icon for page Ecosystem Dynamics and Management: Fall 2013

Ecosystem Dynamics and Management: Fall 2013

A changing world raises great challenges since we need to take steps that either reduce the rate of global change or that manage resources in the face of global change. Both steps require making predictions, which requires theory. But the systems involved are truly complex, so the theory must use mathematics. Despite the long history of mathematical approaches in ecology and other environmental sciences, understanding the resilience of environmental systems in the face of global change presents substantial mathematical challenges that require novel approaches...

icon for page Mathematical Neuroscience 2012-2013

Mathematical Neuroscience 2012-2013

In 2012-13 MBI will return to the subject of mathematical neuroscience, which was the subject of its first emphasis year in 2002-3. Mathematics both elucidates key dynamical mechanisms for patterns of neural activity and quantifies levels of information in these patterns. At the same time, new mathematical questions and techniques...

icon for page Stochastics in Biological Systems September 2011 - August 2012

Stochastics in Biological Systems September 2011 - August 2012

Stochasticity is fundamental to biological systems. While in many situations the system can be viewed as a large number of similar agents interacting in a homogeneously mixing environment so the dynamics are captured well by ordinary differential equations or other...

icon for page Evolution, Synchronization, and Environmental Interactions: Insights from Plants and Insects 2010-2011

Evolution, Synchronization, and Environmental Interactions: Insights from Plants and Insects 2010-2011

Myriad influences shape the patterns of evolution, timing, behavior and ecology of living organisms. These influences range from biochemical cues to configurations of temperature, space and light, to interactions with other organisms. This one-year program focuses on connecting influence to pattern for processes involving plants and insects...

icon for page Molecular interactions within the cell: Network, scale, and complexity 2009-2010

Molecular interactions within the cell: Network, scale, and complexity 2009-2010

Biological processes can be characterized by different degrees of complexity at microscopic (genes, molecules), mesoscopic (protein-DNA complexes) and macroscopic (cells, organisms) levels. Historically, all biological systems have been studied at different levels. However, an increasing amount of experimental results and theoretical studies suggest that a more comprehensive system approach would tackle better biological problems. It would require a collaboration and intensive exchange between experimental and theoretical researchers from physics, chemistry, biology, mathematics, computer science, and engineering...

icon for page Mathematical Challenges in Developmental Biology 2008-2009

Mathematical Challenges in Developmental Biology 2008-2009

Growth, movement and differentiation of cells are three key processes involved in pattern formation and morphogenesis in developing systems. Pattern formation involves the expression of genes at the correct point in space at the correct time, and this in turn typically involves spatially- and temporally-varying signals, and mechanisms for signal transduction and activation or repression of gene expression. Gene expression during embryonic development is not a cell-autonomous process, because cell fate in a multicellular embryo usually depends on the cell's location. This fact led to the theory of positional information, which posits that a cell must `know' its position relative to other cells in order to adopt the correct developmental pathway...

icon for page Mathematical Bioengineering 2007-2008

Mathematical Bioengineering 2007-2008

Bioengineering lies at the interfaces of biology, the applied sciences and engineering. It combines the excitement of multi-disciplinary research with the promise of making improvements to society, especially in health care, e.g. in the diagnosis and treatments of degenerative diseases. However, it is a relatively new field that is still finding its way among the established engineering and biological disciplines. As a multi-discipline it presents particular problems for the seasoned researcher as much as for the new student: indeed, we are all new students when it comes to subfields in which we have not trained...

icon for page Systems Physiology 2006-2007

Systems Physiology 2006-2007

Much of the biological investigation of the past can be described as a compilation and categorization of the list of parts, whether as the delineation of genomic sequences, genes, proteins, or species. The past decade for example has uncovered the genetic basis for many diseases. A remaining and larger challenge is to provide an understanding of how the interactions of these biological entities across spatial and temporal scales lead to observable behavior and function. This is what systems biology is concerned with...

icon for page Ecology and Evolution 2005-2006

Ecology and Evolution 2005-2006

Ecology and evolutionary biology have historically been two of the areas of biology which have most benefited from, and made use of, mathematical methods. Many distinguished mathematical biologists have contributed to these areas, and their efforts have illuminated much of ecological and evolutionary theory over the past century. An objective of this special year is to focus on specialized areas that offer particularly challenging mathematical problems, which are relatively unexplored and are of potentially great interest to observational biologists. Thus, an underlying goal of the proposed activities is to maintain direct connections to observable biology...

icon for page Genomics, Proteomics, and Bioinformatics 2004-2005

Genomics, Proteomics, and Bioinformatics 2004-2005

GENOMICS was defined in the 1980s as the new discipline of mapping, sequencing, and analyzing genomes, that is, the study of genes and their function in organisms on a global rather than a local scale. Proteomics, the study of the PROTEin complement to a genOME, emerged in the 1990s as the qualitative and quantitative comparison of proteomes under different conditions to further unravel biological processes. Both subject areas are at the forefront of the revolution taking place in biological and medical research, which is transforming them from data poor to data rich fields...

icon for page Mathematical Modeling Of Cell Processes 2003-2004

Mathematical Modeling Of Cell Processes 2003-2004

In the past few years, the importance of mathematical models in the study of cellular processes has become widely accepted. Mathematical models have played an important role, for example, in understanding how oscillations in cell cycles lead to regular cell division, and how intercellular calcium waves coordinate cellular response over large areas. In this year, we shall explore topics from cell growth and death, to intercellular communications, and to the behaviors of large populations of cells such at those found in the immune system...

icon for page Mathematical Neuroscience 2002-2003

Mathematical Neuroscience 2002-2003

The use of mathematics in studying the brain has had great impact on the field of neuroscience and simultaneously motivated important research in mathematics. Research aimed at understanding the nervous system has two major lines of inquiry: How is a signal from the external world represented in the brain, and what are the mechanistic models at the circuit and system levels? The program this year will address both questions...