Biblio infotopo

Bibliographical references for information topology: 

[1] Cathelineau, J. Sur l’homologie de sl2 a coefficients dans l’action adjointe, Math. Scand., 63, 51-86, 1988. PDF

[2] Kontsevitch, M. The 1+1/2 logarithm. Unpublished note, Reproduced in Elbaz-Vincent & Gangl, 2002, 1995 PDF

[3] Elbaz-Vincent, P., Gangl, H. On poly(ana)logs I., Compositio Mathematica, 130(2), 161-214. 2002. PDF

[4] Connes, A., Consani, C., Characteristic 1, entropy and the absolute point. preprint arXiv:0911.3537v1. 2009. PDF

[5] Marcolli, M. & Thorngren, R. Thermodynamic Semirings, arXiv 10.4171 / JNCG/159, Vol. abs/1108.2874, 2011. PDF

[6] Abramsky, S., Brandenburger, A.. The Sheaf-theoretic structure of non-locality and contextuality, New Journal of Physics, 13 (2011). PDF

[7] Marcolli, M. & Tedeschi, R. Entropy algebras and Birkhoff factorization, arXiv, Vol. abs/1108.2874, 2014. PDF

[8] Baez, J.; Fritz, T. & Leinster, T. A Characterization of Entropy in Terms of Information Loss Entropy, 13, 1945-1957, 2011. PDF

[9] Baez J. C.; Fritz, T. A Bayesian characterization of relative entropy. Theory and Applications of Categories, Vol. 29, No. 16, p. 422-456. 2014. PDF

[10] Baudot P., Bennequin D. The homological nature of entropy. Entropy, 17, 1-66; 2015. PDF

[11] Gromov, M. Symmetry, probability, entropy. Entropy 2015. PDF

[12] Elbaz-Vincent, P., Gangl, H., Finite polylogarithms, their multiple analogues and the Shannon entropy. (2015) Vol. 9389 Lecture Notes in Computer Science. 277-285, Archiv. PDF

[13] M. Marcolli, Information algebras and their applications. International Conference on Geometric Science of Information (2015), 271-276 PDF

[14] T. Leinster, Entropy modulo a prime, (2019) arXiv:1903.06961 PDF

[15] T. Leinster, E. Roff, The maximum entropy of a metric space, (2019) arXiv:1908.11184  PDF

[16] T.  Maniero, Homological Tools for the Quantum Mechanic. arXiv 2019, arXiv:1901.02011. PDF

[17] M. Marcolli, Motivic information, Bollettino dell'Unione Matematica Italiana (2019) 12 (1-2), 19-41 PDF

[18] J.P. Vigneaux, Information theory with finite vector spaces, in IEEE Transactions on Information Theory, vol. 65, no. 9, pp. 5674-5687, Sept. (2019) PDF

[19] Baudot P., Tapia M., Bennequin, D. , Goaillard J.M., Topological Information Data Analysis. (2019), Entropy, 21(9), 869 PDF

[20] Baudot P., The Poincaré-Shannon Machine: Statistical Physics and Machine Learning aspects of Information Cohomology. (2019), Entropy , 21(9), PDF

[21] G. Sergeant-Perthuis, Bayesian/Graphoid intersection property for factorisation models, (2019),  arXiv:1903.06026 PDF

[22] J.P. Vigneaux, Topology of Statistical Systems: A Cohomological Approach to Information Theory, PhD Thesis (2019). PDF

[23] Y.  Manin, M. Marcolli Homotopy Theoretic and Categorical Models of Neural Information Networks. arXiv (2020) preprint arXiv:2006.15136 PDF

[24] D. Bennequin. G. Sergeant-Perthuis, O. Peltre, and J.P. Vigneaux, Extra-fine sheaves and interaction decompositions,  (2020) arXiv:2009.12646 PDF

[25] J.P. Vigneaux, Information structures and their cohomology, in Theory and Applications of Categories, Vol. 35, (2020), No. 38, pp 1476-1529. PDF

[26] O. Peltre, Message-Passing Algorithms and Homology, PhD Thesis (2020),      arXiv:2009.11631 PDF

[27] G. Sergeant-Perthuis, Interaction decomposition for presheafs, (2020) arXiv:2008.09029 PDF

[28]  Baudot P., On Information links. Lecture Notes in Computer Science Springer, 2021 PDF

