Survival and weak chaos

Caputo Fractional Derivative and Quantum-Like Coherence

We study two forms of anomalous diffusion, one equivalent to replacing the ordinary time derivative of the standard diffusion equation with the Caputo fractional derivative, and the other equivalent to replacing the time independent diffusion coefficient of the standard diffusion equation with a monotonic time dependence. We discuss the joint use of these prescriptions, with a phenomenological method and a theoretical projection method, leading to two apparently different diffusion equations. We prove that the two diffusion equations are equivalent and design a time series that corresponds to the anomalous diffusion equation proposed. We discuss these results in the framework of the growing interest in fractional derivatives and the emergence of cognition in nature. We conclude that the Caputo fractional derivative is a signature of the connection between cognition and self-organization, a form of cognition emergence different from the other source of anomalous diffusion, which is closely related to quantum coherence. We propose a criterion to detect the action of self-organization even in the presence of significant quantum coherence. We argue that statistical analysis of data using diffusion entropy should help the analysis of physiological processes hosting both forms of deviation from ordinary scaling.

Physical models of infant mortality: implications for defects in biological systems

Reliability engineering concerned with failure of technical inanimate systems usually uses the vocabulary and notions of human mortality, e.g., infant mortality vs. senescence mortality. Yet, few data are available to support such a parallel description. Here, we focus on early-stage (infant) mortality for two inanimate systems, incandescent light bulbs and soap films, and show the parallel description is clearly valid. Theoretical considerations of the thermo-electrical properties of electrical conductors allow us to link bulb failure to inherent mechanical defects. We then demonstrate the converse, that is, knowing the failure rate for an ensemble of light bulbs, it is possible to deduce the distribution of defects in wire thickness in the ensemble. Using measurements of lifetimes for soap films, we show how this methodology links failure rate to geometry of the system; in the case presented, this is the length of the tube containing the films. In a similar manner, for a third example, the time-dependent death rate due to congenital aortic valve stenosis is related to the distribution of degrees of severity of this condition, as a function of time. The results not only validate clearly the parallel description noted above, but also point firmly to application of the methodology to humans, with the consequent ability to gain more insight into the role of abnormalities in infant mortality.