On the Foundations of Constructive Mathematics – Especially in Relation to the Theory of Continuous Functions

We discuss the foundations of constructive mathematics, including recursive mathematics and intuitionism, in relation to classical mathematics. There are connections with the foundations of physics, due to the way in which the different branches of mathematics reflect reality. Many different axioms and their interrelationship are discussed. We show that there is a fundamental problem in BISH (Bishop’s school of constructive mathematics) with regard to its current definition of ‘continuous function’. This problem is closely related to the definition in BISH of ‘locally compact’. Possible approaches to this problem are discussed. Topology seems to be a key to understanding many issues. We offer several new simplifying axioms, which can form bridges between the various branches of constructive mathematics and classical mathematics (‘reuniting the antipodes’). We give a simplification of basic intuitionistic theory, especially with regard to so-called ‘bar induction’. We then plead for a limited number of axiomatic systems, which differentiate between the various branches of mathematics. Finally, in the appendix we offer BISH an elegant topological definition of ‘locally compact’, which unlike the current definition is equivalent to the usual classical and/or intuitionistic definition in classical and intuitionistic mathematics, respectively.     

Antioxidant survey to assess antagonism to redox stress using a prokaryotic and an eukaryotic system

Using a prokaryote (Escherichia coli) and a metazoa-resembling eukaryote (Ochromonas danica), we surveyed antioxidants which might overcome redox stress imposed by menadione sodium bisulphite (MD) and buthionine sulphoximine (BSO). BSO oxidant stress was evident only inO. danica; MD oxidant stress was evident in both organisms. Glutathione, its precursors, e.g. cysteine, homocysteine, and 2-oxo-4-thiazolidine carboxylic acid, and red blood cells, emerged as prime antioxidants for relieving BSO and MD oxidant stress. BSO and MD oxidant activity and antioxidant-annulling effect inO. danica were judged comparable to those found in animal cells whereas the resultsE. coli were not entirely equivalent. TheO. danica system emerged as a practical, rapid, and useful system for pinpointing oxidant stressors and antioxidants, and shows promise for studies with mammalian systems.     

Experimental validation of inter-subspecific genetic diversity in rice represented by the differences between the DNA sequences of ‘Nipponbare’ and ‘93-11’

The pedigrees of three sequenced rice cultivars were analyzed to show that a majority of the genetic composition of 'Nipponbare' originates from japonica cultivars while the minority originates from indica cultivars. In contrast, '93-11' is derived mainly from indica cultivars with a smaller contribution from japonica cultivars. All ancestors of 'Guang lu ai 4' appeared to be indica lines. A set of molecular markers (46 InDels and 53 SSRs) polymorphic between 'Nipponbare' and '93-11' were examined in 46 typical indica and 47 typical japonica cultivars selected from 443 accessions according to Cheng's index. All cultivars were divided into indica and japonica groups without overlapping when clustered by Cheng's index, InDels and SSRs. Much higher InDel and SSR diversity between groups than within groups implies that the marker polymorphisms between 'Nipponbare' and '93-11' represent a large proportion of inter-subspecific diversity. About 85% of indica cultivars and more than 90% of japonica cultivars were confirmed to have the same PCR banding patterns as '93-11' and 'Nipponbare', respectively. Some polymorphic loci between 'Nipponbare' and '93-11' cannot be validated in other indica and japonica cultivars, either as subspecies-specific but not predominant alleles, or alleles not specific between the two groups. It was concluded that molecular markers developed from sequence polymorphism between 'Nipponbare' and '93-11' often represent inter-subspecific diversity, although some exceptions were sensitive to either particular marker loci or particular cultivars.     

