Congruences for critical values of higher derivatives of twisted Hasse-Weil L-functions

Let A be an abelian variety over a number field k and F a finite cyclic extension of k of p-power degree for an odd prime p. Under certain technical hypotheses, we obtain a reinterpretation of the equivariant Tamagawa number conjecture (eTNC) for A, F/k and p as an explicit family of p-adic congru- ences involving values of derivatives of the Hasse-Weil L-functions of twists of A, normalised by completely explicit twisted regulators. This reinterpretation makes the eTNC amenable to numerical verification and furthermore leads to explicit predictions which refine well-known conjectures of Mazur and Tate

Increasing Returns and All That: A View From Trade

Do scale economies contribute to our understanding of international trade? Do international trade flows encode information about the extent of scale economies? To answer these questions we examine the large class of general equilibrium theories that imply Helpman-Krugman variants of the Vanek factor content prediction. Using an ambitious database on output, trade flows, and factor endowments, we find that scale economies significantly increase our understanding of the sources of comparative advantage. Further, the Helpman-Krugman framework provides a remarkable lens for viewing the general equilibrium scale elasticities encoded in trade flows. In particular, we find that a third of all goods-producing industries are characterized by scale. (The modal range of scale elasticities for this group is 1.10-1.20 and the economy-wide scale elasticity is 1.05.) Implications are drawn for the trade-and-wages debate (skill-biased scale effects) and endogenous growth.

Towards a Reference Terminology for Ontology Research and Development in the Biomedical Domain

Ontology is a burgeoning field, involving researchers from the computer science, philosophy, data and software engineering, logic, linguistics, and terminology domains. Many ontology-related terms with precise meanings in one of these domains have different meanings in others. Our purpose here is to initiate a path towards disambiguation of such terms. We draw primarily on the literature of biomedical informatics, not least because the problems caused by unclear or ambiguous use of terms have been there most thoroughly addressed. We advance a proposal resting on a distinction of three levels too often run together in biomedical ontology research: 1. the level of reality; 2. the level of cognitive representations of this reality; 3. the level of textual and graphical artifacts. We propose a reference terminology for ontology research and development that is designed to serve as common hub into which the several competing disciplinary terminologies can be mapped. We then justify our terminological choices through a critical treatment of the ‘concept orientation’ in biomedical terminology research