Tucker’s lemma states that if we triangulate the unit disc centered at the origin and color the vertices with {1,−1, 2,−2} in an antipodal way (if |z| = 1, then the sum of the colors of z and −z is zero), then there must be an edge for which the sum of the colors of its endpoints is zero. But how hard is it to find such an edge? We show that if the triangulation is exponentially large and the c...

We derive and analyse a scheme for the approximation of order d tensors A ∈ R n×···×n in the hierarchical (H-) Tucker format, a dimension-multilevel variant of the Tucker format and strongly related to the TT format. For a fixed rank parameter k, the storage complexity of a tensor in H-Tucker format is O(dk 3 + dnk) and we present a (heuristic) algorithm that finds an approximation to a tensor ...

Multivariate Behavioral Genetic Analysis of Parenting in Early Childhood Amanda K. Cheung, K. Paige Harden & Elliot M. Tucker-Drob To cite this article: Amanda K. Cheung, K. Paige Harden & Elliot M. Tucker-Drob (2016) Multivariate Behavioral Genetic Analysis of Parenting in Early Childhood, Parenting, 16:4, 257-283, DOI: 10.1080/15295192.2016.1184926 To link to this article: http://dx.doi.org/1...

For a locally optimal solution to the nonlinear semidefinite programming problem, under Robinson’s constraint qualification, the following conditions are proved to be equivalent: the strong second order sufficient condition and constraint nondegeneracy; the nonsingularity of Clarke’s Jacobian of the Karush-Kuhn-Tucker system; the strong regularity of the Karush-Kuhn-Tucker point; and others.