Learning to Discretize: Solving 1D Scalar Conservation Laws via Deep Reinforcement Learning

Conservation laws are considered to be fundamental laws of nature. It has broad applications in many fields, including physics, chemistry, biology, geology, and engineering. Solving the differential equations associated with conservation laws is a major branch in computational mathematics. The recent success of machine learning, especially deep learning in areas such as computer vision and natural language processing, has attracted a lot of attention from the community of computational mathematics and inspired many intriguing works in combining machine learning with traditional methods. In this paper, we are the first to view numerical PDE solvers as an MDP and to use (deep) RL to learn new solvers. As proof of concept, we focus on 1-dimensional scalar conservation laws. We deploy the machinery of deep reinforcement learning to train a policy network that can decide on how the numerical solutions should be approximated in a sequential and spatial-temporal adaptive manner. We will show that the problem of solving conservation laws can be naturally viewed as a sequential decision-making process, and the numerical schemes learned in such a way can easily enforce long-term accuracy. Furthermore, the learned policy network is carefully designed to determine a good local discrete approximation based on the current state of the solution, which essentially makes the proposed method a meta-learning approach. In other words, the proposed method is capable of learning how to discretize for a given situation mimicking human experts. Finally, we will provide details on how the policy network is trained, how well it performs compared with some state-of-the-art numerical solvers such as WENO schemes, and supervised learning based approach L3D and PINN, and how well it generalizes.     

铜绿假单胞菌噬菌体PaP3生物学特性的研究

目的测定铜绿假单胞菌噬菌体PaP3的最佳感染复数、一步生长曲线和吸附K值及交叉吸附K值等基本生物学特性。方法按照感染复数（MOI）分别为0．0001、0．001、0．01、0．1、1和10加入噬菌体纯培养液和宿主菌，充分裂解细菌后，测定噬菌体滴度；以MOI=10的比例加入噬菌体及宿主菌，进行一步生长实验；纯化PaP3颗粒，免疫家兔，获得抗血清，通过中和反应实验测定PaP3和其抗血清之间的吸附反应常数K值。同时，利用抗血清交叉中和试验确定本室分离的三株噬菌体之间的血清学关系。结果当MOI=0．001时PaP3感染其宿主菌产生的子代噬菌体滴度最高；根据一步生长实验结果绘制一步生长曲线；通过血清交叉中和反应得出不同的吸附常数。结论PaP3最佳感染复数为0．001，感染宿主菌的潜伏期是20min，爆发期是60min，平均爆发量约为31，其抗血清反应的吸附常数K值为262。     

影响颅脑外伤术后颅内感染的危险因素分析

目的探讨影响颅脑外伤开颅术后颅内感染的危险因素。方法采用回顾性研究比较分析了912例颅脑损伤术后出现颅内感染与未出现颅内感染组间的差异因素。结果非感染 770例,颅内感染142例(15．6％)。感染类型有无菌性脑膜炎、细菌性脑膜炎、脑室炎及脑室积脓、脑脓肿、硬膜下腔积脓、术区皮下或(和)骨瓣下化脓或合并骨髓炎、切口感染。细菌检出率占感染的27．5％。颅脑外伤术后感染与高温季节、高龄、重度以上损伤、短期内两次以上手术、连续两侧开颅术、长时间 (>5 h)手术、显微外科手术、颅底与后颅凹手术、脑室外引流、皮下或硬膜外积液以及急诊手术等因素相关(P<0．05)。结论对具有上述危险冈素的易感患者应给予更密切的关注和预防性的处理。     

医学摄影用光

根据医学摄影不同拍摄对象,结合各种光源特点,介绍了用光的一般方法和掌握的基本原则,对物体的反光控制、透明物体内部结构与质感的表现等难点问题进行了研讨,并对荧光摄影作了简要介绍。     

Correction of frequency and phase variations induced by eddy currents in localized spectroscopy with multiple echo times.

As a consequence of the time-varying magnetic field induced by eddy currents, frequency drifting occurs when the sampling window of localized spectroscopy continuously shifts. The frequency drifting and the concomitant phase variations can severely affect spectroscopy results when data are acquired with multiple echo times (TEs), such as in the measurement of glutamate (Glu) concentration using the TE-averaged method. Specifically, the averaged spectra are further broadened and distorted in the presence of residual eddy currents, and editing of the coupled spins of Glu C4 protons is affected, resulting in errors in the measured relative intensity ratio. Postacquisition correction using unsuppressed water as reference can effectively minimize this detrimental effect, as manifested by the significantly enhanced signal intensity. Also, it is demonstrated that the methyl signals of creatine (Cr) at 3.0 ppm and choline (Cho) at 3.2 ppm can be used as internal references in finding frequency and phase disparities between different TEs.     

