Neuroinformatics

, Volume 10, Issue 3, pp 287–304

The Connection-set Algebra—A Novel Formalism for the Representation of Connectivity Structure in Neuronal Network Models

Original Article

Abstract

The connection-set algebra (CSA) is a novel and general formalism for the description of connectivity in neuronal network models, from small-scale to large-scale structure. The algebra provides operators to form more complex sets of connections from simpler ones and also provides parameterization of such sets. CSA is expressive enough to describe a wide range of connection patterns, including multiple types of random and/or geometrically dependent connectivity, and can serve as a concise notation for network structure in scientific writing. CSA implementations allow for scalable and efficient representation of connectivity in parallel neuronal network simulators and could even allow for avoiding explicit representation of connections in computer memory. The expressiveness of CSA makes prototyping of network structure easy. A C+ + version of the algebra has been implemented and used in a large-scale neuronal network simulation (Djurfeldt et al., IBM J Res Dev 52(1/2):31–42, 2008b) and an implementation in Python has been publicly released.

Keywords

Modeling Connectivity Neuronal networks Computational neuroscience Software Formalism 

References

  1. Binzegger, T., Douglas, R. J., & Martin, K. A. C. (2004). A quantitative map of the circuit of cat primary visual cortex. Journal of Neuroscience, 39, 8441–8453.CrossRefGoogle Scholar
  2. Binzegger, T., Douglas, R. J., & Martin, K. A. C. (2007). Stereotypical bouton clustering of individual neurons in cat primary visual cortex. Journal of Neuroscience, 27(45), 12242–12254.PubMedCrossRefGoogle Scholar
  3. Cannon, R. C., Gewaltig, M.-O., Gleeson, P., Bhalla, U. S., Cornelis, H., Hines, M. L., et al. (2007). Interoperability of neuroscience modeling software: Current status and future directions. Neuroinformatics, 5, 127–138.PubMedCrossRefGoogle Scholar
  4. Crook, S. M., Gleeson, P., & Silver, R. A. (2007). NetworkML: Level 3 of the neuroml standards for multiscale model specification and exchange. In Soc. Neurosci. Abstr. Google Scholar
  5. Davison, A. P., Brüderle, D., Eppler, J., Kremkow, J., Muller, E., Pecevski, D., et al. (2009). PyNN: A common interface for neuronal network simulators. Frontiers in Neuroinformatics, 2, 1–10.Google Scholar
  6. Djurfeldt, M. (2010). CSA implementation in Python. INCF software center. http://software.incf.org/software/csa.
  7. Djurfeldt, M., Ekeberg, Ö., & Lansner, A. (2008a). Large-scale modeling—a tool for conquering the complexity of the brain. Frontiers in Neuroinformatics, 2(1), 1–4. doi:10.3389/neuro.11.001.2008.PubMedCrossRefGoogle Scholar
  8. Djurfeldt, M., Lundqvist, M., Johansson, C., Rehn, M., Ekeberg, Ö., & Lansner, A. (2008b). Brain-scale simulation of the neocortex on the Blue Gene/L supercomputer. IBM Journal of Research and Development, 52(1/2), 31–42.CrossRefGoogle Scholar
  9. Djurfeldt, M., & Lansner, A. (2007). Large-scale modeling of the nervous system. Workshop report, International Neuroinformatics Coordinating Facility (INCF), Stockholm.Google Scholar
  10. Gewaltig, M.-O., & Diesmann, M. (2007). NEST (NEural Simulation Tool). Scholarpedia, 2, 1430.CrossRefGoogle Scholar
  11. Gleeson, P., Crook, S., Cannon, R. C., Hines, M. L., Billings, G. O., Farinella, M., et al. (2010). NeuroML: A language for describing data driven models of neurons and networks with a high degree of biological detail. PLoS Computational Biology, 6(6), 1–19.CrossRefGoogle Scholar
  12. Goddard, N. H., Hucka, M., Howell, F., Cornelis, H., Shankar, K., & Beeman, D. (2001). Towards neuroML: Model description methods for collaborative modelling in neuroscience. Philosophical Transactions of Royal Society London Series B, 356, 1209–1228.CrossRefGoogle Scholar
  13. Goodman, D. (2010). Code generation: A strategy for neural network simulators. Neuroinformatics, 8, 183–196. doi:10.1007/s12021-010-9082-x.PubMedCrossRefGoogle Scholar
  14. Knuth, D. E. (1998). The art of computer programming (2nd edn.). Reading, MA: Addison-Wesley.Google Scholar
  15. Lundqvist, M., Rehn, M., Djurfeldt, M., & Lansner, A. (2006). Attractor dynamics in a modular network model of neocortex. Network: Computation in Neural Systems, 17(3), 253–276.CrossRefGoogle Scholar
  16. Lytton, W. W., Omurtag, A., Neymotin, S. A., & Hines, M. L. (2008). Just-in-time connectivity for large spiking networks. Neural Computation, 20(11), 2745–2756.PubMedCrossRefGoogle Scholar
  17. Nordlie, E., Gewaltig, M.-O., & Plesser, H. E. (2009). Towards reproducible descriptions of neuronal network models. PLoS Computational Biology, 5(8), e1000456. doi:10.1371/journal.pcbi.1000456.PubMedCrossRefGoogle Scholar
  18. Nordlie, E., Plesser, H. E., & Gewaltig, M.-O. (2008). Towards reproducible descriptions of neuronal network models. Presented at the Poster Session at 1st INCF Congress of Neuroinformatics: Databasing and Modeling the Brain (Neuroinformatics 2008).Google Scholar
  19. Plesser, H., & Austvoll, K. (2009). Specification and generation of structured neuronal network models with the NEST topology module. BMC Neuroscience, 10(Suppl 1), P56.CrossRefGoogle Scholar
  20. Raikov, I., Cannon, R., Clewley, R., Cornelis, H., Davison, A., De Schutter, E., et al. (2011). NineML: The network interchange for neuroscience modeling language. BMC Neuroscience, 12, 1–2. doi:10.1186/1471-2202-12-S1-P330.CrossRefGoogle Scholar
  21. Strey, A. (1997). EpsiloNN—a specification language for the efficient parallel simulation of neural networks. In IWANN ’97: Proceedings of the international work-conference on artificial and natural neural networks (pp. 714–722). London: Springer-Verlag.Google Scholar
  22. Thomson, A. M., & Lamy, C. (2007). Functional maps of neocortical local circuitry. Frontiers in Neuroscience, 1(1), 19–42.PubMedCrossRefGoogle Scholar
  23. Thomson, A. M., West, D. C., Wang, Y., & Bannister, A. P. (2002). Synaptic connections and small circuits involving excitatory and inhibitory neurons in layer 2–5 of adult rat and cat neocortex: Triple intracellular recordings and biocytin labelling in vitro. Cerebral Cortex, 12, 936–953.PubMedCrossRefGoogle Scholar
  24. Tootell, B., Switkes, E., Silverman, M., & Hamilton, S. (1988). Functional anatomy of the macaque striate cortex. ii. retinotopic organization. Journal of Neuroscience, 8(5), 1531–1568.PubMedGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.School of Computer Science and CommunicationKTHStockholmSweden

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