[29] Lang L., Baudot P., Quax R., Forré P., Information Decomposition Diagrams Applied beyond Shannon Entropy: A Generalization of Hu's Theorem. arXiv:2202.09393. 2022 . PDF

[30] Belfiore JC., Bennequin D. Topos and Stacks of Deep Neural Networks. 2022. arXiv:2106.14587 PDF

[31] Mainiero, T., Higher Information from Families of Measures. Springer (in press) GSI 2023 Proc. PDF

[32] Hamilton G, Leditzky F.,  Probing multipartite entanglement through persistent homology  arXiv:2307.07492  2023 PDF

[33] Dubé H., on the structure of information cohomology. PhD thesis 2023 PDF 

Related important mathematical works on information, probability, topology and geometry (recommended to read):

[1] Cencov, N.N. Statistical Decision Rules and Optimal Inference. Translations of Mathematical Monographs. 1982. PDF

[2] Ay, N. and Jost, J. and Lê, H.V. and Schwachhöfer, L. Information geometry and sufficient statistics. Probability Theory and Related Fields 2015 PDF

[3] Tomasic, I., Independence, measure and pseudofinite fields. Selecta Mathematica, 12 271-306. Archiv. 2006. PDF

[4] Gromov, M. In a Search for a Structure, Part 1: On Entropy, unpublished manuscript, 2013. PDF

[5] McMullen, C.T., Entropy and the clique polynomial, 2013. PDF

[6] Drummond-Cole, G.-C., Park., J.-S., Terrila, J., Homotopy probability theory I. J. Homotopy Relat. Struct. November 2013. PDF

[7] Drummond-Cole, G.-C., Park., J.-S., Terrila, J., Homotopy probability theory II. J. Homotopy Relat. Struct. April 2014. PDF

[8] Burgos Gil J.I., Philippon P., Sombra M., Arithmetic geometry of toric varieties. Metrics, measures and heights, Astérisque 360. 2014 . PDF

[9] Gromov, M. Morse Spectra, Homology Measures, Spaces of Cycles and Parametric Packing Problems, april 2015. PDF

[10] Park., J.-S., Homotopy theory of probability spaces I: classical independence and homotopy Lie algebras. Archiv . 2015 

[11] M. Nguiffo Boyom, Foliations-Webs-Hessian Geometry-Information Geometry-Entropy and Cohomology. Entropy 18(12): 433 (2016) PDF

[12] M. Nguiffo Boyom, A. Zeglaoui, Amari Functors and Dynamics in Gauge Structures. GSI 2017: 170-178 PDF

[13] G.-C. Drummond-Cole, Terila, Homotopy probability theory on a Riemannian manifold and the Euler equation, New York Journal of Mathematics, Volume 23 (2017) 1065-1085. PDF

[14] P. Forré,, JM. Mooij. Constraint-based Causal Discovery for Non-Linear Structural Causal Models with Cycles and Latent Confounders. In A. Globerson, & R. Silva (Eds.) (2018), pp. 269-278) PDF

[15] T. Fritz and P. Perrone, Bimonoidal Structure of Probability Monads. Proceedings of MFPS 34, ENTCS, (2018). PDF

[16] Jae-Suk Park, Homotopical Computations in Quantum Fields Theory, (2018) arXiv:1810.09100 PDF

[17] G.C. Drummond-Cole,  An operadic approach to operator-valued free cumulants. Higher Structures (2018) 2, 42–56.PDF

[18] G.C. Drummond-Cole, A non-crossing word cooperad for free homotopy probability theory. MATRIX Book (2018) Series 1, 77–99. PDF

[19] T. Fritz and P. Perrone, A Probability Monad as the Colimit of Spaces of Finite Samples, Theory and Applications of Categories 34, 2019. PDF.

[20] M. Esfahanian, A new quantum probability theory, quantum information functor and quantum gravity. (2019) PDF

[22] T. Leinster  The categorical origins of Lebesgue integration (2020) arXiv:2011.00412 PDF   

[23] T. Fritz, T. Gonda, P. Perrone, E. Fjeldgren Rischel, Representable Markov Categories and Comparison of Statistical Experiments in Categorical Probability. (2020) arXiv:2010.07416  PDF

[24] T. Fritz, E. Fjeldgren Rischel,  Infinite products and zero-one laws in categorical probability (2020) arXiv:1912.02769 PDF

[25] T. Fritz, A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics (2020) arXiv:1908.07021 PDF

[26] T. Fritz and P. Perrone, Stochastic Order on Metric Spaces and the Ordered Kantorovich Monad, Advances in Mathematics 366, 2020. PDF

[27] T. Fritz and P. Perrone, Monads, partial evaluations, and rewriting. Proceedings of MFPS 36, ENTCS, 2020. PDF.

