We consider arithmetic circuits over the semiring ((; min; concat) and show that such circuits require super-polynomial size to compute the lexicographically minimum perfect matching of a bipartite graph. By deening monotone analogues of optimization classes such as OptP, OptL and OptSAC 1 using the monotone analogues of their arithmetic circuit characterizations 13, 1], our lower bound implies...

We study the computability of one-way functions and pseudorandom generators by monotone circuits, showing a substantial gap between the two: On one hand, there exist one-way functions that are computable by (uniform) polynomial-size monotone functions, provided (of course) that one-way functions exist at all. On the other hand, no monotone function can be a pseudorandom generator.

We show that, for monotone graph map f , all the ω-limit sets are finite whenever f has periodic point and for monotone dendrite map, any infinite ω-limit set does not contain periodic points. As a consequence, monotone graph and dendrite maps have no Li-Yorke pairs. However, we built a homeomorphism on a dendroid with a scrambled set having nonempty interior.

Several deeper results on maximal monotone operators have recently found simpler proofs using Fitzpatrick functions. In this paper, we study a sequence of Fitzpatrick functions associated with a monotone operator. The first term of this sequence coincides with the original Fitzpatrick function, and the other terms turn out to be useful for the identification and characterization of cyclic monot...

This paper considers k-monotone estimation and the related asymptotic performance analysis over a suitable Hölder class for general k. A novel two stage k-monotone B-spline estimator is proposed: in the first stage, an unconstrained estimator with optimal asymptotic performance is considered; in the second stage, a k-monotone B-spline estimator is constructed by projecting the unconstrained est...