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, $\langle \langle T_a^3 \rangle \rangle$, to the normalized second cumulant $\langle \langle T_a^2 \rangle \rangle$. For a broad Gaussian beam profile it is found that $\langle \langle T_a^3 \rangle \rangle= \frac{16}{5} \langle \langle T_a^2 \rangle \rangle^2$. This is in good agreement with data of optical experiments.Comment: 16 pages revtex, 8 separate postscript figure

Correlation between cohesive energy and mixing rate in ion mixing of metallic bilayers

We have compared the mixing rate of several 5d-4d metal bilayers which form ideal solutions. We observe a strong correlation between the mixing rate and the average cohesive energy of each bilayer. A model based on the thermal spike concept is proposed to explain this behavior. The model leads to a general expression describing mixing rates in metallic bilayers

Influence of chemical driving forces in ion mixing of metallic bilayers

The effective interdiffusion coefficient of metallic bilayers under ion irradiation has been correlated with the heat of mixing of corresponding binary alloys. The results are interpreted according to Darken's theory of chemically enhanced diffusion

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