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This paper proposes a simplified analytical solution considering non-Darcian and wellbore storage effect to investigate the pumping flow in a confined aquifer with barrier and recharge boundaries. The mathematical modelling for the pumping-induced flow in aquifers with different boundaries is developed by employing image-well theory with the superposition principle, of which the non-Darcian effect is characterized by Izbash’s equation. The solutions are derived by Boltzmann and dimensionless transformations. Then, the non-Darcian effect and wellbore storage are especially investigated according to the proposed solution. The results show that the aquifer boundaries have non-negligible effects on pumping, and ignoring the wellbore storage can lead to an over-estimation of the drawdown in the first 10 minutes of pumping. The higher the degree of non-Darcian, the smaller the drawdown.

Abstract Background Feature selection in class-imbalance learning has gained increasing attention in recent years due to the massive growth of high-dimensional class-imbalanced data across many scientific fields. In addition to reducing model complexity and discovering key biomarkers, feature selection is also an effective method of combating overlapping which may arise in such data and become a crucial aspect for determining classification performance. However, ordinary feature selection techniques for classification can not be simply used for addressing class-imbalanced data without any adjustment. Thus, more efficient feature selection technique must be developed for complicated class-imbalanced data, especially in the context of high-dimensionality. Results We proposed an algorithm called sssHD to achieve stable sparse feature selection applied it to complicated class-imbalanced data. sssHD is based on the Hellinger distance (HD) coupled with sparse regularization techniques. We stated that Hellinger distance is not only class-insensitive but also translation-invariant. Simulation result indicates that HD-based selection algorithm is effective in recognizing key features and control false discoveries for class-imbalance learning. Five gene expression datasets are also employed to test the performance of the sssHD algorithm, and a comparison with several existing selection procedures is performed. The result shows that sssHD is highly competitive in terms of five assessment metrics. In addition, sssHD presents limited differences between performing and not performing re-balance preprocessing. Conclusions sssHD is a practical feature selection method for high-dimensional class-imbalanced data, which is simple and can be an alternative for performing feature selection in class-imbalanced data. sssHD can be easily extended by connecting it with different re-balance preprocessing, different sparse regularization structures as well as different classifiers. As such, the algorithm is extremely general and has a wide range of applicability.

Abstract Background The transtibial tunnel technique achieves equal length reconstruction of the anterior cruciate ligament (ACL). This study aimed to investigate whether transtibial tunnel technique can achieve anatomical reconstruction of ACL. Methods For 25 corpses, the anterior soft tissue of the knee joint was detached so that the ligamentous surface was fully exposed, then the knee joint was fixed at 90° with an external fixator and the anterior cruciate ligament was removed. Double-sided laser technology was used to establish spatial conformation of ACL. Results The male to female ratio of the subjects was 19:6, with an average age of 59.52 ± 11.13 years. Patellar tendon length was 35.23 ± 5.10 mm, tibial eminence length and width was 15.75 ± 2.44 and 7.80 ± 1.28 mm, respectively, and femoral attachment length and width was 15.40 ± 2.17 and 8.97 ± 1.61 mm, respectively. When the flexion turned 90°, the tibial tunnel length was 31.83 ± 4.09 mm and the distance to the tibial plateau, patellar tendon, and medial collateral ligament was 16.33 ± 4.56, 10.79 ± 5.85, and 23.12 ± 5.99 mm, respectively. Conclusions With the aid of double-sided laser technology, transtibial tunnel technique can safely achieve single-bundle reconstruction of ACL.

Feature screening is an important and challenging topic in current class-imbalance learning. Most of the existing feature screening algorithms in class-imbalance learning are based on filtering techniques. However, the variable rankings obtained by various filtering techniques are generally different, and this inconsistency among different variable ranking methods is usually ignored in practice. To address this problem, we propose a simple strategy called rank aggregation with re-balance (RAR) for finding key variables from class-imbalanced data. RAR fuses each rank to generate a synthetic rank that takes every ranking into account. The class-imbalanced data are modified via different re-sampling procedures, and RAR is performed in this balanced situation. Five class-imbalanced real datasets and their re-balanced ones are employed to test the RAR’s performance, and RAR is compared with several popular feature screening methods. The result shows that RAR is highly competitive and almost better than single filtering screening in terms of several assessing metrics. Performing re-balanced pretreatment is hugely effective in rank aggregation when the data are class-imbalanced.

Elastic net (Enet) and sparse partial least squares (SPLS) are frequently employed for wavelength selection and model calibration in analysis of near infrared spectroscopy data. Enet and SPLS can perform variable selection and model calibration simultaneously. And they also tend to select wavelength intervals rather than individual wavelengths when the predictors are multicollinear. In this paper, we focus on comparison of Enet and SPLS in interval wavelength selection and model calibration for near infrared spectroscopy data. The results from both simulation and real spectroscopy data show that Enet method tends to select less predictors as key variables than SPLS; thus it gets more parsimony model and brings advantages for model interpretation. SPLS can obtain much lower mean square of prediction error (MSE) than Enet. So SPLS is more suitable when the attention is to get better model fitting accuracy. The above conclusion is still held when coming to performing the strongly correlated NIR spectroscopy data whose predictors present group structures, Enet exhibits more sparse property than SPLS, and the selected predictors (wavelengths) are segmentally successive.