Abstract This paper characterizes a class of regular para-Hermitian transfer matrices and then studies the J-spectral factorization of this class using similarity transformations. A transfer matrix Λ in this class admits a J-spectral factorization if and only if there exists a common nonsingular matrix to similarly transform the A-matrices of Λ and Λ, resp., into 2 × 2 lower (upper, resp.) tria...

Achieving transfer – the ability to apply acquired skills in contexts different from those contexts the skills were mastered in – is, arguably, the sine qua non of education. Capturing transfer of knowledge has been addressed by several user modeling and educational data mining approaches (e.g., AFM, PFA, CFA). While similar, these approaches use different underlying structures to model transfe...

We introduce the notion of 1-vertex transfer matrix for near neighbor Potts models with k kinds of particles. We show that the topological entropy (free energy) of this model can be expressed as the limit the logarithm of spectral radii of 1-vertex transfer matrices. Storage and computations using the 1-vertex transfer matrix are much smaller than storage and computations needed for the standar...

The 6-cube has a total of 7174574164703330195841 matchings of which 16332454526976 are perfect. This was computed with a transfer matrix method associated with polygraphs. For polygraphs of type G × Pm we present a method for compression of the transfer matrix. This compression gives a substantial reduction of the order of the transfer matrix by exploiting the automorphisms of the graph G. We c...

The number of 1-factors in the 6-cube is 16 332 454 526 976. This was computed with the traditional permanent and also with a transfer matrix approach, associated with polygraphs. For polygraphs of the type G×Pm we present a method for compression of the transfer matrix. This compression gives a substantial reduction of the order of the transfer matrix by exploiting the automorphisms of the gra...