Random Walks on Hypergraphs with Edge-Dependent Vertex Weights

Hypergraphs are used in machine learning to model higher-order relationships in data. While spectral methods for graphs are well-established, spectral theory for hypergraphs remains an active area of research. In this paper, we use random walks to develop a spectral theory for hypergraphs with edge-dependent vertex weights: hypergraphs where every vertex $v$ has a weight $\gamma_e(v)$ for each incident hyperedge $e$ that describes the contribution of $v$ to the hyperedge $e$. We derive a random walk-based hypergraph Laplacian, and bound the mixing time of random walks on such hypergraphs. Moreover, we give conditions under which random walks on such hypergraphs are equivalent to random walks on graphs. As a corollary, we show that current machine learning methods that rely on Laplacians derived from random walks on hypergraphs with edge-independent vertex weights do not utilize higher-order relationships in the data. Finally, we demonstrate the advantages of hypergraphs with edge-dependent vertex weights on ranking applications using real-world datasets.Comment: Accepted to ICML 201

Trade Theory and Trade Facts

This paper quantitatively tests the "new trade theory" based on product di.erentiation, increasing returns, and imperfect competition. We employ a standard model, which allows both changes in the distribution of income among industrialized countries, emphasized by Helpman and Krugman (1985), and nonhomothetic preferences, emphasized by Markusen (1986), to e.ect trade directions and volumes. In addition, we generalize the model to allow changes in relative prices to have large e.ects. We test the model by calibrating it to 1990 data and then "backcasting" to 1961 to see what changes in crucial variables between 1961 and 1990 are predicted by the theory. The results show that, although the model is capable of explaining much of the increased concentration of trade among industrialized countries, it is not capable of explaining the enormous increase in the ratio of trade to income. Our analysis suggests that it is policy changes, rather than the elements emphasized in the new trade theory, that have been the most significant determinants of the increase in trade volume.

Trade theory and trade facts

This paper quantitatively tests the “new trade theory” based on product differentiation, increasing returns, and imperfect competition. We employ a standard model, which allows both changes in the distribution of income among industrialized countries, emphasized by Helpman and Krugman (1985), and nonhomothetic preferences, emphasized by Markusen (1986), to effect trade directions and volumes. In addition, we generalize the model to allow changes in relative prices to have large effects. We test the model by calibrating it to 1990 data and then “backcasting” to 1961 to see what changes in crucial variables between 1961 and 1990 are predicted by the theory. The results show that, although the model is capable of explaining much of the increased concentration of trade among industrialized countries, it is not capable of explaining the enormous increase in the ratio of trade to income. Our analysis suggests that it is policy changes, rather than the elements emphasized in the new trade theory, that have been the most significant determinants of the increase in trade volume.Trade ; Product differentiation

The global nuclear liability regime post Fukushima Daiichi

Nuclear liability regimes are important as they ensure that potential victims will be compensated promptly and efficiently after a nuclear accident. The accident at Fukushima Daiichi in Japan in 2011 prompted a review of the global nuclear liability regime that remains on-going. Progress has been slow, but over the next few years the European Union is set to announce its new proposals. Meanwhile, in 2015, another global nuclear liability regime, the Convention on Supplementary Compensation for Nuclear Damage, has entered into force. This paper aims to move the debate in the literature on nuclear liability and focuses on the four following major issues: (1) reviews third-party nuclear liability regimes currently in operation around the world; (2) analyses the international nuclear liability regime following the accident at Fukushima Daiichi; (3) comparatively assesses the liability regimes for nuclear energy and the non-nuclear energy sector; and (4) presents the future outlook for possible developments in the global nuclear liability regime

Development of higher-order modal methods for transient thermal and structural analysis

A force-derivative method which produces higher-order modal solutions to transient problems is evaluated. These higher-order solutions converge to an accurate response using fewer degrees-of-freedom (eigenmodes) than lower-order methods such as the mode-displacement or mode-acceleration methods. Results are presented for non-proportionally damped structural problems as well as thermal problems modeled by finite elements