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This article is part of the supplement: Twentieth Annual Computational Neuroscience Meeting: CNS*2011

Open Access Poster presentation

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

Mikael Djurfeldt

Author Affiliations

PDC, KTH, S-100 44 Stockholm, Sweden

INCF, KI, S-171 77 Stockholm, Sweden

BMC Neuroscience 2011, 12(Suppl 1):P80  doi:10.1186/1471-2202-12-S1-P80

The electronic version of this article is the complete one and can be found online at:

Published:18 July 2011

© 2011 Djurfeldt; licensee 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.

Poster presentation

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.


  1. Djurfeldt M: The Connection-set Algebra?a novel formalism for the representation of connectivity structure in neuronal network models.

    Submitted OpenURL

  2. Djurfeldt M: The Connection-set Algebra: A novel formalism for the representation of connectivity structure in neuronal network models. In 3rd INCF Congress of Neuroinformatics. Kobe, Japan; 2010. OpenURL

  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. Publisher Full Text OpenURL

  4. The Python CSA implementation [] webcite

  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.


    PubMed Abstract | Publisher Full Text | PubMed Central Full Text OpenURL

  6. Raikov I, et al.: NineML: The Network Interchange for Neuroscience Modeling Language.

    CNS 2011.

    this conference