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Cortex: Statistics and Geometry of Neuronal Connectivity
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“This is because the high levels of recurrent connectivity in the source area (Braitenberg and Schüz 1998; Markov et al. 2011) can lead to labeled axon terminals in the vicinity of the retrogradely labeled cells that can be mistaken for long-distance anterograde labeling from the injected target area.”
From A Weighted and Directed Interareal Connectivity Matrix for Macaque Cerebral Cortex (2014) · cites this paper as Braitenberg and Schüz 1998
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Negrello, M., Raikov, I., & Schutter, E. D. (2011) · BMC Neuroscience · doi:10.1186/1471-2202-12-s1-p59 · Cited by 2
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Moca, V. V., Nikolić, D., & Muresan, R. C. (2008) · Lecture notes in computer science · doi:10.1007/978-3-540-87559-8_51 · Cited by 2
“1 Introduction The activity of cortical neurons arises from complex firing patterns that are determined by the intricate brain architecture, the external stimuli and the interaction with subcortical structures [1].”
BackgroundLatency Reduction during Telemetry Transmission in Brain-Machine Interfaces
Oweiss, K. G. (2005) · doi:10.1109/iembs.2005.1616867 · Cited by 2
“synapses (assuming 8,000 synapse/neuron) may exist in a cubic millimeter of cortex tissue [ 2 ].”
BackgroundDoes Soft Computing Classify Research in Spiking Neural Networks?
Maguire, L. (2010) · International Journal of Computational Intelligence Systems · doi:10.2991/ijcis.2010.3.2.5 · Cited by 2
Computational Complexity and the Function-Structure-Environment Loop of the Brain
Juba, B. (2016) · Elsevier eBooks · doi:10.1016/b978-0-12-802452-2.00010-x · Cited by 2
“Indeed, the observed pattern of connectivity of the cortex, which aided Brodmann’s division of the cortex into regions, lends some weak support to such a view. Strikingly, genetics per se appears not to be the primary factor determining the function of the cortex. Sur et al. (1988) determined that the auditory regions…”
BackgroundInfluentialCloverleaf Clusters: A Common Macrostructural Organization across Human Visual and Auditory Cortex
Brewer, A. A., & Barton, B. (2018) · InTech eBooks · doi:10.5772/intechopen.77964 · Cited by 2
“Since the axons contained within one cubic millimeter of cortex can extend 3–4 km in length, efficient connectivity is vital for sustainable energetics in cortex [18].”
BackgroundEmbodied working memory during ongoing input streams
Berberian, N., Ross, M., & Chartier, S. (2021) · PLoS ONE · doi:10.1371/journal.pone.0244822 · Cited by 2
The Pathology of Synapses in Brain Networks Implicated in Depression
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Financial Decision Making Within Thermodynamic Principles
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Ranft, J., & Lindner, B. (2023) · Physical review. E · doi:10.1103/physreve.107.044306 · Cited by 4
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Moreno, Y. (2009) · Springer eBooks · doi:10.1007/978-0-387-93797-7_12 · Cited by 2
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Reichl, L. (2010) · doi:10.53846/goediss-2930 · Cited by 2
Positive youth development and age‐related changes in cortical thickness during adolescence
Paus, T., Leonard, G. T., Lerner, J. V., Lerner, R. M., Perron, M., Pike, G. B., Richer, L., Toro, R., Veillette, S., & Pausová, Z. (2011) · doi:10.1002/9781118092699.ch4 · Cited by 2
Halliday, D. M. (2001) · Lecture notes in computer science · doi:10.1007/3-540-44597-8_21 · Cited by 2
“The present simulations are designed to model accurately the large degree of convergence in central and peripheral mammalian neural systems [28, 29].”
MethodTHE EPIC OF PERSONAL DEVELOPMENT AND THE MYSTERY OF SMALL WORKING MEMORY
Glassman, R. B. (2005) · Zygon® · doi:10.1111/j.1467-9744.2005.00648.x · Cited by 2
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Dzakpasu, R., Patel, K., Robinson, N., et al. (2006) · Chaos An Interdisciplinary Journal of Nonlinear Science · doi:10.1063/1.2401130 · Cited by 2
Neef, A., Hady, A. E., Nagpal, J. K., Bröking, K., Afshar, G., Schlüter, O. M., Geisel, T., Bamberg, E., Fleischmann, R., Stühmer, W., et al. (2013) · arXiv (Cornell University) · doi:10.48550/arxiv.1305.7125 · Cited by 3
Borza, P. N., & Pau, L. F. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1609.07642 · Cited by 2
“The maps of these zones have already been identified [12].”
