Optimal control problems with Atangana‐Baleanu fractional derivative

In this paper, we study fractional‐order optimal control problems (FOCPs) involving the Atangana‐Baleanu fractional derivative. A computational method based on B‐spline polynomials and their operational matrix of Atangana‐Baleanu fractional integration is proposed for the numerical solution of this class of problems. With this numerical technique, the FOCPs are reduced to a system of equations which are solved for the unknown parameters with the help of Mathematica® software. Our results show the applicability and usefulness of the numerical technique.     

基于一测多评多组分定量质控联合主成分分析、正交偏最小二乘法-判别分析及熵权逼近理想解排序法的盐沙苑子饮片综合质量评价

目的 建立一测多评（quantitative analysis of multicomponents by single-marker,QAMS）法同时检测盐沙苑子饮片中杨梅素、扁蓄苷、杨梅素-3-O-β-D-葡萄糖苷、毛蕊异黄酮葡萄糖苷、西伯利亚落叶松黄酮、沙苑子苷B、沙苑子苷A、毛蕊异黄酮、芒柄花素、鼠李柠檬素、豆甾醇、胡萝卜苷、β-谷甾醇含量的方法,并采用主成分分析法（principal component analysis,PCA）、正交偏最小二乘法-判别分析（orthogonal partial least squares-discriminant analysis,OPLS-DA）法及熵权逼近理想解排序（entropy weight-technique for order preference by similarity to ideal solution,EW-TOPSIS）法对其质量进行评价。方法 采用Lichrospher C18色谱柱;乙腈-0.2%磷酸水溶液为流动相梯度洗脱。以沙苑子苷A为内参物,建立内参物与其他12个待测成分的相对校正因子（relative co...     

A Mortar Spectral Element Method for Full-Potential Electronic Structure Calculations

In this paper, we propose an efficient mortar spectral element approximation scheme for full-potential electronic structure calculations. As a subsequent work of [24], the paper adopts a similar domain decomposition that the computational domain is first decomposed into a number of cuboid subdomains satisfying each nucleus is located in the center of one cube, in which a small ball element centered at the site of the nucleus is attached, and the remainder of the cube is further partitioned into six curvilinear hexahedrons. Specially designed Sobolev-orthogonal basis is adopted in each ball. Classic conforming spectral element approximations using mapped Jacobi polynomials are implemented on the curvilinear hexahedrons and the cuboid elements without nuclei. A mortar technique is applied to patch the different discretizations. Numerical experiments are carried out to demonstrate the efficiency of our scheme, especially the spectral convergence rates of the ground state approximations. Essentially the algorithm can be extended to general eigenvalue problems with the Coulomb singularities.     

Adaptive Order WENO Reconstructions for the Semi-Lagrangian Finite Difference Scheme for Advection Problem

We present a new conservative semi-Lagrangian finite difference weighted essentially non-oscillatory scheme with adaptive order. This is an extension of the conservative semi-Lagrangian (SL) finite difference WENO scheme in [Qiu and Shu, JCP, 230 (4) (2011), pp. 863-889], in which linear weights in SL WENO framework were shown not to exist for variable coefficient problems. Hence, the order of accuracy is not optimal from reconstruction stencils. In this paper, we incorporate a recent WENO adaptive order (AO) technique [Balsara et al., JCP, 326 (2016), pp. 780-804] to the SL WENO framework. The new scheme can achieve an optimal high order of accuracy, while maintaining the properties of mass conservation and non-oscillatory capture of solutions from the original SL WENO. The positivity-preserving limiter is further applied to ensure the positivity of solutions. Finally, the scheme is applied to high dimensional problems by a fourth-order dimensional splitting. We demonstrate the effectiveness of the new scheme by extensive numerical tests on linear advection equations, the Vlasov-Poisson system, the guiding center Vlasov model as well as the incompressible Euler equations.     

Reducing unnecessary crossmatching for hip fracture patients by accounting for preoperative hemoglobin concentration

