Algebraic topology and neuroscience: a bibliography

Papers which apply algebraic-topological techniques to problems  of interest to neuroscientists. The goal of this list is completeness; please inform me if I have missed anything.  Last update: February 7, 2018.

​For ease of use, here is the bibtex file from which the following is (essentially) generated. The citation format is (first author last name, year, first word of title), e.g., \cite{giusti2015clique}. -

Published or In Press

  1. Arai, M., Brandt, V. and Dabaghian, Y. (2014). The effects of theta precession on spatial learning and simplicial complex dynamics in a topological model of the hippocampal spatial map. PLoS Comp. Bio. 10 (6): e1003651.
  2. Baas, N. (2017) On the concept of space in neuroscience. Curr. Opin. Syst. Biol. 1: 32-37
  3. Babichev, A. and Dabaghian, Y. (2017) Persistent memories in transient networks. In: Emergent Complexity from Nonlinearity in Physics, Engineering and the Life Sciences, pp. 179-188, Springer
  4. Baryshnikov, Y. and Schlafly, E. (2016) Cyclicity in multivariate time series and applications to functional MRI data. In: 2016 IEEE 55th Conference on Decision and Control, pp. 1625-1630, IEEE
  5. Basso, E., Arai, M. and Dabaghian, Y.(2016)  Gamma synchronization influences map formation time in a topological model of spatial learning. PLOS Comp. Bio. 12 (9): e1005114
  6. Bendich, P., Marron, J., Miller, E., Pieloch, A. and Skwerer, S. (2014). Persistent homology analysis of brain artery trees. Ann. Appl. Stat. 10(1): 198-218.
  7. Brown, J. and Gedeon, T. (2012). Structure of afferent terminals in a terminal ganglion of a cricket and persistent homology. PLOS One 7 (5) e37278
  8. Cassidy, B., Rae, C., and Solo, V. (2015) Brain activity: conditional dissimilarity and persistent homology. In Biomedical Imaging (ISBI), 2015 IEEE 12th International Symposium, pp. 1356-1359, IEEE
  9. Chen, Z., Gomperts, S. N., Yamamoto, J. and Wilson, M. A. (2014). Neural representation of spatial topology in the rodent hippocampus. Neural Comput. 26: 1–39.
  10. Choi, H., Kim, Y. K., Kang, H. and Lee, D. S. (2014) Abnormal metabolic connectivity in the pilocarpine-induced epilepsy rat model: a multiscale network analysis based on persistent homology. NeuroImage 99: 226-236
  11. Chung, M. K., Bubenik, P. and Kim, P. T. (2009). Persistence diagrams of cortical surface data. In Information Processing in Medical Imaging, pp. 386–397: Springer.
  12. Chung, M. K., Hanson, J. L., Ye, J., Davidson, R., and Pollak, S. (2015) Persistent homology in sparse regression and its application to brain morphometry. IEEE Trans. Med. Imaging, 34(9): 1928-1939
  13. Croteau, N., Nathoo, F., Jiguo, C., and Budney, R. (2017) High-dimensional classification for brain decoding. In: Big and Complex Data Analysis, pp. 305-324. Springer.
  14. Curto, C. (2017) What can topology tell us about the neural code? Bull. Amer. Math. Soc. 54(1): 63-78
  15. Curto, C., Gross, E., Jeffries, J., Morrison, K., Omar, M., Rosen, Z., Shiu, A. and Youngs, N. (2017) What makes a neural code convex? SIAM J. Appl. Algebra Geometry, 1: 222-238.
  16. Curto, C. and Itskov, V. (2008). Cell groups reveal structure of stimulus space. PLoS Comp. Bio. 4, e1000205.
  17. Curto, C., Itskov, V., Veliz-Cuba, A. and Youngs, N. (2011) The neural ring: an algebraic tool for analyzing the intrinsic structure of neural codes. Bull. Math. Biol. 75: 1571-1611
  18. Dabaghian, Y. (2016) Maintaining consistency of spatial information in the hippocampal network: a combinatorial geometry model. Neural Comput. 28 
  19. Dabaghian, Y., Brandt, V. L. and Frank, L. M. (2014). Reconceiving the hippocampal map as a topological template. Elife 3: e03476.
  20. Dabaghian, Y., Cohn, A. and Frank, L. (2011). Topological coding in the hippocampus. In Computational modeling and simulation of intellect: Current state and future prospectives, pp. 293-320, IGI Global Hershey, PA
  21. Dabaghian, Y., M ́emoli, F., Frank, L. and Carlsson, G. (2012). A topological paradigm for hippocampal spatial map formation using persistent homology. PLoS Comp. Bio. 8: e1002581.
  22. Ellis, S. and Klein, A. (2014). Describing high-order statistical dependence using “concurrence topology” with application to functional MRI brain data. H.H.A. 16(1): 245-264.
  23. Giusti, C., Ghrist, R. and Bassett, D. (2016) Two’s company, three (or more) is a simplex: Algebraic-topological tools for understanding higher-order structure in neural data. J. Comput. Neurosci. 41 (1): doi:10.1007/s10827-016-0608-6
