We study the combinatorics of weighted trees from the point of view of tropical algebraic geometry and tropical linear spaces. The set of dissimilarity vectors of weighted trees is contained in the tropical Grassmannian, so we describe here the tropical linear space of a dissimilarity vector and its associated family of matroids. This gives a family of complete flags of tropical linear spaces, ...

As a new concept tropical halfspaces are introduced to the (linear algebraic) geometry of the tropical semiring (R,min,+). This yields exterior descriptions of the tropical polytopes that were recently studied by Develin and Sturmfels [2004] in a variety of contexts. The key tool to the understanding is a newly defined sign of the tropical determinant, which shares remarkably many properties wi...

Tropical Extra-tropical thermocline water mass exchanges in the community climate model v.3 Part I: the Atlantic Ocean I. Wainer, A. Lazar, and A. Solomon Department of Physical Oceanography, University of São Paulo, São Paulo, Brazil 2 Laboratoire d’Ocanographie Dynamique et de Climatologie (LODYC), Paris, France 3 National Oceanic Atmospheric Administration-Cooperative Institute Research Envi...

1 NTDs, Liverpool School of Tropical Medicine, Pembroke Place, Liverpool, United Kingdom, 2 University of Edinburgh Medical School, Edinburgh, United Kingdom, 3 Department of Parasitology, Liverpool School of Tropical Medicine, Pembroke Place, Liverpool, United Kingdom, 4 National School of Tropical Medicine, Baylor College of Medicine, Houston, Texas, United States of America, 5 World Health O...

A tropical curve is a graph with specified edge lengths, some of which may be infinite. Various facts and attributes about algebraic curves have analogs for tropical curves. In this article, we focus on divisors and linear series, and prove the Riemann-Roch formula for divisors on tropical curves. We describe two ways in which algebraic curves may be transformed into tropical curves: by aboemas...

malaria parasites? Timothy J.C. Anderson, Shalini Nair, Marina McDew-White, Ian H. Cheeseman, Standwell Nkhoma, Fatma Bilgic, Rose McGready, Elizabeth Ashley, Aung Pyae Phyo, Nicholas J. White, François Nosten Department of Genetics, Texas Biomedical Research Institute, San Antonio, Texas, United States of America Shoklo Malaria Research Unit, Mahidol-Oxford Tropical Medicine Research Unit, Fac...

Tropical geometry has burgeoned in the decade and a half since its coalescence as a field of study. It is a combinatorialization of algebraic geometry, associating to each algebraic variety a so-called tropical variety, a polyhedral complex that is its combinatorial “shadow”. In the simplest cases tropical geometry can be seen as the algebraic geometry over the tropical semiring T = (R ∪ {∞}, m...

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The 40-yr ECMWF Re-Analysis (ERA-40) data are analyzed to demonstrate that wave forcing at lower latitudes plays a crucial role in driving the tropical upwelling portion of the Brewer–Dobson circulation. It is shown that subtropical wave forcing is correlated with tropical upwelling on both intraseasonal and interannual time scales when transient waves are taken into account, and that tropical ...