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From the theoretical point of view, population coding is one of a few mathematically well-formulated problems in neuroscience. It grasps the essential features of neural coding and yet, is simple enough for theoretic analysis <ref name="Wu">S Wu, S Amari, and H Nakahara. 2002. Population Coding and Decoding in a Neural Field: A Computational Study. ''Neural Computation'' 14: 999-1026</ref>. Experimental studies have revealed that this coding paradigm is widely used in the sensor and motor areas of the brain. For example, in the visual area [[lobe|medial temporal]] (MT), neurons are tuned to the moving direction <ref name="Maunsell">Maunsell, J. H. R., and Van Essen, D. C. 1983. Functional properties of neurons in middle temporal visual area of the Macaque monkey. I. Selectivity for stimulus direction, speed, and orientation. ''Journal of Neurophysiology'' 49:1127–1147</ref>. In response to an object moving in a particular direction, many neurons in MT fire, with a noise-corrupted and [[bell curve| bell-shaped]] activity pattern across the population. The moving direction of the object is retrieved from the population activity, to be immune from the fluctuation existing in a single neuron’s signal.
Population coding has a number of advantages, including reduction of uncertainty due to neuronal [[variability]] and the ability to represent a number of different stimulus attributes simultaneously. Population coding is also much faster than rate coding and can reflect changes in the stimulus conditions nearly instantaneously <ref name="Hubel">Hubel, D. H. and Wiesel, T. N.. 1959. Receptive fields of single neurons in the cat's striate cortex. ''
====Position Coding====
A typical population code involves neurons with a Gaussian tuning curve whose means vary linearly with the stimulus intensity, meaning that the neuron responds most strongly (in terms of spikes per second) to a stimulus near the mean. The actual intensity could be recovered as the stimulus level corresponding to the mean of the neuron with the greatest response. However, the noise inherent in neural responses means that a maximum likelihood estimation function is more accurate.
This type of code is used to encode continuous variables such as joint position, eye position, color, or sound frequency. Any individual neuron is too noisy to faithfully encode the variable using rate coding, but an entire population ensures greater fidelity and precision.
<gallery>
File:PopulationCode.png|Plot of typical position coding.
File:NoisyNeuralResponse.png|Neural responses are noisy and unreliable.
</gallery>
== References ==
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