Approaches to analysis with infinitesimals following Robinson, Nelson, and others

This is a survey of several approaches to the framework for working with infinitesimals and infinite numbers, originally developed by Abraham Robinson in the 1960s, and their constructive engagement with the Cantor-Dedekind postulate and the Intended Interpretation hypothesis. We highlight some applications including (1) Loeb's approach to the Lebesgue measure, (2) a radically elementary approach to the vibrating string, (3) true infinitesimal differential geometry. We explore the relation of Robinson's and related frameworks to the multiverse view as developed by Hamkins. Keywords: axiomatisations, infinitesimal, nonstandard analysis, ultraproducts, superstructure, set-theoretic foundations, multiverse, naive integers, intuitionism, soritical properties, ideal elements, protozoa

Seasonal hydrological and suspended sediment transport dynamics in proglacial streams, James Ross Island, Antarctica

Rapid warming of the Antarctic Peninsula is producing accelerated glacier mass loss and can be expected to have significant impacts on meltwater runoff regimes and proglacial fluvial activity. This study presents analysis of the hydrology and suspended sediment dynamics of two proglacial streams on James Ross Island, Antarctic Peninsula. Mean water discharge during 8 January 2015 to 18 February 2015 reached 0.19 m3 s−1 and 0.06 m3 s−1 for Bohemian Stream and Algal Stream, respectively, equivalent to specific runoff of 76 and 60 mm month−1. The daily discharge regime strongly correlated with air and ground temperatures. The effect of global radiation on proglacial water discharge was found low to negligible. Suspended sediment concentrations of Bohemian Stream were very high (up to 2927 mg L−1) due to aeolian supply and due to the high erodibility of local rocks. Total sediment yield (186 t km−2 yr−1) was high for (nearly) deglaciated catchments, but relatively low in comparison with streams draining more glaciated alpine and arctic catchments. The sediment provenance was mostly local Cretaceous marine and aeolian sediments; volcanic rocks are not an important source for suspended load. High Rb/Sr ratios for some samples suggested chemical weathering. Overall, this monitoring of proglacial hydrological and suspended sediment dynamics contributes to the dearth of such data from Antarctic environments and offers an insight to the nature of the proglacial fluvial activity, which is likely to be in a transient state with ongoing climate change

The causal ladder and the strength of K-causality. I

A unifying framework for the study of causal relations is presented. The causal relations are regarded as subsets of M x M and the role of the corresponding antisymmetry conditions in the construction of the causal ladder is stressed. The causal hierarchy of spacetime is built from chronology up to K-causality and new characterizations of the distinction and strong causality properties are obtained. The closure of the causal future is not transitive, as a consequence its repeated composition leads to an infinite causal subladder between strong causality and K-causality - the A-causality subladder. A spacetime example is given which proves that K-causality differs from infinite A-causality.Comment: 16 pages, one figure. Old title: ``On the relationship between K-causality and infinite A-causality''. Some typos fixed; small change in the proof of lemma 4.

Divergent mathematical treatments in utility theory

In this paper I study how divergent mathematical treatments affect mathematical modelling, with a special focus on utility theory. In particular I examine recent work on the ranking of information states and the discounting of future utilities, in order to show how, by replacing the standard analytical treatment of the models involved with one based on the framework of Nonstandard Analysis, diametrically opposite results are obtained. In both cases, the choice between the standard and nonstandard treatment amounts to a selection of set-theoretical parameters that cannot be made on purely empirical grounds. The analysis of this phenomenon gives rise to a simple logical account of the relativity of impossibility theorems in economic theory, which concludes the paper

Ten Misconceptions from the History of Analysis and Their Debunking

The widespread idea that infinitesimals were "eliminated" by the "great triumvirate" of Cantor, Dedekind, and Weierstrass is refuted by an uninterrupted chain of work on infinitesimal-enriched number systems. The elimination claim is an oversimplification created by triumvirate followers, who tend to view the history of analysis as a pre-ordained march toward the radiant future of Weierstrassian epsilontics. In the present text, we document distortions of the history of analysis stemming from the triumvirate ideology of ontological minimalism, which identified the continuum with a single number system. Such anachronistic distortions characterize the received interpretation of Stevin, Leibniz, d'Alembert, Cauchy, and others.Comment: 46 pages, 4 figures; Foundations of Science (2012). arXiv admin note: text overlap with arXiv:1108.2885 and arXiv:1110.545

Impact of perioperative chemotherapy on survival in patients with advanced primary urethral cancer: results of the international collaboration on primary urethral carcinoma

This is the first series that suggests a prognostic benefit of neoadjuvant treatment in a consecutive series of patients who underwent perioperative chemotherapy plus surgery for advanced primary urethral carcinoma. Further studies should yield a better understanding of how perioperative chemotherapy exerts a positive effect on survival in order to selectively advocate its use in advanced primary urethral carcinom

