<Emphasis Type="Italic">The Mathematical Intelligencer</Emphasis> Flunks the Olympics

The Mathematical Intelligencer recently published a note by Y. Sergeyev that challenges both mathematics and intelligence. We examine Sergeyev’s claims concerning his purported Infinity computer. We compare his grossone system with the classical Levi-Civita fields and with the hyperreal framework of A. Robinson, and analyze the related algorithmic issues inevitably arising in any genuine computer implementation. We show that Sergeyev’s grossone system is unnecessary and vague, and that whatever consistent subsystem could be salvaged is subsumed entirely within a stronger and clearer system (IST). Lou Kauffman, who published an article on a grossone, places it squarely outside the historical panorama of ideas dealing with infinity and infinitesimals.     

Active tactile exploration using a brain-machine-brain interface

Brain-machine interfaces use neuronal activity recorded from the brain to establish direct communication with external actuators, such as prosthetic arms. It is hoped that brain-machine interfaces can be used to restore the normal sensorimotor functions of the limbs, but so far they have lacked tactile sensation. Here we report the operation of a brain-machine-brain interface (BMBI) that both controls the exploratory reaching movements of an actuator and allows signalling of artificial tactile feedback through intracortical microstimulation (ICMS) of the primary somatosensory cortex. Monkeys performed an active exploration task in which an actuator (a computer cursor or a virtual-reality arm) was moved using a BMBI that derived motor commands from neuronal ensemble activity recorded in the primary motor cortex. ICMS feedback occurred whenever the actuator touched virtual objects. Temporal patterns of ICMS encoded the artificial tactile properties of each object. Neuronal recordings and ICMS epochs were temporally multiplexed to avoid interference. Two monkeys operated this BMBI to search for and distinguish one of three visually identical objects, using the virtual-reality arm to identify the unique artificial texture associated with each. These results suggest that clinical motor neuroprostheses might benefit from the addition of ICMS feedback to generate artificial somatic perceptions associated with mechanical, robotic or even virtual prostheses.     

High bacterivory by the smallest phytoplankton in the North Atlantic Ocean

Planktonic algae <5 m in size are major fixers of inorganic carbon in the ocean. They dominate phytoplankton biomass in post-bloom, stratified oceanic temperate waters. Traditionally, large and small algae are viewed as having a critical growth dependence on inorganic nutrients, which the latter can better acquire at lower ambient concentrations owing to their higher surface area to volume ratios. Nonetheless, recent phosphate tracer experiments in the oligotrophic ocean have suggested that small algae obtain inorganic phosphate indirectly, possibly through feeding on bacterioplankton. There have been numerous microscopy-based studies of algae feeding mixotrophically in the laboratory and field as well as mathematical modelling of the ecological importance of mixotrophy. However, because of methodological limitations there has not been a direct comparison of obligate heterotrophic and mixotrophic bacterivory. Here we present direct evidence that small algae carry out 40-95% of the bacterivory in the euphotic layer of the temperate North Atlantic Ocean in summer. A similar range of 37-70% was determined in the surface waters of the tropical North-East Atlantic Ocean, suggesting the global significance of mixotrophy. This finding reveals that even the smallest algae have less dependence on dissolved inorganic nutrients than previously thought, obtaining a quarter of their biomass from bacterivory. This has important implications for how we perceive nutrient acquisition and limitation of carbon-fixing protists as well as control of bacterioplankton in the ocean.     

Stevin Numbers and Reality

We explore the potential of Simon Stevin??s numbers, obscured by shifting foundational biases and by 19th century developments in the arithmetisation of analysis.     

Macrobenthic communities in water bodies and streams of Svalbard,Norway

Diversity of macrobenthic communities was studied from water bodies and streams of Spitsbergen, Svalbard archipelago, Norway. In total 162 quantitative samples from different regions of Spitsbergen were analysed in relation to environmental variables. Macrobenthic communities were found on all kinds of substrates (except for the periglacial zone), representing a wide range of biological communities: solid-bottom, soft-bottom, macrophytes and small brook associated. However, taxonomical structure is very simplified, with particular dominance of the Chironomidae family. Chironomid larvae dominated highly in diversity, abundance and biomass. Overall macrobenthic communities were characteristic, with remarkable dominance of one species and general omnipresent taxonomical scarcity (average 2.8 species per sample). In total we found 30 taxa. We distinguished 16 types of macrobenthis communities, with characteristic dominance of different taxa: chironomids (11 types), oligochaete Enchytraeidae family (3), caddisfly Apatania zonella (1) and gammarid amphipod Gammarus setosus (1). Regarding environmental variables, temperature and pH had the most significant influence on the abundance of macrobenthic organisms. It is hypothesized that the structural convergence of different types of communities is their common response to extreme high Arctic living conditions. On the other hand, different chironomids may dominate in the same habitats and water bodies. This gives the effect of lower average similarity of communities and high β-diversity.     

Is Leibnizian Calculus Embeddable in First Order Logic?

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.     

Pathogen-induced systemic plant signal triggers DNA rearrangements

Plant genome stability is known to be affected by various abiotic environmental conditions, but little is known about the effect of pathogens. For example, exposure of maize plants to barley stripe mosaic virus seems to activate transposable elements and to cause mutations in the non-infected progeny of infected plants. The induction by barley stripe mosaic virus of an inherited effect may mean that the virus has a non-cell-autonomous influence on genome stability. Infection with Peronospora parasitica results in an increase in the frequency of somatic recombination in Arabidopsis thaliana; however, it is unclear whether effects on recombination require the presence of the pathogen or represent a systemic plant response. It is also not clear whether the changes in the frequency of somatic recombination can be inherited. Here we report a threefold increase in homologous recombination frequency in both infected and non-infected tissue of tobacco plants infected with either tobacco mosaic virus or oilseed rape mosaic virus. These results indicate the existence of a systemic recombination signal that also results in an increased frequency of meiotic and/or inherited late somatic recombination.