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1. The five digits of the giraffe metatarsal

   https://doi.org/10.1093/biolinnean/blaa136  

   Yohe, Laurel R; Solounias, Nikos (October 2020, Biological Journal of the Linnean Society)

   null (Ed.)

   Abstract Evolution has shaped the limbs of hoofed animals in specific ways. In artiodactyls, it is the common assumption that the metatarsal is composed of the fusion of digits III and IV, whereas the other three digits have been lost or are highly reduced. However, evidence from the fossil record and internal morphology of the metatarsal challenges these assumptions. Furthermore, only a few taxonomic groups have been analysed. In giraffes, we discovered that all five digits are present in the adult metatarsal and are highly fused and modified rather than lost. We examined high-resolution micro-computed tomography scans of the metatarsals of two mid and late Miocene giraffid fossils and the extant giraffe and okapi. In all the Giraffidae analysed, we found a combination of four morphologies: (1) four articular facets; (2) four or, in most cases, five separate medullary cavities internally; (3) a clear, small digit I; and (4) in the two fossil taxa of unknown genus, the presence of external elongated grooves where the fusions of digits II and V have taken place. Giraffa and Okapia, the extant Giraffidae, show a difference from all the extinct taxa in having more flattened digits tightly packed together, suggesting convergent highly fused digits despite divergent ecologies and locomotion. These discoveries provide evidence that enhances our understanding of how bones fuse and call into question current hypotheses of digit loss. 

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2. Numerical uncertainty in analytical pipelines lead to impactful variability in brain networks

   https://doi.org/10.1371/journal.pone.0250755  

   Kiar, Gregory; Chatelain, Yohan; de_Oliveira_Castro, Pablo; Petit, Eric; Rokem, Ariel; Varoquaux, Gaël; Misic, Bratislav; Evans, Alan C; Glatard, Tristan (November 2021, PLOS ONE)

   Dimitriadis, Stavros I (Ed.)

   The analysis of brain-imaging data requires complex processing pipelines to support findings on brain function or pathologies. Recent work has shown that variability in analytical decisions, small amounts of noise, or computational environments can lead to substantial differences in the results, endangering the trust in conclusions. We explored the instability of results by instrumenting a structural connectome estimation pipeline with Monte Carlo Arithmetic to introduce random noise throughout. We evaluated the reliability of the connectomes, the robustness of their features, and the eventual impact on analysis. The stability of results was found to range from perfectly stable (i.e. all digits of data significant) to highly unstable (i.e. 0 − 1 significant digits). This paper highlights the potential of leveraging induced variance in estimates of brain connectivity to reduce the bias in networks without compromising reliability, alongside increasing the robustness and potential upper-bound of their applications in the classification of individual differences. We demonstrate that stability evaluations are necessary for understanding error inherent to brain imaging experiments, and how numerical analysis can be applied to typical analytical workflows both in brain imaging and other domains of computational sciences, as the techniques used were data and context agnostic and globally relevant. Overall, while the extreme variability in results due to analytical instabilities could severely hamper our understanding of brain organization, it also affords us the opportunity to increase the robustness of findings. 

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3. Efficient Synthesis with Probabilistic Constraints

   Drews, Samuel; Albarghouthi, Aws; D'Antoni, Loris (January 2019, International Conference on Computer Aided Verification)

   We consider the problem of synthesizing a program given a probabilistic specification of its desired behavior. Specifically, we study the recent paradigm of distribution-guided inductive synthesis (digits), which iteratively calls a synthesizer on finite sample sets from a given distribution. We make theoretical and algorithmic contributions: (i) We prove the surprising result that digits only requires a polynomial number of synthesizer calls in the size of the sample set, despite its ostensibly exponential behavior. (ii) We present a property-directed version of digits that further reduces the number of synthesizer calls, drastically improving synthesis performance on a range of benchmarks. 

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4. The Dynamics of Digits: Calculating Pi with Galperin’s Billiards

   https://doi.org/10.3390/math8040509  

   Aretxabaleta, Xabier M.; Gonchenko, Marina; Harshman, Nathan L.; Jackson, Steven Glenn; Olshanii, Maxim; Astrakharchik, Grigory E. (April 2020, Mathematics)

   In Galperin billiards, two balls colliding with a hard wall form an analog calculator for the digits of the number π . This classical, one-dimensional three-body system (counting the hard wall) calculates the digits of π in a base determined by the ratio of the masses of the two particles. This base can be any integer, but it can also be an irrational number, or even the base can be π itself. This article reviews previous results for Galperin billiards and then pushes these results farther. We provide a complete explicit solution for the balls’ positions and velocities as a function of the collision number and time. We demonstrate that Galperin billiard can be mapped onto a two-particle Calogero-type model. We identify a second dynamical invariant for any mass ratio that provides integrability for the system, and for a sequence of specific mass ratios we identify a third dynamical invariant that establishes superintegrability. Integrability allows us to derive some new exact results for trajectories, and we apply these solutions to analyze the systematic errors that occur in calculating the digits of π with Galperin billiards, including curious cases with irrational number bases. 

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5. Structural and functional connectivity of the inferior temporal numeral area

   https://doi.org/10.1093/cercor/bhac492  

   Conrad, Benjamin N.; Pollack, Courtney; Yeo, Darren J.; Price, Gavin R. (December 2022, Cerebral Cortex)

   Abstract A growing body of evidence suggests that in adults, there is a spatially consistent “inferior temporal numeral area” (ITNA) in the occipitotemporal cortex that appears to preferentially process Arabic digits relative to non-numerical symbols and objects. However, very little is known about why the ITNA is spatially segregated from regions that process other orthographic stimuli such as letters, and why it is spatially consistent across individuals. In the present study, we used diffusion-weighted imaging and functional magnetic resonance imaging to contrast structural and functional connectivity between left and right hemisphere ITNAs and a left hemisphere letter-preferring region. We found that the left ITNA had stronger structural and functional connectivity than the letter region to inferior parietal regions involved in numerical magnitude representation and arithmetic. Between hemispheres, the left ITNA showed stronger structural connectivity with the left inferior frontal gyrus (Broca’s area), while the right ITNA showed stronger structural connectivity to the ipsilateral inferior parietal cortex and stronger functional coupling with the bilateral IPS. Based on their relative connectivity, our results suggest that the left ITNA may be more readily involved in mapping digits to verbal number representations, while the right ITNA may support the mapping of digits to quantity representations. 

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