  24. Giusti, C. and Itskov, V. (2013). A no-go theorem for one-layer feedforward networks. Neural Compt. 26: 2527-2540.
  25. Giusti, C., Pastalkova, E., Curto, C. and Itskov, V. (2015). Clique topology reveals intrinsic geometric structure in neural correlations. Proc. Nat. Acad. Sci. USA 112: 13455-13460.
  26. Hoffman, K., Babichev, A. and Dabaghian, Y. (2016) A model of topological mapping of space in bat hippocampus. Hippocampus 26 (10): 1345-1353
  27. Khalid, A., Kim, B. S., Chung, M. K., Ye, J. C. and Jeon, D. (2014). Tracing the evolution of multi-scale functional networks in a mouse model of depression using persistent brain network homology. NeuroImage 101: 351–363.
  28. Kim, E., Kang, H., Lee, H., Lee, H.-J., Suh, M.-W., Song, J.-J., Oh, S.-H. and Lee, D. S. (2014). Morphological brain network assessed using graph theory and network filtration in deaf adults. Hearing Res. 315: 88–98.
  29. Lee, H., Chung, M. K., Kang, H., Kim, B.-N. and Lee, D. S. (2011). Discriminative persistent homology of brain networks. In Biomedical Imaging: From Nano to Macro, 2011 IEEE International Symposium, pp. 841–844, IEEE.
  30. Lee, H., Kang, H., Chung, M. K., Lim, S. Kim, B-N., Lee, D. S. (2017) Integrated multimodal network approach to PET and MRI based on multidimensional persistent homology. Hum. Brain Mapp. 38(3): 1387-1402.
  31. Lienkaemper, C., Shiu, A. and Woodstock, Z. (2017) Obstructions to convexity in neural codes. Adv. Appl. Math. 85: 31-59
  32. Lord, L.-D., Expert, P., Fernandes, H. M., Petri, G., Van Hartevelt, T. J., Vaccarino, F., Deco, G., Turkheimer, F., and Kringelbach, M. L. (2016) Insights into brain architectures from the homological scaffolds of functional connectivity networks Front. Syst. Neurosci. 10: 85
  33. Masulli, P and Villa A., (2016) The topology of the directed clique complex as a network invariant. SpringerPlus. 5(1): 388
  34. Mata, G., Morales, M., Romero, A., and Rubio, J. (2015) Zigzag persistent homology for processing neuronal images. Pattern Recogn. Lett. 62: 55-60
  35. Petri, G., Expert, P., Turkheimer, F., Carhart-Harris, R., Nutt, D., Hellyer, P. and Vaccarino, F. (2014). Homological scaffolds of brain functional networks. J. Roy. Soc. Int. 11: 20140873.
  36. Pirino, V., Riccomagno, E., Martinoia, S. and Massobrio, P. (2014). A topological study of repetitive co-activation networks in in vitro cortical assemblies. Phys. Bio. 12: 016007–016007.
  37. Riemann, M., Nolte, M., Scolamiero, M., Turner, K., Perin, R., Chindemi, G., Dlotko, P., Levi, R., Hess, K., and Markram, H. (2017) Cliques of neurons bound into cavities provide a missing link between structure and function. Front. Comput. Neurosci. 11: doi:10.3389/fncom.2017.00048
  38. Saggar, M., Sporns, O., Gonzalez-Castillo, J., Bandettini, P. A., Carlsson, G., Glover, G., and Reiss, A. L. (2018) Towards a new approach to reveal dynamical organization of the brain using topological data analysis. Nat. Commun. 9(1): 1399
  39. Singh, G., Memoli, F., Ishkhanov, T., Sapiro, G., Carlsson, G. and Ringach, D. L. (2008). Topological analysis of population activity in visual cortex. J. Vis. 8: 11.
  40. Sizemore, A., Giusti, C. and Bassett, D.S. (2016) Classification of weighted networks through mesoscale homological features. J. Complex Netw: doi:10.1093/comnet/cnw013
  41. Sizemore, A, Giusti, C., Kahn, A., Vettel, J. M., Betzel, R.F., and Bassett, D.S. (2018) Cliques and cavities in the human connectome. J. Comput. Neurosci. 44 (1): 115-145
  42. Stolz, B. (2014). Computational topology in neuroscience. MS Thesis, University of Oxford, Oxford
  43. Stolz, B., Harrington, H., and Porter, M. (2017) Persistent homology of time-dependent functional networks constructed from coupled time series. Chaos, 27(4): 047410
  44. Wildani, A., and Sharpee, T.O. (2014) Persistent homology for characterizing stimuli response in the primary visual cortex. In: Proceedings of the International Conference of Machine Learning Workshop on Topology.
  45. Yoo, J., Kim, E.Y., Ahn, Y.M., and Ye, J.C. (2016) Topological persistence vineyard for dynamic functional brain connectivity during resting and gaming stages. J. Neurosci. Methods 267: 1-13.
  46. Zeeman, E. C. (1962). The topology of the brain and visual perception. In: Mathematics and computer science in biology and medicine, pp. 240-256, London: H.M. Stationary Office.
  47. Zhou, Y., Smith, B. H., and Sharpee, T. O. (2018) Hyperbolic geometry of the olfactory space, Sci. Adv. 4(8): eaaq1458


