1,416 research outputs found
Multiple scattering of classical waves: from microscopy to mesoscopy and diffusion
A tutorial discussion of the propagation of waves in random media is
presented. In first approximation the transport of the multiple scattered waves
is given by diffusion theory, but important corrections are present. These
corrections are calculated with the radiative transfer or Schwarzschild-Milne
equation, which describes intensity transport at the ``mesoscopic'' level and
is derived from the ``microscopic'' wave equation. A precise treatment of the
diffuse intensity is derived which automatically includes the effects of
boundary layers. Effects such as the enhanced backscatter cone and imaging of
objects in opaque media are also discussed within this framework. In the second
part the approach is extended to mesoscopic correlations between multiple
scattered intensities which arise when scattering is strong. These correlations
arise from the underlying wave character. The derivation of correlation
functions and intensity distribution functions is given and experimental data
are discussed. Although the focus is on light scattering, the theory is also
applicable to micro waves, sound waves and non-interacting electrons.Comment: Review. 86 pages Latex, 32 eps-figures included. To appear in Rev.
Mod. Phy
Optimal learning rules for discrete synapses
There is evidence that biological synapses have a limited number of discrete weight states. Memory storage with such synapses behaves quite differently from synapses with unbounded, continuous weights, as old memories are automatically overwritten by new memories. Consequently, there has been substantial discussion about how this affects learning and storage capacity. In this paper, we calculate the storage capacity of discrete, bounded synapses in terms of Shannon information. We use this to optimize the learning rules and investigate how the maximum information capacity depends on the number of synapses, the number of synaptic states, and the coding sparseness. Below a certain critical number of synapses per neuron (comparable to numbers found in biology), we find that storage is similar to unbounded, continuous synapses. Hence, discrete synapses do not necessarily have lower storage capacity
A Novel Spike Distance
The discrimination between two spike trains is a fundamental problem for both experimentalists and the nervous system itself. We introduce a measure for the distance between two spike trains. The distance has a time constant as a parameter. Depending on this parameter, the distance interpolates between a coincidence detector and a rate difference counter. The dependence of the distance on noise is studied with an integrate-and-fire model. For an intermediate range of the time constants, the distance depends linearly on the noise. This property can be used to determine the intrinsic noise of a neuron
Mesoscopic phenomena in multiple light scattering
In my thesis I study mesoscopic corrections on diffuse transport. I first
describe the diffuse transport of light, using the scalar approximation and the
radiative transfer approach. Next, I focus on the correlations in transmission,
I discuss the so called C_1, C_2, C_3 decomposition and calculate each term in
detail. Finally, I discuss the full distribution functions in the transmission.
Many references and figures are included. Note, however, that much of the
work was already published or is present on the cond-mat archive.
A limited number is available as hardcopy on request ([email protected])
else 132 pages Postscript.Comment: Ph.D. thesis. 132 pages postscript; hardcopy available on reques
Third Cumulant of the total Transmission of diffuse Waves
The probability distribution of the total transmission is studied for waves
multiple scattered from a random, static configuration of scatterers. A
theoretical study of the second and third cumulant of this distribution is
presented. Within a diagrammatic approach a theory is developed which relates
the third cumulant normalized to the average, , to the normalized second cumulant . For a broad Gaussian beam profile it is found that .
This is in good agreement with data of optical experiments.Comment: 16 pages revtex, 8 separate postscript figure
The effect of neural adaptation of population coding accuracy
Most neurons in the primary visual cortex initially respond vigorously when a
preferred stimulus is presented, but adapt as stimulation continues. The
functional consequences of adaptation are unclear. Typically a reduction of
firing rate would reduce single neuron accuracy as less spikes are available
for decoding, but it has been suggested that on the population level,
adaptation increases coding accuracy. This question requires careful analysis
as adaptation not only changes the firing rates of neurons, but also the neural
variability and correlations between neurons, which affect coding accuracy as
well. We calculate the coding accuracy using a computational model that
implements two forms of adaptation: spike frequency adaptation and synaptic
adaptation in the form of short-term synaptic plasticity. We find that the net
effect of adaptation is subtle and heterogeneous. Depending on adaptation
mechanism and test stimulus, adaptation can either increase or decrease coding
accuracy. We discuss the neurophysiological and psychophysical implications of
the findings and relate it to published experimental data.Comment: 35 pages, 8 figure
A New Type of Intensity Correlation in Random Media
A monochromatic point source, embedded in a three-dimensional disordered
medium, is considered. The resulting intensity pattern exhibits a new type of
long-range correlations. The range of these correlations is infinite and their
magnitude, normalized to the average intensity, is of order , where
and are the wave number and the mean free path respectively.Comment: RevTeX, 8 pages, 3 figures, Accepted to Phys. Rev. Let
Event-driven simulations of a plastic, spiking neural network
We consider a fully-connected network of leaky integrate-and-fire neurons
with spike-timing-dependent plasticity. The plasticity is controlled by a
parameter representing the expected weight of a synapse between neurons that
are firing randomly with the same mean frequency. For low values of the
plasticity parameter, the activities of the system are dominated by noise,
while large values of the plasticity parameter lead to self-sustaining activity
in the network. We perform event-driven simulations on finite-size networks
with up to 128 neurons to find the stationary synaptic weight conformations for
different values of the plasticity parameter. In both the low and high activity
regimes, the synaptic weights are narrowly distributed around the plasticity
parameter value consistent with the predictions of mean-field theory. However,
the distribution broadens in the transition region between the two regimes,
representing emergent network structures. Using a pseudophysical approach for
visualization, we show that the emergent structures are of "path" or "hub"
type, observed at different values of the plasticity parameter in the
transition region.Comment: 9 pages, 6 figure
Deviations from the Gaussian distribution of mesoscopic conductance fluctuations
The conductance distribution of metallic mesoscopic systems is considered.
The variance of this distribution describes the universal conductance
fluctuations, yielding a Gaussian distribution of the conductance. We calculate
diagrammatically the third cumulant of this distribution, the leading deviation
from the Gaussian. We confirm random matrix theory calculations that the
leading contribution in quasi-one dimension vanishes. However, in quasi two
dimensions the third cumulant is negative, whereas in three dimensions it is
positive.Comment: 9 pages, Revtex, with eps figures,to appear in Phys Rev
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