In these notes we present the notion of Negative Association, discuss some of its useful properties, and end with some example applications. The slogan to bear in mind here is “independent, or better”. 1 Negative Association Definition In randomized algorithms, our randomness often takes on the form of independent random variables, allowing us to apply powerful theorems concerning such variable...

A Boolean k-monotone function defined over a finite poset domain D alternates between the values 0 and 1 at most k times on any ascending chain in D. Therefore, k-monotone functions are natural generalizations of the classical monotone functions, which are the 1-monotone functions. Motivated by the recent interest in k-monotone functions in the context of circuit complexity and learning theory,...

In this paper, coupled xed point results of Bhaskar-Lakshmikantham type [T. Gnana Bhaskar, V.Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, NonlinearAnalysis 65 (2006) 1379-1393] are extend, generalized, unify and improved by using monotonemappings instead mappings with mixed monotone property. Also, an example is given to supportthese improvements.

For a graph property P consider the following computational problem. Given an input graph G, what is the minimum number of edge modifications (additions and/or deletions) that one has to apply to G in order to turn it into a graph that satisfies P? Namely, what is the edit distance ∆(G,P) of a graph G from satisfying P. Clearly, the computational complexity of such a problem strongly depends on...

At diverging junctions in vehicular traffic networks, congestion on one outgoing link may impede traffic flow to other outgoing links. This phenomenon is referred to as the first-in-first-out (FIFO) property. Traffic network models that do not include the FIFO property result in monotone dynamics for which powerful analysis techniques exist. This note shows that a large class of FIFO network mo...

*Correspondence: [email protected] School of Science, Sichuan University of Science and Engineering, Zigong, Sichuan 643000, China Abstract We prove quadruple fixed point theorems in partially ordered metric spaces with mixed g-monotone property. Also, we state some examples to show that our results are real generalization of known ones in quadruple fixed point theory. MSC: 46T99; 54H25; 47H10;...

Model Description • Actors: An infinite population of individuals indexed by ei, one’s ability to earn a secular income, and zi, one’s ideal level of doctrinal strictness. – ei ∼ g(e|θ), where θ captures human development and g(e|θ) satisfies the monotone likelihood ratio property (MLRP). – zi ∼ h(z|ρ), where ρ captures society’s overall preference for doctrinal strictness and h(z|ρ) satisfies ...