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Faisal, A. A., & Neishabouri, A. (2016) · Wiley eBooks · doi:10.1002/9781118316757.ch7 · Cited by 2
Spiegler, A., Hansen, E. C. A., Bernard, C., et al. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1602.07311 · Cited by 2
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Liou, J.-Y., Smith, E. H., Bateman, L. M., Bruce, S. L., McKhann, G. M., Goodman, R. R., Emerson, R. G., Schevon, C. A., & Abbott, L. F. (2019) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/724088 · Cited by 2
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Winnubst, J., Bas, E., Ferreira, T., et al. (2019) · SSRN Electronic Journal · doi:10.2139/ssrn.3330557 · Cited by 2
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Leugering, J., Nieters, P., & Pipa, G. (2019) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/690792 · Cited by 2
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Harrach, M. A., Yochum, M., & Wendling, F. (2025) · SoftwareX · doi:10.1016/j.softx.2025.102108 · Cited by 2
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Amroune, K., Fontolan, L., Baude, A., Robbe, D., & Bureau, I. (2025) · eLife · doi:10.7554/elife.106621 · Cited by 2
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Çürüklü, B. (2005) · Cited by 2
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Wang, T., Shi, P., Luo, D., Guo, J. Q., Liu, H., Yuan, J., Jin, H., Wu, X., Zhang, Y., Xiong, Z., et al. (2023) · Brain Sciences · doi:10.3390/brainsci13050711 · Cited by 2
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“In addition, diameters of intracortical axons and dendrites also do not systematically change with brain size (Braitenberg and Schüz 1998; Karbowski 2014).”
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Wong, H. H., Watt, A. J., & Sjöström, P. J. (2025) · Nature Protocols · doi:10.1038/s41596-024-01125-5 · Cited by 1
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“Neurons whose respective dendrites share a given locus are likely to share common afferent inputs (Braitenberg and Schüz 1998; Packer et al. 2013; Peters and Feldman 1976; Wen et al. 2009 ).”
Critical scaling of novelty in the cortex
Ribeiro, T. L., Vakili, A., Gifford, B., Siddiqui, R., Sinfuego, V., Pajevic, S., & Plenz, D. (2026) · Nature Communications · doi:10.1038/s41467-025-68277-0 · Cited by 3
“Second, the sparse synaptic connectivity between L2/3 pyramidal neurons — estimated at only 5 – 8% locally and diminishing sharply within 200 µ m 19 – 23 — further restricts the transmission of novel spikes 24 .”
Tomasello, R., Rezaki, A. D., Carriere, M., Fekonja, L. S., & Friedemann Pulvermüller, A. (2026) · Frontiers in Human Neuroscience · doi:10.3389/fnhum.2026.1854823 · Cited by 1
“…et al., 2017; Jackson et al., 2021; Ueno et al., 2011), yet they often relied on biologically implausible learning mechanisms (backpropagation, Braitenberg and Schüz, 1998; Mazzoni et al., 1991; Raugel et al., 2026; Reilly, 1999) or did not incorporate the range of multimodal hub regions…”
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“For a general discussion of the geometry of the neuronal connectivity we refer the reader to [1].”
BackgroundNoisy Dendrites: Models of Dendritic Integration In Vivo
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“About 85% of cortical neurons are excitatory, and the rest are inhibitory (Braitenberg & Schüz, 1998).”
BackgroundAllocortical ECoG Images Formed by Learning
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“For cortical neurons the number of synaptic contacts n is very large, typically in the range n ∼ 10 3 − 10 4 [43].”
BackgroundMattie, D., Fang, Z., Takahashi, E., Peña‐Castillo, L., & Levman, J. E. D. (2024) · Information · doi:10.3390/info15010066 · Cited by 1
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“However, in the perspective of the size of the cerebral cortex, which contains between 10 to 100 million neurons (Braitenberg and Schüz, 2013), it is still relatively small.”
