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- ItemEstimating the volume of a convex body(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2018) Baldin, NicolaiSometimes the volume of a convex body needs to be estimated, if we cannot calculate it analytically. We explain how statistics can be used not only to approximate the volume of the convex body, but also its shape.
- ItemModelling the spread of brain tumours(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2015) Swan, Amanda; Murtha, AlbertThe study of mathematical biology attempts to use mathematical models to draw useful conclusions about biological systems. Here, we consider the modelling of brain tumour spread with the ultimate goal of improving treatment outcomes.
- ItemTropical geometry(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2018) Brugallé, Erwan; Itenberg, Ilia; Shaw, Kristin; Viro, OlegWhat kind of strange spaces hide behind the enigmatic name of tropical geometry? In the tropics, just as in other geometries, one of the simplest objects is a line. Therefore, we begin our exploration by considering tropical lines. Afterwards, we take a look at tropical arithmetic and algebra, and describe how to define tropical curves using tropical polynomials.
- ItemThe adaptive finite element method(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2016) Gallistl, DietmarComputer simulations of many physical phenomena rely on approximations by models with a finite number of unknowns. The number of these parameters determines the computational effort needed for the simulation. On the other hand, a larger number of unknowns can improve the precision of the simulation. The adaptive finite element method (AFEM) is an algorithm for optimizing the choice of parameters so accurate simulation results can be obtained with as little computational effort as possible.
- ItemDrugs, herbicides, and numerical simulation(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2014) Benner, Peter; Mena, Hermann; Schneider, RenéThe Colombian government sprays coca fields with herbicides in an effort to reduce drug production. Spray drifts at the Ecuador-Colombia border became an international issue. We developed a mathematical model for the herbicide aerial spray drift, enabling simulations of the phenomenon.
- ItemPolyhedra and commensurability(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2016) Guglielmetti, Rafael; Jacquement, MatthieuThis snapshot introduces the notion of commensurability of polyhedra. At its bottom, this concept can be developed from constructions with paper, scissors, and glue. Starting with an elementary example, we formalize it subsequently. Finally, we discuss intriguing connections with other fields of mathematics.
- ItemThe mystery of sleeping sickness – why does it keep waking up?(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2015) Funk, SebastianSleeping sickness is a neglected tropical disease that affects rural populations in Africa. Deadly when untreated, it is being targeted for elimination through case finding and treatment. Yet, fundamental questions about its transmission cycle remain unanswered. One of them is whether transmission is limited to humans, or whether other species play a role in maintaining circulation of the disease. In this snapshot, we introduce a mathematical model for the spread of Trypanosoma brucei, the parasite responsible for causing sleeping sickness, and present some results based on data collected in Cameroon. Understanding how important animals are in harbouring Trypanosoma brucei that can infect humans is important for assessing whether the disease could be reintroduced in human populations even after all infected people have been successfully treated.
- ItemArrangements of lines(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2014) Harbourne, Brian; Szemberg, TomaszWe discuss certain open problems in the context of arrangements of lines in the plane.
- ItemFootballs and donuts in four dimensions(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2016) Klee, StevenIn this snapshot, we explore connections between the mathematical areas of counting and geometry by studying objects called simplicial complexes. We begin by exploring many familiar objects in our three dimensional world and then discuss the ways one may generalize these ideas into higher dimensions.
- ItemProfinite groups(Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach gGmbH, 2016) Bartholdi, LaurentProfinite objects are mathematical constructions used to collect, in a uniform manner, facts about infinitely many finite objects. We shall review recent progress in the theory of profinite groups, due to Nikolov and Segal, and its implications for finite groups.