A vanishing theorem for operators in Fock space

We consider the bosonic Fock space over the Hilbert space of transversal vector fields in three dimensions. This space carries a canonical representation of the group of rotations. For a certain class of operators in Fock space we show that rotation invariance implies the absence of terms which either create or annihilate only a single particle. We outline an application of this result in an operator theoretic renormalization analysis of Hamilton operators, which occur in non-relativistic qed.Comment: 14 page

The heat kernel expansion for the electromagnetic field in a cavity

We derive the first six coefficients of the heat kernel expansion for the electromagnetic field in a cavity by relating it to the expansion for the Laplace operator acting on forms. As an application we verify that the electromagnetic Casimir energy is finite.Comment: 12 page

Existence of the D0-D4 Bound State: a detailed Proof

We consider the supersymmetric quantum mechanical system which is obtained by dimensionally reducing d=6, N=1 supersymmetric gauge theory with gauge group U(1) and a single charged hypermultiplet. Using the deformation method and ideas introduced by Porrati and Rozenberg, we present a detailed proof of the existence of a normalizable ground state for this system

Locating the Source of Diffusion in Large-Scale Networks

How can we localize the source of diffusion in a complex network? Due to the tremendous size of many real networks--such as the Internet or the human social graph--it is usually infeasible to observe the state of all nodes in a network. We show that it is fundamentally possible to estimate the location of the source from measurements collected by sparsely-placed observers. We present a strategy that is optimal for arbitrary trees, achieving maximum probability of correct localization. We describe efficient implementations with complexity O(N^{\alpha}), where \alpha=1 for arbitrary trees, and \alpha=3 for arbitrary graphs. In the context of several case studies, we determine how localization accuracy is affected by various system parameters, including the structure of the network, the density of observers, and the number of observed cascades.Comment: To appear in Physical Review Letters. Includes pre-print of main paper, and supplementary materia

Integration of production and financial models to analyse the financial impact of livestock diseases: a case study of Schmallenberg virus disease on British and French dairy farms

AIMS AND OBJECTIVES: The aim of the study was to investigate and compare the financial impact of Schmallenberg disease for different dairy production types in the United Kingdom and France. MATERIALS AND METHODS: Integrated production and financial models for dairy cattle were developed and applied to Schmallenberg virus (SBV) disease in a British and French context. The five main production systems that prevail in these two countries were considered. Their respective gross margins measuring the holding's profitability were calculated based on public benchmarking, literature and expert opinion data. A partial budget analysis was performed within each production model to estimate the impact of SBV in the systems modelled. Two disease scenarios were simulated: low impact and high impact. RESULTS: The model gross margin obtained per cow space and year ranged from £1014 to £1484 for the UK and from £1037 to £1890 for France depending on the production system considered. In the UK, the net SBV disease costs in £/cow space/year for an average dairy farm with 100 milking spaces were estimated between £16.3 and £51.4 in the high-impact scenario and between £8.2 and £25.9 in the low-impact scenario. For France, the net SBV disease costs in £/cow space/year ranged from £19.6 to £48.6 in the high-impact scenario and £9.7 to £22.8 in the low-impact scenario, respectively. CONCLUSION: The study illustrates how the combination of production and financial models allows assessing disease impact taking into account differing management and husbandry practices and associated price structures in the dairy sector. It supports decision-making of farmers and veterinarians who are considering disease control measures as it provides an approach to estimate baseline disease impact in common dairy production systems in the UK and France