Complexity of Discrete Energy Minimization Problems

Discrete energy minimization is widely-used in computer vision and machine learning for problems such as MAP inference in graphical models. The problem, in general, is notoriously intractable, and finding the global optimal solution is known to be NP-hard. However, is it possible to approximate this problem with a reasonable ratio bound on the solution quality in polynomial time? We show in this paper that the answer is no. Specifically, we show that general energy minimization, even in the 2-label pairwise case, and planar energy minimization with three or more labels are exp-APX-complete. This finding rules out the existence of any approximation algorithm with a sub-exponential approximation ratio in the input size for these two problems, including constant factor approximations. Moreover, we collect and review the computational complexity of several subclass problems and arrange them on a complexity scale consisting of three major complexity classes -- PO, APX, and exp-APX, corresponding to problems that are solvable, approximable, and inapproximable in polynomial time. Problems in the first two complexity classes can serve as alternative tractable formulations to the inapproximable ones. This paper can help vision researchers to select an appropriate model for an application or guide them in designing new algorithms.Comment: ECCV'16 accepte

Pattern and determinants of HIV research productivity in sub-Saharan Africa: bibliometric analysis of 1981 to 2009 PubMed papers

<p>Abstract</p> <p>Background</p> <p>Several bibliometric studies have been published on AIDS. The findings obtained from these studies have provided a general picture of the history and growth of AIDS literature. However, factors related to variation in HIV research productivity in sub-Saharan Africa have not been examined. Therefore, this study aims to fill some of the gap in existing research to provide insights into factors associated with HIV research productivity in sub-Saharan Africa.</p> <p>Methods</p> <p>A bibliometric analysis regarding sub-Saharan Africa HIV/AIDS research was conducted in the PubMed database for the period of 1981 to 2009. The numbers of HIV research articles indexed in PubMed was used as surrogate for total HIV research productivity. Series of univariable and multivariable negative binomial regression models were used to explore factors associated with variation in HIV research productivity in sub-Saharan Africa.</p> <p>Results</p> <p>First authors from South Africa, Uganda and Kenya contributed almost half of the total number of HIV articles indexed in PubMed between 1981 and 2009. Uganda, Zimbabwe and Malawi had better records when the total production was adjusted for gross domestic product (GDP). Comoros, the Gambia and Guinea-Bissau were the most productive countries when the total products were normalized by number of people with HIV. There were strong positive and statistically significant correlation between countries number of indexed journal (Pearson correlation r = 0.77, p = .001), number of higher institutions (r = 0.60, p = .001), number of physicians (r = 0.83, p = .001) and absolute numbers of HIV articles.</p> <p>Conclusions</p> <p>HIV research productivity in Africa is highly skewed. To increase HIV research output, total expenditure on health (% of GDP), private expenditure on health, and adult literacy rate may be important factors to address.</p

Identity and European integration : diversity as a source of integration

This article explores the concept of European Union identity and its significance for European integration by drawing upon insights from theories of nationalism and national identity. European Union identity is viewed as an ongoing process which is banal, contingent and contextual. The central hypothesis is that: European integration facilitates the flourishing of diverse national identities rather than convergence around a single homogeneous European Union identity. The role of the EU as facilitator for diverse understandings of collective identities encourages the enhabitation of the EU at an everyday level and the reinforcement of a sense of banal Europeanism which is a crucial aspect of the European integration process. Facilitating diversity may thus provide a vital source of dynamism for the integration process