[28] K. Hess, Topological adventures in neuroscience, in the Proceedings of the 2018 Abel Symposium: Topological Data Analysis, Springer Verlag, (2020). PDF

[29] C. Curto, N. Youngs. Neural ring homomorphisms and maps between neural codes. Submitted. arXiv.org preprint. PDF

[30] N.C. Combe, Y, Manin, F-manifolds and geometry of information, arXiv:2004.08808v.2, (2020) Bull. London MS. PDF

Topological applications to neuroscience and machine learning (by teams):

Carina Curto, Nora Youngs and Vladimir Itskov and colleagues:

  [1] C. Curto, N. Youngs. Neural ring homomorphisms and maps between  neural codes. Submitted. arXiv.org preprint.

 [2] C. Curto, J. Geneson, K. Morrison. Fixed points of competitive  threshold-linear networks. Neural Computation, in press, 2019.  arXiv.org preprint.

 [3] C. Curto, A. Veliz-Cuba, N. Youngs. Analysis of combinatorial  neural codes: an algebraic approach. Book chapter in Algebraic and  Combinatorial computational Biology. R. Robeva, M. Macaulay (Eds), 2018.

 [4] C. Curto, V. Itskov. Combinatorial neural codes. Handbook of  Discrete and Combinatorial Mathematics, Second Edition, edited by  Kenneth H. Rosen, CRC Press, 2018. pdf [5] C. Curto, E. Gross, J.  Jeffries, K. Morrison, M. Omar, Z. Rosen, A. Shiu, N. Youngs. What 

 makes a neural code convex? SIAM J. Appl. Algebra Geometry, vol. 1, pp. 222-238, 2017. pdf, SIAGA link, and  arXiv.org preprint 

[6] C. Curto. What can topology tells us about the  neural code? Bulletin of the AMS, vol. 54, no. 1, pp. 63-78, 2017. pdf, Bulletin  link.

 [7] C. Curto, K. Morrison. Pattern completion in symmetric  threshold-linear networks. Neural Computation, Vol 28, pp. 2825-2852,  2016. pdf, arXiv.org preprint.

 [8] C. Giusti, E. Pastalkova, C. Curto, V. Itskov. Clique topology  reveals intrinsic geometric structure in neural correlations. PNAS,  vol. 112, no. 44, pp. 3455-13460, 2015. pdf, PNAS link.

 [9] C. Curto, A. Degeratu, V. Itskov. Encoding binary neural codes in  networks of threshold-linear neurons. Neural Computation, Vol 25, pp.  2858-2903, 2013. pdf, arXiv.org preprint.

 [10] K. Morrison, C. Curto. Predicting neural network dynamics via  graphical analysis. Book chapter in Algebraic and Combinatorial  Computational Biology. R. Robeva, M. Macaulay (Eds), 2018. arXiv.org 

 preprint, [11] C. Curto, V. Itskov, A. Veliz-Cuba, N. Youngs. The neural ring: an algebraic tool for analyzing the intrinsic structure of neural  codes. Bulletin of Mathematical Biology, Volume 75, Issue 9, pp. 1571-1611, 2013. arXiv.org preprint.

 [12] C. Curto, V. Itskov, K. Morrison, Z. Roth, J.L. Walker.  Combinatorial neural codes from a mathematical coding theory  perspective. Neural Computation, Vol 25(7):1891-1925, 2013. arXiv.org  preprint.

 [13] C. Curto, A. Degeratu, V. Itskov. Flexible memory networks.  Bulletin of Mathematical Biology, Vol 74(3):590-614, 2012. arXiv.org  preprint.

 [14] V. Itskov, C. Curto, E. Pastalkova, G. Buzsaki. Cell assembly  sequences arising from spike threshold adaptation keep track of time  in the hippocampus. Journal of Neuroscience, Vol. 31(8):2828-2834, 2011.

 [15] K.D. Harris, P. Bartho, et al.. How do neurons work together?  Lessons from auditory cortex. Hearing Research, Vol. 271(1-2), 2011,  pp. 37-53.

