Mathematical Language Models: A Survey

In recent years, there has been remarkable progress in leveraging Language Models (LMs), encompassing Pre-trained Language Models (PLMs) and Large-scale Language Models (LLMs), within the domain of mathematics. This paper conducts a comprehensive survey of mathematical LMs, systematically categorizing pivotal research endeavors from two distinct perspectives: tasks and methodologies. The landscape reveals a large number of proposed mathematical LLMs, which are further delineated into instruction learning, tool-based methods, fundamental CoT techniques, and advanced CoT methodologies. In addition, our survey entails the compilation of over 60 mathematical datasets, including training datasets, benchmark datasets, and augmented datasets. Addressing the primary challenges and delineating future trajectories within the field of mathematical LMs, this survey is positioned as a valuable resource, poised to facilitate and inspire future innovation among researchers invested in advancing this domain.Comment: arXiv admin note: text overlap with arXiv:1705.04146, arXiv:2304.10977, arXiv:2112.00114, arXiv:1905.13319, arXiv:2304.12244, arXiv:2206.01347, arXiv:2006.09265 by other author

Baicalin Protects Mice Brain From Apoptosis in Traumatic Brain Injury Model Through Activation of Autophagy

Autophagy is associated with secondary injury following traumatic brain injury (TBI) and is expected to be a therapeutic target. Baicalin, a neuroprotective agent, has been proven to exert multi-functional bioactive effects in brain injury diseases. However, it is unknown if Baicalin influences autophagy after TBI. In the present study, we aimed to explore the effects that Baicalin had on TBI in a mice model, focusing on autophagy as a potential mechanism. We found that Baicalin administration significantly improved motor function, reduced cerebral edema, and alleviated disruption of the blood-brain barrier (BBB) after TBI in mice. Besides, TBI-induced apoptosis was reversed by Baicalin evidenced by Nissl staining, terminal deoxynucleotidyl transferase dUTP nick end labeling (TUNEL) assay, and the level of cleaved caspase-3. More importantly, Baicalin enhanced autophagy by detecting the autophagy markers (LC3, Beclin 1, and p62) using western blot and LC3 immunofluorescence staining, ameliorating mitochondrial apoptotic pathway evidenced by restoration of the TBI-induced translocation of Bax and cytochrome C. However, simultaneous treatment with 3-MA inhibited Baicalin-induced autophagy and abolished its protective effects on mitochondrial apoptotic pathway. In conclusion, we demonstrated that Baicalin enhanced autophagy, ameliorated mitochondrial apoptosis and protected mice brain in TBI mice model

The Genomes of Oryza sativa: A History of Duplications

We report improved whole-genome shotgun sequences for the genomes of indica and japonica rice, both with multimegabase contiguity, or almost 1,000-fold improvement over the drafts of 2002. Tested against a nonredundant collection of 19,079 full-length cDNAs, 97.7% of the genes are aligned, without fragmentation, to the mapped super-scaffolds of one or the other genome. We introduce a gene identification procedure for plants that does not rely on similarity to known genes to remove erroneous predictions resulting from transposable elements. Using the available EST data to adjust for residual errors in the predictions, the estimated gene count is at least 38,000–40,000. Only 2%–3% of the genes are unique to any one subspecies, comparable to the amount of sequence that might still be missing. Despite this lack of variation in gene content, there is enormous variation in the intergenic regions. At least a quarter of the two sequences could not be aligned, and where they could be aligned, single nucleotide polymorphism (SNP) rates varied from as little as 3.0 SNP/kb in the coding regions to 27.6 SNP/kb in the transposable elements. A more inclusive new approach for analyzing duplication history is introduced here. It reveals an ancient whole-genome duplication, a recent segmental duplication on Chromosomes 11 and 12, and massive ongoing individual gene duplications. We find 18 distinct pairs of duplicated segments that cover 65.7% of the genome; 17 of these pairs date back to a common time before the divergence of the grasses. More important, ongoing individual gene duplications provide a never-ending source of raw material for gene genesis and are major contributors to the differences between members of the grass family

Azimuthal anisotropy of charged jet production in root s(NN)=2.76 TeV Pb-Pb collisions

We present measurements of the azimuthal dependence of charged jet production in central and semi-central root s(NN) = 2.76 TeV Pb-Pb collisions with respect to the second harmonic event plane, quantified as nu(ch)(2) (jet). Jet finding is performed employing the anti-k(T) algorithm with a resolution parameter R = 0.2 using charged tracks from the ALICE tracking system. The contribution of the azimuthal anisotropy of the underlying event is taken into account event-by-event. The remaining (statistical) region-to-region fluctuations are removed on an ensemble basis by unfolding the jet spectra for different event plane orientations independently. Significant non-zero nu(ch)(2) (jet) is observed in semi-central collisions (30-50% centrality) for 20 <p(T)(ch) (jet) <90 GeV/c. The azimuthal dependence of the charged jet production is similar to the dependence observed for jets comprising both charged and neutral fragments, and compatible with measurements of the nu(2) of single charged particles at high p(T). Good agreement between the data and predictions from JEWEL, an event generator simulating parton shower evolution in the presence of a dense QCD medium, is found in semi-central collisions. (C) 2015 CERN for the benefit of the ALICE Collaboration. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).Peer reviewe