  1. Babichev, A., Morozov, D. and Dabaghian, Y. Robust spatial memory maps encoded in networks with transient connections. arXiv:1710.02623 [q-bio.NC] 
  2. Babichev, A. and Dabaghian, Y. Topological schemas of memory spaces. arXiv:1710.05967 [q-bio.NC]
  3. Chowdhury, S., Dai, B., and Mémoli, F.  The importance of forgetting: limiting memory improves recovery of topological characteristics from neural data.  arXiv:1710.11279 [q-bio.NC]
  4. Chung, M. K., Vilalta-Gil, V., Rathouz, P., Lahey, B., and Zald, D. Mapping heritability of large-scale brain networks with a billion connections via persistent homology. arXiv:1509.04771 [cs.AI]
  5. Curto, C. and Youngs, N. Neural ring homomorphisms and maps between neural codes. arXiv:1511.00255 [q-bio.NC]
  6. Dlotko, P., Hess, K., Levi, R., Nolte, M., Reimann, M., Scolamiero, M., Turner, K., Muller, E. and Markram, H. Topological analysis of the connectome of digital reconstructions of neural microcircuits. arXiv:1601.01580 [q-bio.NC]
  7. Emrani, S. and Krim, H. Effective connectivity-based neural decoding: a causal interaction-driven approach arxiv:1607.07078 [cs.NE]
  8. Heras, J., Mata, G., Cuesto, G., Rubio, J., and Morales, M. Neuron detection in stack images: a persistent homology interpretation. arxiv:1509.04420 [cs.CV]
  9. Itskov, V., Kunin, A, and Rosen, Z. Hyperplane neural codes and the polar complex. arXiv:1801.02304 [q-bio.NC]
  10. Jeffs, R. A., Omar, M., Suaysom, N., Wachtel, A. and Youngs, N. Sparse neural codes and convexity. arXiv:1511.00283 [math.CO]
  11. Lee, H., Zhiwei, M., Yuan, W., Chung, M. Topological Distances between networks and its application to brain imaging, arxiv:1701.04171 [q-bio.QM]
  12. Kanari, L., Dlotko, P., Scolamiero, M., Levi, R., Shillcock, J., Hess, K. and Markram, H. Quantifying topological invariants of neuronal morphologies. arXiv:1603.08432 [q-bio.NC]
  13. Li, Y., Ascoli, G., Mitra, P., and Wang, Y. Metrics for comparing neuronal tree shapes based on persistent homology.
  14. Manin, Y. Neural codes and homotopy types: mathematical models of place field recognition. arXiv:1501.00897 [math.HO]
  15. Rybakken, E., Baas, N., and Dunn, B. Decoding of neural data using cohomological learning. arXiv:1711.07205 [q-bio.NC]
  16. Sizemore, A., Phillips-Cremins, J., Ghrist, R., and Bassett, D. The importance of the whole: topological data analysis for the network neuroscientist. arXiv:1806.05167 [q-bio.QM]
  17. Spreeman, G., Dunn, B., Botnan, M. and Baas, N. Using persistent homology to reveal hidden information in neural data. arXiv:1510.06629 [q-bio.NC] ​