In 2012-13 MBI will return to 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, that often bridge information theory, dynamical systems, and statistical mechanics, have been inspired by the complexity of the underlying networks and the computations they perform. Over the past decade, mathematics has entered new subfields of neuroscience, and has begun to suggest unexpected parallels among others. (W1) We will open the emphasis year with a workshop focusing on such parallels, in the form of general challenges posed by dynamics of nonlinear, spiking networks, and will organize a series of workshops to follow that will highlight mathematical impact and possibilities in the most active and exciting areas of neuroscience.
Cognitive neuroscience (W2) presents superb opportunities for mathematical contributions, especially in connecting different theoretical and experimental frameworks. On the experimental side, methods ranging from single-neuron recording to human behavioral tests are flourishing, and mathematical models are beginning to suggest how one leads to the other. Rigorous theoretical treatments from microeconomics are often applied, including Bayesian estimation and optimization, but details of how they might be implemented in stochastic, dynamic neural circuits have only recently been proposed. By bringing together theorists working on different levels, a workshop will move the field closer to a long-held goal of understanding and predicting decision-making and choice behavior.
Another timely and exciting workshop will be the dynamics of neural disease (W3). Recent work has suggested mechanisms for pathological activity patterns in epilepsy and Parkinsons disease, and dynamical models have been used to explain the function and possible improvement of stimulation-based therapies. Mathematical analysis is also being pursued for prosthetics used in sensory systems (i.e., cochlear implants for deafness) and motor systems (i.e., neural implants that drive artificial limbs). Many open questions remain for other disease states, including addictions, mental illnesses, and memory dysfunction. In parallel, rich mathematical questions arise in the exploding area of non-invasive imaging. Algorithms are needed for more efficient data analysis and especially for combining datasets gathered on different spatial and temporal scales (e.g., fMRI, EEG, and single-neuron recordings).
A fourth workshop (W4) will focus on rhythms and oscillations. This field was featured in the 2002-03 emphasis year, and continues to be highly exciting - especially due to increasing evidence that oscillations and appropriate phase relationships are critical for cognitive states and sensory processing.
Moving to the smallest spatial scale, the chemical and molecular mechanisms for the dynamics of brain state regulation, development, repair, and adaptation are being uncovered by modern tools of molecular biology and genetics. These small-scale dynamics affect excitability, and bridging across such multiple scales is a frontier in our understanding of patterns of neuronal activity. There is enormous opportunity for mathematics to contribute by combining models at the levels of systems biology and electrophysiology. We will focus a workshop (W5) on this theme.
In a workshop on sensory systems (W6), we will address separate modalities, as well as consider commonalities for the representation and processing of stimuli with naturalistic statistics. Here, the establishment of maps and associations, the dynamics of synaptic plasticity, the adaptation to scene statistics, and the mechanisms for multi-modal interactions are of central importance. Special focus will be given to active sensing and feedback loops (central to periphery) in sensory processing, to coding strategies, and to streaming (source separation) in the auditory system. Attention throughout the workshop will be given to plausible neuronal mechanisms for these aspects of sensory processing.