The principle of weak monotonicity for cooperative games states that if a game changes so that the worth of the grand coalition and some player’s marginal contribution to all coalitions increase or stay the same, then this player’s payoff should not decrease. We investigate the class of values that satisfy effi ciency, symmetry, and weak monotonicity. It turns out that this class coincides with...

Yaser S. Abu-Mostafa EE and CS Deptartments California Institute of Technology email: [email protected] A hint is any piece of side information about the target function to be learned. We consider the monotonicity hint, which states that the function to be learned is monotonic in some or all of the input variables. The application of mono tonicity hints is demonstrated on two real-world prob...

In the face of the increasing trend in application development to interact with more and more remote services, and cognizant of the fact that issues arising from data consistency and task coordination are core challenges in distributed programming, the systems and data management communities have taken a keen interest in developing eventually consistent coordination-free models of distributed p...

The circular cone Lθ is not self-dual under the standard inner product and includes second-order cone as a special case. In this paper, we focus on the monotonicity of fLθ and circular cone monotonicity of f . Their relationship is discussed as well. Our results show that the angle θ plays a different role in these two concepts.

The aim of this note is to prove the monotonicity formula of Caffarelli-Jerison-Kenig for functions, which are not necessarily continuous. We also give a detailed proof of the multiphase version of the monotonicity formula in any dimension.

In this paper we introduce the concept of quasimonotone maps and some concepts of generalized monotonicity for multimappings, then establish connections between some concepts of generalized monotonicity for multimappings introduced during the last several years.

Given a directed graph G = (V,E) and an integer k ≥ 1, a ktransitive-closure-spanner (k-TC-spanner) of G is a directed graph H = (V,EH) that has (1) the same transitive-closure as G and (2) diameter at most k. Transitive-closure spanners are a common abstraction for applications in access control, property testing and data structures. We show a connection between 2-TC-spanners and local monoton...

Monotonicity with respect to all arguments is fundamental to the definition of aggregation functions. It is also a limiting property that results in many important non-monotonic averaging functions being excluded from the theoretical framework. This work proposes a definition for weakly monotonic averaging functions, studies some properties of this class of functions and proves that several fam...

A system (Pα : α ∈ A) of probability measures on a common state space S indexed by another index set A can be “realized” by a system (Xα : α ∈ A) of S-valued random variables on some probability space in such a way that each Xα is distributed as Pα. Assuming that A and S are both partially ordered, we may ask when the system (Pα : α ∈ A) can be realized by a system (Xα : α ∈ A) with the monoton...