README.md

Mathematical Neuroscience Papers

The below is a list of mathematical neuroscience papers or mathematics-heavy analyses of biological nervous systems. Some may also talk about artificial systems, or are connectionist or Bayesian, but these are not intended to be the central theme of this list. Most papers involving networks also have a biologically plausible aspect like spiking &/or oscillatory dynamics.

The inclusion criteria for papers here is: the work is relevant to biological neurons/nervous systems and mentions biological neurons at least twice, modeling and equations are central to the paper and not relegated to an appendix, and the model/s is/are not exclusively used to analyze an experiment's data -- they should be able to "stand on their own"

---

Papers

• "Action Potential: A Vortex Phenomena; Driving Membrane Oscillations", Sattigeri 2020 https://doi.org/10.3389/fncom.2020.00021
• "Active gel physics", Prost, Jülicher, Joanny 2015 http://dx.doi.org/10.1038/nphys3224
• "Activity induced synchronization: Mutual flocking and chiral self-sorting", Levis, Pagonabarraga, Liebchen 2019 https://doi.org/10.1103/PhysRevResearch.1.023026
• "Adaptation and decorrelation in the cortex", Barlow & Földiàk 1989 https://www.neuroscience.cam.ac.uk/publications/download.php?id=25159
• "Adaptive Dynamical Networks", Berner, Gross, Kuehn, Kurths, & Yanchuk, 2023 https://doi.org/10.48550/arXiv.2304.05652
• "Adaptive Exponential Integrate-and-Fire Model as an Effective Description of Neuronal Activity", Brette & Gerstner 2005 http://dx.doi.org/10.1152/jn.00686.2005
• "Adaptive Rewiring in Non-Uniform Coupled Oscillators", Haqiqatkhah & van Leeuwen 2020 https://doi.org/10.31234/osf.io/eagzd
• "Algebraic Models of Mental Number Axes: Part II", Krysztofiak 2016 https://doi.org/10.1007/s10516-015-9270-2
• "Algorithmic complexity for short binary strings applied to psychology: a primer", Gauvrit, Zenil, & Soler-Toscano 2014 https://doi.org/10.3758/s13428-013-0416-0
• "An algorithmic information theory of consciousness", Ruffini 2016 https://doi.org/10.1093/nc/nix019
• "Alternative Models to Hodgkin-Huxley Equations", Deng 2017 https://doi.org/10.1007/s11538-017-0289-y
• "An attractor network in the hippocampus: Theory and neurophysiology", Rolls 2007 https://doi.org/10.1101/lm.631207
• "Attractor map theory of the hippocampal representation of space", Samsonovich 1997 http://mason.gmu.edu/~asamsono/disser.pdf
• "Attractor-state itinerancy in neural circuits with synaptic depression", Chen & Miller 2020 https://doi.org/10.1186%2Fs13408-020-00093-w
• "Autapse Turns Neuron Into Oscillator", Hermann & Klaus 2002 https://doi.org/10.1142/S0218127404009338
• "Adaptive learning by extremal dynamics and negative feedback", Bak & Chialvo 2000 https://doi.org/10.1103/physreve.63.031912
• "Beyond dimension reduction: Stable electric fields emerge from and allow representational drift", Pintosis & Miller 2022 https://doi.org/10.1016/j.neuroimage.2022.119058
• "Beyond Linear Elastic Modulus: Viscoelastic Models for Brain and Brain Mimetic Hydrogels", Calhoun, Bentil, Elliott, Otero, Winter, & Dupaix 2019 https://doi.org/10.1021/acsbiomaterials.8b01390
• "Beyond Neural Coding? Lessons from Perceptual Control Theory", Ariswalla, Bote, Verschure 2019 https://doi.org/10.1017/s0140525x19001432
• "Bidirectional Associative Memories", Kosko 1988 https://doi.org/10.1109/21.87054
• "Biological Organization Principles: Biogenesis, Cognition and Evolution of Living Systems", Maureira & García, 2020 https://doi.org/10.20944/preprints202008.0647.v1
• "Biologically plausible solutions for spiking networks with efficient coding", Koren & Panzeri 2022 https://proceedings.neurips.cc/paper_files/paper/2022/file/820c61a0cd419163ccbd2c33b268816e-Paper-Conference.pdf
• "A biologically-inspired recurrent oscillator network for computations in high-dimensional state space", Effenberger, Carvalho, Dubinin, Singer 2022 https://doi.org/10.1101/2022.11.29.518360
• "The Boundaries of Synchronization in Oscillator Networks", Medeiros, Medrano-T, Caldas, Feudel 2018 https://doi.org/10.1103/PhysRevE.98.030201
