A mathematical modelling study of an athlete's sprint time when towing a weighted sled

This is the author's accepted manuscript. The final publication is available at Springer via http://dx.doi.org/10.1007/s12283-013-0114-2.This study used a mathematical model to examine the effects of the sled, the running surface, and the athlete on sprint time when towing a weighted sled. Simulations showed that ratio scaling is an appropriate method of normalising the weight of the sled for athletes of different body size. The relationship between sprint time and the weight of the sled was almost linear, as long as the sled was not excessively heavy. The athlete’s sprint time and rate of increase in sprint time were greater on running surfaces with a greater coefficient of friction, and on any given running surface an athlete with a greater power-to-weight ratio had a lower rate of increase in sprint time. The angle of the tow cord did not have a substantial effect on an athlete’s sprint time. This greater understanding should help coaches set the training intensity experienced by an athlete when performing a sled-towing exercise

Cauchy's infinitesimals, his sum theorem, and foundational paradigms

Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy's proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy's proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy's proof closely and show that it finds closer proxies in a different modern framework. Keywords: Cauchy's infinitesimal; sum theorem; quantifier alternation; uniform convergence; foundational paradigms.Comment: 42 pages; to appear in Foundations of Scienc

Bridging knowing and proving in mathematics An essay from a didactical perspective

Text of a talk at the conference "Explanation and Proof in Mathematics: Philosophical and Educational Perspective" held in Essen in November 2006International audienceThe learning of mathematics starts early but remains far from any theoretical considerations: pupils' mathematical knowledge is first rooted in pragmatic evidence or conforms to procedures taught. However, learners develop a knowledge which they can apply in significant problem situations, and which is amenable to falsification and argumentation. They can validate what they claim to be true but using means generally not conforming to mathematical standards. Here, I analyze how this situation underlies the epistemological and didactical complexities of teaching mathematical proof. I show that the evolution of the learners' understanding of what counts as proof in mathematics implies an evolution of their knowing of mathematical concepts. The key didactical point is not to persuade learners to accept a new formalism but to have them understand how mathematical proof and statements are tightly related within a common framework; that is, a mathematical theory. I address this aim by modeling the learners' way of knowing in terms of a dynamic, homeostatic system. I discuss the roles of different semiotic systems, of the types of actions the learners perform and of the controls they implement in constructing or validating knowledge. Particularly with modern technological aids, this model provides a basis designing didactical situations to help learners bridge the gap between pragmatics and theory

Transmissibility of Atypical Scrapie in Ovine Transgenic Mice: Major Effects of Host Prion Protein Expression and Donor Prion Genotype

Atypical scrapie or Nor98 has been identified as a transmissible spongiform encephalopathy (TSE) that is clearly distinguishable from classical scrapie and BSE, notably regarding the biochemical features of the protease-resistant prion protein PrPres and the genetic factors involved in susceptibility to the disease. In this study we transmitted the disease from a series of 12 French atypical scrapie isolates in a transgenic mouse model (TgOvPrP4) overexpressing in the brain ∼0.25, 1.5 or 6× the levels of the PrPARQ ovine prion protein under the control of the neuron-specific enolase promoter. We used an approach based on serum PrPc measurements that appeared to reflect the different PrPc expression levels in the central nervous system. We found that transmission of atypical scrapie, much more than in classical scrapie or BSE, was strongly influenced by the PrPc expression levels of TgOvPrP4 inoculated mice. Whereas TgOvPrP4 mice overexpressing ∼6× the normal PrPc level died after a survival periods of 400 days, those with ∼1.5× the normal PrPc level died at around 700 days. The transmission of atypical scrapie in TgOvPrP4 mouse line was also strongly influenced by the prnp genotypes of the animal source of atypical scrapie. Isolates carrying the AF141RQ or AHQ alleles, associated with increased disease susceptibility in the natural host, showed a higher transmissibility in TgOvPrP4 mice. The biochemical analysis of PrPres in TgOvPrP4 mouse brains showed a fully conserved pattern, compared to that in the natural host, with three distinct PrPres products. Our results throw light on the transmission features of atypical scrapie and suggest that the risk of transmission is intrinsically lower than that of classical scrapie or BSE, especially in relation to the expression level of the prion protein

Influence of Matrix Polarity on the Properties of Ethylene Vinyl Acetate–Carbon Nanofiller Nanocomposites

A series of ethylene vinyl acetate (EVA) nanocomposites using four kinds of EVA with 40, 50, 60, and 70 wt% vinyl acetate (VA) contents and three different carbon-based nanofillers—expanded graphite (EG), multi-walled carbon nanotube (MWCNT), and carbon nanofiber (CNF) have been prepared via solution blending. The influence of the matrix polarity and the nature of nanofillers on the morphology and properties of EVA nanocomposites have been investigated. It is observed that the sample with lowest vinyl acetate content exhibits highest mechanical properties. However, the enhancement in mechanical properties with the incorporation of various nanofillers is the highest for EVA with high VA content. This trend has been followed in both dynamic mechanical properties and thermal conductivity of the nanocomposites. EVA copolymer undergoes a transition from partial to complete amorphousness between 40 and 50 wt% VA content, and this changes the dispersion of the nanofillers. The high VA-containing polymers show more affinity toward fillers due to the large free volume available and allow easy dispersion of nanofillers in the amorphous rubbery phase, as confirmed from the morphological studies. The thermal stability of the nanocomposites is also influenced by the type of nanofiller

