Infinitesimals without Logic

We introduce the ring of Fermat reals, an extension of the real field containing nilpotent infinitesimals. The construction takes inspiration from Smooth Infinitesimal Analysis (SIA), but provides a powerful theory of actual infinitesimals without any need of a background in mathematical logic. In particular, on the contrary with respect to SIA, which admits models only in intuitionistic logic, the theory of Fermat reals is consistent with classical logic. We face the problem to decide if the product of powers of nilpotent infinitesimals is zero or not, the identity principle for polynomials, the definition and properties of the total order relation. The construction is highly constructive, and every Fermat real admits a clear and order preserving geometrical representation. Using nilpotent infinitesimals, every smooth functions becomes a polynomial because in Taylor's formulas the rest is now zero. Finally, we present several applications to informal classical calculations used in Physics: now all these calculations become rigorous and, at the same time, formally equal to the informal ones. In particular, an interesting rigorous deduction of the wave equation is given, that clarifies how to formalize the approximations tied with Hook's law using this language of nilpotent infinitesimals.Comment: The first part of the preprint is taken directly form arXiv:0907.1872 The second part is new and contains a list of example

A dimensionally continued Poisson summation formula

We generalize the standard Poisson summation formula for lattices so that it operates on the level of theta series, allowing us to introduce noninteger dimension parameters (using the dimensionally continued Fourier transform). When combined with one of the proofs of the Jacobi imaginary transformation of theta functions that does not use the Poisson summation formula, our proof of this generalized Poisson summation formula also provides a new proof of the standard Poisson summation formula for dimensions greater than 2 (with appropriate hypotheses on the function being summed). In general, our methods work to establish the (Voronoi) summation formulae associated with functions satisfying (modular) transformations of the Jacobi imaginary type by means of a density argument (as opposed to the usual Mellin transform approach). In particular, we construct a family of generalized theta series from Jacobi theta functions from which these summation formulae can be obtained. This family contains several families of modular forms, but is significantly more general than any of them. Our result also relaxes several of the hypotheses in the standard statements of these summation formulae. The density result we prove for Gaussians in the Schwartz space may be of independent interest.Comment: 12 pages, version accepted by JFAA, with various additions and improvement

Assessing the transferability and reproducibility of 3D in vitro liver models from primary human multi-cellular microtissues to cell-line based HepG2 spheroids

To reduce, replace, and refine in vivo testing, there is increasing emphasis on the development of more physiologically relevant in vitro test systems to improve the reliability of non-animal-based methods for hazard assessment. When developing new approach methodologies, it is important to standardize the protocols and demonstrate the methods can be reproduced by multiple laboratories. The aim of this study was to assess the transferability and reproducibility of two advanced in vitro liver models, the Primary Human multicellular microtissue liver model (PHH) and the 3D HepG2 Spheroid Model, for nanomaterial (NM) and chemical hazard assessment purposes. The PHH model inter-laboratory trial showed strong consistency across the testing sites. All laboratories evaluated cytokine release and cytotoxicity following exposure to titanium dioxide (TiO2) and zinc oxide (ZnO) nanoparticles. No significant difference was observed in cytotoxicity or IL-8 release for the test materials. The data were reproducible with all three laboratories with control readouts within a similar range. The PHH model ZnO induced the greatest cytotoxicity response at 50.0 μg/mL and a dose-dependent increase in IL-8 release. For the 3D HepG2 spheroid model, all test sites were able to construct the model and demonstrated good concordance in IL-8 cytokine release and genotoxicity data. This trial demonstrates the successful transfer of new approach methodologies across multiple laboratories, with good reproducibility for several hazard endpoints.Toxicolog

Biogeochemical silica mass balances in Lake Michigan and Lake Superior

Silica budgets for Lake Michigan and Lake Superior differ in several respects. Mass balance calculations for both lakes agree with previous studies in that permanent burial of biogenic silica in sediments may be only about 5% of the biogenic silica produced by diatoms. Because dissolution rates are large, good estimates of permanent burial of diatoms can not be obtained indirectly from the internal cycle of silica (silica uptake by diatoms and subsequent dissolution) but must be obtained from the sediment stratigraphy. The annual net production of biogenic silica in Lake Michigan requires 71% of the winter maximum silica reservoir which must be maintained primarily by internal cycling in this large lake whereas the comparable silica demand in Lake Superior is only 8.3%. The greater silica demand in Lake Michigan is the result of phosphorus enrichment which has increased diatom production. It is hypothesized that steady-state silica dynamics in Lake Michigan were disrupted by increased diatom production between 1955 and 1970 and that a new steady state based on silica-limited diatom production developed after 1970. Mass balance calculations for Lake Michigan show in contrast with previous work that the hypothesized water column silica depletion of 3.0 g · m −3 could have occurred even though 90% or more of the biogenic silica production is recycled.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42471/1/10533_2004_Article_BF02187199.pd

