ALBERT

Description: Recent years have seen a surge of interest in understanding patterns and processes of plant invasions into mountains. Here, we synthesise current knowledge about the spread of non-native plants along elevation gradients, emphasising the current status and impacts that these species have in alpine ecosystems. Globally, invasions along elevation gradients are influenced by propagule availability, environmental constraints on population growth, evolutionary change and biotic interactions. The highest elevations are so far relatively free from non-native plants. Nonetheless, in total nearly 200 non-native plant species have been recorded from alpine environments around the world. However, we identified only three species as specifically cold-adapted, with the overwhelming majority having their centres of distribution under warmer environments, and few have substantial impacts on native communities. A combination of low propagule availability and low invasibility likely explain why alpine environments host few non-native plants relative to lowland ecosystems. However, experiences in some areas demonstrate that alpine ecosystems are not inherently resistant to invasions. Furthermore, they will face increasing pressure from the introduction of pre-adapted species, climate change, and the range expansion of native species, which are already causing concern in some areas. Nonetheless, because they are still relatively free from non-native plants, preventative action could be an effective way to limit future impacts of invasions in alpine environments.

Description: To explore the extent of embeddability of Leibnizian infinitesimal calculus in first-order logic (FOL) and modern frameworks, we propose to set aside ontological issues and focus on procedural questions. This would enable an account of Leibnizian procedures in a framework limited to FOL with a small number of additional ingredients such as the relation of infinite proximity. If, as we argue here, first order logic is indeed suitable for developing modern proxies for the inferential moves found in Leibnizian infinitesimal calculus, then modern infinitesimal frameworks are more appropriate to interpreting Leibnizian infinitesimal calculus than modern Weierstrassian ones.

Description: The aim of science is the explanation of complicated systems by reducing it to simple subsystems. According to a millennia-old imagination this will be attained by dividing matter into smaller and smaller pieces of it. The popular superstition that smallness implies simplicity seems to be ineradicable. However, since the beginning of quantum theory it would be possible to realize that the circumstances in nature are exactly the other way round. The idea “smaller becomes simpler” is useful only down to the atoms of chemistry. Planck’s formula shows that smaller extensions are related to larger energies. That more and more energy should result in simpler and simpler structures, this does not only sound absurd, it is absurd. A reduction to really simple structures leads one to smallest energies and, thus, to utmost extended quantum systems. The simplest quantum structure, referred to as quantum bit, has a two-dimensional state space, and it establishes a cosmological structure. Taking many of such quantum bits allows also for the construction of localized particles. The non-localized fraction of quantum bits can appear as “dark matter”.

Description: Fossil evidence, phylogeographic analyses, species distribution modelling and ancient DNA analyses have all shown that plant distributions have been highly dynamic through time. We use the geographical distribution of intra- and interspecific hybrids in Sempervivum , a western Eurasian high mountain oreophyte, as evidence for the past range dynamics of their parents. Sequences of the nuclear ribosomal internal transcribed spacer (ITS), parts of the nuclear ribosomal intergenic spacer region (IGS), and the three chloroplast markers atp I– atp H, rps 16-intron and trn Q– rps 16 were generated for 101 individuals of Sempervivum from across its entire distribution range. Hybrid individuals were identified by the presence of double base calls in direct sequencing of polymerase chain reaction products of ITS and IGS. Parentage was inferred from comparison with sequences without double base calls and with cpDNA sequences. We identified 27 hybrid individuals, which were found outside the current distribution range of one parent in 10 cases and with both (or all three) parents in eight cases. Geographical distance of hybrids and allopatric parents ranged from 25 to 2100 km. The distribution of hybrid individuals in relation to their parents provides evidence for past range dynamics and migration over sometimes large geographical distances. As all taxa involved had been postulated to be of Quaternary origin in an earlier study, we hypothesise that hybridisation took place in glacial refugia where the parental species came into contact.

Description: Stem rust, caused by Puccinia graminis f. sp. tritici , can be a serious disease problem of barley in some production areas of the world. Deployment of resistant cultivars is the best means for controlling the disease. In North America, stem rust of barley has been kept in check for more than 70 years through the widespread use of the resistance gene Rpg1 , which was derived from a landrace collected in Switzerland. Rpg1 is effective against many, but not all races of P. graminis f. sp. tritici . With the threat of Rpg1 -virulent races like TTKSK and QCCJB from Africa and North America, respectively, it is important that additional sources of stem rust resistance be identified in barley. Given that resistance was previously identified in germplasm from Switzerland, the primary objective of this study was to characterize a collection of Swiss barley landraces from the mountainous regions of canton Graubünden for their reaction to stem rust races TTKSK and QCCJB as well as HKHJC, which is diagnostic for detecting Rpg1 . From the stem rust phenotyping of 73 barley landraces, we found a remarkably high frequency (〉43 %) of resistance to the virulent P . graminis f. sp. tritici races of TTKSK and QCCJB. In nearly every case, this resistance was due to the rpg4 / Rpg5 gene complex as determined by a molecular assay. Two landraces were also found to carry Rpg1 based on their diagnostic resistant reaction to race HKHJC and presence of an amplicon specific for the gene. These results demonstrate that landraces from the mountainous areas of eastern Switzerland are valuable sources of important resistance genes for protecting barley from the devastating disease of stem rust.