• "Brain Activity: Conditional Dissimilarity and Persistent Homology", Cassidy, Rae, and Solo 2015 https://ieeexplore.ieee.org/iel7/7150573/7163789/07164127.pdf
• "Brain computation by assemblies of neurons", Papadimitriou, Vempala, Mitropolsky, Collns, & Maass 2020 https://doi.org/10.1073/pnas.2001893117
• "Brain and Physics of Many-Body Problems", Ricciardi & Umezawa 1967 https://doi.org/10.1007/BF00292170
• "A Brief Review of Chimera State in Empirical Brain Networks", Wang & Liu 2020 https://doi.org/10.3389/fphys.2020.00724
• "Bursting synchronization in non-locally coupled maps", de Pontes, Viana, Lopes, Batista, & Batista 2008 http://www.fisica.ufpr.br/viana/artigos/2008/bursting_2008.pdf
• "Canard-induced complex oscillations in an excitatory network", Ersöz, Desroches, Guillamon, Rinzel, & Tabak 2020
• "A category theory approach using preradicals to model information flows in networks", Pardo G & Silva 2020 https://doi.org/10.48550/arXiv.2012.02886
• "A cerebellar mechanism for learning prior distributions of time intervals", Narain, Remington, De Zeeuw, Jazayeri 2018 https://doi.org/10.1038/s41467-017-02516-x
• "The cerebellum as a liquid state machine", Yamazaki & Tanaka 2007 https://doi.org/10.1016/j.neunet.2007.04.004
• "Chaotic Itinerancy as a Dynamical Basis of Hermeneutics in Brain and Mind", Tsuda 1991 https://doi.org/10.1080/02604027.1991.9972257
• "Chaotic Itinerancy as a Mechanism of Irregular Changes Between Synchronization and Desynchronization in a Neural Network", Tsuda 2003 https://doi.org/10.1142/S021963520400049X
• "Chaotic itinerancy within the coupled dynamics between a physical body and neural oscillator networks", Park, Mori, Okuyama, & Asada 2017 https://doi.org/10.1371/journal.pone.0182518
• "Chimera States for Coupled Oscillators", Abrams & Strogatz 2004 https://doi.org/10.1103/PhysRevLett.93.174102
• "Chimera States on a Ring of Strongly Coupled Relaxation Oscillators", Rode, Totz, Fengler, & Engel 2019 https://doi.org/10.3389/fams.2019.00031
• "Classification of bursting patterns: A tale of two ducks", Desroches, Rinzel, & Rodrigues, 2022 https://doi.org/10.1371/journal.pcbi.1009752
• "Clique topology reveals intrinsic geometric structure in neural correlations", Giusti, Pastalkova, Curto, Itskov 2015 https://doi.org/10.1073/pnas.150640711
• "Cliques and Cavities in the Human Connectome", Sizemore, Giusti, Kahn, Betzel, & Bassett 2016 https://doi.org/10.1007/s10827-017-0672-6
• "Cliques of Neurons Bound into Cavities Provide a Missing Link between Structure and Function", Reimann, Nolte, Scolamiero, Turner, Perin, Chindemi, Dłotko, Levi, Hess, & Markram 2017 https://doi.org/10.3389/fncom.2017.00048
• "Cognition and Complexity", Manin 2017 https://doi.org/10.1142/9789813109032_0014
• "Collective Behavior of Place and Non-place Neurons in the Hippocampal Network", Meshulam, Gauthier, Brody, Tank, Bialek 2017 https://doi.org/10.1016/j.neuron.2017.10.027
• "Collective motion of cells: from experiments to models", Méhes & Vicsek 2014 https://doi.org/10.1039/c4ib00115j
• "Collective membrane dynamics emerging from curvature-dependent spatial coupling", Wu, Su, Tong, Wu, & Liu 2017 https://doi.org/10.1101/164392
• "Combinatorial neural codes from a mathematical coding theory perspective", Curto, Itskov, Morrison, Roth, Walker 2012 https://doi.org/10.1162/NECO_a_00459
• "Common population codes produce extremely nonlinear neural manifolds", De & Chaudhuri 2023 https://doi.org/10.1101/2022.09.27.509823
• "A Comparison of the Hodgkin–Huxley Model and the Soliton Theory for the Action Potential in Nerves", Appali, van Rienen, Heimburg 2012 https://doi.org/10.1016/B978-0-12-396534-9.00009-X
• "Complex Dynamics and Bifurcations in Neurology", Milton, Longtin, Beuter, Mackey, & Glass 1989 http://faculty.jsd.claremont.edu/jmilton/reprints/jtb_1989.pdf
• "Complexity and irreducibility of dynamics on networks of networks", Rydin Gorjão, Saha, Ansmann, Feudel, Lehnertz 2018 https://doi.org/10.1063/1.5039483
• "The Complexity of Dynamics in Small Neural Circuits", Fasoli, Cattani, Panzeri 2016 https://doi.org/10.1371/journal.pcbi.1004992
