Jacobi-Maupertuis metric of Lienard type equations and Jacobi Last Multiplier

We present a construction of the Jacobi-Maupertuis (JM) principle for an equation of the Lienard type, viz \ddot{x} + f(x)x^2 + g(x) = 0 using Jacobi's last multiplier. The JM metric allows us to reformulate the Newtonian equation of motion for a variable mass as a geodesic equation for a Riemannian metric. We illustrate the procedure with examples of Painleve-Gambier XXI, the Jacobi equation and the Henon-Heiles system

Convergence (and Divergence) in the Biological Standard of Living in the United States, 1820-1900

Standard economic indicators suggest that the United States experienced long-run economic growth throughout the nineteenth century. However, biological indicators, including human stature, offer a different picture, rising early in the century, falling (on average) mid-century, and rising again at the end of the century. This pattern varied across geographical regions. Using a unique data set, consisting of mean adult stature by state, we test for convergence in stature among states in the nineteenth century. We find that during the period of declining mean stature, heights actually diverged. Later in the century we find a type of “negative” convergence indicating that stature among states tended to converge to a new, lower steady state. Only towards the end of the century do we find classic convergence behavior. We argue that the diversity of economic experiences across regions, e.g. urbanization, industrialization, and transportation improvements, explain this pattern of divergence and then convergence.

Vertical distribution of galactic disc stars and gas constrained by a molecular cloud complex

We investigate the dynamical effects of a molecular cloud complex with a mass ~107 M and a size ~ a few 100 pc on the vertical distribution of stars and atomic hydrogen gas in a spiral galactic disc. Such massive complexes have now been observed in a number of spiral galaxies. The extended mass distribution in a complex, with an average mass density 6 times higher than the Oort limit, is shown to dominate the local gravitational field. This results in a significant redistribution or clustering of the surrounding disc components towards the mid-plane, with a resulting decrease in their vertical scaleheights. The modified, self-consistent stellar density distribution is obtained by solving the combined Poisson equation and the force equation along the z-direction for an isothermal stellar disc on which the complex is imposed. The effect of the complex is strongest at its centre, where the stellar mid-plane density increases by a factor of 2.6 and the vertical scaleheight decreases by a factor of 3.4 compared with the undisturbed stellar disc. A surprising result is the large radial distance of ~ 500 pc from the complex centre over which the complex influences the disc; this is due to the extended mass distribution in a complex. The complex has a comparable effect on the vertical distribution of the atomic hydrogen gas in the galactic disc. This 'pinching' or constraining effect should be detectable in the nearby spiral galaxies, as for example has been done for NGC 2403 by Sicking. Thus the gravitational field of a complex results in local corrugations of the stellar and H i vertical scaleheights, and the galactic disc potential is highly non-uniform on scales of the intercomplex separation of ~1 kpc

Impacts of Bacillus thuringiensis var. israelensis and Bacillus sphaericus insect larvicides on mosquito larval densities in Lusaka, Zambia

The study assessed the impact of bio-larvicides- Bacillus thuringiensis var. israelensis (Bti) and B. sphaericus (Bs) on anopheline mosquito larval densities in four selected areas of Lusaka urban district. Larval densities were determined using a standard WHO protocol at each study area prior to and after larviciding. Ninety percent (90%) of the collected mosquito larvae and pupae were preserved in 70% ethanol, while 10% were reared to adults for species identification. Prior to larviciding, the largest number of mosquito larvae collected was culicines. Among the anophelines, Anopheles coustani Laveran (13.5%) (n = 111) and An. squamosus Theobald (9.5%) (n = 78) were identified from all the study areas with An. rufipes Gough (1.1%) (n = 9) collected from one study area only. None of the major malaria vector species reported for Zambia were identified. No mosquito larvae were found in freshwater bodies following the larviciding exercise. Possible reasons for the absence of known major malaria vectors could be the re-introduction of effective vector control and loss of suitable breeding grounds. The study highlights the potential of larviciding using Bti and Bs for malaria vector control and its integration with indoor residual spraying and insecticide treated nets

Uncertainty Quantification Driven Predictive Multi-Scale Model for Synthesis of Mycotoxins

Many toxic molds synthesize and release an array of poisons, termed mycotoxins that have an enormous impact on human health, agriculture and economy [1]. These molds contaminate our buildings, indoor air and crops, cause life threatening human and animal diseases and reduce agricultural output [2]. In order to design appropriate approaches to minimize the detrimental effects of these fungi, it is essential to develop diagnostic methodologies that can rapidly and accurately determine based on fungal strains and their growth patterns, the extent of mycotoxin mediated damage caused to the environment.Here we developed a novel multi-scale predictive mathematical model that could reliably estimate aflatoxin synthesis from growth features extracted fromAspergillusparasiticus, a well-characterized model for studying mycotoxin biosynthesis. We conducted acoustic imaging experiments to observe and extract the growth features from the biomass profiles of the growing Aspergillus colony growing on an aflatoxin-inducing solid growth medium. We employed the probability-based representation of uncertainty and used Bayes’ theorem to infer the uncertain parameters in our mathematical model using biomass observations of the colony at 24h (aflatoxin is not synthesized yet at this time-point) and 48 hours (aflatoxin synthesis occurs at peak levels). We demonstrate that our model could successfully predict with quantified uncertainties the levels of aflatoxin secreted to the environment by the fungus