Description: Human language has the characteristic of being open and in some cases polysemic. The word “infinite” is used often in common speech and more frequently in literary language, but rarely with its precise meaning. In this way the concepts can be used in a vague way but an argument can still be structured so that the central idea is understood and is shared with to the partners. At the same time no precise definition is given to the concepts used and each partner makes his own reading of the text based on previous experience and cultural background. In a language dictionary the first meaning of “infinite” agrees with the etymology: what has no end. We apply the word infinite most often and incorrectly as a synonym for “very large” or something that we do not perceive its completion. In this context, the infinite mentioned in dictionaries refers to the idea or notion of the “immeasurably large” although this is open to what the individual’s means by “immeasurably great.” Based on this linguistic imprecision, the authors present a non Cantorian theory of the potential and actual infinite. For this we have introduced a new concept: the homogon that is the whole set that does not fall within the definition of sets established by Cantor.

Description: The use of mathematics in economics has been widely discussed. The philosophical discussion on what mathematics is remains unsettled on why it can be applied to the study of the real world. We propose to get back to some philosophical conceptions that lead to a language-like role for the mathematical analysis of economic phenomena and present some problems of interest that can be better examined in this light. Category theory provides the appropriate tools for these analytical approach.

Description: In 1975, two experimental groups have independently observed the \(4\pi \) -symmetry of neutrons’ spin, when passing through a static magnetic field, using a three-blade interferometer made from a single perfect Si-crystal (analogous to the Mach Zehnder interferometer of light optics). In this article, we provide a complete analysis of the experiment, both from a theoretical and conceptual point of view. Firstly, we solve the Schrödinger equation in the weak potential approximation, to obtain the amplitude of the refracted and forward refracted beams, produced by the passage of neutrons through one of the three plates of the LLL interferometer. Secondly, we analyze their passage through a static magnetic field region. This allows us to find explicit expressions for the intensities of the four beams exiting the interferometer, two of which will be interfering and show a typical \(4\pi \) -symmetry, when the strength of the magnetic field is varied. In the last part of the article, we provide a conceptual analysis of the experiment, showing that a neutron’s phase change, when passing through the magnetic field, is due to a longitudinal Stern–Gerlach effect, and not to a Larmor precession. We also emphasize that these experiments do not prove the observability of the sign change of the wave function, when a neutron is \(2\pi \) rotated, but strongly indicate that the latter, like any other elementary “particle,” would be a genuinely non-spatial entity.

Description: Although the present paper looks upon the formal apparatus of quantum mechanics as a calculus of correlations, it goes beyond a purely operationalist interpretation. Having established the consistency of the correlations with the existence of their correlata (measurement outcomes), and having justified the distinction between a domain in which outcome-indicating events occur and a domain whose properties only exist if their existence is indicated by such events, it explains the difference between the two domains as essentially the difference between the manifested world and its manifestation. A single, intrinsically undifferentiated Being manifests the macroworld by entering into reflexive spatial relations. This atemporal process implies a new kind of causality and sheds new light on the mysterious nonlocality of quantum mechanics. Unlike other realist interpretations, which proceed from an evolving-states formulation, the present interpretation proceeds from Feynman’s formulation of the theory, and it introduces a new interpretive principle, replacing the collapse postulate and the eigenvalue–eigenstate link of evolving-states formulations. Applied to alternatives involving distinctions between regions of space, this principle implies that the spatiotemporal differentiation of the physical world is incomplete. Applied to alternatives involving distinctions between things, it warrants the claim that, intrinsically, all fundamental particles are identical in the strong sense of numerical identical. They are the aforementioned intrinsically undifferentiated Being, which manifests the macroworld by entering into reflexive spatial relations.

Description: Over the past few decades the notion of symmetry has played a major role in physics and in the philosophy of physics. Philosophers have used symmetry to discuss the ontology and seeming objectivity of the laws of physics. We introduce several notions of symmetry in mathematics and explain how they can also be used in resolving different problems in the philosophy of mathematics. We use symmetry to discuss the objectivity of mathematics, the role of mathematical objects, the unreasonable effectiveness of mathematics and the relationship of mathematics to physics.