• "A Computational Model of Emotional Learning in the Amygdala", Morén & Balkenius 2000 https://doi.org/10.7551/mitpress%2F3120.003.0041
• "Computational Neuroscience: Mathematical and Statistical Perspectives", Kass, Amari, Arai, Brown, Diekman, Diesmann, Doiron, Eden, Fairhall, Fiddyment, Fukai, Grün, Harrison, Helias, Nakahara, Teramae, Thomas, Reimers, Rodu, Rotstein, Shea-Brown, Shimazaki, Shinomoto, Yu, & Kramer 2018 https://doi.org/10.1146/annurev-statistics-041715-033733
• "Computation in a Single Neuron: Hodgkin and Huxley Revisted", Agüera y Arcas, Fairhall, & Bialek 2003 https://doi.org/10.1162/08997660360675017
• "Computing with Continuous Attractors: Stability and Online Aspects", Amari & Wu 2005 https://doi.org/10.1162/0899766054615626
• "Conditional Mixture Model for Correlated Neuronal Spikes", Amari 2010 https://http://doi.org/10.1162/neco.2010.04-08-766
• "Conceptual Circuit Models of Neurons", Deng 2009 https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1069&context=mathfacpub
• "Connection Between Internernal Representation of Rigid Transformation and Cortical Activity Paths", Carlton 1988 https://doi.org/10.1007/bf00336115
• "Continuous attractors for dynamic memories", Spalla, Cornacchia, Treves 2021 https://doi.org/10.7554/eLife.69499
• "Cortical circuits for perceptual inference", Friston & Kiebel 2009 https://doi.org/10.1016/j.neunet.2009.07.023
• "Cortical Learning via Prediction", Papadimitriou & Vempala 2015 http://jmlr.csail.mit.edu/proceedings/papers/v40/Papadimitriou15.pdf
• "Critical brain networks", Chialvo 2004 https://doi.org/10.1016/j.physa.2004.05.064
• "Decoding of neural data using cohomological feature extraction", Rybakken, Baas, Dunn 2018 https://doi.org/10.1162/neco_a_01150
• "Delay Regulated Explosive Synchronization in Multiplex Networks", Kachhvah & Jalan 2018 https://doi.org/10.1088/1367-2630/aaff0e
• "Dendritic Self-Organizing Maps for Continual Learning", Pinitas, Chavlis, Poirazi 2021 https://arxiv.org/abs/2110.13611
• "Differential Geometry of Proteins: A Structural and Dynamical Representation of Patterns", Louie & Somorjai 1982 https://doi.org/10.1016/0022-5193(82)90258-2
• "Diffusion of liquid domains in lipid bilayer membranes", Cicuta, Keller, Veatch 2006 https://doi.org/10.1021/jp0702088
• "Does the Cerebellum Implement or Select Geometries? A Speculative Note", Habas, Berthoz, Flash, & Bennequin 2020 https://doi.org/10.1007/s12311-019-01095-5
• "Dynamic signal tracking in a simple V1 spiking model", Lajoie & Young 2016 https://doi.org/10.1162/NECO_a_00868
• "Dynamics of filaments and membranes in a viscous fluid", Powers 2010 https://doi.org/10.1103/RevModPhys.82.1607
• "The Dynamics of Recurrent Inhibition", Mackey & an der Heiden 1984 https://www.mcgill.ca/mathematical-physiology-lab/files/mathematical-physiology-lab/1984_mcm_uheiden_dynamics_recurrent_inhibition.pdf
• "Dynamics of Sparsely Connected Networks of Excitatory and Inhibitory Spiking Neurons", Brunel 1999 https://doi.org/10.1023/a:1008925309027
• "The Effect of Calcium++ on Bursting Neurons: A Modeling Study" Plant, 1977 https://www.cell.com/biophysj/pdf/S0006-3495(78)85521-0.pdf
• "The effect of inhibition on rate code efficiency indicators", Barta & Kostal 2019 https://doi.org/10.1371/journal.pcbi.1007545
• "Elements of qualitative cognition: An information topology perspective", Pierre Baudot 2019 https://doi.org/10.1016/j.plrev.2019.10.003
• "Embodied neuromechanical chaos through homeostatic regulation", Shim & Husbands 2019 https://doi.org/10.1063/1.5078429
• "Emergence of Irregular Activity in Networks of Strongly Coupled Conductance-Based Neurons", Sanzeni, Histed, & Brunel 2022 https://doi.org/10.1103/PhysRevX.12.011044
• "Emergent complex neural dynamics: the brain at the edge", Chialvo 2010 https://doi.org/10.1038/nphys1803
• "Emergent dynamics in a model of visual cortex", Rangan & Young 2013 https://doi.org/10.1007/s10827-013-0445-9
• "Emergent Spaces for Coupled Oscillators", Thiem, Kooshkbaghi, Bertalan, Laing, Kevrekidis 2020 https://doi.org/10.3389/fncom.2020.00036
