PT - JOURNAL ARTICLE AU - Dinkar Wadhwa TI - The Series of a Four-node Motif can Provide Sensitive Detection over Arbitrary Range of Signal, thereby Explain Weber’s Law in Higher-Order Sensory Processes, and Compute Logarithm AID - 10.1101/2020.04.08.032193 DP - 2020 Jan 01 TA - bioRxiv PG - 2020.04.08.032193 4099 - http://biorxiv.org/content/early/2020/07/17/2020.04.08.032193.short 4100 - http://biorxiv.org/content/early/2020/07/17/2020.04.08.032193.full AB - Weber’s law states that the ratio of the smallest perceptual change in a signal and the background signal is constant. The law is observed across the perception of weight, light intensity, and sound intensity and pitch. Conventionally, two models of perception have been proposed to explain Weber’s law, namely the logarithmic and the linear model. Later, another formulation of Weber’s law was proposed which links it with exact adaptation. This paper argues in favour of the linear model, which requires the sensory system to generate linear signal-response relationship over several orders of magnitude. To this end, a four-node motif is constructed from first principles whose series provides linear relationship between signal and response over arbitrary range of signal. The motif also reproduces the neuronal data of numerosity detection study on monkey. The series of this motif provides a general mechanism for sensitive detection over arbitrary range of signal. The series also provides a general basis for a class of bow-tie architecture where the number of receptors is much lower than the range of signal and response. Besides numerosity processing, another example of this class of bow-tie architecture that the series of this motif is able to produce is absorption spectra of cone opsins of humans. Further, the series can compute logarithm over arbitrary range of signal.Competing Interest StatementThe authors have declared no competing interest.