Performance evaluation of discrete event systems involving Henstock-Kurzweil integral

This paper presents a study on the performance of flexible manufacturing systems (FMSs), by using discrete event system (DES) models, considering resource losses modelled by a parameter entitled coverage factor. We conclude that the resources cell loss distribution between the tasks of a FSM is a real function that cannot be integrated, in order to calculate its primitive, in the classical sense of Riemann or Lebesgue, but only in the sense of Henstock-Kurzweil integral. Our result allows one to study more general processes where highly oscillatory functions occur. The method used to deduce the function describing the resources cell loss distribution is compared with a classical method related in the literature, respectively rational interpolants. An example has been constructed to emphasize what we believe to be, new approaches.     

Interdependence of behavioural variability and response to small stimuli in bacteria

The chemotaxis signalling network in Escherichia coli that controls the locomotion of bacteria is a classic model system for signal transduction. This pathway modulates the behaviour of flagellar motors to propel bacteria towards sources of chemical attractants. Although this system relaxes to a steady state in response to environmental changes, the signalling events within the chemotaxis network are noisy and cause large temporal variations of the motor behaviour even in the absence of stimulus. That the same signalling network governs both behavioural variability and cellular response raises the question of whether these two traits are independent. Here, we experimentally establish a fluctuation-response relationship in the chemotaxis system of living bacteria. Using this relationship, we demonstrate the possibility of inferring the cellular response from the behavioural variability measured before stimulus. In monitoring the pre- and post-stimulus switching behaviour of individual bacterial motors, we found that variability scales linearly with the response time for different functioning states of the cell. This study highlights that the fundamental relationship between fluctuation and response is not constrained to physical systems at thermodynamic equilibrium but is extensible to living cells. Such a relationship not only implies that behavioural variability and cellular response can be coupled traits, but it also provides a general framework within which we can examine how the selection of a network design shapes this interdependence.