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.     

Maternal consumption of ɷ3 attenuates metabolic disruption elicited by saturated fatty acids-enriched diet in offspring rats

Background and aimsHigh-fat diet (HFD) intake during gestation and lactation has been associated with an increased risk of developing cardiometabolic disorders in adult offspring. We investigated whether metabolic alterations resulting from the maternal consumption of HFD are prevented by the addition of omega-3 (?3) in the diet.Methods and resultsWistar rat dams were fed a control (C: 19% of lipids and ?6:?3 = 12), HF (HF: 33% lipids and ?6:?3 = 21), or HF enriched with ?3 (HFω3: 33% lipids and ?6:?3 = 9) diet during gestation and lactation, and their offspring food consumption, murinometric measurements, serum levels of metabolic markers, insulin and pyruvate sensitivity tests were evaluated. The maternal HFD increased body weight at birth, dyslipidemia, and elevated fasting glucose levels in the HF group. The enrichment of ?3 in the maternal HFD led to lower birth weight and improved lipid, glycemic, and transaminase biochemical profile of the HFω3 group until the beginning of adulthood. However, at later adulthood of the offspring, there was no improvement in these biochemical parameters.ConclusionOur findings show the maternal consumption of high-fat ?3-rich diet is able to attenuate or prevent metabolic disruption elicited by HFD in offspring until 90 days old, but not in the long term, as observed at 300 days old of the offspring.     

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。     

大补元煎通过上调BDNF/TrkB/CREB信号通路改善APP/PS1双转基因痴呆小鼠海马突触可塑性

目的:观察大补元煎对APP/PS1痴呆小鼠海马突触可塑性及脑源性神经营养因子(BDNF)/酪氨酸蛋白激酶受体B(TrkB)/环磷酸腺苷反应元件结合蛋白(CREB)信号通路的作用,并探讨其改善突触可塑性的可能机制。方法:将APP/PS1小鼠36只分为模型组、多奈哌齐组(6.5×10~(-4)g·kg~(-1)·d~(-1))和大补元煎组(13.2 g·kg~(-1)·d~(-1)),野生鼠12只设为正常组,正常组和模型组给予等体积生理盐水,各组连续灌胃30 d。应用Morris水迷宫检测各组小鼠的学习记忆能力,应用尼氏染色和高尔基染色观察海马区神经元和突触的病理形态变化,应用免疫荧光(IF)观察海马突触后致密蛋白95(PSD95)及突触素(SYN)的蛋白表达水平,采用蛋白免疫印迹法(Western blot)检测海马中BDNF,TrkB,CREB及磷酸化CREB(p-CREB)的蛋白表达水平。结果:与空白组比较,模型组小鼠平台潜伏期和游泳总路程增加(P0.01),穿越平台次数和目标象限停留时间减少(P0.01),小鼠海马CA3区神经元胞内尼氏体减少或消失,小鼠海马CA3区神经元及树突分支数量、树突棘密度减少(P0.01),小鼠海马SYN,PSD95,BDNF,TrkB及p-CREB的蛋白表达水平减少(P0.01)。与模型组比较,多奈哌齐组和大补元煎组小鼠平台潜伏期和游泳总路程减少(P0.05,P0.01),穿越平台次数和目标象限停留时间增加(P0.05,P0.01),小鼠海马CA3区神经元胞内尼氏体数量增多,小鼠海马CA3区神经元及树突分支数量,树突棘密度增加(P0.05,P0.01),小鼠海马SYN,PSD95,BDNF,TrkB及p-CREB的蛋白表达水平增加(P0.05,P0.01)。结论:大补元煎改善APP/PS1双转基因小鼠突触可塑性的机制可能与其上调小鼠海马中BDNF/TrkB/CREB信号通路有关。