Speaker
Description
In various statistically defined situations, like referendum, epidemic threshold, mass service process or a chemical sensor the probability of overall output coincides with the probability that a threshold $N_0$ number of elementary events has been achieved. The latter depends on the probability $p$ that a single elementary event happens. Elementary event for a referendum case is the positive vote of a single voter; for a chemical sensor $-$ is the ligand binding by a single receptor in the sensor. The probability $p$ of elementary event may depend on some external factor $-$ campaigning type L for the referendum case, or the ligand type L applied in the case of chemical sensor. This constitutes the selectivity of elementary event. Naturally, the probability that the threshold $N_0$ is achieved depends on L as well. This constitutes the selectivity of essential event. Any of the two selectivities can be expressed by means of a dimensionless non-negative number. We derive a concise mathematical expression, for comparing the two selectivities, based on the incomplete beta-function, or on a continued fraction. Possible application in a chemical sensor is discussed.
