Research

The universal questions that have brought together members of the CAMBAM community are:

* How do local dynamics shape and determine global dynamics in large complex systems? For example, how do the dynamics of single cardiac cells, viewed as non-linear oscillators, when coupled in a large interconnected network influence the dynamics of the whole heart?
* How do these properties influence the evolution of these complex systems? For example, how can alterations in the dynamics of the large interconnected network of cardiac cells undergo bifurcations from a normal cardiac rhythm to that of an arrhythmia?
* What is the effectiveness in applied settings of mathematical models? For example, in the application of mathematical models of disease spread to surveillance there has been considerable academic activity to develop models of disease spread retrospectively. However, they are used infrequently in public health practice and even more rarely evaluated to determine how, if at all, they improve outcomes in the context of epidemic detection and management.

Though the members of the CAMBAM work on seemingly disparate problems in a wide spectrum of the biosciences, there is unity in the mathematical tools that we all use. These fall into five categories (with examples cited for each):
o Dynamical systems and probability theory (Neural systems, cell signaling, ecological communities, systems biology, pharmacometrics)
o Signal processing and systems identification (Brain-machine interface, neural network processing, information processing by single and multiple neurons, structure-function relationships in the brain)
o Combinatorics and graph theory (Phylogenetic and sequence analysis, brain-machine interface, neural network structure, gene regulatory networks, systems biology)
o Machine learning and optimization (Development of hierarchical neural network models, decoding of brain signals, pattern recognition by neural networks, models of neural plasticity, models of cognitive processes, models of visual recognition)
o Statistics, including temporal and spatial statistics, will be used to make better inference from all data that is collected.

By using these tools, the CAMBAM will work at several different scales and within different settings, emphasizing multi-scale relationships and the translation of basic research into applied settings.