732 research outputs found
An Algorithm for constructing Hjelmslev planes
Projective Hjelmslev planes and Affine Hjelmselv planes are generalisations
of projective planes and affine planes. We present an algorithm for
constructing a projective Hjelmslev planes and affine Hjelsmelv planes using
projective planes, affine planes and orthogonal arrays. We show that all
2-uniform projective Hjelmslev planes, and all 2-uniform affine Hjelsmelv
planes can be constructed in this way. As a corollary it is shown that all
2-uniform Affine Hjelmselv planes are sub-geometries of 2-uniform projective
Hjelmselv planes.Comment: 15 pages. Algebraic Design Theory and Hadamard matrices, 2014,
Springer Proceedings in Mathematics & Statistics 13
Texture Coding in the Rat Whisker System: Slip-Stick Versus Differential Resonance
Rats discriminate surface textures using their whiskers (vibrissae), but how whiskers extract texture information, and how this information is encoded by the brain, are not known. In the resonance model, whisker motion across different textures excites mechanical resonance in distinct subsets of whiskers, due to variation across whiskers in resonance frequency, which varies with whisker length. Texture information is therefore encoded by the spatial pattern of activated whiskers. In the competing kinetic signature model, different textures excite resonance equally across whiskers, and instead, texture is encoded by characteristic, nonuniform temporal patterns of whisker motion. We tested these models by measuring whisker motion in awake, behaving rats whisking in air and onto sandpaper surfaces. Resonant motion was prominent during whisking in air, with fundamental frequencies ranging from approximately 35 Hz for the long Delta whisker to approximately 110 Hz for the shorter D3 whisker. Resonant vibrations also occurred while whisking against textures, but the amplitude of resonance within single whiskers was independent of texture, contradicting the resonance model. Rather, whiskers resonated transiently during discrete, high-velocity, and high-acceleration slip-stick events, which occurred prominently during whisking on surfaces. The rate and magnitude of slip-stick events varied systematically with texture. These results suggest that texture is encoded not by differential resonant motion across whiskers, but by the magnitude and temporal pattern of slip-stick motion. These findings predict a temporal code for texture in neural spike trains
Stable Propagation of a Burst Through a One-Dimensional Homogeneous Excitatory Chain Model of Songbird Nucleus HVC
We demonstrate numerically that a brief burst consisting of two to six spikes
can propagate in a stable manner through a one-dimensional homogeneous
feedforward chain of non-bursting neurons with excitatory synaptic connections.
Our results are obtained for two kinds of neuronal models, leaky
integrate-and-fire (LIF) neurons and Hodgkin-Huxley (HH) neurons with five
conductances. Over a range of parameters such as the maximum synaptic
conductance, both kinds of chains are found to have multiple attractors of
propagating bursts, with each attractor being distinguished by the number of
spikes and total duration of the propagating burst. These results make
plausible the hypothesis that sparse precisely-timed sequential bursts observed
in projection neurons of nucleus HVC of a singing zebra finch are intrinsic and
causally related.Comment: 13 pages, 6 figure
Hjelmslev Geometry of Mutually Unbiased Bases
The basic combinatorial properties of a complete set of mutually unbiased
bases (MUBs) of a q-dimensional Hilbert space H\_q, q = p^r with p being a
prime and r a positive integer, are shown to be qualitatively mimicked by the
configuration of points lying on a proper conic in a projective Hjelmslev plane
defined over a Galois ring of characteristic p^2 and rank r. The q vectors of a
basis of H\_q correspond to the q points of a (so-called) neighbour class and
the q+1 MUBs answer to the total number of (pairwise disjoint) neighbour
classes on the conic.Comment: 4 pages, 1 figure; extended list of references, figure made more
illustrative and in colour; v3 - one more figure and section added, paper
made easier to follow, references update
Identification of Neural Circuits by Imaging Coherent Electrical Activity with FRET-Based Dyes
AbstractWe show that neurons that underlie rhythmic patterns of electrical output may be identified by optical imaging and frequency-domain analysis. Our contrast agent is a two-component dye system in which changes in membrane potential modulate the relative emission between a pair of fluorophores. We demonstrate our methods with the circuit responsible for fictive swimming in the isolated leech nerve cord. The output of a motor neuron provides a reference signal for the phase-sensitive detection of changes in fluorescence from individual neurons in a ganglion. We identify known and possibly novel neurons that participate in the swim rhythm and determine their phases within a cycle. A variant of this approach is used to identify the postsynaptic followers of intracellularly stimulated neurons
Modeling of Spiking-Bursting Neural Behavior Using Two-Dimensional Map
A simple model that replicates the dynamics of spiking and spiking-bursting
activity of real biological neurons is proposed. The model is a two-dimensional
map which contains one fast and one slow variable. The mechanisms behind
generation of spikes, bursts of spikes, and restructuring of the map behavior
are explained using phase portrait analysis. The dynamics of two coupled maps
which model the behavior of two electrically coupled neurons is discussed.
Synchronization regimes for spiking and bursting activity of these maps are
studied as a function of coupling strength. It is demonstrated that the results
of this model are in agreement with the synchronization of chaotic
spiking-bursting behavior experimentally found in real biological neurons.Comment: 9 pages, 12 figure
Gain without population inversion in V-type systems driven by a frequency-modulated field
We obtain gain of the probe field at multiple frequencies in a closed
three-level V-type system using frequency modulated pump field. There is no
associated population inversion among the atomic states of the probe
transition. We describe both the steady-state and transient dynamics of this
system. Under suitable conditions, the system exhibits large gain
simultaneously at series of frequencies far removed from resonance. Moreover,
the system can be tailored to exhibit multiple frequency regimes where the
probe experiences anomalous dispersion accompanied by negligible
gain-absorption over a large bandwidth, a desirable feature for obtaining
superluminal propagation of pulses with negligible distortion.Comment: 10 pages + 8 figures; To appear in Physical Review
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