Experts of abacus, who have the skills of abacus-based mental calculation (AMC), are able to manipulate numbers via an imagined abacus in mind and demonstrate extraordinary ability in mental calculation. Behavioral studies indicated that abacus experts utilize visual strategy in solving numerical problems, and fMRI studies confirmed the enhanced involvement of visuospatial-related neural resources in AMC. This study aims to explore the possible changes in brain white matter induced by long-term training of AMC. Two matched groups participated: the abacus group consisting of 25 children with over 3-year training in abacus calculation and AMC, the controls including 25 children without any abacus experience. We found that the abacus group showed higher average fractional anisotropy (FA) in whole-brain fiber tracts, and the regions with increased FA were found in corpus callosum, left occipitotemporal junction and right premotor projection. No regions, however, showed decreased FA in the abacus group. Further analysis revealed that the differences in FA values were mainly driven by the alternation of radial rather than axial diffusivities. Furthermore, in forward digit and letter memory span tests, AMC group showed larger digit/letter memory spans. Interestingly, individual differences in white matter tracts were found positively correlated with the memory spans, indicating that the widespread increase of FA in the abacus group result possibly from the AMC training. In conclusion, our findings suggested that long-term AMC training from an early age may improve the memory capacity and enhance the integrity in white matter tracts related to motor and visuospatial processes.

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This paper studies the problem of parameter estimation for the multifrequency sine signals, which have multiple characteristic parameters such as the amplitudes, phases, and frequencies. It is noted that the signal output is nonlinear with respect to the phase and frequency parameters while it is linear with respect to the amplitude parameters. This feature inspires us to separate all of the characteristic parameters into a linear parameter set and a nonlinear parameter set, where the linear set is composed of the amplitude parameters and the nonlinear set is composed of the phase parameters and the frequency parameters. After the parameter separation, two identification submodels are constructed for optimizing the linear parameter set and the nonlinear parameter set. Then the nonlinear identification model becomes a linear identification submodel and a nonlinear identification submodel. Therefore, the nonlinear optimization for minimizing the objective function is converted into the combination of the quadratic optimization and nonlinear optimization. Based on the separable identification submodels, a recursive least squares subalgorithm and a recursive gradient subalgorithm are proposed for identifying the linear parameters and nonlinear parameters, respectively. Moreover, an interactive estimation algorithm is designed to remove the related parameter sets between the subalgorithms and a hierarchical identification method is presented by combining the subalgorithms. For the purpose of tracking the time‐varying, a forgetting factor is introduced to improve the convergence speed. The numerical examples are provided to qualify the performance of the proposed method based on some performance measures.

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