• "Emotional Learning: A Computational Model of the Amygdala", Balkenius & Morën 2001 https://doi.org/10.1080/01969720118947
• "Emotions as Computations", Emanuel & Eldar 2022 https://doi.org/10.1016/j.neubiorev.2022.104977
• "Everything is connected: Inference and attractors in delusions", Adams, Vincent, Benrimoh, Friston, & Parr 2021 https://doi.org/10.1016/j.schres.2021.07.032
• "The Existence of Infinitely Many Traveling Front and Back Waves in the FitzHugh-Nagumo Equations", Deng 1991 https://doi.org/10.1137/0522102
• "Extended active inference: Constructing predictive cognition beyond skulls", Constant, Clark, Kirchhoff, Friston 2019 https://doi.org/10.1111/mila.12330
• "Extending Integrate-and-Fire Model Neurons to Account for the Effects of Weak Electric Fields and Input Filtering Mediated by the Dendrite", Aspart, Ladenbauer, Obermayer 2016 https://doi.org/10.1371/journal.pcbi.1005206
• "An Extension of Combinatorial Contextuality for Cognitive Protocols", Obeid, Bruns, Angus, Bruza, & Moreira 2022 https://doi.org/10.3389%2Ffpsyg.2022.871028
• "Falsification and consciousness", Kleiner & Hoel 2021 https://doi.org/10.1093/nc/niab001
• "Fast–Slow Bursters in the Unfolding of a High Codimension Singularity and the Ultra-slow Transitions of Classes", Saggio, Spiegler, Bernard, & Jirsa, 2017 https://doi.org/10.1186/s13408-017-0050-8
• "FitzHugh-Nagumo Revisited: Types of Bifurcations, Periodical Forcing and Stability Regions by a Lyapunov Functional", Kostova, Ravindran, & Shonbek 2003 http://www.its.caltech.edu/~matilde/FHNLyapunov.pdf
• "A Framework for Mesencephalic Dopamine Systems Based on Predictive Hebbian Learning", Montague, Dayan, Sejnowski 1996 https://doi.org/10.1523/jneurosci.16-05-01936.1996
• "Free Energy, Value, Attractors", Friston & Ao 2011 https://doi.org/10.1155/2012/937860
• "From Coupled Dynamical Systems to Biological Irreversibility", Kaneko 2002 https://doi.org/10.48550/arXiv.nlin/0203040
• "Forgetting Leads to Chaos in Attractor Networks", Pereira-Obilinovic, Aljadeff, Brunel 2023 https://doi.org/10.1103/PhysRevX.13.011009
• "Functional geometry of the horizontal connectivity in the primary visual cortex", Sarti, Citti, Petitot 2009 http://dx.doi.org/10.1016/j.jphysparis.2009.05.004
• "Functional random effects modeling of brain shape and connectivity", Lila & Aston 2022 https://doi.org/10.48550/arXiv.2009.06059
• "A Generalized Linear Integrate-and-Fire Neural Model Produces Diverse Spiking Behaviors", Mihalaş & Niebur 2009 https://doi.org/10.1162/neco.2008.12-07-680
• "Generalized Shape Metrics on Neural Representations", Williams, Kunz, Kornblith, & Linderman 2021 https://doi.org/10.48550/arXiv.2110.14739
• "Generic theory of active polar gels: a paradigm for cytoskeletal dynamics", Kruse, Joanny, Jülicher, Prost, & Sekimoto 2005 https://doi.org/10.1140/epje/e2005-00002-5
• "Geometric constraints on human brain function", Pang, Aquino, Oldehinkel, Robinson, Fulcher, Breakspear, & Fornito 2022 https://doi.org/10.1101/2022.10.04.510897
• "Graph-Laplacian Features for Neural Waveform Classification", Ghanbari 2011 https://doi.org/10.1109/TBME.2010.2090349
• "Grid cells generate an analog error-correcting code for singularly precise neural computation", Sreenivasan & Fiete 2011 https://doi.org/10.1038/nn.2901
• "Homological scaffolds of brain functional networks", Petri, Expert, Turkheimer, Carhat-Harris, Nutt, Hellyer, & Vaccarino 2014 https://doi.org/10.1098/rsif.2014.0873
• "Homotopy Theoretic and Categorical Models of Neural Information Networks", Manin & Marcolli 2020 https://doi.org/10.48550/arXiv.2006.15136
• "Hopf Bifurcation in Mean Field Explains Critical Avalanches in Excitation-Inhibition Balanced Neuronal Networks: A Mechanism for Multiscale Variability", Liang, Zhou, & Zhou 2020 https://doi.org/10.3389/fnsys.2020.580011
• "How should we define Information Flow in Neural Circuits?", Venkatesh, Dutta, Grover 2019 https://doi.org/10.1109/ISIT.2019.8849411
• "How the brain keeps the eyes still", Seung 1996 https://doi.org/10.1073/pnas.93.23.13339