Enhancements of energetic particles near the heliospheric termination shock

The spacecraft Voyager 1 is at a distance greater than 85 au from the Sun, in the vicinity of the termination shock that marks the abrupt slowing of the supersonic solar wind and the beginning of the extended and unexplored distant heliosphere. This shock is expected to accelerate 'anomalous cosmic rays', as well as to re-accelerate Galactic cosmic rays and low-energy particles from the inner Solar System. Here we report a significant increase in the numbers of energetic ions and electrons that persisted for seven months beginning in mid-2002. This increase differs from any previously observed in that there was a simultaneous increase in Galactic cosmic ray ions and electrons, anomalous cosmic rays and low-energy ions. The low-intensity level and spectral energy distribution of the anomalous cosmic rays, however, indicates that Voyager 1 still has not reached the termination shock. Rather, the observed increase is an expected precursor event. We argue that the radial anisotropy of the cosmic rays is expected to be small in the foreshock region, as is observed.     

Signal Diffusion Mapping: Optimal Forecasting with Time‐Varying Lags

We introduce a new methodology for forecasting, which we call signal diffusion mapping. Our approach accommodates features of real‐world financial data which have been ignored historically in existing forecasting methodologies. Our method builds upon well‐established and accepted methods from other areas of statistical analysis. We develop and adapt those models for use in forecasting. We also present tests of our model on data in which we demonstrate the efficacy of our approach. Copyright © 2015 John Wiley & Sons, Ltd.     

Infection of young Douglas-firs by dwarf mistletoe in the Southwest

Studies in several areas in Arizona and New Mexico show that dwarf mistletoe ( Arceuthobium douglasii ) is rare in young Douglas-firs growing under infected overstories. Less than 5% of the Douglas-firs under 26 years old and less than 6% of those under 1.4m tall were infected in 77 mistletoe-infested stands. Both percent infection and mean dwarf mistletoe rating of young Douglas-firs increased as tree age, height, and stand dwarf mistletoe ratings increased.     

Winter macroinvertebrate communities in two montane Wyoming streams

Macroinvertebrate communities were examined on 4 winter dates over a 4-yr period in 2 high-altitude Rocky Mountain streams to document overwintering assemblages potentially experiencing spring acid pulses. Taxa richness values were comparable to other published lists for alpine and montane stream systems despite the fact that most literature reflected summer collections. Mean benthic density ranged from 1406 to 19,734 organisms/m 2 , and drift rates ranged from 0 to 1740 organisms/100 m 3 . Benthic collections showed higher taxa richness than drift collections while the Ephemeroptera and Plecoptera occurred in greater proportions in drift than in benthos. The Nemouridae (Plecoptera), Ephemerellidae and Heptageniidae (Ephemeroptera), Chironomidae (Diptera), and Hydracarina were the numerically dominant taxa in benthic collections. Grazer/scrapers and shredder/detritivores were always the numerically dominant functional feeding groups at all sites, composing 60-90% of the benthos. Predators, constituting approximately 15% of the community, occurred in the same relative proportion at all sites on all dates. Winter macroinvertebrate communities in these low-order, montane streams exhibit high taxonomic richness and benthic densities as great as lower-elevation mountain streams in the West.     

Cartilage biology, pathology, and repair

Osteoarthritis is one of the most common forms of musculoskeletal disease and the most prominent type of arthritis encountered in all countries. Although great efforts have been made to investigate cartilage biology and osteoarthritis pathology, the treatment has lagged behind that of other arthritides, as there is a lack of effective disease-modifying therapies. Numerous approaches for dealing with cartilage degradation have been tried, but enjoyed very little success to develop approved OA treatments with not only symptomatic improvement but also structure-modifying effect. In this review we discuss the most recent findings regarding the regulation of cartilage biology and pathology and highlight their potential therapeutic values.     

Mathematics, technics, and courtly life in Late Renaissance Urbino

The present article seeks to provide an overview of the general characteristics of the cultural and scientific climate in the Duchy of Urbino. Three of the Duchy’s milieus seem to have been particularly important for scholars who were engaged in the study of mathematics: the so-called “School of Urbino”, the environment of the court, and the world of the technicians and engineers. While the Urbino School has already been the object of previous studies, the other two milieus and their effect on the mathematicians’ work have been rather neglected and are, consequently, addressed here. The paper’s final section presents some documents that attest the importance of Renaissance scholars’ interaction with these environments to their actual scientific activity, taking the case of Guidobaldo dal Monte as an example.