The fundamental cycle of concept construction underlying various theoretical frameworks

In this paper, the development of mathematical concepts over time is considered. Particular reference is given to the shifting of attention from step-by-step procedures that are performed in time, to symbolism that can be manipulated as mental entities on paper and in the mind. The development is analysed using different theoretical perspectives, including the SOLO model and various theories of concept construction to reveal a fundamental cycle underlying the building of concepts that features widely in different ways of thinking that occurs throughout mathematical learning

4f spin density in the reentrant ferromagnet SmMn2Ge2

The spin contribution to the magnetic moment in SmMn2Ge2 has been measured by magnetic Compton scattering in both the low and high temperature ferromagnetic phases. At low temperature, the Sm site is shown to possess a large 4f spin moment of 3.4 +/- 0.1 Bohr magnetons, aligned antiparallel to the total magnetic moment. At high temperature, the data show conclusively that ordered magnetic moments are present on the samarium site.Comment: 5 pages, 2 figures, transferred from PRL to PRB (Rapid Comm.

Substructures in lens galaxies: PG1115+080 and B1555+375, two fold configurations

We study the anomalous flux ratio which is observed in some four-image lens systems, where the source lies close to a fold caustic. In this case two of the images are close to the critical curve and their flux ratio should be equal to unity, instead in several cases the observed value differs significantly. The most plausible solution is to invoke the presence of substructures, as for instance predicted by the Cold Dark Matter scenario, located near the two images. In particular, we analyze the two fold lens systems PG1115+080 and B1555+375, for which there are not yet satisfactory models which explain the observed anomalous flux ratios. We add to a smooth lens model, which reproduces well the positions of the images but not the anomalous fluxes, one or two substructures described as singular isothermal spheres. For PG1115+080 we consider a smooth model with the influence of the group of galaxies described by a SIS and a substructure with mass $\sim 10^{5} M_{\odot}$ as well as a smooth model with an external shear and one substructure with mass $\sim 10^{8} M_{\odot}$ . For B1555+375 either a strong external shear or two substructures with mass $\sim 10^{7} M_{\odot}$ reproduce the data quite well.Comment: 26 pages, updated bibliography, Accepted for publication in Astrophysics & Space Scienc

The programme on ecosystem change and society (PECS)–a decade of deepening social-ecological research through a place-based focus

The Programme on Ecosystem Change and Society (PECS) was established in 2011, and is now one of the major international social-ecological systems (SES) research networks. During this time, SES research has undergone a phase of rapid growth and has grown into an influential branch of sustainability science. In this Perspective, we argue that SES research has also deepened over the past decade, and helped to shed light on key dimensions of SES dynamics (e.g. system feedbacks, aspects of system design, goals and paradigms) that can lead to tangible action for solving the major sustainability challenges of our time. We suggest four ways in which the growth of place-based SES research, fostered by networks such as PECS, has contributed to these developments, namely by: 1) shedding light on transformational change, 2) revealing the social dynamics shaping SES, 3) bringing together diverse types of knowledge, and 4) encouraging reflexive researchers

Genome-wide association and Mendelian randomisation analysis provide insights into the pathogenesis of heart failure

Heart failure (HF) is a leading cause of morbidity and mortality worldwide. A small proportion of HF cases are attributable to monogenic cardiomyopathies and existing genome-wide association studies (GWAS) have yielded only limited insights, leaving the observed heritability of HF largely unexplained. We report results from a GWAS meta-analysis of HF comprising 47,309 cases and 930,014 controls. Twelve independent variants at 11 genomic loci are associated with HF, all of which demonstrate one or more associations with coronary artery disease (CAD), atrial fibrillation, or reduced left ventricular function, suggesting shared genetic aetiology. Functional analysis of non-CAD-associated loci implicate genes involved in cardiac development (MYOZ1, SYNPO2L), protein homoeostasis (BAG3), and cellular senescence (CDKN1A). Mendelian randomisation analysis supports causal roles for several HF risk factors, and demonstrates CAD-independent effects for atrial fibrillation, body mass index, and hypertension. These findings extend our knowledge of the pathways underlying HF and may inform new therapeutic strategies

Erratum: "A Gravitational-wave Measurement of the Hubble Constant Following the Second Observing Run of Advanced LIGO and Virgo" (2021, ApJ, 909, 218)

[no abstract available