• "How the brain transitions from conscious to subliminal perception", Lucini, Ferraro, Sigman, & Makse 2019 https://doi.org/10.1016%2Fj.neuroscience.2019.03.047
• "Hyperstructures and memory evolutive systems", Baas, Ehresmann, & Vanbremeersch 2007 https://doi.org/10.1080/0308107042000193534
• "Influence fields: a quantitative framework for representation and analysis of active dendrites", Rathour & Narayanan 2012 https://doi.org/10.1371/journal.pcbi.1006485
• "Information Flow in Computational Systems", Venkatesh, Dutta, & Grover 2020 https://doi.org/10.48550/arXiv.1902.02292
• "An Information Processing Approach to Understanding the Visual Cortex", Crick, Marr, & Poggio 1980 https://dspace.mit.edu/bitstream/handle/1721.1/6332/AIM-557.ps?sequence=1&isAllowed=y
• "Information Processing Capacity of Dynamical Systems", Dambre, Verstraeten, Schrauwen, & Massar 2012 https://doi.org/10.1038/srep00514
• "Information topology of gene expression profile in dopaminergic neurons", Pacheco, Baudot, Dufour, Formisano-Tréziny, Temporal, Lasserre, Gabert, Kobayashi, Goaillard 2017 https://doi.org/10.1101/168740
• "Inners and Biocontrol Models", Clark, Krishnan, & Stark 1975 https://doi.org/10.1016/S0092-8240(75)80023-1
• "Insights into Brain Architectures from the Homological Scaffolds of Functional Connectivity Networks", Lord, Expert, Fernandes, Petri, Van Hartevelt, Vaccarino, Deco, Turkheimer, & Kringelbach 2016 https://doi.org/10.3389/fnsys.2016.00085
• "Integrated information and dimensionality in continuous attractor dynamics", Tajima & Kanai 2017 https://academic.oup.com/nc/article-pdf/doi/10.1093/nc/nix011/25023944/nix011.pdf
• "Interaction of Canard and Singular Hopf Mechanisms in a Neural Model", Curtu & Rubin 2011 http://homepage.math.uiowa.edu/~rcurtu/RCfiles/CurtuRubin_SIADS2011.pdf
• "Interactions of multiple rhythms in a biophysical network of neurons", Gelastopoulos & Kobell 2020 https://doi.org/10.1186/s13408-020-00096-7
• "Intracellular Oscillations and Waves", Beta & Kruse 2017 https://doi.org/10.1146/annurev-conmatphys-031016-025210
• "Landmarks for Neurogeometry", Petitot 2015 http://jeanpetitot.com/ArticlesPDF/Petitot_Landmarks.pdf
• "Laplace–Beltrami eigenvalues and topological features of eigenfunctions for statistical shape analysis", Reuter, Wolter, Shenton, & Niethamer, 2009 https://doi.org/10.1016/j.cad.2009.02.007
• "The Lost Art of Mathematical Modelling" Gyllingberg, Birhane, Sumpter 2023 https://doi.org/10.48550/arXiv.2301.08559
• "Maintaining Consistency of Spatial Information in the Hippocampal Network: A Combinatorial Geometry Model", Dabaghian 2016 https://doi.org/10.1162/NECO_a_00840
• "Markov blankets in the brain", Hipólito, Ramstead, Convertino, Bhat, Friston, Parr 2021 https://doi.org/10.1016/j.neubiorev.2021.02.003
• "Mathematical Analysis of Static and Plastic Biological Neural Circuits", Wang 2018 https://dspace.mit.edu/bitstream/handle/1721.1/127445/1192966398-MIT.pdf?sequence=1&isAllowed=y
• "Mathematical Biophysics and Psychology", Rashevsky 1936 https://doi.org/10.1007/BF02287920
• "Mathematical Modeling of the Brain: Principles and Challenges", Tenti, Sivaloganathan, & Drake, 2007 https://doi.org/10.1227/01.NEU.0000313132.04702.EA
• "Mathematical modelling of central pattern generators", Ermentrout & Kopell 1989 https://doi.org/10.1016/B978-0-12-287960-9.50013-7
• "Mathematical modelling of the enteric nervous network I: cholinergic neuron", Miftakhov & Wingate 1993 https://doi.org/10.1016/1350-4533(94)90013-2
• "Mathematical modelling of the enteric nervous network II: facilitation and inhibition of the cholinergic transmission", Miftakhov & Wingate 1993 https://doi.org/10.1016/0141-5425(93)90008-M
• "Mathematical modelling of the enteric nervous network 3. Adrenergic neuron", Miftakhov & Wingate 1994 https://doi.org/10.1016/1350-4533(94)90068-x
• "Mathematical modelling of the enteric nervous network 4. Analysis of adrenergic transmission", Miftakhov & Wingate 1994 https://doi.org/10.1016/1350-4533(95)01003-B
• "Mathematical modelling of the enteric nervous network 5. Excitation propagation in a planar neural network", Miftakhov & Wingate 1995 https://doi.org/10.1016/1350-4533(95)90372-I
