Improving the Representation and Conversion of Mathematical Formulae by Considering their Textual Context

Mathematical formulae represent complex semantic information in a concise form. Especially in Science, Technology, Engineering, and Mathematics, mathematical formulae are crucial to communicate information, e.g., in scientific papers, and to perform computations using computer algebra systems. Enabling computers to access the information encoded in mathematical formulae requires machine-readable formats that can represent both the presentation and content, i.e., the semantics, of formulae. Exchanging such information between systems additionally requires conversion methods for mathematical representation formats. We analyze how the semantic enrichment of formulae improves the format conversion process and show that considering the textual context of formulae reduces the error rate of such conversions. Our main contributions are: (1) providing an openly available benchmark dataset for the mathematical format conversion task consisting of a newly created test collection, an extensive, manually curated gold standard and task-specific evaluation metrics; (2) performing a quantitative evaluation of state-of-the-art tools for mathematical format conversions; (3) presenting a new approach that considers the textual context of formulae to reduce the error rate for mathematical format conversions. Our benchmark dataset facilitates future research on mathematical format conversions as well as research on many problems in mathematical information retrieval. Because we annotated and linked all components of formulae, e.g., identifiers, operators and other entities, to Wikidata entries, the gold standard can, for instance, be used to train methods for formula concept discovery and recognition. Such methods can then be applied to improve mathematical information retrieval systems, e.g., for semantic formula search, recommendation of mathematical content, or detection of mathematical plagiarism.Comment: 10 pages, 4 figure

Mathematical Formulae in Wikimedia Projects 2020

This poster summarizes our contributions to Wikimedia's processing pipeline for mathematical formulae. We describe how we have supported the transition from rendering formulae as course-grained PNG images in 2001 to providing modern semantically enriched language-independent MathML formulae in 2020. Additionally, we describe our plans to improve the accessibility and discoverability of mathematical knowledge in Wikimedia projects further.Comment: Submitted to JCDL 2020: Proceedings of the ACM/ IEEE Joint Conference on Digital Libraries in 2020 (JCDL '20), August 1-5, 2020, Virtual Event, Chin

Impairment of Auditory-Motor Timing and Compensatory Reorganization after Ventral Premotor Cortex Stimulation

Integrating auditory and motor information often requires precise timing as in speech and music. In humans, the position of the ventral premotor cortex (PMv) in the dorsal auditory stream renders this area a node for auditory-motor integration. Yet, it remains unknown whether the PMv is critical for auditory-motor timing and which activity increases help to preserve task performance following its disruption. 16 healthy volunteers participated in two sessions with fMRI measured at baseline and following rTMS (rTMS) of either the left PMv or a control region. Subjects synchronized left or right finger tapping to sub-second beat rates of auditory rhythms in the experimental task, and produced self-paced tapping during spectrally matched auditory stimuli in the control task. Left PMv rTMS impaired auditory-motor synchronization accuracy in the first sub-block following stimulation (p<0.01, Bonferroni corrected), but spared motor timing and attention to task. Task-related activity increased in the homologue right PMv, but did not predict the behavioral effect of rTMS. In contrast, anterior midline cerebellum revealed most pronounced activity increase in less impaired subjects. The present findings suggest a critical role of the left PMv in feed-forward computations enabling accurate auditory-motor timing, which can be compensated by activity modulations in the cerebellum, but not in the homologue region contralateral to stimulation

The tropical peatland archaeal lipidome – influence of vegetation and redox on diversity

This is the final version. Available from the European Association of Geoscientists & Engineers via the DOI in this record. The nature, variability, and diversity of environmental microbiomes and lipidomes are vital to understanding soil health, biogeochemical processes and reconstructing past climates. Such research on peatlands – especially tropical peatlands – is limited, despite their importance to the global carbon cycle through the sequestration of organic matter (OM) and production of methane. Here, we explore the distribution of archaea and their isoprenoidal glycerol dialkyl glycerol tetraether lipids (isoGDGTs) across a range of wetlands, in order to ascertain the controls on their distribution. We focus specifically on vegetation and OM composition to explore the relationships between archaeal ecology and carbon cycling in tropical contexts. Through international collaboration, we created a database of core archaeal and bacteria lipid distributions of hundreds of peats from globally widespread sites (the TGRES Peat Database, Naafs et al., 2017). This formed the basis for peat-specific temperature and pH proxies based on the distribution of bacterial branched GDGTs as initially pioneered for mineral soils. However, clear environmental controls and patterns in the distribution of archaeal lipids are ambiguous (Naafs et al., 2018). For example, isoGDGT-5 is restricted to high temperature and low pH settings, but other isoGDGT and overly methylated isoprenoidal GDGT (Me-GDGTs) ring indices are poorly correlated with temperature and pH (Blewett et al., 2020). This suggests that in comparison to previously established GDGT-based environmental proxies the archaeal GDGTs of peatlands derive from an ecologically diverse group of organisms that confound simple environmental comparisons. Given the increased recognition of archaeal metabolic diversity, including a range of heterotrophic, methanotrophic and methanogen ecologies, it seems likely that changes in vegetation, peat OM composition and water level depth will impose significant controls on the archaeal community – and that of the lipids they produce

