应理学院和科研处邀请西安理工大学刘英博士、西安工程大学李玲玲博士、西安邮电大学王永恒博士将于10月21日为我校师生做学术讲座，欢迎广大师生参加！报告的具体安排如下：

报告时间：2023年10月21日（周六）14:30-16:20

报告地点：理学院442会议室

报告主题1：抛物方程弱有限元方法的先验和后验误差估计

报 告 人1：刘英（西安理工大学）

报告主题2：Mathematical Modeling the Order of Driver Gene Mutations in Colorectal Cancer

报 告 人2：李玲玲（西安工程大学）

报告主题3：针对运动的不规则区域上的分数阶FitzHugh-Nagumo单域模型的一种虚拟结构体有限差分方法

报 告 人3：王永恒（西安邮电大学）

报告摘要1：We derive the priori and a posteriori error estimates of the weak Galerkin finite element method with the Crank-Nicolson time discretization for the parabolic equation in this paper. The priori error estimate is deduced based on existing priori error results of the corresponding elliptic projection problem. For the a posteriori error estimates, the elliptic reconstruction technique is introduced to decompose the true error into elliptic error and parabolic error,where the elliptic part is bounded by the a posteriori error estimates of the auxiliary elliptic reconstruction problem. The temporal and spatial a posteriori error estimators are further used to develop the  time-space adaptive algorithm. Numerical results in the uniform and adaptive meshes are provided to validate the proposed estimators.

报告人简介1：刘英，博士毕业于西北工业大学，研究方向是自适应有限元方法、自适应弱有限元方法。在Advances in Computational Mathematics，Computers & Mathematics with Applications，Applied Numerical Mathematics等国际著名期刊发表学术论文5篇，被评为2023届西北工业大学研究生优秀毕业生。现入职西安理工大学，获批主持国家自然科学基金青年项目、陕西省教育厅自然科学专项。

报告摘要2：Tumor heterogeneity is a large obstacle for cancer study and treatment. Different cancer patients may involve different combinations of gene mutations or the distinct regulatory pathways for inducing the progression of tumor. Investigating the pathways of gene mutations which can cause the formation of tumor can provide a basis for the personalized treatment of cancer. Studies suggested that KRAS, APC and TP53 are the most significant driver genes for colorectal cancer. However, it is still an open issue regarding the detailed mutation order of these genes in the development of colorectal cancer. For this purpose, we analyze the mathematical model considering all orders of mutations in oncogene, KRAS and tumor suppressor genes, APC and TP53, and fit it on data describing the incidence rates of colorectal cancer at different age from the Surveillance Epidemiology and End Results registry in the United States for the year 1973–2013. The specific orders that can induce the development of colorectal cancer are identified by the model fitting. The fitting results indicate that the mutation order with KRAS→APC→TP53, APC→TP53→KRAS and APC→KRAS→TP53 explain the age–specific risk of colorectal cancer with very well. Furthermore, eleven pathways of gene mutations can be accepted for the mutation order of genes with KRAS→APC→TP53, APC→TP53→KRAS and APC→KRAS→TP53, and the alternation of APC acts as the initiating or promoting event in the colorectal cancer. The estimated mutation rates of cells in the different pathways demonstrate that genetic instability must exist in colorectal cancer with alterations of genes, KRAS, APC and TP53.

报告人简介2：李玲玲于华中师范大学获得统计学博士学位，现在陕西师范大学数学与统计学院做博士后，主要从事交叉学科在癌症研究中的应用，围绕着价肿瘤患病风险的评价、如何从数学角度分析癌症形成的机制、如何利用多尺度数据来研究影响癌症风险的因子以及这些因子如何影响癌症风险等关键问题展开研究，主持国家自然科学基金青年基金、中国博士后科学基金面上项目、陕西省博士后项目（特别资助）、陕西省科协青年人才托举计划项目、陕西省教育厅自然专项和优博培育计划项目，在PLoS Computational Biology、Journal of Theoretical Biology等SCI期刊发表学术论文十余篇。

报告摘要3：本文提出了一种虚拟结构体有限差分方法，用于模拟运动的不规则区域内的分数阶FitzHugh-Nagumo (FHN)单域模型。在虚拟结构体有限差分方法中，移动的不规则区域将转化为固定的规则区域，跨膜电势通过欧拉坐标进行描述，膜动力学通过拉格朗日坐标进行描述，拉格朗日变量和欧拉变量之间的相互变换通过含有Delta函数的积分变换来实现。虚拟结构体有限差分方法允许在固定的规则区域内使用笛卡尔网格上的有限差分方法计算跨膜电势，这在逼近与计算区域相关的分数阶导数方面具有巨大的优势。数值算例证明了所提出的虚拟结构体有限差分法的有效性。

报告人简介3：王永恒，博士毕业于西北工业大学，现就职于西安邮电大学理学院应用数学系，研究方向为科学工程计算的模型、理论与方法，主要从事心脏方面的相关研究，特别是心脏的数学建模及其数值求解方面的研究，在Journal of Computational Physics、Scientific Reports和Plos One等期刊上发表多篇论文。