On the compounding of higher order monotonic pseudo-Boolean functions

  title={On the compounding of higher order monotonic pseudo-Boolean functions},
  author={Paul Ressel},
  • P. Ressel
  • Published 23 June 2021
  • Mathematics
  • Positivity
Compounding submodular monotone (i.e. 2-alternating) set functions on a finite set preserves this property, as shown in 2010. A natural generalization to k-alternating functions was presented in 2018, however hardly readable because of page long formulas. We give an easier proof of a more general result, exploiting known properties of higher order monotonic functions. 

Monotonicity properties of multivariate distribution and survival functions - With an application to Lévy-frailty copulas

Copulas, stable tail dependence functions, and multivariate monotonicity

  • P. Ressel
  • Computer Science
    Dependence Modeling
  • 2019
It will turn out that for nested Archimedean copulas and stable tail dependence functions the basic degree of monotonicity is the only one possible, apart from the (trivial) independence functions.

Higher order monotonic functions of several variables

Multivariate functions with a specific degree of higher order monotonicity in each variable are introduced. When normalized, they turn out to form a simplex whose extreme points are precisely the

Submodularity of Influence in Social Networks: From Local to Global

The results demonstrate that “local” submodularity is preserved “globally” under this diffusion process, which is of natural computational interest, as many optimization problems have good approximation algorithms for submodular functions.

Maximizing the spread of influence through a social network

An analysis framework based on submodular functions shows that a natural greedy strategy obtains a solution that is provably within 63% of optimal for several classes of models, and suggests a general approach for reasoning about the performance guarantees of algorithms for these types of influence problems in social networks.

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