Books
2019
B. Pasdeloup, V. Gripon, R. Alami and M. Rabbat, "Uncertainty Principle on Graphs," L. Stankovic and E. Sejdic, VertexFrequency Analysis of Graph Signals, April 2019.
2012

B. Pasdeloup, V. Gripon, R. Alami and M. Rabbat, "Uncertainty Principle on Graphs," L. Stankovic and E. Sejdic, VertexFrequency Analysis of Graph Signals, April 2019.
Bibtex@inbook{PasGriAlaRab20194,
author = {Bastien Pasdeloup and Vincent Gripon and
Réda Alami and Michael Rabbat},
editor = {L. Stankovic and E. Sejdic},
title = {Uncertainty Principle on Graphs},
publisher = {Springer Nature},
year = {2019},
series = {VertexFrequency Analysis of Graph
Signals},
month = {April},
}

We know much about the neuron, the fundamental brain component. But we know almost nothing about mental information. On what kind of support does the brain memorize known faces, poems or phone numbers? How does it return those? Neurobiologists and neuroanatomists are unable to clarify those purely informational questions. If it is necessary to understand the neuron functioning principles, it seems not to be sufficient in order to answer the speculative question of mental information. Other concepts, coming from scientific domains foreign to biology such as information theory and redundant coding, may help finding adequate answers. This work brings a first concrete idea, mathematically justified and biologically plausible, on the way the neural network sets and retrieve its knowledge items. This novel theory mixes neurons and graphs, error correcting codes and cortical columns, stationnary messages and sequences and finally neural cliques and tournaments. Development prospects offered by this theory and by the fully digital brain memory model are many and promising, in neuroscience as well as in artificial intelligence.
This book is currently only available in french.
Bibtex@book{BerGri201209,
author = {Claude Berrou and Vincent Gripon},
editor = {Odile Jacob},
title = {Petite mathématique du cerveau},
year = {2012},
month = {September},
}


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