An algorithm is described for the nonnegative rank factorization (NRF) of some completely positive (CP) matrices whose rank is equal to their CP-rank. The algorithm can compute the symmetric NRF of any nonnegative symmetric rank-r matrix that contains a diagonal principal submatrix of that rank and size with leading cost O(rm) operations in the dense case. The algorithm is based on geometric co...

This paper introduces the order-theoretic concept of lattices along with the concept of consistent quantification where lattice elements are mapped to real numbers in such a way that preserves some aspect of the ordertheoretic structure. Symmetries, such as associativity, constrain consistent quantification, and lead to a constraint equation known as the sum rule. Distributivity in distributive...

Let n and r be two integers such that 0 < r ≤ n; we denote by γ(n, r) [η(n, r)] the minimum [maximum] number of the non-negative partial sums of a sum ∑ n 1=1 ai ≥ 0, where a1, · · · , an are n real numbers arbitrarily chosen in such a way that r of them are non-negative and the remaining n − r are negative. Inspired by some interesting extremal combinatorial sum problems raised by Manickam, Mi...

We provide an extensive study of the differential properties of the functions x 7→ x t −1 over F2n , for 1 < t < n. We notably show that the differential spectra of these functions are determined by the number of roots of the linear polynomials x t + bx + (b + 1)x where b varies in F2n .We prove a strong relationship between the differential spectra of x 7→ x t −1 and x 7→ x s −1 for s = n− t+ ...