Proving Ground Confluence of Equational Specifications Modulo Axioms

Terminating functional programs should be deterministic, i.e., should evaluate to a unique result, regardless of the evaluation order. For equational functional programs such determinism is exactly captured by the ground confluence property. For terminating equations this is equivalent to ground local confluence, which follows from local confluence. Checking local confluence by computing critical pairs is the standard way to check ground confluence. The problem is that some perfectly reasonable equational programs are not locally confluent and it can be very hard or even impossible to make them so by adding more equations. We propose a three-step strategy to prove that an equational program as is is ground confluent: First: apply the strategy proposed in [8] to use non-joinable critical pairs as completion hints to either achieve local confluence or reduce the number of critical pairs. Second: use the inductive inference system proposed in this paper to prove the remaining critical pairs ground joinable. Third: to show ground confluence of the original specification, prove also ground joinable the equations added. These methods apply to order-sorted and possibly conditional equational programs modulo axioms such as, e.g., Maude functional modules.This work has been partially supported by NRL under contract number N00173-17-1-G002.Ope

Serum antibodies against genitourinary infectious agents in prostate cancer and benign prostate hyperplasia patients: a case-control study

<p>Abstract</p> <p>Background</p> <p>Infection plays a role in the pathogenesis of many human malignancies. Whether prostate cancer (PCa) - an important health issue in the aging male population in the Western world - belongs to these conditions has been a matter of research since the 1970 s. Persistent serum antibodies are a proof of present or past infection. The aim of this study was to compare serum antibodies against genitourinary infectious agents between PCa patients and controls with benign prostate hyperplasia (BPH). We hypothesized that elevated serum antibody levels or higher seroprevalence in PCa patients would suggest an association of genitourinary infection in patient history and elevated PCa risk.</p> <p>Methods</p> <p>A total of 434 males who had undergone open prostate surgery in a single institution were included in the study: 329 PCa patients and 105 controls with BPH. The subjects' serum samples were analysed by means of enzyme-linked immunosorbent assay, complement fixation test and indirect immunofluorescence for the presence of antibodies against common genitourinary infectious agents: human papillomavirus (HPV) 6, 11, 16, 18, 31 and 33, herpes simplex virus (HSV) 1 and 2, human cytomegalovirus (CMV), Chlamydia trachomatis, Mycoplasma hominis, Ureaplasma urealyticum, Neisseria gonorrhoeae and Treponema pallidum. Antibody seroprevalence and mean serum antibody levels were compared between cases and controls. Tumour grade and stage were correlated with serological findings.</p> <p>Results</p> <p>PCa patients were more likely to harbour antibodies against Ureaplasma urealyticum (odds ratio (OR) 2.06; 95% confidence interval (CI) 1.08-4.28). Men with BPH were more often seropositive for HPV 18 and Chlamydia trachomatis (OR 0.23; 95% CI 0.09-0.61 and OR 0.45; 95% CI 0.21-0.99, respectively) and had higher mean serum CMV antibody levels than PCa patients (p = 0.0004). Among PCa patients, antibodies against HPV 6 were associated with a higher Gleason score (p = 0.0305).</p> <p>Conclusions</p> <p>Antibody seropositivity against the analyzed pathogens with the exception of Ureaplasma does not seem to be a risk factor for PCa pathogenesis. The presence or higher levels of serum antibodies against the genitourinary pathogens studied were not consistently associated with PCa. Serostatus was not a predictor of disease stage in the studied population.</p

Global maps of soil temperature

Research in global change ecology relies heavily on global climatic grids derived from estimates of air temperature in open areas at around 2 m above the ground. These climatic grids do not reflect conditions below vegetation canopies and near the ground surface, where critical ecosystem functions occur and most terrestrial species reside. Here, we provide global maps of soil temperature and bioclimatic variables at a 1-km² resolution for 0–5 and 5–15 cm soil depth. These maps were created by calculating the difference (i.e., offset) between in-situ soil temperature measurements, based on time series from over 1200 1-km² pixels (summarized from 8500 unique temperature sensors) across all the world’s major terrestrial biomes, and coarse-grained air temperature estimates from ERA5-Land (an atmospheric reanalysis by the European Centre for Medium-Range Weather Forecasts). We show that mean annual soil temperature differs markedly from the corresponding gridded air temperature, by up to 10°C (mean = 3.0 ± 2.1°C), with substantial variation across biomes and seasons. Over the year, soils in cold and/or dry biomes are substantially warmer (+3.6 ± 2.3°C) than gridded air temperature, whereas soils in warm and humid environments are on average slightly cooler (-0.7 ± 2.3°C). The observed substantial and biome-specific offsets emphasize that the projected impacts of climate and climate change on near-surface biodiversity and ecosystem functioning are inaccurately assessed when air rather than soil temperature is used, especially in cold environments. The global soil-related bioclimatic variables provided here are an important step forward for any application in ecology and related disciplines. Nevertheless, we highlight the need to fill remaining geographic gaps by collecting more in-situ measurements of microclimate conditions to further enhance the spatiotemporal resolution of global soil temperature products for ecological applications