The skeleton of the Jacobian, the Jacobian of the skeleton, and lifting meromorphic functions from tropical to algebraic curves

Let K be an algebraically closed field which is complete with respect to a nontrivial, non-Archimedean valuation and let \Lambda be its value group. Given a smooth, proper, connected K-curve X and a skeleton \Gamma of the Berkovich analytification X^\an, there are two natural real tori which one can consider: the tropical Jacobian Jac(\Gamma) and the skeleton of the Berkovich analytification Jac(X)^\an. We show that the skeleton of the Jacobian is canonically isomorphic to the Jacobian of the skeleton as principally polarized tropical abelian varieties. In addition, we show that the tropicalization of a classical Abel-Jacobi map is a tropical Abel-Jacobi map. As a consequence of these results, we deduce that \Lambda-rational principal divisors on \Gamma, in the sense of tropical geometry, are exactly the retractions of principal divisors on X. We actually prove a more precise result which says that, although zeros and poles of divisors can cancel under the retraction map, in order to lift a \Lambda-rational principal divisor on \Gamma to a principal divisor on X it is never necessary to add more than g extra zeros and g extra poles. Our results imply that a continuous function F:\Gamma -> R is the restriction to \Gamma of -log|f| for some nonzero meromorphic function f on X if and only if F is a \Lambda-rational tropical meromorphic function, and we use this fact to prove that there is a rational map f : X --> P^3 whose tropicalization, when restricted to \Gamma, is an isometry onto its image.Comment: 21 pages, 1 figur

On the structure of nonarchimedean analytic curves

Let K be an algebraically closed, complete nonarchimedean field and let X be a smooth K-curve. In this paper we elaborate on several aspects of the structure of the Berkovich analytic space X^an. We define semistable vertex sets of X^an and their associated skeleta, which are essentially finite metric graphs embedded in X^an. We prove a folklore theorem which states that semistable vertex sets of X are in natural bijective correspondence with semistable models of X, thus showing that our notion of skeleton coincides with the standard definition of Berkovich. We use the skeletal theory to define a canonical metric on H(X^an) := X^an - X(K), and we give a proof of Thuillier's nonarchimedean Poincar\'e-Lelong formula in this language using results of Bosch and L\"utkebohmert.Comment: 23 pages. This an expanded version of section 5 of arXiv:1104.0320 which appears in the conference proceedings "Tropical and Non-Archimedean Geometry

Innovation, Intellectual Property, and Development: A Better Set of Approaches for the 21st Century

This paper aims to provide an intellectual basis to think about the relationship between development, intellectual property and innovation; where we currently are and what alternatives are available. For the most part, we are concerned less with the implications of current IP laws for the advanced countries as we are with their impact on developing countries. We focus here not only on the current pathologies of the system and on potential alternative ways to tackle its most egregious excesses; but on a more positive note, on what kind of "system" would best promote development and well-being in the developing world. We are looking for a world with new and better rules for intellectual property. Just as some have begun to think about re-writing the rules of the American economy to ensure a more just and efficient system, the time is ripe for doing the same for the global economy, especially with regard to the IP system

What Lies Beneath: Treatment of Canvas-backed Pennsylvania Coal Mining Maps for Digitization

An ongoing program to preserve approximately seven hundred oversized, canvas-backed, coal mining maps from the CONSOL Energy Mining Map Collection was initiated by the University of Pittsburgh (Pitt) in 2007, supported by funding from the United States Department of the Interior Office of Surface Mining and Reclamation (OSM) and the Pennsylvania Department of Environmental Protection (PA-DEP). The main goal of this project is to stabilize and clean the mining maps for digitization at the OSM National Mine Map Repository (NMMR) located in Pittsburgh, Pennsylvania. The digitized data of the underground mines will be incorporated into Geographical Information Systems relative to mine safety, land reclamation, current mining operations, and new development

Lifting harmonic morphisms II: tropical curves and metrized complexes

In this paper we prove several lifting theorems for morphisms of tropical curves. We interpret the obstruction to lifting a finite harmonic morphism of augmented metric graphs to a morphism of algebraic curves as the non-vanishing of certain Hurwitz numbers, and we give various conditions under which this obstruction does vanish. In particular we show that any finite harmonic morphism of (non-augmented) metric graphs lifts. We also give various applications of these results. For example, we show that linear equivalence of divisors on a tropical curve C coincides with the equivalence relation generated by declaring that the fibers of every finite harmonic morphism from C to the tropical projective line are equivalent. We study liftability of metrized complexes equipped with a finite group action, and use this to classify all augmented metric graphs arising as the tropicalization of a hyperelliptic curve. We prove that there exists a d-gonal tropical curve that does not lift to a d-gonal algebraic curve. This article is the second in a series of two.Comment: 35 pages, 18 figures. This article used to be the second half of arXiv:1303.4812, and is now its seque

The Effects of Private Insurance on Measures of Health: Evidence from the Health and Retirement Study

In this paper we investigate whether the presence of private insurance leads to improved health status. Using the Health and Retirement study we focus on adults in late middle age who are nearing entry into Medicare. Estimation addresses endogeneity of the insurance participation decision in health outcome regressions. Two models are tested, an instrumental variables models, and a model with endogenous treatment effects due to Heckman (1978). Insurance participation and health behaviors enter with a lag to allow their effects to dissipate over time. Separate regressions were run for groupings of chronic conditions. We find that the overall impact of insurance on health tends to be significantly downwards biased if no adjustment for endogeneity is made. With corrections there is a four-fold increase in the insurance effect; yielding a 7 percent increase in the overall health measure for the uninsured. Results are consistent across IV and treatment effects models, and for all major groupings of medical conditions. Thus, the effect of private insurance on health may be larger than previously estimated. As for policy, expanding coverage to the uninsured should result in substantial health improvement. By conjecture, this is likely to reduce the need for health care when individuals retire and enter Medicare, potentially leading to savings.

MooseGuard: secure file sharing at scale in untrusted environments

Shared storage systems provide cheap, scalable, and reliable storage, but secure sharing in these systems requires users to encrypt their data and limit efficient sharing or trust a service provider to faithfully keep their data private. Current research has explored the use of trusted execution environments (TEEs) to operate on sensitive data and sharing policies in isolated execution. That work enables the utilization of untrusted shared resources to store and share sensitive data while maintaining stronger security guarantees. However, current research has limitations in scaling these solutions, as it bottlenecks both metadata and data operations within the same physical TEE, whereas a scaled file system distributes metadata and data operations to separate devices. This paper explores the use of two TEEs specialized for metadata and data operations to provide file sharing at scale with less overhead in addition to strong security guarantees. This approach achieves scaled metadata and concurrent use by utilizing a server-side TEE for isolated execution on a master server and provides data privacy and efficient access revocation through a client-side TEE. MooseGuard is the prototype implementation of this design, utilizing Intel SGX as a TEE and extending the MooseFS distributed file system. MooseGuard's implementation details the modifications needed to provide security and shows how this approach can be applied to a typical distributed file system. An evaluation of MooseGuard demonstrates that TEEs specialized for metadata and data operations allow a secured distributed file system to maintain its scale with only constant overheads. As TEEs and secure hardware become more widely available in public clouds, enterprise, and personal devices, MooseGuard presents a way for users to get the best of both worlds in data privacy and efficient sharing when using scaled, shared storage systems