Quantum Geometry as a Relational Construct

The problem of constructing a quantum theory of gravity is considered from a novel viewpoint. It is argued that any consistent theory of gravity should incorporate a relational character between the matter constituents of the theory. In particular, the traditional approach of quantizing a space-time metric is criticized and two possible avenues for constructing a satisfactory theory are put forward.Comment: 14 pages, revtex file. Submitted to MPL

Majorana lattices from the quantized Hall limit of a proximitized spin-orbit coupled electron gas

Motivated by recent experiments demonstrating intricate quantum Hall physics on the surface of elemental bismuth, we consider proximity coupling an $s$-wave superconductor to a two-dimensional electron gas with strong Rashba spin-orbit interactions in the presence of a strong perpendicular magnetic field. We focus on the high-field limit so that the superconductivity can be treated as a perturbation to the low-lying Landau levels. In the clean case, wherein the superconducting order parameter takes the form of an Abrikosov vortex lattice, we show that a lattice of hybridized Majorana modes emerges near the plateau transition of the lowest Landau level. However, unless magnetic-symmetry-violating perturbations are present, the system always has an even number of chiral Majorana edge modes and thus is strictly speaking Abelian in nature, in agreement with previous work on related setups. Interestingly, however, a weak topological superconducting phase can very naturally be stabilized near the plateau transition for the square vortex lattice. The relevance of our findings to potential near-term experiments on proximitized materials such as bismuth will be discussed.Comment: 13 pages, 9 figure

Bayesian Optimization with Unknown Constraints

Recent work on Bayesian optimization has shown its effectiveness in global optimization of difficult black-box objective functions. Many real-world optimization problems of interest also have constraints which are unknown a priori. In this paper, we study Bayesian optimization for constrained problems in the general case that noise may be present in the constraint functions, and the objective and constraints may be evaluated independently. We provide motivating practical examples, and present a general framework to solve such problems. We demonstrate the effectiveness of our approach on optimizing the performance of online latent Dirichlet allocation subject to topic sparsity constraints, tuning a neural network given test-time memory constraints, and optimizing Hamiltonian Monte Carlo to achieve maximal effectiveness in a fixed time, subject to passing standard convergence diagnostics.Comment: 14 pages, 3 figure

Knowledge, Legitimacy, Efficiency and the Institutionalization of Dispute Settlement Procedures at the World Trade Organization and the World Intellectual Property Organization

International legal research regarding international economic dispute settlement tends to be a-theoretical. A theoretically-grounded analytic framework is employed in this article which draws from scholarship from political science, sociology, and economics regarding institutions and international governmental organizations. The knowledge-legitimacy-efficiency analytic framework is applied in this article to studies of General Agreement on Tariffs and Trade (GA TT)/World Trade Organization (WTO) dispute settlement in order to relate this relevant scholarship to the economic field under primary study, Internet domain names. GA TT/WTO knowledge regarding international trade law has thickened through multi-lateral trade negotiations and dispute settlement decisions. The WTO\u27s legitimacy is increasingly questioned by disenchanted members, in particular by those from developing countries, and by outside critics who believe the organization to be undemocratic in process and unfair in outcome. However the WTO\u27s efficiency with respect to quasi-judicial dispute settlement procedure is perhaps a model for emulation by other multilateral institutions. Likewise, World Intellectual Property Organization ( WIPO\u27) knowledge regarding trademark law is deep and relevant to Internet-domain-name-dispute settlement. WIPO legitimacy has been earned through the sponsorship ofpublic forums, fair, independent decisions, and by virtue of its United Nations status. WIPO arbitration quickly established itself as a more efficient alternative to national courts. Knowledge, legitimacy, and efficiency account for the rapid increase in the number of users of WIPO Internet domain name arbitration

Strategy and Compliance with Bilateral Trade Dispute Settlement Agreements: USTR\u27s Section 301 Experience in the Pacific Basin

The paper is laid out in five parts. First, the conceptual linkages among strategy, goals, and agreement compliance are developed. Second, the study research design and findings are reported. Third, the strategy of trade dispute settlement negotiation is discussed with regard to bureaucratic politics. Fourth, case evidence that illustrates the key study findings is reviewed. Finally, effective monitoring and the notion of unilateral surveillance within the context of the present GATT-based, multilateral trading system are explored