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We study several classes of operadic ideals of the unital associative algebra operad uAss. As an application, we classify quotient operads of uAss of GK-dimension no more than 6. This corresponds to a classification of all T-ideals of codimension growth no more than 5 (or equivalently, varieties of grade no more than 5). 

Active Learning (AL) has gained prominence in integrating data-intensive machine learning (ML) models into domains with limited labeled data. However, its effectiveness diminishes significantly when the labeling budget is low. In this paper, we first empirically observe the performance degradation of existing AL algorithms in the low-budget settings, and then introduce Direct Acquisition Optimization (DAO), a novel AL algorithm that optimizes sample selections based on expected true loss reduction. Specifically, DAO utilizes influence functions to update model parameters and incorporates an additional acquisition strategy to mitigate bias in loss estimation. This approach facilitates a more accurate estimation of the overall error reduction, without extensive computations or reliance on labeled data. Experiments demonstrate DAO's effectiveness in low budget settings, outperforming state-of-the-arts approaches across seven benchmarks. 

We present measurements of the total and differential cross sections for near-threshold $J/\psi$photoproduction obtained with the CLAS12 detector at the Thomas Jefferson National Accelerator Facility. The results are based on data collected during the fall 2018 and spring 2019 running periods, using electron beams with energies of 10.6 and 10.2 GeV, respectively, scattered off a liquid-hydrogen target. Near-threshold $J/\psi$photoproduction offers a unique sensitivity to the strong interaction in the nonperturbative regime of quantum chromodynamics (QCD). The energy dependence of the cross section constrains the underlying $J/\psi$production mechanisms, including multigluon exchange and potential baryonic excitations. Additionally, the $t$dependence of the differential cross section can be related to the transverse spatial distribution of gluons in the proton, providing critical input for theoretical descriptions of the gluonic structure of the proton. An interpretation of the results in terms of the gluon content of the proton is presented, providing new experimental constraints on QCD-inspired models of the proton structure and the role of gluonic degrees of freedom in hadronic mass generation.