nach oben

Cognitive Neurodynamics

Erschienen in:

18.05.2020 | Research Article

Neural computing in four spatial dimensions

verfasst von: Arturo Tozzi, Muhammad Zubair Ahmad, James F. Peters

Erschienen in: Cognitive Neurodynamics | Ausgabe 2/2021

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

Relationships among near set theory, shape maps and recent accounts of the Quantum Hall effect pave the way to neural networks computations performed in higher dimensions. We illustrate the operational procedure to build a real or artificial neural network able to detect, assess and quantify a fourth spatial dimension. We show how, starting from two-dimensional shapes embedded in a 2D topological charge pump, it is feasible to achieve the corresponding four-dimensional shapes, which encompass a larger amount of information. Synthesis of surface shape components, viewed topologically as shape descriptions in the form of feature vectors that vary over time, leads to a 4D view of cerebral activity. This novel, relatively straightforward architecture permits to increase the amount of available qbits in a fixed volume.

Vorheriger Artikel Complex bifurcation analysis and synchronization optimal control for Hindmarsh–Rose neuron model under magnetic flow effect

Nächster Artikel Primal-size neural circuits in meta-periodic interaction

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Ahmad MZ, Peters JF (2018) Descriptive unions. A fibre bundle characterization of the union of descriptively near sets, arXiv:1811.11129

Borsuk K (1957–1958) Concerning the classification of topological spaces from the standpoint of the theory of retracts. XLVI:177–190

Di Concilio A, Guadagni C, Peters JF, Ramanna S (2018) Descriptive proximities. Properties and interplay between classical proximities and overlap. Math Comput Sci 12(1):91–106. https://doi.org/10.1007/s11786-017.0328-yCrossRef

Dmochowski JP, Ki JJ, DeGuzman P, Sajda P, Parra LC (2017) Extracting multidimensional stimulus-response correlations using hybrid encoding-decoding of neural activity. Neuroimage. https://doi.org/10.1016/j.neuroimage.2017.05.037CrossRefPubMedPubMedCentral

Don A, Peters JF, Ramanna S, Tozzi A (2020) Topological view of flows inside the BOLD spontaneous activity of the human brain. Front Comput Neurosci. https://doi.org/10.3389/fncom.2020.00034CrossRefPubMedPubMedCentral

Garcia JO, Ashourvan A, Muldoon SF, Vettel J, Bassett DS (2018) Applications of community detection techniques to brain graphs: algorithmic considerations and implications for neural function. Proc IEEE. https://doi.org/10.1109/jproc.2017.2786710CrossRef

Hall E (1879) On a new action of the magnet on electric currents. Am J Math 2(3):287–292. https://doi.org/10.2307/2369245CrossRef

Izhikevich EM (2010) Dynamical systems in neuroscience—the geometry of excitability and bursting. ISBN: 9780262514200

Kraus YE, Ringel Z, Zilberberg O (2013) Four-dimensional quantum Hall effect in a two-dimensional quasicrystal. Phys Rev Lett 111:226401CrossRef

Lohse M, Schweizer C, Price HM, Zilberberg O, Bloch I (2018) Exploring 4D quantum Hall physics with a 2D topological charge pump. Nature 553:55–58. https://doi.org/10.1038/nature25000CrossRefPubMed

Matoušek J (2003) Using the Borsuk–Ulam theorem. Lectures on topological methods in combinatorics and geometry. Springer, Berlin

Novoselov KS, Jiang Z, Zhang Y, Morozov SV, Stormer HL et al (2007) Room-temperature quantum Hall effect in graphene. Science 315(5817):1379CrossRef

Peters JF (2007) Near sets. Special theory about nearness of objects. Fundam Inf 75(1–4):407–433

Peters JF (2014) Topology of digital images. Visual pattern discovery in proximity spaces. In: Intelligent systems reference library. Springer, Berlin, pp 1–342, vol 63. ISBN 978-3-642-53844-5. https://doi.org/10.1007/978-3-642-53845-2

Riley SN, Davies J (2020) A spiking neural network model of spatial and visual mental imagery. Cogn Neurodyn 14:239–251. https://doi.org/10.1007/s11571-019-09566-5CrossRefPubMed

Sen S, Daimi SN, Watanabe K et al (2020) Switch or stay? Automatic classification of internal mental states in bistable perception. Cogn Neurodyn 14:95–113. https://doi.org/10.1007/s11571-019-09548-7CrossRefPubMed

