Bounds on the Norms of Uniform Low Degree Graph Matrices

The Sum Of Squares hierarchy is one of the most powerful tools we know of for solving combinatorial optimization problems. However, its performance is only partially understood. Improving our understanding of the sum of squares hierarchy is a major open problem in computational complexity theory. A key component of analyzing the sum of squares hierarchy is understanding the behavior of certain matrices whose entries are random but not independent. For these matrices, there is a random input graph and each entry of the matrix is a low degree function of the edges of this input graph. Moreoever, these matrices are generally invariant (as a function of the input graph) when we permute the vertices of the input graph. In this paper, we bound the norms of all such matrices up to a polylogarithmic factor

Social Ecological Factors Affecting Substance Abuse in Ghana (West Africa) Using Photovoice

Introduction: substance abuse is an important public health issue affecting West Africa; however, there is currently a dearth of literature on the actions needed to address it. The aim of this study was to assess the risks and protective factors of substance abuse in Ghana, West Africa, using the photovoice method. Methods: this study recruited and trained 10 participants in recovery from substance abuse and undergoing treatment in the greater Accra region of Ghana on the photovoice methodology. Each participant received a disposable camera to take pictures that represented the risk and protective factors pertinent to substance abuse in their communities. They were also given the opportunity to provide narratives of the pictures using pre-identified themes and the different levels of the social-ecological model and participatory action research (PAR). Results: participants identified at the individual level: ignorance; interpersonal level: family and peer pressure; organizational level: lack of regulation; community level: media, availability of drugs, cost of drugs, urbanization, slum communities and cultural factors; and policy level: lack of regulations and their enforcement. Education and beliefs were cited at the individual level; family at the interpersonal level; religion at the organizational level; organizing youth, media and narcotics anonymous at the community level; and nothing at the policy level. Conclusion: this is an exploratory study that will add to the limited body of knowledge in the scientific literature with respect to substance abuse in the country and also help develop interventions to address the respective needs of several communities in Ghana

Proper Distance in Edge-Colored Hypercubes

An edge-colored path is called properly colored if no two consecutive edges have the same color. An edge-colored graph is called properly connected if, between every pair of vertices, there is a properly colored path. Moreover, the proper distance between vertices u and v is the length of the shortest properly colored path from u to v. Given a particular class of properly connected colorings of the hypercube, we consider the proper distance between pairs of vertices in the hypercube