 [16] P. Bartho, C. Curto, A. Luczak, S. Marguet, K.D. Harris. Population coding of tone stimuli in auditory cortex: dynamic rate  vector analysis. European Journal of Neuroscience, Vol. 30(9), 2009,  pp. 1767-1778.

 [17] C. Curto, V. Itskov. Cell groups reveal structure of stimulus  space. PLoS Computational Biology, Vol. 4(10): e1000205, 2008.

 [18] E. Gross , N. K. Obatake , N. Youngs, Neural ideals and stimulus  space visualization, Adv. Appl.Math., 95 (2018), pp. 65–95.

 [19] C. Giusti, V. Itskov. A no-go theorem for one-layer feedforward  networks. Neural Computation, 26 (11):2527-2540, 2014.

 [20] V. Itskov, L.F. Abbott. Capacity of a Perceptron for Sparse  Discrimination . Phys. Rev. Lett. 101(1), 2008.

 [21] V. Itskov, E. Pastalkova, K. Mizuseki, G. Buzsaki, K.D. Harris.  Theta-mediated dynamics of spatial information in hippocampus. 

 Journal of Neuroscience, 28(23), 2008.

 [22] V. Itskov, C. Curto, K.D. Harris. Valuations for spike train  prediction. Neural Computation, 20(3), 644-667, 2008.

 [23] E. Pastalkova, V. Itskov , A. Amarasingham , G. Buzsaki.  Internally Generated Cell Assembly Sequences in the Rat Hippocampus. 

 Science 321(5894):1322 - 1327, 2008.

 [24] V. Itskov, A. Kunin, Z. Rosen. Hyperplane neural codes and the  polar complex. To appear in the Abel Symposia proceedings, Vol. 15,  2019.

 Alexander Ruys de Perez and colleagues:

 [25] A. Ruys de Perez, L.F. Matusevich, A. Shiu, Neural codes and the  factor complex, Advances in Applied Mathematics 114 (2020).

 Sunghyon Kyeong and colleagues:

 [26] Sunghyon Kyeong, Seonjeong Park, Keun-Ah Cheon, Jae-Jin Kim,  Dong-Ho Song, and Eunjoo Kim, A New Approach to Investigate the 

 Association between Brain Functional Connectivity and Disease  Characteristics of Attention-Deficit/Hyperactivity Disorder:  Topological Neuroimaging Data Analysis, PLOS ONE, 10 (9): e0137296,  DOI: 10.1371/journal.pone.0137296 (2015)

 Jonathan Pillow and colleagues:

 [27] Aoi MC & Pillow JW (2017). Scalable Bayesian inference for  high-dimensional neural receptive fields. bioRxiv 212217; doi: https://doi.org/10.1101/212217

 [28] Aoi MC, Mante V, & Pillow JW. (2020). Prefrontal cortex exhibits  multi-dimensional dynamic encoding during decision-making. Nat Neurosci.

 [29] Calhoun AJ, Pillow JW, & Murthy M. (2019). Unsupervised  identification of the internal states that shape natural behavior. Nature Neuroscience 22:2040-20149.

 [30] Dong X, Thanou D, Toni L, et al., 2020, Graph Signal Processing  for Machine Learning: A Review and New Perspectives, Ieee Signal  Processing Magazine, Vol:37, ISSN:1053-5888, Pages:117-127

 Michael Bronstein, Federico Monti, Giorgos Bouritsas and colleagues:

 [31] G. Bouritsas, F. Frasca, S Zafeiriou, MM Bronstein, Improving  graph neural network expressivity via subgraph isomorphism counting.  arXiv (2020) preprint arXiv:2006.09252 

[32] M. Bronstein , G.  Pennycook, L. Buonomano, T.D. Cannon, Belief in fake news,  responsiveness to cognitive conflict, and analytic reasoning  engagement, Thinking and Reasoning (2020), ISSN: 1354-6783 

[33] X.  Dong, D. Thanou, L. Toni, M. Bronstein, P. Frossard, Graph Signal  Processing for Machine Learning: A Review and New Perspectives, IEEE 

