On mathematical modeling of networks and implementation aspects

Regina Bernhaupt; Jochen Pfalzgraf

doi:10.1007/3-540-45470-5

On mathematical modeling of networks and implementation aspects

Regina Bernhaupt, Jochen Pfalzgraf

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

1 Citation (Scopus)

Abstract

Based on existing work where categorical and geometrical methods were used to establish a mathematical model of neural net structures, we develop a new very general model for artificial neural networks (ANN), where all basic components of a network are described abstractly. This mathematical model serves as a guideline for design and implementation of a new ANN-simulator. The proposed model of neuron types will be illustrated by the discussion of an example, using the Single Spiking Neuron Model (SSM). The main building blocks of the simulation tool, a new construction principle for ANN, and abstract modeling of connection weights are presented.

Original language	English
Title of host publication	Artificial Intelligence, Automated Reasoning and Symbolic Computation - Joint International Conferences AISC 2002 and Calculemus 2002, Proceedings
Editors	Laurent Henocque, Jacques Calmet, Belaid Benhamou, Olga Caprotti, Volker Sorge
Publisher	Springer
Pages	168-180
Number of pages	13
ISBN (Print)	3540438653, 9783540438656
DOIs	https://doi.org/10.1007/3-540-45470-5
Publication status	Published - 1 Jan 2002
Externally published	Yes
Event	Joint Conferences on 6th Artificial Intelligence and Symbolic Computation, AISC 2002 and 10th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning, Calculemus 2002 - Marseille, France Duration: 1 Jul 2002 → 5 Jul 2002

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2385
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	Joint Conferences on 6th Artificial Intelligence and Symbolic Computation, AISC 2002 and 10th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning, Calculemus 2002
Country	France
City	Marseille
Period	1/07/02 → 5/07/02

Access to Document

10.1007/3-540-45470-5

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Bernhaupt, R., & Pfalzgraf, J. (2002). On mathematical modeling of networks and implementation aspects. In L. Henocque, J. Calmet, B. Benhamou, O. Caprotti, & V. Sorge (Eds.), Artificial Intelligence, Automated Reasoning and Symbolic Computation - Joint International Conferences AISC 2002 and Calculemus 2002, Proceedings (pp. 168-180). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2385). Springer. https://doi.org/10.1007/3-540-45470-5

Bernhaupt, Regina ; Pfalzgraf, Jochen. / On mathematical modeling of networks and implementation aspects. Artificial Intelligence, Automated Reasoning and Symbolic Computation - Joint International Conferences AISC 2002 and Calculemus 2002, Proceedings. editor / Laurent Henocque ; Jacques Calmet ; Belaid Benhamou ; Olga Caprotti ; Volker Sorge. Springer, 2002. pp. 168-180 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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Bernhaupt, R & Pfalzgraf, J 2002, On mathematical modeling of networks and implementation aspects. in L Henocque, J Calmet, B Benhamou, O Caprotti & V Sorge (eds), Artificial Intelligence, Automated Reasoning and Symbolic Computation - Joint International Conferences AISC 2002 and Calculemus 2002, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2385, Springer, pp. 168-180, Joint Conferences on 6th Artificial Intelligence and Symbolic Computation, AISC 2002 and 10th Symposium on the Integration of Symbolic Computation and Mechanized Reasoning, Calculemus 2002, Marseille, France, 1/07/02. https://doi.org/10.1007/3-540-45470-5

On mathematical modeling of networks and implementation aspects. / Bernhaupt, Regina; Pfalzgraf, Jochen.

Artificial Intelligence, Automated Reasoning and Symbolic Computation - Joint International Conferences AISC 2002 and Calculemus 2002, Proceedings. ed. / Laurent Henocque; Jacques Calmet; Belaid Benhamou; Olga Caprotti; Volker Sorge. Springer, 2002. p. 168-180 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2385).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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Bernhaupt R, Pfalzgraf J. On mathematical modeling of networks and implementation aspects. In Henocque L, Calmet J, Benhamou B, Caprotti O, Sorge V, editors, Artificial Intelligence, Automated Reasoning and Symbolic Computation - Joint International Conferences AISC 2002 and Calculemus 2002, Proceedings. Springer. 2002. p. 168-180. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/3-540-45470-5