The name is absent

86

visual scenes in the rod network. Generally, rod-rod coupling reduces the spatial resolution
of a visual image because signals are allowed to ’’diffuse” into neighboring rods. In exchange,
noise in adjacent rods is reduced by averaging the noise over a larger area, making individ-
ual rods less noisy. In order to answer the question of how coupling between salamander
rods improves the signal-to-noise ratio in visual scenes, we use the measurements made in
the first part of this work to create a linear, two-dimensional model of the salamander rod
network.

5.4.1 Cableequationinonedimension

The cable equation describes the electrical potential as a function of time and space in a lossy
conductor when current is injected along its length. Such a conductor has terms represent-
ing the resistivity, distributed radial capacitance, and radial loss resistance, and gives rise
to the differential equation 5.2. The originator of this equation is William Thompson, who
studied it in describing the electrical losses in the first undersea cable between the US and
Britain for telegraph communications, built in the mid 19th century. At that time there was
no way to amplify the signal in the cable as it lay beneath the Atlantic ocean, so the quality of
the conductor was very important. From his theoretical analysis, he advocated new ways of
manufacturing to reduce the parasitic capacitance and resistance. For work on the subma-
rine telegraph cable and thermodynamics, Thompson was knighted, and later adopted the
title of Lord Kelvin [21]. More recently, the cable equation has been used extensively in neu-
roscience to describe the propagation of electrical potential along the axons and dendrites

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