 Signal Processing Magazine (2020), Vol: 37, Pages: 117-127, ISSN: 1053-5888

[34] Y. Wang, Y. Sun, Z. Liu, S.E. Sarma, M. Bronstein, J.M. Solomon, Dynamic Graph CNN for Learning on Point Clouds, ACM Transactions on 

 graphics (2020), Vol: 38, ISSN: 0730-0301 

[35] M. Bronstein, J. Everaert, A. Castro, J. Joormann,  T. D. Cannon, Pathways to paranoia: Analytic thinking and belief flexibility., Behav Res Ther (2019), Vol: 113, Pages: 18-24 

[36] G.  Bouritsas, S. Bokhnyak, S. Ploumpis, M. Bronstein, S. Zafeiriou, Neural 3D Morphable Models: Spiral Convolutional Networks 

 for 3D Shape Representation Learning and Generation, (2019) IEEE/CVF  ICCV 2019, 7212 

[37] O. Litany, A. Bronstein, M. Bronstein, A. Makadia et al., Deformable Shape Completion with Graph Convolutional  Autoencoders (2018), Pages: 1886-1895, ISSN: 1063-6919 

[38] R. Levie,  F. Monti, X. Bresson X, M. Bronstein, CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters, IEEE Transactions on Signal Processing (2018), Vol: 67, Pages: 97-109, ISSN: 1053-587X

 [39] F. Monti, K. Otness, M. Bronstein,  Motifnet: a motif-based  graph convolutional network for directed graphs (2018), Pages:  225-228 

[40] F. Monti, M. Bronstein, X. Bresson, Geometric matrix  completion with recurrent multi-graph neural networks, Neural  Information Processing Systems (2017), Pages: 3700-3710, ISSN:  1049-5258 

[41] F. Monti F, D. Boscaini, J. Masci, E. Rodola, J. Svoboda, M. Bronstein, Geometric deep learning on graphs and manifolds using  mixture model CNNs, (2017) IEEE Conference on Computer Vision and  Pattern Recognition, p: 3-3 [42] M. Bronstein, J. Bruna, Y. LeCun, A.  Szlam, P. Vandergheynst et al., Geometric Deep Learning Going beyond  Euclidean data, IEEE Signal Processing Magazine (2017), Vol: 34,  Pages: 18-42, ISSN: 1053-5888

 Kathryn Hess  and colleagues:

 [43] L. Kanari, H. Dictus, W. Van Geit, A. Chalimourda, B. Coste, J.  Shillcock, K. Hess, and H. Markram, Computational synthesis of 

 cortical dendritic morphologies, bioRvix (2020)  10.1101/2020.04.15.040410, submitted.

 [44] G. Tauzin, U. Lupo, L. Tunstall, J. Burella Prez, M. Caorsi, A.  Medina-Mardones, A, Dassatti, and K. Hess, giotto-tda: a topological 

 data analysis toolkit for machine learning and data exploration,  arXiv:2004.02551

 [45] E. Mullier, J. Vohryzek, A. Griffa, Y. Alemàn-Gómez, C. Hacker,  K. Hess, and P. Hagmann, Functional brain dynamics are shaped by  connectome n-simplicial organization, (2020) submitted.

 [46] M. Fournier, M. Scolamiero, etal., Topology predicts long-term functional outcome in early psychosis, Molecular Psychiatry (2020). https://doi.org/10.1038/s41380-020-0826-1.

 [47] K. Hess, Topological adventures in neuroscience, in the Proceedings of the 2018 Abel Symposium: Topological Data Analysis, Springer Verlag, (2020).

 [48] A. Doerig, A. Schurger, K. Hess, and M. H. Herzog, The unfolding  argument: why IIT and other causal structure theories of  consciousness are  empirically untestable, Consciousness and Cognition  72 (2019) 49-59.

 [49] L. Kanari, S. Ramaswamy, et al., Objective classification of  neocortical pyramidal cells, Cerebral Cortex (2019) bhy339, https://doi.org/10.1093/cercor/bhy339.

 [50] J.-B. Bardin, G. Spreemann, K. Hess, Topological exploration of  artificial neuronal network dynamics, Network Neuroscience (2019) https://doi.org/10.1162/netn_a_00080.

 [51] L. Kanari, P. Dłotko, M. Scolamiero, R. Levi, J. C. Shillcock, K. Hess, and H. Markram, A topological representation of branching  morphologies, Neuroinformatics (2017) doi: 10.1007/s12021-017-9341-1.

 [52] M. W. Reimann, M. Nolte,et al., Cliques of neurons bound into  cavities provide a missing link between structure and function,  Front. Comput. Neurosci., 12 June (2017), doi: 10.3389/fncom.2017.00048.