Tropical peatland biogeochemistry along an ecological transect: the enigmatic fate of organic matter

This is the final version. Available from the European Association of Geoscientists & Engineers via the DOI in this record. Peatlands play a pivotal role in the global carbon cycle. Despite only covering 3% of the world’s surface, peatlands hold 500–700 Gt of carbon (Page & Baird, 2016). These dense carbon stocks are sensitive to direct and/or indirect human intervention and can quickly turn from carbon sink to carbon source when perturbed. Additionally, peat deposits are crucial for our understanding of terrestrial environmental change by recording environmental parameters such as temperature and biogeochemical cycling through geological time (Naafs et al., 2019). Constraining the magnitude and rate of change during past periods of climatic change in the terrestrial realm is essential for accurately predicting the effects of anthropogenic global warming. Most peatland studies have focussed on reconstructing environmental parameters such as water table depth, temperature, vegetation, and pH, because those are readily available through quick observation or meteorological data. However, changes in the nature of the organic matter (OM) is often harder to characterize but is imperative to the tight balance between accumulation and degradation of peat. Especially in tropical peatlands, the nature of OM is largely understudied. Tropical peats are more carbon-dense compared to boreal peatlands, have a more active methane cycle, and can have a wider range of vegetation, which makes understanding their biogeochemistry vitally important. We investigated the biogeochemistry of a tropical peat along an ecological transect consisting of 5 sites: mangrove, mixed tropical forest, hardwood tropical forest, stunted forest with sawgrass and ombrotrophic (i.e., rain-fed) sawgrass bog. From each site, a 1–2 meter core was collected and analysed by pyrolysis-GC/MS, GC/MS (of apolar and polar fractions), 16S rRNA genomic profiling and, UPLC-QToF-MS. Our unique dataset allows for a direct comparison of the biogeochemistry of tropical peats under different vegetation and nutrient concentrations, but constant temperature

Intact polar lipids in the water column of the eastern tropical North Pacific: abundance and structural variety of non-phosphorus lipids

Intact polar lipids (IPLs) are the main building blocks of cellular membranes and contain chemotaxonomic, ecophysiological and metabolic information, making them valuable biomarkers in microbial ecology and biogeochemistry. This study investigates IPLs in suspended particulate matter (SPM) in the water column of the eastern tropical North Pacific Ocean (ETNP), one of the most extensive open-ocean oxygen minimum zones (OMZs) in the world, with strong gradients of nutrients, temperature and redox conditions. A wide structural variety in polar lipid head-group composition and core structures exists along physical and geochemical gradients within the water column, from the oxygenated photic zone to the aphotic OMZ. We use this structural diversity in IPLs to evaluate the ecology and ecophysiological adaptations that affect organisms inhabiting the water column, especially the mid-depth OMZ in the context of biogeochemical cycles. Diacylglycerol phospholipids are present at all depths, but exhibit the highest relative abundance and compositional variety (including mixed acyl/ether core structures) in the upper and core OMZ where prokaryotic biomass was enriched. Surface ocean SPM is dominated by diacylglycerol glycolipids that are found in photosynthetic membranes. These and other glycolipids with varying core structures composed of ceramides and hydroxylated fatty acids are also detected with varying relative abundances in the OMZ and deep oxycline, signifying additional non-phototrophic bacterial sources for these lipids. Betaine lipids (with zero or multiple hydroxylations in the core structures) that are typically assigned to microalgae are found throughout the water column down to the deep oxycline but do not show a depth-related trend in relative abundance. Archaeal IPLs comprised of glycosidic and mixed glycosidic-phosphatidic glycerol dibiphytanyl glycerol tetraethers (GDGTs) are most abundant in the upper OMZ, where nitrate maxima point to ammonium oxidation but increase in relative abundance in the core OMZ and deep oxycline. The presence of non-phosphorus substitute lipids within the OMZ suggest that the indigenous microbes might be phosphorus limited (P starved) at ambient phosphate concentrations of 1 to 3.5&thinsp;µM, although specific microbial sources for many of these lipids still remain unknown.</p

