The notions of relaxed submonotone and relaxed monotone mappings in Banach spaces are introduced and many of their properties are investigated. For example, the Clarke subdifferential of a locally Lipschitz function in a separable Banach space is relaxed submonotone on a residual subset. For example, it is shown that this property need not be valid on the whole space. We prove, under certain hy...

Inferring inductive invariants is one of the main challenges formal verification. The theory abstract interpretation provides a rich framework to devise invariant inference algorithms. One latest breakthroughs in property-directed reachability (PDR), but research community views PDR and as mostly unrelated techniques. This paper shows that, surprisingly, propositional can be formulated an algor...

This paper establishes a global contraction property for networks of phase-coupled oscillators characterized by a monotone coupling function. The contraction measure is a total variation distance. The contraction property determines the asymptotic behavior of the network, which is either finite-time synchronization or asymptotic convergence to a splay state.

Cores are, besides connectivity components, one among few concepts that provides us with efficient decompositions of large graphs and networks. In the paper a generalization of the notion of core of a graph based on vertex property function is presented. It is shown that for the local monotone vertex property functions the corresponding cores can be determined in time.

Strongly monotone systems of ordinary differential equations which have a certain translationinvariance property are shown to have the property that all projected solutions converge to a unique equilibrium. This result may be seen as a dual of a well-known theorem of Mierczyński for systems that satisfy a conservation law. As an application, it is shown that enzymatic futile cycles have a globa...

Topology control is the problem of assigning power levels to the nodes of an ad hoc network so as to create a specified network topology while minimizing the energy consumed by the network nodes. While considerable theoretical attention has been given to the issue of topology control in wireless ad hoc networks, all of that prior work has concerned stationary networks. When the nodes are mobile...