Data-driven PDE discovery with evolutionary approach

The data-driven models allow one to define the model structure in cases when a priori information is not sufficient to build other types of models. The possible way to obtain physical interpretation is the data-driven differential equation discovery techniques. The existing methods of PDE (partial derivative equations) discovery are bound with the sparse regression. However, sparse regression is restricting the resulting model form, since the terms for PDE are defined before regression. The evolutionary approach described in the article has a symbolic regression as the background instead and thus has fewer restrictions on the PDE form. The evolutionary method of PDE discovery (EPDE) is described and tested on several canonical PDEs. The question of robustness is examined on a noised data example

The Farmer Field School: a method for enhancing the role of rural communities in malaria control ?

Malaria has strong linkages with agriculture, and farmers in malarious regions have a central position in creating or controlling the conditions that favour disease transmission. An interdisciplinary and integrated approach is needed to involve farmers and more than one sector in control efforts. It is suggested that malaria control can benefit from a complementary intervention in rural development, the Farmer Field School (FFS) on Integrated Pest Management (IPM). This is a form of education that uses experiential learning methods to build farmers' expertise, and has proven farm-level and empowerment effects. The benefits of incorporating malaria control into the IPM curriculum are discussed. An example of a combined health-agriculture curriculum, labeled Integrated Pest and Vector Management (IPVM), developed in Sri Lanka is presented. Institutional ownership and support for IPVM could potentially be spread over several public sectors requiring a process for institutional learning and reform

A Calculation of the Full Neutrino Phase Space in Cold+Hot Dark Matter Models

This paper presents a general-relativistic N-body technique for evolving the phase space distribution of massive neutrinos in linear perturbation theory. The method provides a much more accurate sampling of the neutrino phase space for the HDM initial conditions of N-body simulations in a cold+hot dark matter universe than previous work. Instead of directly sampling the phase space at the end of the linear era, we first compute the evolution of the metric perturbations by numerically integrating the coupled, linearized Einstein, Boltzmann, and fluid equations for all particle species. We then sample the phase space shortly after neutrino decoupling at redshift z=10^9 when the distribution is Fermi-Dirac. To follow the trajectory of each neutrino, we subsequently integrate the geodesic equations for each neutrino in the perturbed background spacetime from z=10^9 to z=13.55, using the linearized metric found in the previous calculation to eliminate discreteness noise. The positions and momenta resulting from this integration represent a fair sample of the full neutrino phase space and can be used as HDM initial conditions for N-body simulations of nonlinear structure evolution in this model. A total of 21 million neutrino particles are used in a 100 Mpc box, with Omega_cdm=0.65, Omega_hdm=0.30, Omega_baryon=0.05, and Hubble constant H_0=50. We find that correlations develop in the neutrino densities and momenta which are absent when only the zeroth-order Fermi-Dirac distribution is considered.Comment: 20 pages, AAS LaTeX v3.0, figures and/or postscript available by anonymous ftp to arcturus.mit.edu, MIT CSR-93-1