Through his invited lecture, Toward a Mathematical Theory of Climate Sensitivity, Michael Ghil (Ecole Normale Superieure de Paris) elegantly described the mathematics behind the estimation of climate sensitivity by applying random dynamical systems (RDS) theory. He gave an overview of random attractors, and their significance in the analysis of such nonlinear, stochastically perturbed systems. Describing the interplay between statistical mechanics and physics’ and dynamical systems theories in climate research, Ghil emphasized that a systemic view was important in order to apply engineering to tackle uncertainties about the future of climate change.
“We have a second brain; this brain, unfortunately does not do mathematics,” began Kerry Landman (University of Melbourne), in her talk, Our “Second Brain”: Modelling Its Development and Disease. The second brain or enteric nervous system is so described because of a system of nerves almost comparable to the central nervous system in scope and intricacy. “If you have a gut feeling, now you know why, because you have billions of neurons in the second brain,” she said. Landman described a stochastic approach and a cellular content model to describe the proliferation of neural crest cells in the gut, a process that is key to colonization of the human gut wall in embryonic development. Such models are significant in quantifying the growth and in the understanding of Hirschsprung’s disease (HD), a congenital condition that causes chronic constipation and can be fatal.
In the talk, Adaptive Evolution: A Population View, Benoit Perthame (Ecole Normale Superieure) described the mathematics behind the processes of multiplication, mutation and selection, which allow evolution of distinct species through the survival of “fittest traits” in nature.
Shigeo Kusuoka (University of Tokyo) described financial methods involved in the computation of expectation related to diffusion models in high dimensional state spaces in the invited lecture, Numerical Computation for the Expectation on Diffusion Processes.
Bin Yu (University of California) gave a talk on Sparse Modeling for High Dimensional Data, illustrating models for the collection of vast amounts of data in science, engineering, social science, and finance as well as issues involved with model validation.
The invited talk, The Variational Viewpoint in Fracture Mechanics by Gilles Francfort (Université de Paris Nord) discussed the impact of variational viewpoint on crack initiation and path prediction, in addition to its amenability to numerical implementation and predictive computational ability.
The minisymposium on Current Interests in Mathematical Physics organized by Michael Loss (Georgia Institute of Technology) described just what the name indicates: the recent expansion in the field to include various significant areas of research such as condensed matter physics, quantum computing and quantum information.
The Cancer Modelling minisymposium organized by Antonio Fasano (University of Florence) tackled the very significant topic of applying mathematics to the diagnosis and treatment of one of the world’s most debilitating diseases. A panel of experts discussed recent research in mathematical modelling into the growth, spread and metabolism of the disease. Avner Friedman gave a detailed description of the multiscale features of solid tumors (such as carcinomas and sarcomas), describing mathematical models of the quiescent-to-proliferative switch in cancer cells that can simulate, and hence be used to study the phenomenon. In addition, he described modeling of different types of cancers, which is dependent on time scales of cancer development at the genetic and molecular level, and the influence of cell type and microenvironment. He also explained mathematical analysis of different types of cancers, such as breast, prostate and colorectal cancers. Irina Kareva (Arizona State University) provided a very engaging game theory analogy to cancer metabolism: the inability of a cancer cell to break out of its glycolytic phenotype and creating a toxic environment was described as a game of prisoner’s dilemma. She proposed a mathematical model illustrating that changing the environment can take the cells out of this equilibrium while cooperation can push them further into this glycolytic state. “Cooperation is not always good,” Kareva concluded.
A minisymposium on Mathematical Models and Numerical Methods for Cardiac Electromechanics described multidomain modeling of heterogenous cardiac tissue and advances in the development of “in-silico” cardiac simulations, which provide non-invasive tools to model and better understand its dynamics. Optimization of different imaging techniques, methods to produce high-resolution data of cardiac tissue, and statistical methods to analyze such data were also discussed.
A minisymposium on Immunology described a wide range of models such as those to develop vaccines against the multifaceted immune dynamics of Shigella bacteria and combat uenza virus infections. Mathematical models to study the regulation of T-cells, which play a central role in cell-mediated immunity, were also discussed. A comprehensive overview of stochastic modeling in the case of HIV infections was provided, including determining risk of infection, the effects of pre- and post-exposure prophylaxis, and the dynamics of HIV interactions with cytotoxic T-lymphocytes.
The CAIMS/Mprime/SIAM Awards Lunch took place this afternoon, and SIAM President Nick Trefethan honored the following SIAM prize recipients:
The John von Neumann Lecture: Dr. Ingrid Daubechies, Duke University
AWM/SIAM Sonia Kovalevsky Lecture: Dr. Susanne C. Brenner, Louisiana State University
Peter Henrici Prize (awarded jointly by the Eidgenössische Technische Hochschule-Zürich (ETH Zurich) and SIAM): Dr. Bjorn Engquist, University of Texas at Austin
Ralph E. Kleinman Prize: Gunther Uhlmann (University of California & University of Washington)
W.T. and Idalia Reid Prize: Irena Lasiecka (University of Virginia)
SIAM Prize for Distinguished Service to the Profession: David Keyes (Columbia University & King Abdullah University of Science and Technology)
SIAM Outstanding Paper Prizes:
Justin Brickell, Inderjit Dhillon, Suvrit Sra, and Joel A. Tropp
Constantinos Daskalakis, Paul W. Goldberg, and Christos H. Papadimitriou
Iftach Haitner, Minh-Huyen Nguyen, Shien Jin Ong, Omer Reingold, and Salil Vadhan
SIAM Award in the Mathematical Contest in Modeling
Enhao Gong, Rongsha Li, Xiaoyun Wang, Tsinghua University, P.R.China and
Daniel Furlong, Dylan Marriner, Louis Ryan, Harvey Mudd College
SIAM Student Paper Prize
Necdet Serhat Aybat, Columbia University
Sungwoo Park, University of Maryland, College Park
Xiangxiong Zhang, Brown University
In addition, the 2011 Class of SIAM Fellows were acknowledged.
CAIMS and Mprime prizes were also awarded at the luncheon.
Chris Budd (University of Bath) gave a very engaging talk on Math In and Out of the Zoo. The lecture covered everything from the math that goes behind artificial incubation of penguin eggs to adjusting the temperature of aquariums, and the organization of animals in social groups, such as shoals and flocks, as well as crowd dynamics of humans. He proceeded to demonstrate the latter with an illustration of a hypothetical mad dash for dessert from last night’s Marsden reception. Budd concluded with the mathematics behind origami, the elegant geometry that can produce such artful shapes as a moose and a stag beetle.
The talk was followed by a special screening of the movie, Achieving the Unachievable by celebrated documentary filmmaker, Jean Bergeron, which describes the work of artist Maurits Cornelis Escher and the completion of one his famous paintings by mathematician Hendrik Lenstra.
From the Twitterverse:
dr_pyser: bashing away at the thesis introduction in a cafe. is this more important than seeing ‘math in the zoo’ at #ICIAM2011? probably hey.
Picture of the day:
MINOTAUR’s Soft-Wear Stack Courtesy of @SvenLeyffer