The Consecutive-Ones Property (C1P) in binary matrices is a combinatorial concept with applications in several area, from graph planarity testing to computational biology. Tucker patterns are families of submatrices that characterize non-C1P matrices, and thus represent natural certificates of non-C1P matrices. However, there are very few algorithmic results regarding Tucker patterns. In the pr...

Sequential optimality conditions provide adequate theoretical tools to justify stopping criteria for nonlinear programming solvers. Here, nonsmooth approximate gradient projection and complementary approximate Karush-Kuhn-Tucker conditions are presented. These sequential optimality conditions are satisfied by local minimizers of optimization problems independently of the fulfillment of constrai...

Th is paper is concerned w i th the problem of dete rmin ing the indirect effects or ramifications of actions. We argue that the standard framework in which background knowledge is given in the fo rm of state constraints is inadequate and that background knowledge should instead be given in the fo rm of "causal laws." We represent "causal laws" f irst as inference rules and later as sentences i...

There is a increasing interest in analysis of large-scale multiway data. The concept of multiway data refers to arrays of data with more than two dimensions, that is, taking the form of tensors. To analyze such data, decomposition techniques are widely used. The two most common decompositions for tensors are the Tucker model and the more restricted PARAFAC model. Both models can be viewed as ge...

The 2-D Tucker search problem is shown to be PPA-hard under many-one reductions; therefore it is complete for PPA. The same holds for k-D Tucker for all k ≥ 2. This corrects a claim in the literature that the Tucker search problem is in PPAD.

The hierarchical Tucker format is a way to decompose a high-dimensional tensor recursively into sums of products of lower-dimensional tensors. The number of degrees of freedom in such a representation is typically many orders of magnitude lower than the number of entries of the original tensor. This makes the hierarchical Tucker format a promising approach to solve ordinary differential equatio...