Global offensive kk-alliances in digraphs

In this paper, we initiate the study of global offensive $k$-alliances in digraphs. Given a digraph $D=(V(D),A(D))$, a global offensive $k$-alliance in a digraph $D$ is a subset $S\subseteq V(D)$ such that every vertex outside of $S$ has at least one in-neighbor from $S$ and also at least $k$ more in-neighbors from $S$ than from outside of $S$, by assuming $k$ is an integer lying between two minus the maximum in-degree of $D$ and the maximum in-degree of $D$. The global offensive $k$-alliance number $\gamma_{k}^{o}(D)$ is the minimum cardinality among all global offensive $k$-alliances in $D$. In this article we begin the study of the global offensive $k$-alliance number of digraphs. For instance, we prove that finding the global offensive $k$-alliance number of digraphs $D$ is an NP-hard problem for any value $k\in \{2-\Delta^-(D),\dots,\Delta^-(D)\}$ and that it remains NP-complete even when restricted to bipartite digraphs when we consider the non-negative values of $k$ given in the interval above. Based on these facts, lower bounds on $\gamma_{k}^{o}(D)$ with characterizations of all digraphs attaining the bounds are given in this work. We also bound this parameter for bipartite digraphs from above. For the particular case $k=1$, an immediate result from the definition shows that $\gamma(D)\leq \gamma_{1}^{o}(D)$ for all digraphs $D$, in which $\gamma(D)$ stands for the domination number of $D$. We show that these two digraph parameters are the same for some infinite families of digraphs like rooted trees and contrafunctional digraphs. Moreover, we show that the difference between $\gamma_{1}^{o}(D)$ and $\gamma(D)$ can be arbitrary large for directed trees and connected functional digraphs

Social Learning and Networking : How multiple actors can learn through joint analysis, dialogue and co-creation

We are facing complex societal problems such as climate change, human conflict, poverty and inequality, and need innovative solutions. Multi-stakeholder processes (MSPs) are more and more seen as a critical way of coming to such innovative solutions. It is thought that when multiple stakeholders are able to meet, share experiences, learn together and contribute to decisions, new and innovative ways of dealing with problems are found and turned into action. Still, much remains to be understood about the role and effectiveness of social learning in multi-stakeholder settings. This report summarizes the deliberations of the seminar “Social learning and networking: How multiple actors can learn through joint analysis, dialogue and co-creation”, which was held in Wageningen on 16 September 2010

Global defensive k-alliances in directed graphs: combinatorial and computational issues

In this paper we define the global defensive k-alliance (number) in a digraph D, and give several bounds on this parameter with characterizations of all digraphs attaining the bounds. In particular, for the case k = -1, we give a lower (an upper) bound on this parameter for directed trees (rooted trees). Moreover, the characterization of all directed trees (rooted trees) for which the equality holds is given. Finally, we show that the problem of finding the global defensive k-alliance number of a digraph is NP-hard for any suitable non-negative value of k, and in contrast with it, we also show that finding a minimum global defensive (-1)-alliance for any rooted tree is polynomial-time solvable

The value question in India: Ethnographic reflections on an ongoing debate

The terms of the debate about anthropological approaches to the value question in India have been set by Dumont, whose theories were based on his ethnographic studies in North and South India, his knowledge of the Sanskrit literature, his synthesis of the comparative ethnography of India, and his studies on the history of European economic thought. His theory of affinity as a value, one element of this general theory, was based on a critique of L�vi-Strauss and was, in turn, critiqued by Trautmann, among others. On the basis of fieldwork done in Central India, I draw attention to an unexamined assumption that all three theorists share, and I also consider its consequences