-fire network models
Leaky integrate-and-fire (LIF) network models are commonly used to study how the spiking dynamics of neural networks changes with stimuli, tasks or dynamic network states. However, neurophysiological studies in vivo often rather measure the mass activity of neuronal microcircuits with the local field potential (LFP). Given that LFPs are generated by spatially separated currents across the neuronal membrane, they cannot be computed directly from quantities defined in models of point-like LIF neurons. Here, we explore the best approximation for predicting the LFP based on standard output from point-neuron LIF networks. To search for this best "LFP proxy", we compared LFP predictions from candidate proxies based on LIF network output (e.g, firing rates, membrane potentials, synaptic currents) with "ground-truth" LFP obtained when the LIF network synaptic input currents were injected into an analogous three-dimensional (3D) network model of multi-compartmental neurons with realistic morphology, spatial distributions of somata and synapses. We found that a specific fixed linear combination of the LIF synaptic currents provided an accurate LFP proxy, accounting for most of the variance of the LFP time course observed in the 3D network for all recording locations. This proxy performed well over a broad set of conditions, including substantial variations of the neuronal morphologies. Our results provide a simple formula for estimating the time course of the LFP from LIF network simulations in cases where a single pyramidal population dominates the LFP generation, and thereby facilitate quantitative comparison between computational models and experimental LFP recordings in vivo
Estimation of Thalamocortical and Intracortical Network Models from Joint Thalamic Single-Electrode and Cortical Laminar-Electrode Recordings in the Rat Barrel System
A new method is presented for extraction of population firing-rate models for
both thalamocortical and intracortical signal transfer based on stimulus-evoked
data from simultaneous thalamic single-electrode and cortical recordings using
linear (laminar) multielectrodes in the rat barrel system. Time-dependent
population firing rates for granular (layer 4), supragranular (layer 2/3), and
infragranular (layer 5) populations in a barrel column and the thalamic
population in the homologous barreloid are extracted from the high-frequency
portion (multi-unit activity; MUA) of the recorded extracellular signals. These
extracted firing rates are in turn used to identify population firing-rate
models formulated as integral equations with exponentially decaying coupling
kernels, allowing for straightforward transformation to the more common
firing-rate formulation in terms of differential equations. Optimal model
structures and model parameters are identified by minimizing the deviation
between model firing rates and the experimentally extracted population firing
rates. For the thalamocortical transfer, the experimental data favor a model
with fast feedforward excitation from thalamus to the layer-4 laminar population
combined with a slower inhibitory process due to feedforward and/or recurrent
connections and mixed linear-parabolic activation functions. The extracted
firing rates of the various cortical laminar populations are found to exhibit
strong temporal correlations for the present experimental paradigm, and simple
feedforward population firing-rate models combined with linear or mixed
linear-parabolic activation function are found to provide excellent fits to the
data. The identified thalamocortical and intracortical network models are thus
found to be qualitatively very different. While the thalamocortical circuit is
optimally stimulated by rapid changes in the thalamic firing rate, the
intracortical circuits are low-pass and respond most strongly to slowly varying
inputs from the cortical layer-4 population
Excitons in type-II quantum dots: Finite offsets
Quantum size effects for an exciton attached to a spherical quantum dot are
calculated by a variational approach. The band line-ups are assumed to be
type-II with finite offsets. The dependence of the exciton binding energy upon
the dot radius and the offsets is studied for different sets of electron and
hole effective masses
Non-Hermitian von Roos Hamiltonian's -weak-pseudo-Hermiticity, isospectrality and exact solvability
A complexified von Roos Hamiltonian is considered and a Hermitian first-order
intertwining differential operator is used to obtain the related position
dependent mass -weak-pseudo-Hermitian Hamiltonians. Using a
Liouvillean-type change of variables, the -weak-pseudo-Hermitian von Roos
Hamiltonians H(x) are mapped into the traditional Schrodinger Hamiltonian form
H(q), where exact isospectral correspondence between H(x) and H(q) is obtained.
Under a user-friendly position dependent mass settings, it is observed that for
each exactly-solvable -weak-pseudo-Hermitian reference-Hamiltonian
H(q)there is a set of exactly-solvable -weak-pseudo-Hermitian isospectral
target-Hamiltonians H(x). A non-Hermitian PT-symmetric Scarf II and a
non-Hermitian periodic-type PT-symmetric Samsonov-Roy potentials are used as
reference models and the corresponding -weak-pseudo-Hermitian isospectral
target-Hamiltonians are obtained.Comment: 11 pages, no figures
Reversal of the Charge Transfer between Host and Dopant Atoms in Semiconductor Nanocrystals
We present ab initio density functional calculations that show P (Al) dopant
atoms in small hydrogen-terminated Si crystals to be negatively (positively)
charged. These signs of the dopant charges are reversed relative to the same
dopants in bulk Si. We predict this novel reversal of the dopant charge (and
electronic character of the doping) to occur at crystal sizes of order 100 Si
atoms. We explain it as a result of competition between fundamental principles
governing charge transfer in bulk semiconductors and molecules and predict it
to occur in nanocrystals of most semiconductors.Comment: 4 pages, 4 figures (3 in color), 2 table
Ordering ambiguity revisited via position dependent mass pseudo-momentum operators
Ordering ambiguity associated with the von Roos position dependent mass (PDM)
Hamiltonian is considered. An affine locally scaled first order differential
introduced, in Eq.(9), as a PDM-pseudo-momentum operator. Upon intertwining our
Hamiltonian, which is the sum of the square of this operator and the potential
function, with the von Roos d-dimensional PDM-Hamiltonian, we observed that the
so-called von Roos ambiguity parameters are strictly determined, but not
necessarily unique. Our new ambiguity parameters' setting is subjected to
Dutra's and Almeida's [11] reliability test and classified as good ordering.Comment: 10 pages, no figures, revised/expanded, mathematical presentations in
section 2 (Especially, the typological Errors in Eqs.(9)-(12))are now
corrected. To appear in the Int. J. Theor. Phy
Applications of Information Theory to Analysis of Neural Data
Information theory is a practical and theoretical framework developed for the
study of communication over noisy channels. Its probabilistic basis and
capacity to relate statistical structure to function make it ideally suited for
studying information flow in the nervous system. It has a number of useful
properties: it is a general measure sensitive to any relationship, not only
linear effects; it has meaningful units which in many cases allow direct
comparison between different experiments; and it can be used to study how much
information can be gained by observing neural responses in single trials,
rather than in averages over multiple trials. A variety of information
theoretic quantities are commonly used in neuroscience - (see entry
"Definitions of Information-Theoretic Quantities"). In this entry we review
some applications of information theory in neuroscience to study encoding of
information in both single neurons and neuronal populations.Comment: 8 pages, 2 figure
Shape-invariant quantum Hamiltonian with position-dependent effective mass through second order supersymmetry
Second order supersymmetric approach is taken to the system describing motion
of a quantum particle in a potential endowed with position-dependent effective
mass. It is shown that the intertwining relations between second order partner
Hamiltonians may be exploited to obtain a simple shape-invariant condition.
Indeed a novel relation between potential and mass functions is derived, which
leads to a class of exactly solvable model. As an illustration of our
procedure, two examples are given for which one obtains whole spectra
algebraically. Both shape-invariant potentials exhibit harmonic-oscillator-like
or singular-oscillator-like spectra depending on the values of the
shape-invariant parameter.Comment: 16 pages, 5 figs; Present e-mail of AG: [email protected]
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