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+ ...

A sum rule relation is proposed for direct CP asymmetries in B → Kπ decays. Leading terms are identical in the isospin symmetry limit, while subleading terms are equal in the flavor SU(3) and heavy quark limits. The sum rule predicts ACP(B 0 → Kπ) = −0.17±0.06 using current asymmetry measurements for the other three B → Kπ decays. A violation of the sum rule would be evidence for New Physics in...

We will discuss recent results for the spin structure functions, with an emphasis on g2. High precision g2 data allows for tests of the Burkhardt–Cottingham sum rule, and is needed to consistently evaluate higher twist effects.