• "A mathematical model of embodied consciousness", Rudrauf, Bennequin, Granic, Landini, Friston, Williford 2017 https://doi.org/10.1016/j.jtbi.2017.05.032
• "The Mathematical Structure of Integrated Information Theory", Kleiner & Tull 2021 https://doi.org/10.3389/fams.2020.602973
• "A Mathematical Theory of Visual Hallucination Patterns", Ermentrout & Cowan 1979 https://doi.org/10.1007/BF00336965
• "Mathematics and the Brain: A Category Theoretical Approach to Go Beyond the Neural Correlates of Consciousness", Northoff, Tsuchiya, & Saigo 2019 https://doi.org/10.3390/e21121234
• "Memetics and neural models of conspiracy theories", Duch 2021 https://doi.org/10.1016/j.patter.2021.100353
• "Memory psychophysics", Hubbard 1993 https://doi.org/10.1007/BF00419654
• "Memory via Temporal Delays in weightless Spiking Neural Network", Hazan, Caby, Earl, Siegelmann, Levin 2022 https://doi.org/10.48550/arXiv.2202.07132
• "Mesoscopic Segregation of Excitation and Inhibition in a Brain Network Model", Malagarriga, Villa, Garcia-Ojalvo, Pons 2014 https://doi.org/10.1371/journal.pcbi.1004007
• "Metastability And Plasticity In A Conceptual Model of Neurons", Deng 2010 https://core.ac.uk/download/pdf/188092910.pdf
• "A Method of Statistical Neurodynamics", Amari 1973 https://doi.org/10.1007/BF00274806
• "Metrics for comparing Neuronal Tree Shapes based on Persistent Homology", Li, Ascoli, Mitra, & Wang 2016 https://doi.org/10.1371/journal.pone.0182184
• "Minimum-Jerk, Two-Thirds Power Law, and Isochrony: Converging Approaches to Movement Planning", Viviani & Flash 1995 https://doi.org/10.1037/0096-1523.21.1.32
• "Model of the Human Sleep Wake System", Rogers & Holmes 2012 https://doi.org/10.48550/arXiv.1208.3228
• "A model of neocortex", Bienenstock 1994 https://doi.org/10.1088/0954-898X_6_2_004
• "Modeling brain reorganization after hemispherectomy", Seoane & Solé 2020 https://doi.org/10.1101/2020.12.25.424412
• "Modeling Extracellular Field Potentials and the Frequency-Filtering Properties of Extracellular Space", Bédard, Kröger, & Destexhe 2004 https://doi.org/10.1016/S0006-3495(04)74250-2
• "Modeling synchronization in human musical rhythms using Impulse Pattern Formulation (IPF)", Linke, Bader, Mores 2021 https://doi.org/10.48550/arXiv.2112.03218
• "Modelling Cochlear Mechanics", Ni, Elliott, Ayat, & Teal 2014 https://doi.org/10.1155/2014/150637
• "Modern temporal network theory: A colloquium", Holme 2015 https://doi.org/10.1140/epjb/e2015-60657-4
• "Modularization of grid cells constrained by the pyramidal patch lattice", Wang, Yang, Wang, Zhang, Wang, Liu 2021 https://doi.org/10.1016/j.isci.2021.102301
• "Modulated Noisy Biological Dynamics", Chialvo & Apkarian 1993 https://doi.org/10.1007/BF01053974
• "Modulation of excitatory synaptic coupling facilitates synchronization and complex dynamics in a biophysical model of neuronal dynamics", Breakspear, Terry, & Friston 2009 https://doi.org/10.1088/0954-898X_14_4_305
• "Molecular Motors: A Theorist's Perspective", Kolomeisky & Fisher 2007 https://doi.org/10.1146/annurev.physchem.58.032806.104532
• "Movement Timing and Invariance Arise from Several Geometries", Bennequin, Fuchs, Berthoz, & Flash 2009 https://doi.org/10.1371/journal.pcbi.1000426
• "Multi-periodic neural coding for adaptive information transfer", Yoo, Koyluoglu, Vishwanath, & Fiete 2015 https://doi.org/10.1016/j.tcs.2016.02.026
• "Multifrequency Hebbian plasticity in coupled neural oscillators", Kim & Large 2021 https://doi.org/10.1007/s00422-020-00854-6
• "A neural circuit model for human sensorimotor timing", Egger, Le, Jazayeri 2020 https://doi.org/10.1038/s41467-020-16999-8
• "Neural Codes and Homotopy Types: Mathematical Models of Place Field Recognition", Manin 2015 https://doi.org/10.48550/arXiv.1501.00897
• "Neural Excitability, Bursting and Spiking", Izhikevich, 1999 https://www.izhikevich.org/publications/nesb.pdf
• "Neural Ideals and Stimulus Space Visualization", Gross, Obatake, & Youngs 2016 https://doi.org/10.1016/j.aam.2017.10.002
