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

Dynamic patterns make the premotor cortex interested in objects: Influence of stimulus and task revealed by fMRI

Research in monkey and man indicates that the ventrolateral premotor cortex (PMv) underlies not only the preparation of manual movements, but also the perceptual representation of pragmatic object properties. However, visual stimuli without any pragmatic meaning were recently found to elicit selective PMv responses if they were subjected to a perceivable pattern of change. We used functional magnetic resonance imaging (fMRI) to investigate if perceptual representations in the PMv might apply not only to pragmatic, but also to dynamic stimulus properties. To this end, a sequential figure matching task that required the processing of dynamic features was contrasted with a non-figure control task (Experiment 1) and an individual figure matching task (Experiment 2). In order to control for potential influences of stimulus properties that might be associated with pragmatic attributes, different types of abstract visual stimuli were employed. The experiments yielded two major findings: if their dynamic properties are attended, then abstract 2D visual figures are sufficient to trigger activation within premotor areas involved in hand-object interaction. Moreover, these premotor activations are independent from stimulus properties that might relate to pragmatic features. The results imply that the PMv is engaged in the processing of stimuli that are usually or actually embedded within either a pragmatic or a dynamic context

A blueprint for target motion: fMRI reveals perceived sequential complexity to modulate premotor cortex

The execution of movements that are guided by an increasingly complex target motion is known to draw on premotor cortices. Whole-brain functional magnetic resonance imaging was used to investigate whether, in the absence of any movement, attending to and predicting increasingly complex target motion also rely on premotor cortices. Complexity was varied as a function of number of sequential elements and amount of dynamic sequential trend in a pulsing target motion. As a result, serial prediction caused activations in premotor and parietal cortices, particularly within the right hemisphere. Parametric analyses revealed that the right ventrolateral premotor cortex and the right anterior intraparietal sulcus were the only areas that, in addition, covaried positively with both behavioral and physical measures of sequential complexity. Further areas that covaried positively with increasing task difficulty reflected influences of both number and trend manipulation. In particular, increasing element number drew on dorsal premotor and corresponding posterior intraparietal regions, whereas increasing trend drew on the visual motion area and area V4. The present findings demonstrate that premotor involvement directly reflects perceptual complexity in attended and predicted target motion. It is suggested that when we try to predict how a target will move, the motor system generates a “blueprint” of the observed motion that allows potential sensorimotor integration. In the absence of any motor requirement, this blueprint appears to be not a by-product of motor planning, but rather the basis for target motion prediction

burleszk-operette 3 felvonásban - írta Báron Rezső és Fellner Pál - zenéjét szerzé Báron Rezső

Városi Szinház. Debreczen, 1913. évi szeptember hó 5 -én, pénteken: Ujdonság. Itt először.Debreceni Egyetem Egyetemi és Nemzeti Könyvtá

Premotor cortex in observing erroneous action: An fMRI study

The lateral premotor cortex (PMC) is involved during action observation in monkeys and humans, reflecting a matching process between observed actions and their corresponding motor schemata. In the present study, functional magnetic resonance imaging (fMRI) was used to investigate if paying attention to the two observable action components, objects and movements, modulates premotor activation during the observation of actions. Participants were asked to classify presented movies as showing correct actions, erroneous actions, or senseless movements. Erroneous actions were incorrect either with regard to employed objects, or to performed movements. The experiment yielded two major results: (1) The ventrolateral premotor cortex (vPMC) and the anterior part of the intraparietal sulcus (aIPS) are strongly activated during the observation of actions in humans. Premotor activation was dominantly located within Brodmann Area (BA) 6, and sometimes extended into BA 44. (2) The presentation of object errors and movements errors allowed to disentangle brain activations corresponding to the analysis of movements and objects in observed actions. Left premotor areas were more involved in the analysis of objects, whereas right premotor areas were dominant in the analysis of movements. It is suggested that the analysis of categorical information, like objects, and that of coordinate information, like movements, are pronounced in different hemispheres

Why you think Milan is larger than Modena: Neural correlates of the recognition heuristic

