Quantum formalisms applied to human cognition have shown a great potential for certain applications in the social sciences. However, one must ask how this is so, and also how predictive they are. For instance, as showed above, it is possible to devi…
In this appendix, we follow all the same notation in Section 9. Our aim is to prove that the constant δ(Λ) does not appear in the lower bound, showing also that the frame inequality in (4.9) in Theorem 4.4 is indeed the Parseval identity.
We finish with two venues for future research. First, one can associate several matroids to a signed graph, most prominently Zaslavsky’s frame matriod and (extended) lift matroid [12, 14]. It is a natural question to ask about possible connections b…
Unless specified otherwise, a monoid in this section means a commutative and cancellative monoid, possibly with torsion, i.e., no longer is the group gp(M) assumed to be torsion free.
In the last section, we will prove our main theorem. We first need to study the spectral property of the quasi-product form. Suppose now the pair (R,B) is in the quasi-product form
Our goal in this section is to prove Theorem 4. We will need a few identities that are slightly technical but straightforward. For x∈R and m∈Z>0, we denote by [x]m the smallest nonnegative real number congruent to x mod m.
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