 Mathilde Marcoli, Yuri Manin, and colleagues:

[53] Y. Manin, M. Marcolli Homotopy Theoretic and Categorical Models  of Neural Information Networks. arXiv (2020) preprint  arXiv:2006.15136 [54] M. Marcolli, Lumen Naturae: Visions of the  Abstract in Art and Mathematics, MIT Press (2020) 

[55] A. Port, T.  Karidi, M. Marcolli, Topological Analysis of Syntactic Structures  (2019) arXiv preprint arXiv:1903.05181 [56] M. Marcolli, Motivic information, Bollettino dell'Unione Matematica Italiana (2019) 12  (1-2), 19-41 

[57] A. Port, I. Gheorghita, D. Guth, J.M. Clark, C.  Liang, S. Dasu, M. Marcolli, Persistent topology of syntax,  Mathematics in Computer Science (2018) 12 (1), 33-50 20 

[58] K. Shu,  S. Aziz, VL Huynh, D Warrick, M Marcolli, Syntactic phylogenetic trees, Foundations of Mathematics and Physics One Century After 

 Hilbert (2018), 417-441 

[59] K. Shu, A. Ortegaray, R Berwick, M. Marcolli Phylogenetics of Indo-European language families via an algebro-geometric analysis of their syntactic structures. arXiv (2018) preprint arXiv:1712.01719 

[60] K. Shu, M. Marcolli, Syntactic structures and code parameters Mathematics in Computer Science (2018)  11 (1), 79-90 

[61] K Siva, J Tao, M Marcolli. Syntactic Parameters and Spin Glass Models of Language Change Linguist. Anal (2017) 41  (3-4), 559-608 

[62] M. Marcolli, N. Tedeschi, Entropy algebras and Birkhoff factorization. Journal of Geometry and Physics (2015) 97,  243-265 

[63] M. Marcolli, Information algebras and their applications. International Conference on Geometric Science of Information (2015), 271-276

[64] K. Siva, J. Tao, M. Marcolli Spin glass models of syntax and  language evolution,  arXiv preprint (2015) arXiv:1508.00504 

[65]  Y.  Manin, M. Marcolli, Kolmogorov complexity and the asymptotic bound  for error-correcting codes Journal of Differential Geometry

 (2014) 97 (1), 91-108

[66] M. Marcolli, R. Thorngren, Thermodynamic semirings, ArXiv  preprint (2011) arXiv:1108.2874

 Bosa Tadić and colleagues:

 [67] M. Andjelkovic, B. Tadic, R. Melnik, The topology of  higher-order complexes associated with brain-function hubs in human  connectomes , available on  arxiv.org/abs/2006.10357<http://arxiv.org/abs/2006.10357>, published  in Scientific Reports 10:17320 (2020) [68] B. Tadic, M. Andjelkovic, 

 M. Suvakov, G.J. Rodgers, Magnetisation Processes in Geometrically Frustrated Spin Networks with Self-Assembled Cliques, Entropy 22(3),  336 (2020) 

[69] B. Tadic, M. Andjelkovic, R. Melnik, Functional Geometry of Human Connectomes published in ScientificReports Nature:ScientificReports 9:12060 (2019) previous version: Functional Geometry of Human Connectome and Robustness of Gender Differences, arXiv preprint arXiv:1904.03399 April 6, 2019 

[70] B. Tadic, M. Andjelkovic, M. Suvakov, Origin of hyperbolicity in brain-to-brain coordination networks, FRONTIERS in PHYSICS vol.6, ARTICLE{10.3389/fphy.2018.00007}, (2018) OA 

[71] B. Tadic, M.  Andjelkovic, Algebraic topology of multi-brain graphs: Methods to study the social impact and other factors onto functional brain connections, in Proceedings of BELBI (2016) 

[72] B. Tadic, M. Andjelkovic, B.M. Boskoska, Z. Levnajic, Algebraic Topology of Multi-Brain Connectivity Networks Reveals Dissimilarity in Functional Patterns during Spoken Communications, PLOS ONE Vol 11(11), e0166787 (2016) 

[73] M. Mitrovic and B. Tadic, Search for Weighted Subgraphs on Complex Networks with MLM, Lecture Notes in Computer Science, Vol. 5102 pp. 551-558 (2008)

 Giovanni Petri, Francesco Vaccarino and collaborators:

