2019 Summer School on Mathematical Biology will be hosted from July 1 - July 5, 2019 by the Institute of Natural Sciences at Shanghai Jiao Tong University, China. Top experts will be invited to deliver lectures on mathematical modeling, theoretical analysis, scientific computing, and their applications in biology and life sciences. The summer school aims to introduce important research topics with modern styles and to provide participants new perspectives in the frontiers of mathematical biology and applied mathematics.
July 1-5, 2019
Room 706, No.6 Science Building, Minhang Campus, Shanghai Jiao Tong University
No registration fee. Please register online. Apply Online
Participants should cover their own lodging and meals.
|Time||July 1||July 2||July 3||July 4||July 5|
|09:00 ~ 09:45||Qing Nie||Michael Jeffrey Ward||Sepideh Mirrahimi||Nicolas Vauchelet|
|10:00 ~ 10:45||Qing Nie||Marie Doumic||Marie Doumic||Marie Doumic||Marie Doumic|
|10:45 ~ 11:15||Group Photo & Coffee Break||Coffee Break||Coffee Break||Coffee Break||Coffee Break|
|11:15 ~ 12:00||Michael Jeffrey Ward||Michael Jeffrey Ward||Nicolas Vauchelet||Michael Jeffrey Ward||Benoit Perthame|
|14:00 ~ 14:45||Qing Nie||Nicolas Vauchelet||Peter Markowich||Nicolas Vauchelet|
|15:00 ~ 15:45||Qing Nie||Sepideh Mirrahimi||Sepideh Mirrahimi||Sepideh Mirrahimi|
By Marie Doumic
The aim of this course is an introduction to structured population models, to their mathematical analysis and to the inverse problem consisting in estimating the division features of the population and selecting the most convenient “structuring” variable, i.e. the variable which best characterizes the division. We call “division features” on the one hand the division rate, rate at which individuals of the population divide, and on the other hand the so-called “division kernel”, which characterizes how from a given value for the parent the structuring variable is distributed in offspring.
We present an ab-initio approach to the modeling of (biological) transportation networks, which leads to a highly complex nonlinear PDE system featuring (fractal-type) structures, locally large variations of solutions and moving ‚free boundaries‘ and thin transition layers. The system has applications in many different areas of biology (leaf venation, neural networks, blood flow…..) and exploits the well known biological principle that transportation drives network growth.
We study a class of parabolic integro-differential equations coming from evolutionary biology. Such equations describe the dynamics of a phenotypically structured population under the effect of selection and mutations. The solutions to such equations concentrate, in the limit of small diffusion (mutation) and in long time, as a sum of Dirac masses corresponding to dominant traits. In the first part of this talk, we present the basic ingredients of an approach based on Hamilton-Jacobi equations with constraint to study such problems. In the second part, we consider a more restricted framework with more regularity, where we are able to obtain the well-posedness of the corresponding Hamilton-Jacobi equation with constraint, and where we can obtain a rather precise approximation of the phenotypic distribution of the population. Finally, we show how this approach can lead to quantitative results in biological applications, in particular, in the case of a time periodic environment.
By Qing Nie
In 2009, US National Research Council of the National Academies published a report, called “A New Biology for the 21st Century”. One of the major emphases in the New Biology is the integration between biology and mathematics. As explosion of biological measurements takes place in biology due to rapid technology development in recent years, the challenge lies in how to connect and make sense of the massive experimental data collected in various forms at different spatial and temporal scales. Modeling is becoming an increasingly important tool that enables better understanding of the complex data in biology. In this four-hour lecture series, I will focus on several topics in mathematical and computational analysis of modern cell and developmental biology.
Lecture 1: Gene Regulatory Network Modeling and Computation
Lecture 2 & 3: Spatial Models of Development and Patterning
Lecture 4: Multiscale Models of Dynamic Cell Fates
The mechanical modeling of living tissues has attracted much attention in the last decade. Applications include tissue repair and growth models of solid tumors. These models contain several levels of complexity, both in terms of the biological and mechanical effects, and therefore in their mathematical description. Multiphase models describe the dynamics of several types of cells, liquid, fibers (extra-cellular matrix) and both compressible and incompressible models are used in the literature.
In this talk I shall discuss the analysis of multiphase models based on Darcy’s assumption. The compactness issue leads us to use Aronson-Benilan estimate and to build new variants. I shall also discuss the incompressible limit in special cases.
Due the complexity and the importance of this phenomenon, tumor growth has raised the attention of many mathematicians. Indeed, cancer has become a major cause of death in western countries. Partial differential equations (PDE) may be an interesting tool to model and describe the expansion of tumoral cells.
The aim of this course is to review some classes of PDE models used to describe tumor growth. In particular, we will distinguish two main classes of models: cell mechanical model and free boundary model. In the former, the tumor is described through the dynamics of cell density of tumoral cells. In the latter, we focus on the dynamics of the domain of the tumor subjected to internal pressure. Then we will explain a link between both classes of model.
Localized spatial patterns for various classes of linear and nonlinear diffusive processes arise in a wide variety of biological applications. In the workshop we will highlight some problems in this area and outline a singular perturbation method, known as strong localized perturbation theory (SLPT), that is designed specifically for analyzing diffusive problems with small localized features in multi-dimensional domains.
Lecture 1: We will briefly illustrate localized patterns in several distinct biological problems. We will then discuss the SLPT approach and apply it to the determination of the mean first capture time for a Brownian particle in a 2-D or a 3-D domain.
Lecture 2: We will apply SLPT to two distinct problems. With applications to ecology we will optimize the persistence threshold of a species in a 2-D landscape with patchy food resources and analyze the effects of fragmentation of resources. Secondly, we will discuss the Berg-Purcell problem of biophysics for the capture of a Brownian particle by a sphere with many localized nanotraps. The homogenized limit will also be considered.
Lecture 3: We will analyze a new class of PDE/ODE models of quorum and diffusing sensing in a multi-dimensional domain in which a passively diffusing species (autoinducer) can trigger synchronous oscillations between small, spatially but spatially segregated, dynamically active cells.
Lecture 4: Results and open problems for localized spot patterns in singularly perturbed activator-inhibitor reaction-diffusion systems in 2-D are discussed.