• "Neural Ideal Preserving Homomorphisms", Jeffs, Omar, & Youngs 2016 https://doi.org/10.48550/arXiv.1612.06150
• "Neural Interactions in Developing Rhythmogenic Spinal Networks: Insights From Computational Modeling", Shevstova, Ha, Rybak, & Dougherty 2020 https://doi.org/10.3389/fncir.2020.614615
• "A neural network model of sensoritopic maps with predictive short-term memory properties", Droulez & Berthoz 1991 https://doi.org/10.1073/pnas.88.21.9653
• "The Neural Mechanism of Logical Thinking", Rashevsky 1946 https://doi.org/10.1007/BF02478469
• "Neural Modeling", Harmon & Lewis 1966 https://doi.org/10.1152/physrev.1966.46.3.513
• "The neural ring: an algebraic tool for analyzing the intrinsic structure of neural codes", Curto, Itskov, & Veliz-Cuba 2013 https://doi.org/10.1007/s11538-013-9860-3
• "The Neural Ring: Using Algebraic Geometry to Analyze Neural Codes", Youngs 2014 https://doi.org/10.48550/arXiv.1409.2544
• "Neurogeometry of perception: isotropic and anisotropic aspects", Citti & Sarti 2022 https://doi.org/10.1007/s10516-019-09426-1
• "A neuro-mathematical model for size and context related illusions", Franceschiello, Sarti, & Citti 2019 https://doi.org/10.1007/978-3-030-57227-3_5
• "Neuronal Morphology Generates High-Frequency Firing Resonance", Ostojic, Szapiro, Schwartz, Barbour, Brunel, & Hakim 2015 https://doi.org/10.1523/JNEUROSCI.3924-14.2015
• "Neuron Model with Conductance-Resistance Symmetry", Deng 2019 https://doi.org/10.1016/j.physleta.2019.125976
• "Neurons, Dynamics and Computation", Hopfield 1994 http://dx.doi.org/10.1063/1.881412
• "Next-generation neural mass and field modeling", Byrne, O'Dea, Forrester, Ross, & Coombes 2019 https://doi.org/10.1152/jn.00406.2019
• "Noise as a Resource for Computation and Learning in Networks of Spiking Neurons", Maass 2014 https://doi.org/10.1109/JPROC.2014.2310593
• "Noise in biology", Tsimring 2013 https://doi.org/10.1088/0034-4885/77/2/026601
• "Noncommutative Biology: Sequential Regulation of Complex Networks", Letsou, Cai 2016 https://doi.org/10.1371/journal.pcbi.1005089
• "Nonequilibrium landscape theory of neural networks", Yan, Zhao, Hu, Wang, Wang, & Wang 2013 https://doi.org/10.1073/pnas.1310692110
• "Nonlinear brain dynamics as macroscopic manifestation of underlying many-body field dynamics", Freeman, Vitiello 2005 https://doi.org/10.1016/j.plrev.2006.02.001
• "Nonlinear mixed selectivity supposrts reliable neural computation", Jonston, Palmer, & Freedman 2020 https://doi.org/10.1371/journal.pcbi.1007544
• "On Matrices of Neural Nets", Wei 1948 https://doi.org/10.1007/BF02477433
• "On The Concept of Space in Neuroscience", Baas 2017 https://doi.org/10.1016/j.coisb.2016.12.002
• "On the Origin and Nature of Neurogeometry", Sarti & Citti http://www.dm.unibo.it/~citti/curri/neurogeometry.pdf
• "On the relationship between synaptic input and spike output jitter in individual neurons", Maršálek, Koch, & Maunsell 1996 https://doi.org/10.1073/pnas.94.2.735
• "Oriented Matroids and Combinatorial Neural Codes", Kunin, Lienkaemper, & Rosen 2020 https://doi.org/10.48550/arXiv.2002.03542
• "Oscillations in a refractory neural net", Curtu & Ermentrout 2000 https://doi.org/10.1007/s002850100089
• "An Oscillatory Neural Autoencoder Based on Frequency Modulation and Multiplexing", Soman, Muralidharan, & Chakravarthy 2018 https://doi.org/10.3389/fncom.2018.00052
• "Oscillatory Tracking of Continuous Attractor Neural Networks Account for Phase Precession and Procession of Hippocampal Place Cells", Chu, Ji, Zuo, Zhang, Huang, Mi, Wu 2022 https://proceedings.neurips.cc/paper_files/paper/2022/file/d6797a91df19b768409b5178642dcb26-Paper-Conference.pdf
• "Outline of a Matrix Calculus for Neural Nets", Landahl & Runge 1946 https://doi.org/10.1007/BF02478464
• "Parabolic Bursting in an Excitable System Coupled With a Slow Oscillation", Ermentrout & Kopell, 1986 http://utw10729.utweb.utexas.edu/wp-content/uploads/2019/01/KopelErmentrout.pdf
• "Parabolic bursting revisited", Soto-Treviño, Kopell, & Watson, 1996 https://doi.org/10.1007/s002850050046