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“T o further simplify the model, we assume random intracorticalconnectivity,leadingto N ib = N eb forall b (Braitenberg and Schüz, 1998).”
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BackgroundIntegrating Time-Space and Orientation. A Case Study on fMRI + DTI Brain Data
Kasabov, N. K. (2018) · Springer series on bio- and neurosystems · doi:10.1007/978-3-662-57715-8_11 · Cited by 1
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(2014) · Frontiers research topics · doi:10.3389/978-2-88919-288-5 · Cited by 1
Wavelet Approach to the Study of Rhythmic Neuronal Activity
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Friedemann Pulvermüller, A. (2023) · The Project Repository Journal · doi:10.54050/prj1820736
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Chakrabartty, S., Gore, A., & Oweiss, K. G. (2006) · doi:10.1109/iembs.2006.259512 · Cited by 1
“Next generation of prosthesis will host even larger number of electrodes and recording channels considering that approximately 30,000 neurons and 2.4x10 8 synapses (assuming 8,000 synapses/neuron) may exist in a cubic millimeter of cortex tissue [2].”
BackgroundSpike and Burst Synchronization in a Detailed Cortical Network Model with I-F Neurons
Çürüklü, B., & Lansner, A. (2001) · Lecture notes in computer science · doi:10.1007/3-540-44668-0_152 · Cited by 1
“This resulted in a very spread connection probability of 15-80% for neuron pairs, and led to a connectivity of 50-60% between neurons inside a minicolumn [ 8 ].”
BackgroundInfluentialStructure and plasticity potential of neural networks in the cerebral cortex
Fares, T. (2010) · Digital Repository Service (Northeastern University) · doi:10.17760/d20000285 · Cited by 1
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“On the basis of several neuroanatomical studies (see for instance [1]) these quantities have been estimated by counting synapses, and their numerical values is given in table 1.”
BackgroundOn the Computational Power of Neural Microcircuit Models: Pointers to the Literature
Maass, W. (2002) · Lecture notes in computer science · doi:10.1007/3-540-46084-5_42 · Cited by 1
“Biological neural microcircuits are highly recurrent and consist of heterogeneous types of neurons and synapses, which are each endowed with an individual complex dynamics [4], [6], [3], [7], [8], [23], [20].”
BackgroundPsychology of Science/Theology of Science: Reaching Out or Narrowing?
Glassman, R. B. (2007) · Zygon® · doi:10.1111/j.1467-9744.2007.00858.x · Cited by 1
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Odinaev, K., Raichelgauz, I., & Zeevi, Y. Y. (2006) · International Joint Conference on Neural Networks (IJCNN) · doi:10.1109/ijcnn.2006.246693 · Cited by 1
“Liquid-currents from presented inputs to cliques are the dynamic realizations by means of the neural ensembles.”
BackgroundMethodMaimon, M., & Manevitz, L. M. (2007) · Journal of Combinatorial Optimization · doi:10.1007/s10878-007-9103-3 · Cited by 1
Connectivity in real and evolved associative memories
Adams, R., Calcraft, L., & Davey, N. (2006) · University of Hertfordshire Research Archive (University of Hertfordshire) · Cited by 1
Review Neuron-glia metabolic coupling and plasticity
Magistretti, P. J. (2006) · Cited by 1
Roger, R. D., & Whittington, M. A. (2010) · Oxford University Press eBooks · doi:10.1093/acprof:oso/9780195342796.003.0012 · Cited by 1
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Bullmann, T., Radivojević, M., Huber, S., Deligkaris, K., Hierlemann, A. R., & Frey, U. (2017) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/139436 · Cited by 1
“…to their typical waveform [47] and this information could be used for the subsequent reconstruction of their connectivity according to an extension of “Peter’s rule” [46][8]: the probability of two neurons being connected is proportional to the overlap of their axonal and dendritic fields [50].”