[74] F. Battiston, G. Cencetti, et al., Networks beyond pairwise interactions: structure and dynamics, Physics Reports (2020), arXiv:2006.01764

[75] M. Guerra, A. De Gregorio, U. Fugacci, G. Petri, F. Vaccarino, Homological scaffold via minimal homology bases. arXiv (2020) preprint ArXiv:2004.11606 

[76] J. Billings, R. Tivadar, M.M. Murray, B. Franceschiello, G. Petri, Topological Features of Electroencephalography are  Reference-Invariant, bioRxiv 2020 [77] J. Billings, M. Saggar, S. Keilholz, G. Petri, Topological Segmentation of Time-Varying Functional Connectivity Highlights the Role of Preferred Cortical 

 Circuits, bioRxiv 2020 

[78] E. Ibáñez-Marcelo, L. Campioni, et al., Topology highlights mesoscopic functional equivalence between imagery and perception: The case of hypnotizability. NeuroImage (2019) 200, 437-449 

[79] P. Expert, L.D. Lord, M.L. Kringelbach, G. Petri. Topological neuroscience. Network Neuroscience (2019) 3 (3), 653-655

[80] C. Geniesse, O. Sporns, G. Petri, M. Saggar, Generating dynamical neuroimaging spatiotemporal representations (DyNeuSR) using topological data analysis. Network Neuroscience  (2019) 3 (3), 763-778 

[81] A. Patania, P. Selvaggi, M. Veronese, O. Dipasquale, P. Expert, G. Petri, Topological gene expression networks recapitulate brain anatomy and function. Network Neuroscience (2019) 3 (3),  744-762 

[82] E. Ibáñez‐Marcelo, L. Campioni, D.et al.. Spectral and topological analyses of the cortical representation of the head position: Does hypnotizability matter? Brain and behavior (2018) 9 (6), e01277 

[83] G. Petri, A. Barrat, Simplicial activity driven  model, Physical review letters 121 (22), 228301 

[84] A. Phinyomark, E. Ibanez-Marcelo, G. Petri. Resting-state fmri functional connectivity: Big data preprocessing pipelines and topological data 

 analysis. IEEE Transactions on Big Data (2017) 3 (4), 415-428 

[85] G. Petri, S. Musslick, B. Dey, K. Ozcimder, D. Turner, N.K. Ahmed, T. Willke. Topological limits to parallel processing 

 capability of network architectures. arXiv preprint (2017) arXiv:1708.03263

[86] K. Ozcimder, B. Dey, S. Musslick, G. Petri, N.K. Ahmed, T.L. Willke, J.D. Cohen, A Formal Approach to Modeling the Cost of Cognitive Control, arXiv preprint (2017) arXiv:1706.00085 

[87] L.D. Lord, P. Expert, et al. , Insights into brain architectures from the homological scaffolds of functional connectivity networks, Frontiers in systems neuroscience (2016) 10, 85 

[88] J. Binchi, E. Merelli, M. Rucco, G. Petri, F. Vaccarino. jHoles: A Tool for Understanding Biological Complex Networks via Clique Weight Rank Persistent Homology. Electron. Notes Theor. Comput. Sci. (2014) 306, 5-18

[89] G. Petri, P. Expert, F. Turkheimer, R. Carhart-Harris, D. Nutt, P.J. Hellyer et al., Homological scaffolds of brain functional networks. Journal of The Royal Society Interface (2014) 11 (101), 20140873

[90] G. Petri, M. Scolamiero, I. Donato, F. Vaccarino, Topological strata of weighted complex networks. PloS one (2013) 8 (6), e66506 

[91] G. Petri, M. Scolamiero, I. Donato, ., Networks and cycles: a persistent homology approach to complex networks Proceedings of the european conference on complex systems (2013), 93-99

 Daniel Bennequin, Juan-Pablo Vigneaux, Olivier Peltre, Grégoire Sergeant Perthuis, Pierre Baudot and colleagues:

[92] D. Bennequin. G. Sergeant-Perthuis, O. Peltre, and J.P. Vigneaux, Extra-fine sheaves and interaction decompositions, (2020) arXiv:2009.12646

[93] O. Peltre, Message-Passing Algorithms and Homology, PhD Thesis (2020), arXiv:2009.11631 

[94] G. Sergeant-Perthuis, Interaction decomposition for presheafs, (2020) arXiv:2008.09029

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