美國俄亥俄州立大學Avner Friedman教授在中國人民大學信息學院作了題為什么是數(shù)學生物學?以及有什么作用的講座,中國人民大學信息學院是培養(yǎng)信息領(lǐng)域高素質(zhì)專業(yè)人才的基地。Avner Friedman教授在中國人民大學所作講座的主要內(nèi)容是:
生物學過程的數(shù)學建?梢哉嫌绊戇^程中的許多因素,從而提供新的見解參與這一過程的機制。如果模型的預測一致與實驗結(jié)果,則該模型可以用于使新的假設,新的預測。在這個演講中,我會給這種模式的幾個例子。第一個是在慢性創(chuàng)傷的建模和氧氣治療的作用。第二個例子是關(guān)于免疫系統(tǒng)對感染的肺反應,重點是結(jié)核病。第三個例子是關(guān)于腎臟纖維化,一種疾病的量沒有治愈。在所有這些例子的數(shù)學模型,提出新的方法,可能有利于治療。該模型由微分方程組的代表,并特別必須注意參數(shù)的確定。有些車型還可能會出現(xiàn)在偏微分方程新的數(shù)學開放題。
Avner Friedman,美國俄亥俄州立大學數(shù)學特聘教授,美國科學院院士,美國藝術(shù)與科學院院士,國際著名數(shù)學家,在偏微分方程、隨機PDE、自由邊界問題、控制論和數(shù)學生物學等領(lǐng)域取得了杰出成就。曾任美國工業(yè)與應用數(shù)學學會主席,明尼蘇達大學工業(yè)數(shù)學與應用研究所所長,美國數(shù)學生命科學習究所所長,近20個國際著名數(shù)學雜志編委。出版著作20余部,發(fā)表研究論文500余篇,其中絕大多數(shù)著作和論文被美國數(shù)學會數(shù)學評論網(wǎng)超高次數(shù)引用。
原文:Mathematical modeling of a biological process can integrate many factors that affect the process and thereby provide new insight into the mechanisms involved in this process. If the model predictions agree with the experimental results, then the model may be used to make new hypotheses and new predictions. In this talk I will give several examples of such models. The first one is on modeling of chronic wounds and the role of oxygen treatment. The second example is about the response of the immune system to infection in the lung, with focus on tuberculosis. The third example is concerned with fibrosis of the kidney, a disease for which there is no cure. In all these examples the mathematical models suggest new approaches that may benefit medical treatment. The models are represented by systems of differential equations, and special care must be taken to determine the parameters. Some of the models may also present new mathematical open problems in PDEs.