On the basis of the evident ability of neuronal olfactory systems to evaluate the intensity of an odorous stimulus and also recognize the identity of the odorant over a large range of concentrations, a few biologically-realistic hypotheses on some of the underlying neural processes are made.  The mathematical implementation of such phenomenological postulates allows to infer quite simply a functional relationship between the mean firing-rate of the neural population and the concentration of any odorant as well as the statistical distribution of the sensitivity of any receptor neuron to any odorant across the population; both of them turn out to be power-laws and an arithmetic, testable relationship between the respective exponents naturally appears . In order to compare quantitatively the prediction of power-law dependence of population mean firing-rate on odorant concentration, a probabilistic model is created to extract information from data available in the experimental literature which, inter alia, allows to pool together several data-sets and hence increase statistical accuracy . The values of the free parameters of the model are estimated by a Bayesian maximum likelihood inference which keeps into account the prior distribution of the parameters making use of theorems from Information Geometry . The eventual goodness of fit is quantified by means of a distribution-independent test. The probabilistic model results to be accurate, thus confirming the theoretical prediction of a power-law dependence on odorant concentration. The experimental data available about the distribution of sensitivities also agree with the other predictions, though they are not statistically sufficient for a very stringent verification. The theory also suggests a possible explanation for the range of values of the exponent of the sensitivity power-law found in experiments.
On the basis of the evident ability of neuronal olfactory systems to evaluate the intensity of an odorous stimulus and at the same time also recognise the identity of the odorant over a large range of concentrations, a few biologically-realistic hypotheses on some of the underlying neural processes are made. In particular, it is assumed that the receptor neurons mean firing-rate scale monotonically with odorant intensity, and that the receptor sensitivities range widely across odorants and receptor neurons hence leading to highly distributed representations of the stimuli. The mathematical implementation of the phenomenological postulates allows for inferring explicit functional relationships between some measurable quantities. It results that both the dependence of the mean firing-rate on odorant concentration and the statistical distribution of receptor sensitivity across the neuronal population are power-laws , whose respective exponents are in an arithmetic, testable relationship . In order to test quantitatively the prediction of power-law dependence of population mean firing-rate on odorant concentration, a probabilistic model is created to extract information from data available in the experimental literature . The values of the free parameters of the model are estimated by an info-geometric Bayesian maximum-likelihood inference which keeps into account the prior distribution of the parameters . The eventual goodness of fit is quantified by means of a distribution-independent test. CONTINUES
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at the same time also recognise
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In particular, it is assumed that the receptor neurons mean firing-rate scale monotonically with odorant intensity, and that the receptor sensitivities range widely across odorants and receptor neurons hence leading to highly distributed representations of the stimuli.
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to infer quite simply a functional relationship between the
for inferring explicit functional relationships between some measurable quantities. It results that both the dependence of the
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firing-rate of the neural population and the concentration of any odorant as well as the
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the sensitivity of any receptor neuron to any odorant across the population; both of them turn out to be
receptor sensitivity across the neuronal population are
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between the respective exponents naturally appears
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test
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which, inter alia, allows to pool together several data-sets and hence increase statistical accuracy
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a Bayesian maximum likelihood
an info-geometric Bayesian maximum-likelihood
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making use of theorems from Information Geometry
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The probabilistic model results to be accurate, thus confirming the theoretical prediction of a power-law dependence on odorant concentration. The experimental data available about the distribution of sensitivities also agree with the other predictions, though they are not statistically sufficient for a very stringent verification. The theory also suggests a possible explanation for the range of values of the exponent of the sensitivity power-law found in experiments.
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