Convergence and multiplicities for the Lempert function

Given a domain $\Omega \subset \mathbb C$, the Lempert function is a functional on the space Hol (\D,\Omega) of analytic disks with values in $\Omega$, depending on a set of poles in $\Omega$. We generalize its definition to the case where poles have multiplicities given by local indicators (in the sense of Rashkovskii's work) to obtain a function which still dominates the corresponding Green function, behaves relatively well under limits, and is monotonic with respect to the indicators. In particular, this is an improvement over the previous generalization used by the same authors to find an example of a set of poles in the bidisk so that the (usual) Green and Lempert functions differ.Comment: 24 pages; many typos corrected thanks to the referee of Arkiv for Matemati

Jacobi Identity for Vertex Algebras in Higher Dimensions

Vertex algebras in higher dimensions provide an algebraic framework for investigating axiomatic quantum field theory with global conformal invariance. We develop further the theory of such vertex algebras by introducing formal calculus techniques and investigating the notion of polylocal fields. We derive a Jacobi identity which together with the vacuum axiom can be taken as an equivalent definition of vertex algebra.Comment: 35 pages, references adde

Malaria elimination campaigns in the Lake Kariba region of Zambia: a spatial dynamical model

Background As more regions approach malaria elimination, understanding how different interventions interact to reduce transmission becomes critical. The Lake Kariba area of Southern Province, Zambia, is part of a multi-country elimination effort and presents a particular challenge as it is an interconnected region of variable transmission intensities. Methods In 2012-13, six rounds of mass-screen-and-treat drug campaigns were carried out in the Lake Kariba region. A spatial dynamical model of malaria transmission in the Lake Kariba area, with transmission and climate modeled at the village scale, was calibrated to the 2012-13 prevalence survey data, with case management rates, insecticide-treated net usage, and drug campaign coverage informed by surveillance. The model was used to simulate the effect of various interventions implemented in 2014-22 on reducing regional transmission, achieving elimination by 2022, and maintaining elimination through 2028. Findings The model captured the spatio-temporal trends of decline and rebound in malaria prevalence in 2012-13 at the village scale. Simulations predicted that elimination required repeated mass drug administrations coupled with simultaneous increase in net usage. Drug campaigns targeted only at high-burden areas were as successful as campaigns covering the entire region. Interpretation Elimination in the Lake Kariba region is possible through coordinating mass drug campaigns with high-coverage vector control. Targeting regional hotspots is a viable alternative to global campaigns when human migration within an interconnected area is responsible for maintaining transmission in low-burden areas