Physics in Riemann's mathematical papers

Riemann's mathematical papers contain many ideas that arise from physics, and some of them are motivated by problems from physics. In fact, it is not easy to separate Riemann's ideas in mathematics from those in physics. Furthermore, Riemann's philosophical ideas are often in the background of his work on science. The aim of this chapter is to give an overview of Riemann's mathematical results based on physical reasoning or motivated by physics. We also elaborate on the relation with philosophy. While we discuss some of Riemann's philosophical points of view, we review some ideas on the same subjects emitted by Riemann's predecessors, and in particular Greek philosophers, mainly the pre-socratics and Aristotle. The final version of this paper will appear in the book: From Riemann to differential geometry and relativity (L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017

Looking backward: From Euler to Riemann

We survey the main ideas in the early history of the subjects on which Riemann worked and that led to some of his most important discoveries. The subjects discussed include the theory of functions of a complex variable, elliptic and Abelian integrals, the hypergeometric series, the zeta function, topology, differential geometry, integration, and the notion of space. We shall see that among Riemann's predecessors in all these fields, one name occupies a prominent place, this is Leonhard Euler. The final version of this paper will appear in the book \emph{From Riemann to differential geometry and relativity} (L. Ji, A. Papadopoulos and S. Yamada, ed.) Berlin: Springer, 2017

The prescribed mean curvature equation in weakly regular domains

We show that the characterization of existence and uniqueness up to vertical translations of solutions to the prescribed mean curvature equation, originally proved by Giusti in the smooth case, holds true for domains satisfying very mild regularity assumptions. Our results apply in particular to the non-parametric solutions of the capillary problem for perfectly wetting fluids in zero gravity. Among the essential tools used in the proofs, we mention a \textit{generalized Gauss-Green theorem} based on the construction of the weak normal trace of a vector field with bounded divergence, in the spirit of classical results due to Anzellotti, and a \textit{weak Young's law} for $(\Lambda,r_{0})$-minimizers of the perimeter.Comment: 23 pages, 1 figure --- The results on the weak normal trace of vector fields have been now extended and moved in a self-contained paper available at: arXiv:1708.0139

Seamless Gene Tagging by Endonuclease-Driven Homologous Recombination

Gene tagging facilitates systematic genomic and proteomic analyses but chromosomal tagging typically disrupts gene regulatory sequences. Here we describe a seamless gene tagging approach that preserves endogenous gene regulation and is potentially applicable in any species with efficient DNA double-strand break repair by homologous recombination. We implement seamless tagging in Saccharomyces cerevisiae and demonstrate its application for protein tagging while preserving simultaneously upstream and downstream gene regulatory elements. Seamless tagging is compatible with high-throughput strain construction using synthetic genetic arrays (SGA), enables functional analysis of transcription antisense to open reading frames and should facilitate systematic and minimally-invasive analysis of gene functions

Skeletal Muscle NADPH Oxidase Is Increased and Triggers Stretch-Induced Damage in the mdx Mouse

Recent studies have shown that oxidative stress contributes to the pathogenesis of muscle damage in dystrophic (mdx) mice. In this study we have investigated the role of NADPH oxidase as a source of the oxidative stress in these mice. The NADPH oxidase subunits gp91phox, p67phox and rac 1 were increased 2–3 fold in tibilais anterior muscles from mdx mice compared to wild type. Importantly, this increase occurred in 19 day old mice, before the onset of muscle necrosis and inflammation, suggesting that NADPH oxidase is an important source of oxidative stress in mdx muscle. In muscles from 9 week old mdx mice, gp91phox and p67phox were increased 3–4 fold and NADPH oxidase superoxide production was 2 times greater than wild type. In single fibers from mdx muscle NADPH oxidase subunits were all located on or near the sarcolemma, except for p67phox,which was expressed in the cytosol. Pharmacological inhibition of NADPH oxidase significantly reduced the intracellular Ca2+ rise following stretched contractions in mdx single fibers, and also attenuated the loss of muscle force. These results suggest that NADPH oxidase is a major source of reactive oxygen species in dystrophic muscle and its enhanced activity has a stimulatory effect on stretch-induced Ca2+ entry, a key mechanism for muscle damage and functional impairment

Diversity in action: Exchange of perspectives and reflections on taxonomies of individual differences

Throughout the last 2500 years, the classification of individual differences in healthy people and their extreme expressions in mental disorders has remained one of the most difficult challenges in science that affects our ability to explore individuals' functioning, underlying psychobiological processes and pathways of development. To facilitate analyses of the principles required for studying individual differences, this theme issue brought together prominent scholars from diverse backgrounds of which many bring unique combinations of cross-disciplinary experiences and perspectives that help establish connections and promote exchange across disciplines. This final paper presents brief commentaries of some of our authors and further scholars exchanging perspectives and reflecting on the contributions of this theme issue

Climate simulations for 1880-2003 with GISS modelE

We carry out climate simulations for 1880-2003 with GISS modelE driven by ten measured or estimated climate forcings. An ensemble of climate model runs is carried out for each forcing acting individually and for all forcing mechanisms acting together. We compare side-by-side simulated climate change for each forcing, all forcings, observations, unforced variability among model ensemble members, and, if available, observed variability. Discrepancies between observations and simulations with all forcings are due to model deficiencies, inaccurate or incomplete forcings, and imperfect observations. Although there are notable discrepancies between model and observations, the fidelity is sufficient to encourage use of the model for simulations of future climate change. By using a fixed well-documented model and accurately defining the 1880-2003 forcings, we aim to provide a benchmark against which the effect of improvements in the model, climate forcings, and observations can be tested. Principal model deficiencies include unrealistically weak tropical El Nino-like variability and a poor distribution of sea ice, with too much sea ice in the Northern Hemisphere and too little in the Southern Hemisphere. The greatest uncertainties in the forcings are the temporal and spatial variations of anthropogenic aerosols and their indirect effects on clouds.Comment: 44 pages; 19 figures; Final text accepted by Climate Dynamic

Expansion of the Preimmune Antibody Repertoire by Junctional Diversity in Bos taurus

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