Frame Invariance and Scalability of Neural Operators for Partial Differential Equations

Partial differential equations (PDEs) play a dominant role in the mathematical modeling of many complex dynamical processes. Solving these PDEs often requires prohibitively high computational costs, especially when multiple evaluations must be made for different parameters or conditions. After training, neural operators can provide PDEs solutions significantly faster than traditional PDE solvers. In this work, invariance properties and computational complexity of two neural operators are examined for transport PDE of a scalar quantity. Neural operator based on graph kernel network (GKN) operates on graph-structured data to incorporate nonlocal dependencies. Here we propose a modified formulation of GKN to achieve frame invariance. Vector cloud neural network (VCNN) is an alternate neural operator with embedded frame invariance which operates on point cloud data. GKN-based neural operator demonstrates slightly better predictive performance compared to VCNN. However, GKN requires an excessively high computational cost that increases quadratically with the increasing number of discretized objects as compared to a linear increase for VCNN.     

从五运六气角度探析己亥年冬瘟

2019年为己亥之年,土运不足,厥阴风木司天,少阳相火在泉。下半年相火淫胜,火气流行,克金、刑水。风木盛则克制土运,土运本不足,致虚者更虚,强者更强,此谓之不相得,不相得则病;且气克运,古称之为天刑,天刑之年多灾害。2019年,冬季主气太阳寒水之上少阳相火客临,致冬不藏反长,天不寒反暖。地气封藏不固,水中阳气不藏,本应该被抑制或杀灭的微生物却因火热而未灭,并得少阳火毒助长而毒性更猛,化生为火疫。2020年为庚子年,主行金运,金克木,可平复2019年偏盛之木运,故瘟毒会被2020年之金运削弱或肃杀。针对此次瘟疫,未病之人预防要点为:虚邪贼风,避之有时;精神内守,病安从来;正气存内,邪不可干;饮食宜忌,尤为重要;避秽化浊,芳香化湿。已病之人的治疗,依据此次瘟疫"少阳火毒夹湿"病机,以咸补之,以甘泻之,以咸耎之,岁谷宜丹,间谷宜豆。此次瘟毒的性质虽为湿热火毒,但患者体质却有寒热虚实之别,感染后症状、病情和预后亦不同,故中医临证时应遵循辨证论治,三因治宜的原则;若体质素有湿热,邪从本气而化,可遵循运气病机施治;若体质本热,湿去而化为火毒,则应以制火为主;若体质本寒,热去而化寒湿,则应温化寒湿,芳香化浊;若体质素虚,出现危重证候,则应在祛邪时,重视固护元气。     

Prospective Analysis Using a Novel CNN Algorithm to Distinguish Atypical Ductal Hyperplasia From Ductal Carcinoma in Situ in Breast

IntroductionWe previously developed a convolutional neural networks (CNN)-based algorithm to distinguish atypical ductal hyperplasia (ADH) from ductal carcinoma in situ (DCIS) using a mammographic dataset. The purpose of this study is to further validate our CNN algorithm by prospectively analyzing an unseen new dataset to evaluate the diagnostic performance of our algorithm.Materials and MethodsIn this institutional review board-approved study, a new dataset composed of 280 unique mammographic images from 140 patients was used to test our CNN algorithm. All patients underwent stereotactic-guided biopsy of calcifications and underwent surgical excision with available final pathology. The ADH group consisted of 122 images from 61 patients with the highest pathology diagnosis of ADH. The DCIS group consisted of 158 images from 79 patients with the highest pathology diagnosis of DCIS. Two standard mammographic magnification views (craniocaudal and mediolateral/lateromedial) of the calcifications were used for analysis. Calcifications were segmented using an open source software platform 3D slicer and resized to fit a 128 × 128 pixel bounding box. Our previously developed CNN algorithm was used. Briefly, a 15 hidden layer topology was used. The network architecture contained 5 residual layers and dropout of 0.25 after each convolution. Diagnostic performance metrics were analyzed including sensitivity, specificity, accuracy, and area under the receiver operating characteristic curve. The “positive class” was defined as the pure ADH group in this study and thus specificity represents minimizing the amount of falsely labeled pure ADH cases.ResultsArea under the receiver operating characteristic curve was 0.90 (95% confidence interval, ± 0.04). Diagnostic accuracy, sensitivity, and specificity was 80.7%, 63.9%, and 93.7%, respectively.ConclusionProspectively tested on new unseen data, our CNN algorithm distinguished pure ADH from DCIS using mammographic images with high specificity.     

脑血管畸形致脑出血患者手术治疗效果观察

目的分析脑血管畸形致脑出血患者应用手术治疗的临床疗效。方法纳入本院2018年1月—2020年1月收治的60例脑血管畸形致脑出血患者,随机分组(每组样本容量共计30例),参照组给予保守治疗,观察组给予手术治疗,对比两组临床疗效、治疗前、治疗1月后NIHSS评分、住院时间。结果临床总有效率观察组(93.33%)明显高于参照组(63.33%),观察组治疗1月后NIHSS评分明显低于参照组,观察组住院时间明显比参照组短,差异均具有统计学意义(P<0.05)。结论脑血管畸形致脑出血患者采纳手术治疗,可有效减轻患者神经功能受损情况,缩短治疗时间。