Among the most important questions of neuroscience  are how information is encoded in neural activity, what an appropriate framework (including a mathematical definition) of cortical computation should look like, and how the highly specialized cortical subsystems are able to coordinate with one another. The importance of these questions extends way beyond the field of neuroscience, and potential answers have technological relevance. However, despite the efforts dedicated to these questions in the recent years, no conclusive answers could be given.
In particular, the ways by which biological systems compute are still largely unknown. It is, however, imperative to understand these systems, as there are a number of properties in which biological computation excels. Their low (variable) clock-time and the ease of how they deal with noise are of central technological interest. Presently, thermal noise resulting from high integration and short clock-times, drive hardware chips of the conventional paradigms into conditions where noise and how to deal with it become the dominating issues [2-3]. Beyond the few systems that could be shown to use stochastic resonance techniques, it is still unknown how biological systems deal efficiently with noise and imperfections. As an example, starting with only a one- or two-dimensional time series (the sound wave at one or two ears), the auditory system extracts a rich portrait of the auditory environment; accurately segmenting and locating auditory objects in the presence of noise, distortion, echos and other signal imperfections.
A prominent paradigm where noise and reliable computation-like processes are irresolvably intertwined, is phase-coupling, which was proposed as a computational paradigm by the applicant already in 1997 [4-6]. In a small-size project funded by SNF , the conditions under which locking is able to persist, how emerging chaotic response can be controlled, and how phase-coupling can help to synchronize events in distal parts of the network was investigated. The result of these investigations was that locking can persist under biologically realistic conditions and that it offers a promising explanation of cortical coding and computation.Recently, the locking paradigm has attracted increased interest among the more mathematically oriented groups of the neuroscience community [8-11].
Novel techniques now allow to extract phases also in the case of driven phase-locked interactions that are prominent in the working brain.
Therefore, the time seems optimal for making phase-coupled computation a specific research focus. Seamlessly, we will be able to connect to the previously posed and partly resolved questions. In our research project, we propose to investigate:
1) what kind of computations can be achieved by means of phase-coupling (this involves the definition of appropriate computational classes),
2) how the efficiency of phase-coupled computation can be measured and how this efficiency rates compared to other computational paradigms,
3) how phase-coupled computation can be implemented to solve technological problems.This agenda will force us to go beyond the nonlinear dynamics approach of phase-coupling. In order to answer the most basic question of what aspects of biological computation can be explained by phase-locking, we will combine our knowledge from the fields of mathematics (discrete mathematics, network analysis, nonlinear dynamics), physics (synchronization theory), theoretical and applied computer sciences, and electronic engineering, to work out a comprehensive model of biological computation. We will extend and refine the mathematical description of phase-locking in networks, and explore corresponding new fields of phase-locked computation. We will investigate theoretically and simulate numerically complex networks of phase-coupled neurons, and implement phase-coupled limit-cycle oscillators electronically. Our main focus will be to identify and work out toy situations where phase-coupled neurons perform efficient computations. This strategy will enable us to introduce a new kind of computational models, where noise-robustness is already introduced on the level of the coding symbols (Arnold tongue coding), to learn about the dependence of the computation in biological information processing systems on the underlying architecture, and to come up with electronic circuits implementations for result verification and as a basis for technical computational applications.Based on our earlier work, we are in the position to quickly publish a number of results that have been achieved in the meantime. This will direct and add momentum to the proposed research. In addition, we will investigate the connection between phase-coupled computational networks and sparse representations, searching for a link between the two. Here, we can profit from recent insight obtained in the field of the sparse signal processing performed by the auditory cortex .
 Eagleman, D. and Churchland, P.
Ten Unsolved Questions of Neuroscience (MIT Press, 2006).
 Kish, L.B.
End of Moore's Law: thermal (noise) death of integration in micro and nano electronics.
Phys. Lett. A 305, 144-149 (2002).
 Stoop, R., Schindler, K. and Bunimovich, L.A.
When pyramidal neurons lock, when they respond chaotically, and when they like to synchronize.
Neuroscience Research 36 (2000).
 Stoop, R., Schindler, K. and Bunimovich, L.A.
Neocortical networks of pyramidal neurons: from local locking and chaos to macroscopic chaos and synchronization. Nonlinearity 13, 5 (2000).
 Stoop, R., Bunimovich, L.A. and Steeb, W.-H.
Generic origins of irregular spiking in neocortical networks.
Biol. Cybern. 83, 481-489 (2000).
 SNF grant SNF2100-065293 to R. Stoop.
 Preyer, A.J. and Butera, R.J.
Neuronal Oscillators in Aplysia californica that Demontrate Weak Coupling In Vitro.
Phys. Rev. Lett. 95 138103 (2005).
 Galan, R.F., Ermentrout, G.B.
Efficient estimation of Phase-Resetting Curves in Real Neurons and its Significance for Neural-Network Modeling, Phys. Rev. Lett. 94, 158101(2005)
 Haken, H.
Synchronization and pattern recognition in a pulse-coupled neural net.
Physica D 205, 1-6 (2005).
 Netoff, T.I, Banks, M.I., Dorval, A.D., Acker, C.D., Haas, J.S., Kopell, N., and Whilte, J.A.
Synchronization in Hybrid Neuronal Networks of the Hippocampal Formation.
J. Neurophysiol. 93,1197-1208 (2005).
 Kern, A., Nagy, O., and Stoop, R.
Sparse time-frequency analysis of speech signals.
IEEE Conf. on Nonlinear Theory and its Applications NOLTA 2005 (2005).