Size Doesn't Matter: Towards a More Inclusive Philosophy of Biology

notes: As the primary author, O’Malley drafted the paper, and gathered and analysed data (scientific papers and talks). Conceptual analysis was conducted by both authors.publication-status: Publishedtypes: ArticlePhilosophers of biology, along with everyone else, generally perceive life to fall into two broad categories, the microbes and macrobes, and then pay most of their attention to the latter. ‘Macrobe’ is the word we propose for larger life forms, and we use it as part of an argument for microbial equality. We suggest that taking more notice of microbes – the dominant life form on the planet, both now and throughout evolutionary history – will transform some of the philosophy of biology’s standard ideas on ontology, evolution, taxonomy and biodiversity. We set out a number of recent developments in microbiology – including biofilm formation, chemotaxis, quorum sensing and gene transfer – that highlight microbial capacities for cooperation and communication and break down conventional thinking that microbes are solely or primarily single-celled organisms. These insights also bring new perspectives to the levels of selection debate, as well as to discussions of the evolution and nature of multicellularity, and to neo-Darwinian understandings of evolutionary mechanisms. We show how these revisions lead to further complications for microbial classification and the philosophies of systematics and biodiversity. Incorporating microbial insights into the philosophy of biology will challenge many of its assumptions, but also give greater scope and depth to its investigations

Methotrexate and interstitial lung disease: Controversies and questions. A narrative review of the literature

MTX, which is the anchor-drug for the treatment of RA, has been associated with lung injury and in particular with MTX-related pneumonitis (M-pneu). Although the frequency of M-pneu has been reported to range between 0.3 and 11.6%, more recent studies and meta-analyses have challenged that, suggesting that it is less common than previously thought. M-pneu is considered a hypersensitivity reaction usually occuring early after MTX commencement, and to be dose-independent. Furthermore, it does not seem to be truly related to the development of interstitial lung disease observed in some patients as part of the natural history of RA (RA-ILD). On the other hand, there are data suggesting that clinicians should be cautious when commencing MTX in patients with pre-existing lung disease. However, treatment should not be delayed or limited in progressive RA that could lead to RA-ILD, and MTX remains one of the central players in the treat-to-target approach. In this review, we aimed to summarize the current evidence from observational studies and clinical trials on lung disease in MTX-treated RA patients. We focus the discussion on the lack of association between M-pneu and RA-ILD. © 2019 The Author(s)

Methotrexate-Associated Pneumonitis and Rheumatoid Arthritis-Interstitial Lung Disease: Current Concepts for the Diagnosis and Treatment

Rheumatoid arthritis (RA) is a type of inflammatory arthritis that affects ~1% of the general population. Although arthritis is the cardinal symptom, many extra-articular manifestations can occur. Lung involvement and particularly interstitial lung disease (ILD) is among the most common. Although ILD can occur as part of the natural history of RA (RA-ILD), pulmonary fibrosis has been also linked with methotrexate (MTX); a condition also known as MTX-pneumonitis (M-pneu). This review aims to discuss epidemiological, diagnostic, imaging and histopathological features, risk factors, and treatment options in RA-ILD and M-pneu. M-pneu, usually has an acute/subacute course characterized by cough, dyspnea and fever. Several risk factors, including genetic and environmental factors have been suggested, but none have been validated. The diagnosis is based on clinical and radiologic findings which are mostly consistent with non-specific interstitial pneumonia (NSIP), more so than bronchiolitis obliterans organizing pneumonia (BOOP). Histological findings include interstitial infiltrates by lymphocytes, histiocytes, and eosinophils with or without non-caseating granulomas. Treatment requires immediate cessation of MTX and commencement of glucocorticoids. RA-ILD shares the same symptomatology with M-pneu. However, it usually has a more chronic course. RA-ILD occurs in about 3–5% of RA patients, although this percentage is significantly increased when radiologic criteria are used. Usual interstitial pneumonia (UIP) and NSIP are the most common radiologic patterns. Several risk factors have been identified for RA-ILD including smoking, male gender, and positivity for anti-citrullinated peptide antibodies and rheumatoid factor. Diagnosis is based on clinical and radiologic findings while pulmonary function tests may demonstrate a restrictive pattern. Although no clear guidelines exist for RA-ILD treatment, glucocorticoids and conventional disease modifying antirheumatic drugs (DMARDs) like MTX or leflunomide, as well as treatment with biologic DMARDs can be effective. There is limited evidence that rituximab, abatacept, and tocilizumab are better options compared to TNF-inhibitors. © Copyright © 2019 Fragoulis, Nikiphorou, Larsen, Korsten and Conway