Maximal Sensitive Dependence and the Optimal Path to Epidemic Extinction

Extinction of an epidemic or a species is a rare event that occurs due to a large, rare stochastic fluctuation. Although the extinction process is dynamically unstable, it follows an optimal path that maximizes the probability of extinction. We show that the optimal path is also directly related to the finite-time Lyapunov exponents of the underlying dynamical system in that the optimal path displays maximum sensitivity to initial conditions. We consider several stochastic epidemic models, and examine the extinction process in a dynamical systems framework. Using the dynamics of the finite-time Lyapunov exponents as a constructive tool, we demonstrate that the dynamical systems viewpoint of extinction evolves naturally toward the optimal path.Comment: 21 pages, 5 figures, Final revision to appear in Bulletin of Mathematical Biolog

Hypertemporal Imaging of NYC Grid Dynamics

Hypertemporal visible imaging of an urban lightscape can reveal the phase of the electrical grid granular to individual housing units. In contrast to in-situ monitoring or metering, this method offers broad, persistent, real-time, and non-permissive coverage through a single camera sited at an urban vantage point. Rapid changes in the phase of individual housing units signal changes in load (e.g., appliances turning on and off), while slower building- or neighborhood-level changes can indicate the health of distribution transformers. We demonstrate the concept by observing the 120 Hz flicker of lights across a NYC skyline. A liquid crystal shutter driven at 119.75 Hz down-converts the flicker to 0.25 Hz, which is imaged at a 4 Hz cadence by an inexpensive CCD camera; the grid phase of each source is determined by analysis of its sinusoidal light curve over an imaging "burst" of some 25 seconds. Analysis of bursts taken at ~15 minute cadence over several hours demonstrates both the stability and variation of phases of halogen, incandescent, and some fluorescent lights. Correlation of such results with ground-truth data will validate a method that could be applied to better monitor electricity consumption and distribution in both developed and developing cities.Comment: This paper uses astronomical techniques applied to the study of urban lights. This research is reproducible but the data access is restricted. A Github repository contains all code supporting this research as well as additional material: https://github.com/fedhere/detect12

Recurrent deficit irrigation and fruit harvest affect tree water relations and fruitlet growth in ‘Valencia’ orange

Background. Partial rootzone drying is an irrigation strategy known for increasing water use efficiency without significantly affecting tree water status. ‘Valencia’ oranges have a very long development period and nearly mature fruit and new fruitlets may be present at the same time on the tree, competing for water and assimilates. Objectives. The present study investigates the effect of recurrent deficit irrigation and fruit harvest on tree water status and fruitlet growth of ‘Valencia’ orange. Methods. Forty-eight adult trees were exposed to three irrigation treatments for seven years (2007-2013): irrigation with 100% of ETc (CI), continuous deficit irrigation (DI, 50% of CI) and partial root-zone drying (PRD, 50% of CI on alternated sides of the root-zone). In spring 2014, stem water potential (Ψstem) and continuous measurements of sap flow and fruitlet growth were recorded before (May) and after (June) the harvest of mature fruit. Results. No differences in Ψstem were found among irrigation treatments, while Ψstem was lower in June than in May at midday. In both May and June, sap flow density (not sap flow per tree) was higher in DI than in CI and PRD trees suggesting more efficient water uptake/transport in the former. In May, DI and PRD fruit showed lower daily relative growth rate (RGR) than CI fruit due to a possible shortage of carbon and nutrients. After removing mature fruits, differences among irrigation treatments were canceled. Sap flow was directly related to fruit RGR at low sap flow rates, but inversely related to RGR at high sap flow rates. Conclusions. Our data show that the presence of maturing fruit does not impact the water status of ‘Valencia’ trees, while it may transiently limit fruitlet growth (by source limitation) in deficit irrigated trees

On the Mass to Charge Ratio of Neutron Cores and Heavy Nuclei

We determine theoretically the relation between the total number of protons $N_{p}$ and the mass number $A$ (the charge to mass ratio) of nuclei and neutron cores with the model recently proposed by Ruffini et al. (2007) and we compare it with other $N_p$ versus $A$ relations: the empirical one, related to the Periodic Table, and the semi-empirical relation, obtained by minimizing the Weizs\"{a}cker mass formula. We find that there is a very good agreement between all the relations for values of $A$ typical of nuclei, with differences of the order of per cent. Our relation and the semi-empirical one are in agreement up to $A\sim 10^4$; for higher values, we find that the two relations differ. We interprete the different behaviour of our theoretical relation as a result of the penetration of electrons (initially confined in an external shell) inside the core, that becomes more and more important by increasing $A$; these effects are not taken into account in the semi-empirical mass-formula.Comment: Some misprints of the published version corrected (value of nuclear density and eq. 7). Talk given at the 4th Italian-Sino Workshop, July 20-30 (2007), Pescara (Italy