BACKGROUNDMaximum surgical blood order schedules were designed to eliminate unnecessary preoperative crossmatching prior to surgery in order to conserve blood bank resources. Most protocols recommend type and cross of 2 red blood cell (RBC) units for patients undergoing surgery for treatment of hip fracture. Preoperative hemoglobin has been identified as the strongest predictor of inpatient transfusion, but current maximum surgical blood order schedules do not consider preoperative hemoglobin values to determine the number of RBC units to prepare prior to surgery. AIMTo determine the preoperative hemoglobin level resulting in the optimal 2:1 crossmatch-to-transfusion (C:T) ratio in hip fracture surgery patients.METHODSIn 2015 a patient blood management (PBM) program was implemented at our institution mandating a single unit-per-occurrence transfusion policy and a restrictive transfusion threshold of < 7 g/dL hemoglobin in asymptomatic patients and < 8 g/dL in those with refractory symptomatic anemia or history of coronary artery disease. We identified all hip fracture patients between 2013 and 2017 and compared the preoperative hemoglobin which would predict a 2:1 C:T ratio in the pre PBM and post PBM cohorts. Prediction profiling and sensitivity analysis were performed with statistical significance set at P < 0.05. RESULTSFour hundred and ninety-eight patients who underwent hip fracture surgery between 2013 and 2017 were identified, 291 in the post PBM cohort. Transfusion requirements in the post PBM cohort were lower (51% vs 33%, P < 0.0001) than in the pre PBM cohort. The mean RBC units transfused per patient was 1.15 in the pre PBM cohort, compared to 0.66 in the post PBM cohort (P < 0.001). The 2:1 C:T ratio (inpatient transfusion probability of 50%) was predicted by a preoperative hemoglobin of 12.3 g/dL [area under the curve (AUC) 0.78 (95% confidence interval (CI), 0.72-0.83), Sensitivity 0.66] in the pre PBM cohort and 10.7 g/dL [AUC 0.78 (95%CI, 0.73-0.83), Sensitivity 0.88] in the post PBM cohort. A 50% probability of requiring > 1 RBC unit was predicted by 11.2g/dL [AUC 0.80 (95%CI, 0.74-0.85), Sensitivity 0.87] in the pre PBM cohort and 8.7g/dL [AUC 0.78 (95%CI, 0.73-0.83), Sensitivity 0.84] in the post-PBM cohort.CONCLUSIONThe hip fracture maximum surgical blood order schedule should consider preoperative hemoglobin in determining the number of units to type and cross prior to surgery.     

角膜波前像差引导的TransPRK和常规TransPRK矫正中度近视的疗效比较

目的 比较角膜波前像差引导(WFG)的经上皮准分子激光屈光性角膜切削术(TransPRK)和常规TransPRK矫正中度近视的疗效差异。方法 回顾性分析2021年1～12月在安徽省第二人民医院接受双眼TransPRK治疗的60例中度近视患者临床资料,根据是否采用WFG,分为WFG-TransPRK组(30例,60眼)和TransPRK组(30例,60眼)。在术前和术后6个月时,测量两组患者视力、屈光度、角膜高阶像差和中央角膜厚度等变量,记录两组患者术后6个月内的并发症发生情况,计算两组疗效指数和安全指数,并进行比较。结果 术前,两组等效球镜度、中央角膜厚度和角膜高阶像差比较,差异均无统计学意义(P>0.05)。TransPRK组手术前后总高阶相差和球差升幅高于WFG-TransPRK组(P<0.05),两组手术前后等效球镜度升幅、中央角膜厚度降幅比较,差异均无统计学意义(P>0.05)。随访6个月,两组疗效指数(t=1.913)、安全指数(t=0.775)和并发症发生率(χ²=0.162)比较,差异均无统计学意义(P=0.061、0.442、0....     

苯并嘧啶衍生物的合成和抗糖尿病活性评价

硫氧还蛋白相互作用蛋白(thioredoxin-interacting protein, TXNIP)主要调节胰岛β细胞中葡萄糖的稳态,是治疗糖尿病的新颖靶点。本研究以4-羟基苯并嘧啶为原料,通过不同长度的碳链,引入吡唑、甲基哌嗪、咪唑、吗啡啉等4种含氮杂环,设计合成靶向TXNIP的苯并嘧啶骨架拼合含氮杂环的衍生物,并考察化合物对棕榈酸(palmitate acid, PA)刺激的胰岛β细胞损伤的保护作用。共设计合成20个苯并嘧啶衍生物,结构经¹H NMR、ESI-MS确证;药理活性表明大部分化合物对胰岛β细胞有保护作用,其中化合物C-1、C-2、C-4、D-2保护作用较强,相较PA模型组细胞活力为38.3%,这4个化合物细胞活力高于70%,其中化合物D-2细胞活力最高,达到87.2%;化合物D-2可以作为潜在的抗糖尿病新化学实体。     

Bihemispheric Collateralization of the Cortical and Subcortical Afferents to the Rat's Visual Cortex

