College of Science
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 Creator(s):
 Dan Bates, David Eklund, Jonathan Hauenstein, Chris Peterson
 Description:
A fundamental problem in algebraic geometry is to decompose the solution set of a given polynomial system. A numerical description of this solution set is called a numerical irreducible decomposition and currently all standard algorithms use a sequence of homotopies forming a dimensionbydimension approach. In this article, we pair a classical result to compute a smooth point on every irreducible component in every dimension using a single homotopy together with the theory of isosingular s…
 Date Created:
 20190426

 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

 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

4
Dataset
 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):
 Sunny Boyd
 Description:
Mate choice strategies in a spatiallyexplicit model environment
Giordano B. S. Ferreira1, Matthias Scheutz1, and Sunny K. Boyd2 1Department of Computer Science, Tufts University, Medford, MA 02155, USA Matthias.scheutz@tufts.edu and Giordano.Ferreira@tufts.edu 2Department of Biological Sciences, University of Notre Dame, Notre Dame, IN 46556, USA Boyd.1@nd.edu (Corresponding author; phone: 5746315021; fax: 5746317413)
Keywords: mate choice, decisionmaking, agentbased modeling, f…
 Date Created:
 20171214

6
Dataset
 Creator(s):
 Jennifer Tank
 Description:
This dataset contains data from 17 stream 15NNH4 tracer addition experiments conducted globally, with data partitioned by autotrophic uptake compartments (i.e., epilithic biofilm, filamentous algae, bryophytes/macrophytes) and heterotrophic uptake compartments (i.e., leaves, small wood, and fine particles) that comprise the base of stream food webs. The dataset includes compartmental data on N biomass and uptake as well as other physiochemical variable that describe conditions in each stream.
 Date Created:
 20170912

 Creator(s):
 Jonathan Hauenstein
 Description:
The Kuramoto model describes synchronization behavior among coupled oscillators and enjoys successful application in a wide variety of fields. Many of these applications seek phasecoherent solutions, i.e., equilibria of the model. Historically, research has focused on situations where the number of oscillators, n, is extremely large and can be treated as being infinite. More recently, however, applications have arisen in areas such as electrical engineering with more modest values of n. For…
 Date Created:
 20170407

 Creator(s):
 Jonathan Hauenstein
 Description:
StewartGough platforms are mechanisms which consist of two rigid objects, a base and a platform, connected by six legs via spherical joints. For fixed leg lengths, a generic StewartGough platform is rigid with 40 assembly configurations (over the complex numbers) while exceptional StewartGough platforms have infinitely many assembly configurations and thus have selfmotion. We define a family of exceptional StewartGough platforms called Segredependent StewartGough platforms which aris…
 Date Created:
 20170117

 Creator(s):
 Jonathan Hauenstein
 Description:
We define tensors, most of which correspond with cubic polynomials, which have the same exponent w as the matrix multiplication tensor. In particular, we study the symmetrized matrix multiplication tensor defined on an nxn matrix A by trace(A^3). The use of polynomials enables the introduction of additional techniques from algebraic geometry in the study of the matrix multiplication exponent w.
 Date Created:
 20170107

 Creator(s):
 Jonathan Hauenstein
 Description:
A computationally challenging classical elimination theory problem is to compute polynomials which vanish on the set of tensors of a given rank. By moving away from computing polynomials via elimination theory to computing pseudowitness sets via numerical elimination theory, we develop computational methods for computing ranks and border ranks of tensors along with decompositions. More generally, we present our approach using joins of any collection of irreducible and nondegenerate projecti…
 Date Created:
 20160831