主动呼吸控制技术(ABC)在肺癌放射治疗中的应用

目的：使用主动呼吸控制技术（aetive brething control,ABC）治疗非小细胞肺癌患者，评价呼吸运动时肺部肿瘤动度的影响及ABC技术的优势和可行性，并评价近期疗效和急性放射反应。方法：选择9例使用ABC技术联合三维造型放疗技术治疗的非小细胞系癌患者进行分析。CT定位扫描时分别采集ABC和自由呼吸（free breath.FB）状态下的图像，评价呼吸运动对肺部肿瘤动度和PTV边界的影响唾弃；并比较两种计划的DVH，放疗剂量为54-60Gy/18-20次。3Gy/次，1次/天，5天/周，定期随访，评价近期疗效及急性放射反应。结果：应用ABC技术后，隔肌的平均位移从FB时的43.5mm（20.0-32.0mm）降低为3.6mm（0.5-72.mm）,胸壁的侧方位移从FB时的3.2mm（2.8-4.0mm）降低为1.2mm（0.5-1.6mm）.PTV边界可以从FB时的1.5mm减少为0.75cm;肺的V20从21.8%降低为15.0%,减少了30.6%.中位随访6个月时,9例患者中有6例CR,3例PR.急性放射副反应都很轻微,仅为I-II.结论：在肺癌的精确放射治疗中,呼吸动度的影响不可忽视.而ABC系统可以有效的降低呼吸运动时治疗的影响,提高放疗的精确性,减少副反应.,但该系统使用较为复杂,延长了治疗的时间,个别患者不能忍受.     

166Ho-DOTMP radiation-absorbed dose estimation for skeletal targeted radiotherapy.

166Ho-1,4,7,10-tetraazacyclododecane-1,4,7,10-tetramethylene-phosphonate (DOTMP) is a tetraphosphonate molecule radiolabeled with 166Ho that localizes to bone surfaces. This study evaluated pharmacokinetics and radiation-absorbed dose to all organs from this beta-emitting radiopharmaceutical. METHODS: After two 1.1-GBq administrations of 166Ho-DOTMP, data from whole-body counting using a gamma-camera or uptake probe were assessed for reproducibility of whole-body retention in 12 patients with multiple myeloma. The radiation-absorbed dose to normal organs was estimated using MIRD methodology, applying residence times and S values for 166Ho. Marrow dose was estimated from measured activity retained after 18 h. The activity to deliver a therapeutic dose of 25 Gy to the marrow was determined. Methods based on region-of-interest (ROI) and whole-body clearance were evaluated to estimate kidney activity, because the radiotracer is rapidly excreted in the urine. The dose to the surface of the bladder wall was estimated using a dynamic bladder model. RESULTS: In clinical practice, gamma-camera methods were more reliable than uptake probe-based methods for whole-body counting. The intrapatient variability of dose calculations was less than 10% between the 2 tracer studies. Skeletal uptake of 166Ho-DOTMP varied from 19% to 39% (mean, 28%). The activity of 166Ho prescribed for therapy ranged from 38 to 67 GBq (1,030-1,810 mCi). After high-dose therapy, the estimates of absorbed dose to the kidney varied from 1.6 to 4 Gy using the whole-body clearance-based method and from 8.3 to 17.3 Gy using the ROI-based method. Bladder dose ranged from 10 to 20 Gy, bone surface dose ranged from 39 to 57 Gy, and doses to other organs were less than 2 Gy for all patients. Repetitive administration had no impact on tracer biodistribution, pharmacokinetics, or organ dose. CONCLUSION: Pharmacokinetics analysis validated gamma-camera whole-body counting of 166Ho as an appropriate approach to assess clearance and to estimate radiation-absorbed dose to normal organs except the kidneys. Quantitative gamma-camera imaging is difficult and requires scatter subtraction because of the multiple energy emissions of 166Ho. Kidney dose estimates were approximately 5-fold higher when the ROI-based method was used rather than the clearance-based model, and neither appeared reliable. In future clinical trials with 166Ho-DOTMP, we recommend that dose estimation based on the methods described here be used for all organs except the kidneys. Assumptions for the kidney dose require further evaluation.