On the fractionality of the path packing problem

Given an undirected graph G=(N,E), a subset T of its nodes and an undirected graph (T,S), G and (T,S) together are often called a network. A?collection of paths in G whose end-pairs lie in S is called an integer multiflow. When these paths are allowed to have fractional weight, under the constraint that the total weight of the paths traversing a single edge does not exceed 1, we have a fractional multiflow in G. The problems of finding the maximum weight of paths with end-pairs in S over all fractional multiflows in G is called the fractional path packing problem. In 1989, A. Karzanov had defined the fractionality of the fractional path packing problem for a class of networks {G,(T,S)} as the smallest natural D such that for any network from the class, the fractional path packing problem has a solution which becomes integer-valued when multiplied by D (see A.?Karzanov in Linear Algebra Appl. 114–115:293–328, 1989). He proved that the fractional path packing problem has infinite fractionality outside a very specific class of networks, and conjectured that within this class, the fractionality does not exceed 4. A.?Karzanov also proved that the fractionality of the path packing problem is at most 8 by studying the fractionality of the dual problem. Special cases of Karzanov’s conjecture were proved in or are implied by the works of L.R.?Ford and D.R.?Fulkerson, Y.?Dinitz, T.C.?Hu, B.V.?Cherkassky, L.?Lov?sz and H.?Hirai. We prove Karzanov’s conjecture by showing that the fractionality of the path packing problem is at most 4. Our proof is stand-alone and does not rely on Karzanov’s results.     

Feeling Social Movements: Theoretical Contributions to Social Movement Research on Emotions

Recent literature provides evidence that emotions are intrinsic to the constitution of social movements. The present review examines how scholars theorize emotions in their empirical studies and focuses on the following topics: emotion work, emotional framing, emotional cultures and emotional opportunity structures. The combination of several constructs in the analysis of emotions signals a shift toward integration of preexisting perspectives common in the field of social movements.     

Interorganizational Partnerships as a Strategy for Lobbying: Nonprofit Administrators’ Perspectives on Collaborating for Systems-Level Change

Participation in coalitions has been identified as a policy advocacy behavior for nonprofit organizations, although few studies have examined nonprofit leaders’ perceptions of coalition building as a strategy for lobbying. This study conducted focus groups and in-person interviews with nonprofit administrators to explore how interorganizational collaboration is utilized to address their organizations’ policy advocacy goals. The findings indicate that nonprofit administrators view their participation in coalitions as a means of achieving several policy advocacy goals, including increasing their capacity to lobby and protecting them from exposure as lobbyists. Implications for practice and research are provided.     

Translation sociology and social capital in rural development initiatives. A case study from the Italian Alps

This article analyses the results of a European ‘research and demonstration’ project promoting multifunctional and sustainable agriculture in Alpine regions through a participatory approach. It focuses in particular on initiatives undertaken by a local farmers group in the Italian Alpine area of Val di Sole, the purpose being to draw attention to the role of social dynamics in fostering sustainable rural development in a participatory context. In order to accomplish this objective, two key sociological approaches to the study of rural development, namely social capital and the sociology of translation, are considered. The former focuses on the relational capital available to a group of actors and which can be mobilised in a development initiative. The latter views change in social practices as resulting from a cycle of phases where the problem, its solution, and the identity of the actors are constantly transformed and negotiated. By contrasting the two theoretical approaches in relation to the outcomes of two specific actions implemented in the valley we suggest that the sociology of translation offers a more effective tool with which to capture the complexity of social dynamics involved in a rural development initiative.