Analysis of Neural Networks:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1980
|
| Schriftenreihe: | Lecture Notes in Biomathematics
35 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The purpose of this work is a unified and general treatment of activity in neural networks from a mathematical pOint of view. Possible applications of the theory presented are indica ted throughout the text. However, they are not explored in de tail for two reasons : first, the universal character of n- ral activity in nearly all animals requires some type of a general approach~ secondly, the mathematical perspicuity would suffer if too many experimental details and empirical peculiarities were interspersed among the mathematical investigation. A guide to many applications is supplied by the references concerning a variety of specific issues. Of course the theory does not aim at covering all individual problems. Moreover there are other approaches to neural network theory (see e.g. Poggio-Torre, 1978) based on the different lev els at which the nervous system may be viewed. The theory is a deterministic one reflecting the average be havior of neurons or neuron pools. In this respect the essay is written in the spirit of the work of Cowan, Feldman, and Wilson (see sect. 2.2). The networks are described by systems of nonlinear integral equations. Therefore the paper can also be read as a course in nonlinear system theory. The interpretation of the elements as neurons is not a necessary one. However, for vividness the mathematical results are often expressed in neurophysiological terms, such as excitation, inhibition, membrane potentials, and impulse frequencies. The nonlinearities are essential constituents of the theory |
| Beschreibung: | 1 Online-Ressource (X, 164 p) |
| ISBN: | 9783642455179 9783540099666 |
| ISSN: | 0341-633X |
| DOI: | 10.1007/978-3-642-45517-9 |
Internformat
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Datensatz im Suchindex
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| dewey-hundreds | 600 - Technology (Applied sciences) |
| dewey-ones | 612 - Human physiology |
| dewey-raw | 612.8 |
| dewey-search | 612.8 |
| dewey-sort | 3612.8 |
| dewey-tens | 610 - Medicine and health |
| discipline | Mathematik Medizin |
| doi_str_mv | 10.1007/978-3-642-45517-9 |
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| indexdate | 2024-07-10T01:21:11Z |
| institution | BVB |
| isbn | 9783642455179 9783540099666 |
| issn | 0341-633X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027857909 |
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| spelling | Heiden, Uwe an der 1942- Verfasser (DE-588)1013536835 aut Analysis of Neural Networks by Uwe Heiden Berlin, Heidelberg Springer Berlin Heidelberg 1980 1 Online-Ressource (X, 164 p) txt rdacontent c rdamedia cr rdacarrier Lecture Notes in Biomathematics 35 0341-633X The purpose of this work is a unified and general treatment of activity in neural networks from a mathematical pOint of view. Possible applications of the theory presented are indica ted throughout the text. However, they are not explored in de tail for two reasons : first, the universal character of n- ral activity in nearly all animals requires some type of a general approach~ secondly, the mathematical perspicuity would suffer if too many experimental details and empirical peculiarities were interspersed among the mathematical investigation. A guide to many applications is supplied by the references concerning a variety of specific issues. Of course the theory does not aim at covering all individual problems. Moreover there are other approaches to neural network theory (see e.g. Poggio-Torre, 1978) based on the different lev els at which the nervous system may be viewed. The theory is a deterministic one reflecting the average be havior of neurons or neuron pools. In this respect the essay is written in the spirit of the work of Cowan, Feldman, and Wilson (see sect. 2.2). The networks are described by systems of nonlinear integral equations. Therefore the paper can also be read as a course in nonlinear system theory. The interpretation of the elements as neurons is not a necessary one. However, for vividness the mathematical results are often expressed in neurophysiological terms, such as excitation, inhibition, membrane potentials, and impulse frequencies. The nonlinearities are essential constituents of the theory Medicine Neurosciences Biomedicine Mathematical and Computational Biology Medizin Analysis (DE-588)4001865-9 gnd rswk-swf Biomathematik (DE-588)4139408-2 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Nervensystem (DE-588)4041643-4 gnd rswk-swf Neuronales Netz (DE-588)4226127-2 gnd rswk-swf 1\p (DE-588)4113937-9 Hochschulschrift gnd-content Nervensystem (DE-588)4041643-4 s Mathematisches Modell (DE-588)4114528-8 s 2\p DE-604 Neuronales Netz (DE-588)4226127-2 s Biomathematik (DE-588)4139408-2 s 3\p DE-604 Analysis (DE-588)4001865-9 s 4\p DE-604 https://doi.org/10.1007/978-3-642-45517-9 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Heiden, Uwe an der 1942- Analysis of Neural Networks Medicine Neurosciences Biomedicine Mathematical and Computational Biology Medizin Analysis (DE-588)4001865-9 gnd Biomathematik (DE-588)4139408-2 gnd Mathematisches Modell (DE-588)4114528-8 gnd Nervensystem (DE-588)4041643-4 gnd Neuronales Netz (DE-588)4226127-2 gnd |
| subject_GND | (DE-588)4001865-9 (DE-588)4139408-2 (DE-588)4114528-8 (DE-588)4041643-4 (DE-588)4226127-2 (DE-588)4113937-9 |
| title | Analysis of Neural Networks |
| title_auth | Analysis of Neural Networks |
| title_exact_search | Analysis of Neural Networks |
| title_full | Analysis of Neural Networks by Uwe Heiden |
| title_fullStr | Analysis of Neural Networks by Uwe Heiden |
| title_full_unstemmed | Analysis of Neural Networks by Uwe Heiden |
| title_short | Analysis of Neural Networks |
| title_sort | analysis of neural networks |
| topic | Medicine Neurosciences Biomedicine Mathematical and Computational Biology Medizin Analysis (DE-588)4001865-9 gnd Biomathematik (DE-588)4139408-2 gnd Mathematisches Modell (DE-588)4114528-8 gnd Nervensystem (DE-588)4041643-4 gnd Neuronales Netz (DE-588)4226127-2 gnd |
| topic_facet | Medicine Neurosciences Biomedicine Mathematical and Computational Biology Medizin Analysis Biomathematik Mathematisches Modell Nervensystem Neuronales Netz Hochschulschrift |
| url | https://doi.org/10.1007/978-3-642-45517-9 |
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