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Gautschi proposed a method for computing incomplete beta functions I x ( a , b ) using Miller’s algorithm with a three-term recurrence relation and showed a computation program in ALGOL. In this paper, first, Miller’s algorithm using the recurrence relation satisfied by f k ( x ) = I x ( a + k , b ) is described. Next, another solution that is first-order independent of f k ( x ) of the recurrence relation is given, and its general solution can be expressed as a linear sum of these. Using this general solution, an error analysis for the function I x ( a , b ) is performed for the first time. The relative error of the function values is then expressed in a new formula to a trend of the error behavior. Also, Miller’s algorithm with a normalizing sum is explained and its error analysis is performed. Since Miller’s algorithm requires a predefined number of iterations of the recurrence relation, it is necessary to repeat the computation of the recurrence relation with increasing number of iterations until the required accuracy will be met. Therefore, in this paper, we apply Deuflhard’s algorithm, which can automatically obtain the function value with the required accuracy. This algorithm requires far fewer iterations than Gautschi’s algorithm to obtain the same accuracy.

Objective Oral leukoplakia is keratinized lesions in the buccal mucosa, tongue, and gingiva. It is the most common oral precancerous lesion; oxidative stresses and irrelevant autophagy have been reported to be the cause of oncogenesis. p62, a cytoplasmic protein induced by oxidative stress, is an adaptor protein involved in the formation of protein aggregates and induction and inhibition of autophagy. The inhibition of autophagy induces p62 overexpression and promotes oncogenesis via the oncogenic signaling pathway. The aim of the present study was to elucidate the involvement of intracellular expression of p62 in oral leukoplakia and to address its potential clinical implementation as a biomarker to predict malignant transformation. Material and Methods Fifty samples from subjects with confirmed oral leukoplakia were evaluated by immunohistochemical staining for the expression of p62, 8‐hydroxy‐2′‐deoxyguanosine (8‐OHdG), Ki67, and p53. Univariate and multivariate logistic regression analyses were performed to evaluate the association between p62, 8‐OHdG, Ki67, and p53 and clinical characteristics, including epithelial dysplasia. Results Significant associations were observed between p62 expression in the nucleus, p62 aggregation, and epithelial dysplasia (adjusted odds ratio [OR] = 5.75; 95% confidence interval [CI]: [1.28, 26.2]; .024 and OR = 6.16; 95% CI: [1.01, 37.4]; .048, respectively). The expression of p62 in the cytoplasm and the levels of 8‐OHdG, Ki67, and p53 were not significantly associated with epithelial dysplasia. A significant relationship was found between p62 expression in the nucleus and p53 expression (OR = 3.94; 95% CI: [1.14, 13.6]; .031). Conclusions The results suggested that p62 expression in the nucleus and p62 aggregation can be potential markers to predict the malignant transformation of oral leukoplakia.

Two taxa of Meconopsis, growing on metalliferous mountains adjacent to Wanba () valley, Jiulong Xian (), southwestern Sichuan, China, are described as new and accompanied by photographs. The first taxon, M. wanbaensis, is distinguished from related species by such unique features as the prominently undulate petals and obconical style. The second taxon, M. pulchella var. melananthera, is distinguished from var. pulchella by features of the anthers and bristles.

Meconopsis castanea and the related M. georgei and M. bijiangensis are revised, and a related new species, M. atrovinosa, is described and illustrated. A distribution map of the treated species is provided.

Meconopsis section Forrestianae is revised. Three new species, M. aprica, M. purpurea, and M. wengdaensis; two new subspecies of M. lancifolia, subsp. daliensis and subsp. shikaensis; and a new variety of M. yaoshanensis, var. luojiensis, are described and illustrated. A new combination is proposed, Meconopsis lancifolia subsp. xiangchengensis. Distribution maps of the taxa treated are provided.

Meconopsis castanea and the related M. georgei and M. bijiangensis are revised, and a related new species, M. atrovinosa, is described and illustrated. A distribution map of the treated species is provided.

Meconopsis section Forrestianae is revised. Three new species, M. aprica, M. purpurea, and M. wengdaensis; two new subspecies of M. lancifolia, subsp. daliensis and subsp. shikaensis; and a new variety of M. yaoshanensis, var. luojiensis, are described and illustrated. A new combination is proposed, Meconopsis lancifolia subsp. xiangchengensis. Distribution maps of the taxa treated are provided.

In this paper, we describe a robotic ultrasound (US) probe scanning system for reducing the manual tasks of US technicians and assisting in interventional procedures. The system consists of a probe scanning robot that uses McKibben artificial muscles, an optical tracking device, and in-house software for volume reconstruction and automatic guidance of surgical tools. The proposed system is lightweight and safe due to the use of artificial muscles, and allows positional control of the B-scan plane through transformation of US calibration. We applied the robotic system to robotic three-dimensional (3D) ultrasound and automatic ultrasound guidance. To clarify the system's feasibility, we performed phantom and human liver volume reconstructions, as well as needle guidance. The volume qualities of the reconstruction were validated by cross-correlation with reference echograms and reslicing of the reconstructed volumes. The correlation values were 0.80 ± 0.06 for the phantom and 0.53 ± 0.06 for the human liver. Regarding needle guidance, we confirmed that the B-scan plane automatically followed the needle. The translation error was −0.10 ± 1.26 mm and rotation error was −0.22 ± 1.81 degrees. Analysis of frequency response confirmed that the system was able to stably follow a motion at frequencies less than 0.3 Hz. The experimental results demonstrate that the robotic probe scanning system has great potential for yielding acceptable 3D volumes using two-dimensional (2D) ultrasound and assisting interventional procedures under US guidance.

Four new species of Meconopsis—M. huanglongensis, M. inaperta, M. hispida, and M. trichogyna—are described and illustrated, M. barbiseta is redescribed, and a new series of Meconopsis, series Barbisetae, is proposed.