When ranking two alternatives by some criteria and only one of the alternatives is recognized, participants overwhelmingly adopt the strategy, termed the recognition heuristic (RH), of choosing the recognized alternative. Understanding the neural correlates underlying decisions that follow the RH could help determine whether people make judgments about the RH's applicability or simply choose the recognized alternative. We measured brain activity by using functional magnetic resonance imaging while participants indicated which of two cities they thought was larger (Experiment 1) or which city they recognized (Experiment 2). In Experiment 1, increased activation was observed within the anterior frontomedian cortex (aFMC), precuneus, and retrosplenial cortex when participants followed the RH compared to when they did not. Experiment 2 revealed that RH decisional processes cannot be reduced to recognition memory processes. As the aFMC has previously been associated with self-referential judgments, we conclude that RH decisional processes involve an assessment about the applicability of the RH

Quantifying the effects of hydrogen on carbon assimilation in a seafloor microbial community associated with ultramafic rocks

Thermodynamic models predict that H2 is energetically favorable for seafloor microbial life, but how H2 affects anabolic processes in seafloor-associated communities is poorly understood. Here, we used quantitative 13C DNA stable isotope probing (qSIP) to quantify the effect of H2 on carbon assimilation by microbial taxa synthesizing 13C-labeled DNA that are associated with partially serpentinized peridotite rocks from the equatorial Mid-Atlantic Ridge. The rock-hosted seafloor community was an order of magnitude more diverse compared to the seawater community directly above the rocks. With added H2, peridotite-associated taxa increased assimilation of 13C-bicarbonate and 13C-acetate into 16S rRNA genes of operational taxonomic units by 146% (±29%) and 55% (±34%), respectively, which correlated with enrichment of H2-oxidizing NiFe-hydrogenases encoded in peridotite-associated metagenomes. The effect of H2 on anabolism was phylogenetically organized, with taxa affiliated with Atribacteria, Nitrospira, and Thaumarchaeota exhibiting the most significant increases in 13C-substrate assimilation in the presence of H2. In SIP incubations with added H2, an order of magnitude higher number of peridotite rock-associated taxa assimilated 13C-bicarbonate, 13C-acetate, and 13C-formate compared to taxa that were not associated with peridotites. Collectively, these findings indicate that the unique geochemical nature of the peridotite-hosted ecosystem has selected for H2-metabolizing, rock-associated taxa that can increase anabolism under high H2 concentrations. Because ultramafic rocks are widespread in slow-, and ultraslow-spreading oceanic lithosphere, continental margins, and subduction zones where H2 is formed in copious amounts, the link between H2 and carbon assimilation demonstrated here may be widespread within these geological settings

Surmising synchrony of sound and sight: Factors explaining variance of audiovisual integration in hurdling, tap dancing and drumming.

Auditory and visual percepts are integrated even when they are not perfectly temporally aligned with each other, especially when the visual signal precedes the auditory signal. This window of temporal integration for asynchronous audiovisual stimuli is relatively well examined in the case of speech, while other natural action-induced sounds have been widely neglected. Here, we studied the detection of audiovisual asynchrony in three different whole-body actions with natural action-induced sounds-hurdling, tap dancing and drumming. In Study 1, we examined whether audiovisual asynchrony detection, assessed by a simultaneity judgment task, differs as a function of sound production intentionality. Based on previous findings, we expected that auditory and visual signals should be integrated over a wider temporal window for actions creating sounds intentionally (tap dancing), compared to actions creating sounds incidentally (hurdling). While percentages of perceived synchrony differed in the expected way, we identified two further factors, namely high event density and low rhythmicity, to induce higher synchrony ratings as well. Therefore, we systematically varied event density and rhythmicity in Study 2, this time using drumming stimuli to exert full control over these variables, and the same simultaneity judgment tasks. Results suggest that high event density leads to a bias to integrate rather than segregate auditory and visual signals, even at relatively large asynchronies. Rhythmicity had a similar, albeit weaker effect, when event density was low. Our findings demonstrate that shorter asynchronies and visual-first asynchronies lead to higher synchrony ratings of whole-body action, pointing to clear parallels with audiovisual integration in speech perception. Overconfidence in the naturally expected, that is, synchrony of sound and sight, was stronger for intentional (vs. incidental) sound production and for movements with high (vs. low) rhythmicity, presumably because both encourage predictive processes. In contrast, high event density appears to increase synchronicity judgments simply because it makes the detection of audiovisual asynchrony more difficult. More studies using real-life audiovisual stimuli with varying event densities and rhythmicities are needed to fully uncover the general mechanisms of audiovisual integration