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  • Poster presentation
  • Open Access

The Connection-set Algebra: a formalism for the representation of connectivity structure in neuronal network models, implementations in Python and C++, and their use in simulators

BMC Neuroscience201112 (Suppl 1) :P80

  • Published:


  • Network Model
  • Network Structure
  • Neuronal Network
  • Network Connectivity
  • Network Simulator

The connection-set algebra (CSA) [1, 2] is a novel and general formalism for the description of connectivity in neuronal network models, from its small-scale to its large-scale structure. It provides operators to form more complex sets of connections from simpler ones and also provides parameterization of such sets.

The CSA is expressive enough to describe a wide range of connectivities 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.

Here, a Python implementation [4] of the connection-set algebra is presented together with its application to describing various network connectivity patterns. In addition, it is shown how CSA can be used to describe network models in the PyNN [5] and NineML [6] network model description languages.

Authors’ Affiliations

PDC, KTH, S-100 44 Stockholm, Sweden
INCF, KI, S-171 77 Stockholm, Sweden


  1. Djurfeldt M: The Connection-set Algebra?a novel formalism for the representation of connectivity structure in neuronal network models. Submitted.Google Scholar
  2. Djurfeldt M: The Connection-set Algebra: A novel formalism for the representation of connectivity structure in neuronal network models. 3rd INCF Congress of Neuroinformatics. 2010, Kobe, JapanGoogle Scholar
  3. Djurfeldt M, Lundqvist M, Johansson C, Rehn M, Ekeberg Ö, Lansner A: Brain-scale simulation of the neocortex on the Blue Gene/L supercomputer. IBM J Research and Development. 2008, 52 (1/2): 31-42. 10.1147/rd.521.0031.View ArticleGoogle Scholar
  4. The Python CSA implementation. []
  5. Davison AP, Brüderle D, Eppler JM, Kremkow J, Muller E, Pecevski DA, Perrinet L, Yger P: PyNN: a common interface for neuronal network simulators. Front. Neuroinform. 2008, 2: 11-10.3389/neuro.11.011.2008. doi:10.3389/neuro.11.011.2008PubMed CentralView ArticlePubMedGoogle Scholar
  6. Raikov I: NineML: The Network Interchange for Neuroscience Modeling Language. CNS. 2011, this conferenceGoogle Scholar


© Djurfeldt; licensee BioMed Central Ltd. 2011

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.