A fluorescent dye (usually fast blue or rhodamine tagged latex microspheres) was injected into cortical area 17 (or area 17 and the lateral part of area 18b) of adult and juvenile (15 - 22 day old) Sprague-Dawley albino rats. Another fluorescent dye (usually diamidino yellow) was injected into cortical areas 17, 18a and 18b of the opposite hemisphere. The injections involved only the cortical grey matter. After postinjection survival of 2 - 14 days the distribution of retrogradely labelled mesencephalic and prosencephalic cells was analysed. Both small and large injections labelled retrogradely a substantial number of cells in specific and nonspecific dorsal thalamic nuclei (lateral geniculate, lateral posterior, ventromedial, several intralaminar nuclei and nucleus Reuniens) as well as a small number of cells in the preoptic area of the hypothalamus and the mesencephalic ventral tagmental area (VTA). While labelled thalamic cells contained only the dye injected into the ipsilateral cortex, a small proportion of hypothalamic and VTA cells was labelled with the dye injected into the contralateral cortex. Virtually none of the cells in these areas were double labelled with both dyes. Both small and large injections labelled cells in the ipsilateral telencephalic magnocellular nuclei of the basal forebrain and the caudal claustrum. A substantial minority of labelled cells in these structures was labelled by the dye injected into the contralateral cortex. Furthermore, a small proportion (about 1%) of claustral cells projecting to the ipsilateral cortex were double labelled with both dyes. In several cortical areas ipsilateral to the injected area 17, associational neurons were intermingled with commissural neurons projecting to the contralateral visual cortex. A substantial proportion of associational neurons projecting to ipsilateral area 17 also projected to the contralateral visual cortex (associational-commissural neurons). Thus, in visual area 18a, the associational-commissural neurons were located in all laminae, with the exception of lamina 1 and the bottom of lamina 6, and constituted about 30% of the neurons projecting to ipsilateral area 17. In paralimbic association area 35/13, associational-commissural neurons were located in lamina 5 and constituted about 20% of neurons projecting to ipsilateral area 17. In the limbic area 29d, the associational-commissural neurons were located in laminae 4, 5 and the upper part of lamina 6 and constituted about 10% of the associational-commissural neurons projecting to ipsilateral area 17. In oculomotor area 8, double-labelled neurons were located in lamina 5 and constituted about 10% of the neurons projecting to ipsilateral area 17. Thus, it appears that the axons of mesencephalic and diencephalic neurons projecting to the visual cortex do not send collaterals into both hemispheres. The bihemispheric projection to the rat's visual cortex originates almost exclusively in the retinotopically organized cortical area 18a and in integrative cortical areas 35/13, 29d and 8.     

Prechiasmatic Reordering of Fibre Diameter Classes in the Retinofugal Pathway of Ferrets

This study examines the distribution of fibre diameter classes at various sites along the retinofugal pathway of adult ferrets. Light microscopic observations were made on semi-thin sections, and regional fibre diameter spectra were constructed from diameter measurements taken from electron micrographs of thin sections of the intraorbital optic nerve (2.5 mm from the optic disc), the intracranial optic nerve (1 mm rostral to the fusion of the nerves), and the optic tract (just caudal to the optic chiasm).
Whereas diameter types are relatively evenly distributed behind the eye in the postoptic nerve, they begin to segregate along its prechiasmatic course. Within this prechiasmatic region, coarse and fine calibre fibres are confined increasingly to more ventral locations in the nerve, leaving a dorsal band populated predominantly by intermediate calibre fibres. In conjunction with this redistribution of axon size classes, the fascicular arrangement of axons which is present distally, changes to a non-fascicular organization. The prechiasmatic organization of fibre types approximates that found in the optic tract where the coarse and fine calibre fibres lie further ventrally towards the pial surface.
The prechiasmatic region can be viewed as a region of transition where the order of fibres in the nerve (retinotopic) starts to change to that present in the optic tract (chronotopic), resulting in the first-born beta cell axons becoming segregated dorsally, and rostral to the coarse and fine calibre classes which segregate at further caudal locations. Further, since the sorting of fibres according to diameter appears before the fibres reach the optic chiasm, the segregation of diameter classes is not dependent on the chiasmatic sorting of fibres according to their crossed or uncrossed course.     

Methods for in vivo haematoporphyrin derivative quantification: a review

Photodynamic therapy is a new treatment for early carcinomas. Although undergoing phase 1/2 clinical assays, clinical indications for this therapy remain rare mainly because of the approximate dosimetry of HPD uptake by tumour tissues in human beings.In this review we present the potential interest and limits of both direct fluorescence detection or dosimetry of HPD and in vivo measurements of singlet oxygen, produced during photodynamic therapy. Clinical applications of such measurements should represent one of the main conditions for the future development of photodynamic therapy.

---

Résumé La photochimiothérapie est un nouveau traitement des cancers débutants. Alors que des essais cliniques de phase 1–2 sont entrepris, les indications pour ce type de traitement demeurent rares, principalement du fait d'une dosimétrie approximative de la captation de l'hématoporphyrine dérivée par les tissus cancéreux humains. La fluorescence émise par l'HPD peut Être utilisée in-vivo pour un diagnostique topographique de la répartition de l'HPD, mais aussi le dosage quantitatif des espèces fluorescentes présentes dans le mélange HPD. Le dosage de l'oxygène singulet, généré lors de la réaction photochimique, est nettement plus difficile à réaliser mais a été proposé pour le dosage in-vivo des formes porphyriniques actives présentes dans le milieu. Les applications cliniques de telles mesures représentent une condition essentielle pour le developpement de la photochimiothérapie car à côté des possibilités de diagnotiques offertes par l'analyse de la répartition intratumorale de l'HPD, un dosage précis permettrait d'optimiser le moment du traitement, arbitrairement fixé aujourd'hui à 72 heures.