Facile synthesis of B/g-C3N4 composite materials for the continuous-flow selective photo-production of acetone

In this work versatile boron–carbon nitride composite materials were synthesized and utilized in a sustainable process using sunlight as the energy source for the continuous-flow selective photocatalytic production of acetone from 2-propanol. It is worth highlighting that the sample preparation was carried out by an environmentally friendly strategy, without a solvent or additional reagents. Samples containing boron in 1–10 wt% were subjected to physico-chemical characterization using XRD, porosimetry, UVvisible spectroscopy, TEM, energy-dispersive X-ray spectroscopy and XPS. The reaction output was analyzed on the basis of the reaction rate, selectivity and quantum efficiency of the process. A correlation analysis between catalytic properties with two observables, the boron phase distribution in the materials and charge handling efficiency (measured using photoluminescence), rationalizes photoactivity. Such an analysis indicates that the presence of an amorphous boron metallic phase and its contact with the carbon nitride component are key to setting up a renewable and easily scalable chemical process to obtain acetone.MINECO (Spain) ENE2016-77798-C4-1-RConsejo Superior de Investigaciones Cientificas (CSIC)Secretaria de Ciencia Tecnologia e Innovacion of CDMX (SECTEI, Mexico)MINECO CTQ2016-78289-PEuropean Union (EU)RUDN University Program 5-10

The Physical Relationship between Infectivity and Prion Protein Aggregates Is Strain-Dependent

Prions are unconventional infectious agents thought to be primarily composed of PrPSc, a multimeric misfolded conformer of the ubiquitously expressed host-encoded prion protein (PrPC). They cause fatal neurodegenerative diseases in both animals and humans. The disease phenotype is not uniform within species, and stable, self-propagating variations in PrPSc conformation could encode this ‘strain’ diversity. However, much remains to be learned about the physical relationship between the infectious agent and PrPSc aggregation state, and how this varies according to the strain. We applied a sedimentation velocity technique to a panel of natural, biologically cloned strains obtained by propagation of classical and atypical sheep scrapie and BSE infectious sources in transgenic mice expressing ovine PrP. Detergent-solubilized, infected brain homogenates were used as starting material. Solubilization conditions were optimized to separate PrPSc aggregates from PrPC. The distribution of PrPSc and infectivity in the gradient was determined by immunoblotting and mouse bioassay, respectively. As a general feature, a major proteinase K-resistant PrPSc peak was observed in the middle part of the gradient. This population approximately corresponds to multimers of 12–30 PrP molecules, if constituted of PrP only. For two strains, infectivity peaked in a markedly different region of the gradient. This most infectious component sedimented very slowly, suggesting small size oligomers and/or low density PrPSc aggregates. Extending this study to hamster prions passaged in hamster PrP transgenic mice revealed that the highly infectious, slowly sedimenting particles could be a feature of strains able to induce a rapidly lethal disease. Our findings suggest that prion infectious particles are subjected to marked strain-dependent variations, which in turn could influence the strain biological phenotype, in particular the replication dynamics

Atypical/Nor98 Scrapie Infectivity in Sheep Peripheral Tissues

Atypical/Nor98 scrapie was first identified in 1998 in Norway. It is now considered as a worldwide disease of small ruminants and currently represents a significant part of the detected transmissible spongiform encephalopathies (TSE) cases in Europe. Atypical/Nor98 scrapie cases were reported in ARR/ARR sheep, which are highly resistant to BSE and other small ruminants TSE agents. The biology and pathogenesis of the Atypical/Nor98 scrapie agent in its natural host is still poorly understood. However, based on the absence of detectable abnormal PrP in peripheral tissues of affected individuals, human and animal exposure risk to this specific TSE agent has been considered low. In this study we demonstrate that infectivity can accumulate, even if no abnormal PrP is detectable, in lymphoid tissues, nerves, and muscles from natural and/or experimental Atypical/Nor98 scrapie cases. Evidence is provided that, in comparison to other TSE agents, samples containing Atypical/Nor98 scrapie infectivity could remain PrPSc negative. This feature will impact detection of Atypical/Nor98 scrapie cases in the field, and highlights the need to review current evaluations of the disease prevalence and potential transmissibility. Finally, an estimate is made of the infectivity loads accumulating in peripheral tissues in both Atypical/Nor98 and classical scrapie cases that currently enter the food chain. The results obtained indicate that dietary exposure risk to small ruminants TSE agents may be higher than commonly believed