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 Creator(s):
 Rob Wieck
 Description:
Commonly known as the yellow fever mosquito, Aedes aegypti invaded Madeira Island in 2005 and was the vector of the island’s first dengue outbreak in 2012. We have studied genetic variation at 16 microsatellites and 2 mitochondrial DNA genes in temporal samples of Madeira Island, in order to assess the origin of the invasion and the population structure of this mosquito vector.
 Date Created:
 20180724

 Creator(s):
 Jonathan Hauenstein, Alan Liddell, Yi Zhang
 Description:
Standard interior point methods in semidefinite programming track a solution path for a homotopy defined by a system of polynomial equations. By viewing this in the context of numerical algebraic geometry, we are able to employ techniques to handle various cases which can arise. Adaptive precision path tracking techniques can help navigate around illconditioned areas. When the optimizer is singular with respect to the firstorder optimality conditions, endgames can be used to efficiently and…
 Date Created:
 20180410

20
Dataset

 Creator(s):
 Jonathan Hauenstein
 Description:
A common problem when analyzing models, such as a mathematical modeling of a biological process, is to determine if the unknown parameters of the model can be determined from given inputoutput data. Identifiable models are models such that the unknown parameters can be determined to have a finite number of values given inputoutput data. The total number of such values over the complex numbers is called the identifiability degree of the model. Unidentifiable models are models such that th…
 Date Created:
 20180309

 Creator(s):
 Samantha Sherman, Jonathan Hauenstein
 Description:
Computational tools in numerical algebraic geometry can be used to numerically approximate solutions to a system of polynomial equations. If the system is wellconstrained (i.e., square), Newton’s method is locally quadratically convergent near each nonsingular solution. In such cases, Smale’s alpha theory can be used to certify that a given point is in the quadratic convergence basin of some solution. This was extended to certifiably determine the reality of the corresponding sol…
 Date Created:
 20180308

 Creator(s):
 Margaret Regan, Jonathan Hauenstein
 Description:
A common computational problem is to compute topological information about a real surface defined by a system of polynomial equations. Our software, called polyTop, leverages numerical algebraic geometry computations from Bertini and Bertini_real with topological computations in javaPlex to compute the Euler characteristic, genus, Betti numbers, and generators of the fundamental group of a real surface. Several examples are used to demonstrate this new software.
 Date Created:
 20180302