Abstract. We consider Tucker-like approximations with an r × r × r core tensor for threedimensional n×n×n arrays in the case of r ¿ n and possibly very large n (up to 104−106). As the approximation contains only O(rn + r3) parameters, it is natural to ask if it can be computed using only a small amount of entries of the given array. A similar question for matrices (two-dimensional tensors) was ...

This paper extends the work of Bird, Warner, Stewart, Sørensen, Larson, Ottinger, Vukadinovic, and Forest et al., who have applied Spherical Harmonics to numerically solve certain types of partial differential equations on the two-dimensional sphere. We present a systematic approach and implementation for solving such equations with efficient numerical solutions. In particular we are able to so...

In (Tucker, J. V. and Zucker, J. I. (2007) Computability of analog networks. Theoret. Comput. Sci., 371, 115–146; Tucker, J. V. and Zucker, J. I. (2011) Continuity of operators on continuous and discrete time streams. Theoret. Comput. Sci., 412, 3378–3403), Tucker and Zucker present a model for the semantics of analog networks operating on streams from topological algebras. Central to their mod...

We give a new algorithm to construct optimal alphabetic ternary trees, where every internal node has at most three children. This algorithm generalizes the classic Hu-Tucker algorithm, though the overall computational complexity has yet to be determined.

Recensión del libro Entender el cambio climático. Información y recursos para profesorado, de Laura Tucker Lois Sherwood (2020).

Tensor decomposition methods are effective tools for modelling multidimensional array data (i.e., tensors). Among them, nonparametric Bayesian models, such as Infinite Tucker Decomposition (InfTucker), are more powerful than multilinear factorization approaches, including Tucker and PARAFAC, and usually achieve better predictive performance. However, they are difficult to handle massive data du...

A solution of the standard formulation of a linear program with linear complementarity constraints (LPCC) does not satisfy a constraint qualification. A family of relaxations of an LPCC, associated with a probability-one homotopy map, proposed here is shown to have several desirable properties. The homotopy map is nonlinear, replacing all the constraints with nonlinear relaxations of NCP functi...

Infinite Tucker Decomposition (InfTucker) and random function prior models, as nonparametric Bayesian models on infinite exchangeable arrays, are more powerful models than widely-used multilinear factorization methods including Tucker and PARAFAC decomposition, (partly) due to their capability of modeling nonlinear relationships between array elements. Despite their great predictive performance...

In this paper we obtain secondand first-order optimality conditions of Kuhn-Tucker type and Fritz John one for weak efficiency in the vector problem with inequality constraints. In the necessary conditions we suppose that the objective function and the active constraints are continuously differentiable. We introduce notions of KTSP-invex problem and second-order KTSP-invex one. We obtain that t...

Flair and Loathing on the Front Page, by Jim Tucker. New Plymouth, NZ: Tucker Media. 2022, 283 pages.
 'NAMES make news' is a mantra drummed into head of every young reporter heaven help those who can’t identify vital quote or face. It lesson that veteran journalist educator never forgot. The evidence lies in pages first part his memoir spanning career began Taranaki 1965 which has gone fu...