MethodSimulating semantic dementia in a brain-constrained model of action and object words learningPreprint
Efremov, A., Kuptsova, A., Wennekers, T., Юрьевич, Ш. Ю., Gutkin, B. S., & Garagnani, M. (2022) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2022.03.03.482066 · Cited by 1
“…between-and within-area connections, with the probability of the existence of a synaptic link between two cells falling off with their distance (29, 30) (see Appendix (Detailed Model Implementation) for specifications); 3) local lateral inhibition (Fig.2) and area-specific global regulation…”
BackgroundRolls, E. T. (2023) · doi:10.1093/oso/9780198887911.005.0002 · Cited by 1
Biomimetic model of corticostriatal micro-assemblies discovers new neural codePreprint
Pathak, A., Brincat, S. L., Organtzidis, H., Strey, H. H., Senneff, S., Antzoulatos, E. G., Mujica-Parodi, L. R., Miller, E. K., & Granger, R. (2023) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2023.11.06.565902 · Cited by 1
“Yet, while these can accurately simulate brain-wide phenomena (7) such as epileptic seizure genesis and propagation (8, 9), they are not designed to generate cognitive processes, such as learning.”
BackgroundThalamic Influence Over Adaptive Cortical Dynamics Across Conscious StatesPreprint
Müller, E. J., Munn, B., Baracchini, G., Fulcher, B., Medel, V., Redinbaugh, M. J., Saalmann, Y. B., Brunton, B. W., Brunton, S. L., & Shine, J. M. (2024) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2024.07.02.601788 · Cited by 1
A universal dynamic routing architecture governs the flow of human cortical activityPreprint
Vinao-Carl, M., Peach, R. L., Gosztolai, A., David, M., Mallas, E., Kurtin, D. L., Alania, K., Jaramillo, V., Violante, I. R., Sharp, D. J., et al. (2025) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2025.09.05.674413 · Cited by 1
Sommer, M. (2014) · KTH Publication Database DiVA (KTH Royal Institute of Technology) · Cited by 1
The role of hypoxia in neuroinflammatory disease
Desai, R. (2013) · UCL Discovery (University College London) · Cited by 1
Chauvière, L. (2010) · theses.fr (ABES) · doi:10.70675/2a39bc21zed63z4f59z9650zbd80d49c1e37 · Cited by 1
Cayol, Z. (2021) · theses.fr (ABES) · doi:10.70675/9065d90dz0542z42d3zbf7ezc3297a27ff6f · Cited by 1
Attention reshapes the information dynamics of thalamic and cortical prediction-error learningPreprint
Äijälä, J., Jensen, M. A., Miller, K. J., Hermes, D., Blenkmann, A. O., Ince, R. A. A., Bekinschtein, T. A., Vinck, M. A., Garagnani, M., & Canales‐Johnson, A. (2026) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.64898/2026.07.10.737794 · Cited by 1
“…values; 4) Local lateral inhibition 80,81 and area-specific global regulation mechanisms (referred to as local and global inhibition, respectively) 77,81,82 ; 5) Single cells’ neurophysiological dynamics, including sigmoid transformation of membrane potentials into neuronal outputs, as well as…”
InfluentialAn Energy Budget for Signaling in the Grey Matter of the Brain
Attwell, D., & Laughlin, S. B. (2001) · Journal of Cerebral Blood Flow & Metabolism · doi:10.1097/00004647-200110000-00001 · Cited by 3,543
Metadata
- Authors
- Braitenberg, V., & Schüz, A.
- Affiliations
- Max Planck Society (DE)
- Venue
- Springer eBooks
- Publisher
- Springer Berlin Heidelberg
- Published
- 1998
- OpenAlex
- W1603661052
- Cited by
- 1,178
- References
- 0
- Citations by year
- 2026: 14 · 2025: 30 · 2024: 38 · 2023: 62 · 2022: 38 · 2021: 54 · 2020: 34 · 2019: 57 · 2018: 49 · 2017: 44 · 2016: 42 · 2015: 57 · 2014: 53 · 2013: 51 · 2012: 64
- FWCI
- 4.64
- Type
- book
- Language
- en
- Open access
- closed
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Springer eBooks (publishedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion)
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Functional Brain Connectivity Studies
- Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
- Health Sciences › Medicine › Radiology, Nuclear Medicine and Imaging › Advanced Neuroimaging Techniques and Applications
- Keywords
- cerebral cortex, neuronal connectivity, cortical networks, mouse cortex, cortical geometry, corticocortical connections
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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