We prove that the fully asynchronous dynamics of a Boolean network f : {0, 1} → {0, 1} without negative loop can be simulated, in a very specific way, by a monotone Boolean network with 2n components. We then use this result to prove that, for every even n, there exists a monotone Boolean network f : {0, 1} → {0, 1}, an initial configuration x and a fixed point y of f such that: (i) y can be re...

Any negative moment of an increasing Lamperti process (Yt, t ≥ 0) is a completely monotone function of t. This property enticed us to study systematically, for a given Markov process (Yt, t ≥ 0), the functions f such that the expectation of f(Yt) is a completely monotone function of t. We call these functions temporally completely monotone (for Y ). Our description of these functions is deduced...

Let Ω be an open subset in C. PSH(Ω) will stand for the set of all plurisubharmonic (psh) functions on Ω. We use the standard notations d = ∂ + ∂ and d = i (∂ − ∂). The complex Monge-Ampère operator (dd) is, via integrations by parts, well defined on PSH(Ω) ∩ Lloc(Ω) and is continuous under monotone limits, that is, (dd uj) n → (ddu) in the sense of currents if the monotone sequence of function...

Since monotone methods have been initiated by Kamke 1 and Müler 2 , and developed further by Krasnoselskii 3, 4 , Matano 5 , and Smith 6 , the theory and application of monotone dynamics have become increasingly important see 7–18 . It is well known that the quasimonotone condition is very important in studying the asymptotic behaviors of dynamical systems. If this condition is satisfied, the s...

It is shown that a set-valued map M : R ⇒ R is maximal monotone if and only if the following five conditions are satisfied: (i) M is monotone; (ii) M has a nearly convex domain; (iii) M is convex-valued; (iv) the recession cone of the values M(x) equals the normal cone to the closure of the domain of M at x; (v) M has a closed graph. We also show that the conditions (iii) and (v) can be replace...

We investigate the power of Katm-style datattow networks, with processes that may exhibit indeterminate behavior. Our main result is a theorem about networks of "monotone" processes, which shows: (1) that the input/output relation of such a network is a total and monotone relation; and (2) every relation that is total, monotone, and continuous in a certain sense, is the input/output relation of...

This paper is concerned with the class of distributions, continuous or discrete, whose shape is monotone of finite integer order t. A characterization is presented as a mixture of a minimum of t independent uniform distributions. Then, a comparison of t-monotone distributions is made using the s-convex stochastic orders. A link is also pointed out with an alternative approach to monotonicity ba...

The monotone crossing number of G is defined as the smallest number of crossing points in a drawing of G in the plane, where every edge is represented by an x-monotone curve, that is, by a connected continuous arc with the property that every vertical line intersects it in at most one point. It is shown that this parameter can be strictly larger than the classical crossing number cr(G), but it ...

We study the construction of the minimum cost spanning geometric graph of a given rooted point set P where each point of P is connected to the root by a path that satisfies a given property. We focus on two properties, namely the monotonicity w.r.t. a single direction (y-monotonicity) and the monotonicity w.r.t. a single pair of orthogonal directions (xy-monotonicity). We propose algorithms tha...

For two classes of monotone maps on the n-dimensional positive orthant we show that for a discrete dynamical system induced by a map the origin of Rn+ is globally asymptotically stable, if and only if the map Γ is such that for any point in s ∈ R+, s 6= 0, the image-vector Γ(s) is such that at least one component is strictly less than the corresponding component of s. One class is the set of n ...