Tafreshi TF, Daliri MR, Ghodousi M (2019) Functional and effective connectivity based features of EEG signals for object recognition. Cogn Neurodyn 13:555–566. https://doi.org/10.1007/s11571-019-09556-7CrossRefPubMedPubMedCentral

Tozzi A (2019) The multidimensional brain. Phys Life Rev. https://doi.org/10.1016/j.plrev.2018.12.004(in press)CrossRefPubMed

Tozzi A, Peters JF (2016a) Towards a fourth spatial dimension of brain activity. Cogn Neurodyn 10(3):189–199. https://doi.org/10.1007/s11571-016-9379-zCrossRefPubMedPubMedCentral

Tozzi A, Peters JF (2016b) A topological approach unveils system invariances and broken symmetries in the brain. J Neurosci Res 94(5):351–365. https://doi.org/10.1002/jnr.23720CrossRefPubMed

Tozzi A, Peters JF (2019) The Borsuk–Ulam theorem solves the curse of dimensionality: comment on “the unreasonable effectiveness of small neural ensembles in high-dimensional brain” by Alexander N. Gorban et al. Phys Life Rev. https://doi.org/10.1016/j.plrev.2019.04.008CrossRefPubMed

Tozzi A, Peters JF (2020) Removing uncertainty in neural networks. Cogn Neurodyn. https://doi.org/10.1007/s11571-020-09574-wCrossRefPubMed

Tozzi A, Peters JF, Fingelkurts AA, Fingelkurts AA, Marijuán PC (2017) Topodynamics of metastable brains. Phys Life Rev 21:1–20. https://doi.org/10.1016/j.plrev.2017.03.001CrossRefPubMed

Ursino M, Cuppini C, Cappa SF et al (2018) A feature-based neurocomputational model of semantic memory. Cogn Neurodyn 12:525–547. https://doi.org/10.1007/s11571-018-9494-0CrossRefPubMedPubMedCentral

Zhang S-C, Hu J (2001) A four-dimensional generalization of the quantum Hall effect. Science 294:823–828CrossRef

Zilberberg O, Huang S, Guglielmon J, Wang M, Chen KP et al (2018) Photonic topological boundary pumping as a probe of 4D quantum Hall physics. Nature 553(7686):59–62. https://doi.org/10.1038/nature25011CrossRefPubMed

Titel: Neural computing in four spatial dimensions
verfasst von: Arturo Tozzi
Muhammad Zubair Ahmad
James F. Peters
Publikationsdatum: 18.05.2020
Verlag: Springer Netherlands
Erschienen in: Cognitive Neurodynamics / Ausgabe 2/2021
Print ISSN: 1871-4080
Elektronische ISSN: 1871-4099
DOI: https://doi.org/10.1007/s11571-020-09598-2

Neuer Inhalt

Bildnachweise

VDI-Icon, Profil Icon, inhalt2, Springer Professional Modul/© Springer Fachmedien Wiesbaden GmbH, Nachhaltigkeitsaward Key Visual/© Cometis AG/Global ESG Monitor | Daniel Rupp | Generiert mit KI, Search Icon, Banner Hanser, Kryptowährungen/© gopixa / Getty Images / iStock, MG4 aus China auf dem Prüfstand im ADAC-Technik-Zentrum in Landsberg am Lech/© ADAC e.V., Chassis eines Elektrofahrzeugs/© chesky / stock.adobe.com, Zeitschrift Wissensmanagement Cover, PatentFit-Logo/© Springer Fachmedien Wiesbaden GmbH, Sustainibility Finance/© Robert Kneschke / stock.adobe.com / Springer Fachmedien Wiesbaden GmbH, Zukunftswerkstatt Sales Excellence 2024/© AndreyPopov / Getty Images / iStock, 2023_Antrieb/© supervisuell

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Weitere Artikel der Ausgabe 2/2021

Complex bifurcation analysis and synchronization optimal control for Hindmarsh–Rose neuron model under magnetic flow effect

Application of expert system and LSTM in extracting index of synaptic plasticity

Role of joint language control during cross-language communication: evidence from cross-frequency coupling

Synaptic dendritic activity modulates the single synaptic event

Major depressive disorder diagnosis based on effective connectivity in EEG signals: a convolutional neural network and long short-term memory approach

A dynamic center and multi threshold point based stable feature extraction network for driver fatigue detection utilizing EEG signals

Neuer Inhalt

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.