This paper provides an expository introduction to monotone and near-monotone biochemical network structures. Monotone systems respond in a predictable fashion to perturbations, and have very robust dynamical characteristics. This makes them reliable components of more complex networks, and suggests that natural biological systems may have evolved to be, if not monotone, at least close to monoto...

This paper provides an expository introduction to monotone and nearmonotone biochemical network structures. Monotone systems respond in a predictable fashion to perturbations, and have very robust dynamical characteristics. This makes them reliable components of more complex networks, and suggests that natural biological systems may have evolved to be, if not monotone, at least close to monoton...

We survey an algebraic approach to proving impossibility results in distributed computing. The approach is emerging around monotone groups, a new class of algebraic groups we define here as a tight suit to monotone Read&Modify&Write (or RMW) operations in a distributed system. The yields of this approach have been the first impossibility results for implementations of monotone RMW operations th...

In this paper, we present an example in which the sum of two maximal abstract monotone operators is maximal. Also, we shall show that the necessary condition for Rockafellar’s surjectivity which was obtained in ([19], Theorem 4.3) can be sufficient.

In this article, we provide a splitting method for solving monotone inclusions in real Hilbert space involving four operators: maximally monotone, monotone-Lipschitzian, cocoercive, and monotone-continuous operator. The proposed takes advantage of the intrinsic properties each operator, generalizing forward–backward–half-forward Tseng’s algorithm with line search. At iteration, our defines step...

For classification problems with ordinal attributes very often the class attribute should increase with each or some of the explanatory attributes. These are called classification problems with monotonicity constraints. Standard classification tree algorithms such as CART or C4.5 are not guaranteed to produce monotone trees, even if the data set is completely monotone. We look at pruning based ...

We prove tight lower bounds, of up to n , for the monotone depth of functions in monotone-P. As a result we achieve the separation of the following classes. 1. monotone-NC 6 = monotone-P. 2. For every i 1, monotone-NC i 6 = monotone-NC i+1. 3. More generally: For any integer function D(n), up to n (for some > 0), we give an explicit example of a monotone Boolean function, that can be computed b...