Formation of ethane and propane via abiotic reductive conversion of acetic acid in hydrothermal sediments

A mechanistic understanding of formation pathways of lowmolecular- weight hydrocarbons is relevant for disciplines such as atmospheric chemistry, geology, and astrobiology. The patterns of stable carbon isotopic compositions (δ13C) of hydrocarbons are commonly used to distinguish biological, thermogenic, and abiotic sources. Here, we report unusual isotope patterns of nonmethane hydrocarbons in hydrothermally heated sediments of the Guaymas Basin; these nonmethane hydrocarbons are notably 13Cenriched relative to sedimentary organic matter and display an isotope pattern that is reversed relative to thermogenic hydrocarbons (i.e., δ13C ethane > δ13C propane > δ13C n-butane > δ13C n-pentane). We hypothesized that this pattern results from abiotic reductive conversion of volatile fatty acids, which were isotopically enriched due to prior equilibration of their carboxyl carbon with dissolved inorganic carbon. This hypothesis was tested by hydrous pyrolysis experiments with isotopically labeled substrates at 350°C and 400 bar that demonstrated 1) the exchange of carboxyl carbon of C2 to C5 volatile fatty acids with 13C-bicarbonate and 2) the incorporation of 13C from 13C-2-acetic acid into ethane and propane. Collectively, our results reveal an abiotic formation pathway for nonmethane hydrocarbons, which may be sufficiently active in organic-rich, geothermally heated sediments and petroleum systems to affect isotopic compositions of nonmethane hydrocarbons

Generation and Utilization of Volatile Fatty Acids and Alcohols in Hydrothermally Altered Sediments in the Guaymas Basin, Gulf of California

Volatile fatty acids (VFAs) and alcohols are key intermediates of anaerobic carbon metabolism, yet their biogeochemical cycling remains poorly constrained in hydrothermal systems. We investigated the abundance, stable carbon isotopic composition, and metabolic cycling of VFAs and alcohols to elucidate their generation and utilization pathways in hydrothermally influenced sediments (4 °C to 90 °C) from the Guaymas Basin. Acetate (up to 229 μM) and methanol (up to 37 μM) were abundant in porewaters. The δ13C values of acetate varied between −35.6‰ and −18.1‰. Carbon isotopic signatures, thermodynamic predictions, and experimental incubations suggested biological sources such as fermentation and acetogenesis for acetate. Acetate and methanol were predominantly consumed by nonmethanogenic processes (e.g., sulfate reduction), as reflected in high oxidation rates versus low methanogenesis rates, and further evidenced through inhibition experiments with molybdate. These results reveal an important role for VFAs and alcohols as energy sources for diverse chemoheterotrophs in organic-rich hydrothermally influenced sediments

The prediction of visual stimuli influences auditory loudness discrimination

The brain combines information from different senses to improve performance on perceptual tasks. For instance, auditory processing is enhanced by the mere fact that a visual input is processed simultaneously. However, the sensory processing of one modality is itself subject to diverse influences. Namely, perceptual processing depends on the degree to which a stimulus is predicted. The present study investigated the extent to which the influence of one processing pathway on another pathway depends on whether or not the stimulation in this pathway is predicted. We used an action–effect paradigm to vary the match between incoming and predicted visual stimulation. Participants triggered a bimodal stimulus composed of a Gabor and a tone. The Gabor was either congruent or incongruent compared to an action–effect association that participants learned in an acquisition phase.We tested the influence of action–effect congruency on the loudness perception of the tone. We observed that an incongruent–task-irrelevant Gabor stimulus increases participant’s sensitivity to loudness discrimination. An identical result was obtained for a second condition in which the visual stimulus was predicted by a cue instead of an action. Our results suggest that prediction error is a driving factor of the crossmodal interplay between vision and audition