• "Pattern Recognition Via Synchronization in Phase-Locked Loop Neural Networks", Hoppensteadt & Izhikevich 2000 https://doi.org/10.1109/72.846744
• "Periodically kicked feedforward chains of simple exitable FitzHugh-Nagumo neurons", Ambrosio & Mintchev 2021 https://doi.org/10.1007/s11071-022-07757-0
• "Persistent memories in transient networks", Babichev & Dabaghian 2018 https://doi.org/10.1007/978-3-319-47810-4_14
• "Physics of Psychophysics: it is critical to sense", Copelli 2006 https://doi.org/10.1063/1.2709581
• "Physic of Psychophysics: two coupled square lattices of spiking neurons have huge dynamic range at criticality", Galera, Kinouchi 2020 https://doi.org/10.48550/arXiv.2006.11254
• "Physics, Computation, and Why Biology Looks so Different", Hopfield 1994 https://doi.org/10.1006/jtbi.1994.1211
• "Predictive coding in balanced neural networks with noise, chaos and delays", Kadmon, Timcheck, & Ganguli 2020 https://proceedings.neurips.cc/paper/2020/file/c236337b043acf93c7df397fdb9082b3-Paper.pdf
• "Predictive Hebbian Learning", Sejnowski, Dayan, & Montague 1995 https://doi.org/10.1523/JNEUROSCI.16-05-01936.1996
• "Problems of Information Processing in the Nervous System", Güttinger 1972 https://doi.org/10.3109/00207457209147014
• "Propagation of chaos in neural fields", Touboul 2014 https://doi.org/10.1214/13-AAP950
• "Psychologically Simple Motions as Geodesic Paths I. Asymmetric Objects", Carlton & Shepard 1990 https://doi.org/10.1016/0022-2496(90)90001-P
• "Psychologically Simple Motions as Geodesic Paths II. Symmetric Objects", Carlton & Shepard 1990 https://doi.org/10.1016/0022-2496(90)90002-Q
• "Quantified symmetry for entorhinal spatial maps", Chastain & Liu 2007 https://doi.org/10.1016/j.neucom.2006.10.050
• "Quantifying collectivity", Daniels, Ellison, Krakauer, & Flack 2016 http://dx.doi.org/10.1016/j.conb.2016.01.012
• "Refractory Neuron Circuits", Sarpeshkar, Watts, & Mead 1992 https://authors.library.caltech.edu/60111/1/Refractory%20Neuron%20Circuits.pdf
• "Regular spiking in high-conductance states: The essential role of inhibition", Barta & Kostal 2021 https://doi.org/10.1103/PhysRevE.103.022408
• "A Remark on Landahl's Theory of Learning", Rashevsky 1950 https://doi.org/10.1007/BF02478323
• "Replay as context-driven memory reactivation", Zhou, Kahana, Schapiro 2023 https://doi.org/10.1101/2023.03.22.533833
• "Routes to extreme events in dynamical systems: Dynamical and Statistical Characteristics", Mishra, Kingston, Hens, Kapitaniak, Feudel, & Dana 2020 https://doi.org/10.1063/1.5144143
• "Shape Analysis of Human Brain: A Brief Survey", Nitzken, Casanova, Gimel’farb, Inanc, Zurada, & El-Baz, 2013 https://ieeexplore.ieee.org/iel7/6221020/6846381/06704321.pdf
• "Shared input and recurrency in neural networks for metabolically efficient information transmission", Barta & Kostal 2023 https://doi.org/10.1101/2023.03.13.532471
• "The Sign Rule and Beyond: Boundary Effects, Flexibility, and Noise Correlations in Neural Population Codes", Hu, Zylberberg, Shea-Brown 2014 https://doi.org/10.1371/journal.pcbi.1003469
• "A Simple Chaotic Neuron", Pasemann 1997 https://doi.org/10.1016/S0167-2789(96)00239-4
• "Simulating brain rhythms using an ODE with stochastically varying coefficients", Ambrosio & Young 2020 https://doi.org/10.48550/arXiv.2006.04039
• "Some Physico-Mathematical Aspects of Nerve Conduction. I", Rashevsky 1933 https://doi.org/10.1063/1.1745203
• "Some Physico-Mathematical Aspects of Nerve Conduction. II", Rashevsky 1935 https://doi.org/10.1063/1.1745337
• "Some Properties of Randomly Connected Networks of Neuron-Like Elements with Refractory", Yoshizawa 1974 https://doi.org/10.1007/BF00271721
• "Sparse Neural Codes and Convexity", Jeffs, Omar, Suaysom, Watchtel, Youngs 2015 https://doi.org/10.48550/arXiv.1511.00283
• "Spatially localized cluster solutions in inhibitory neural networks", Ryu, Miller, Teymuroglu, Wang, Booth, & Campbell 2020 https://doi.org/10.1101/2020.07.30.229542
• "Stability, bifurcation and phase-locking of time-delayed excitatory-inhibitory neural networks", Ryu & Campbell 2020 https://doi.org/10.3934/mbe.2020403
• "Statistical Inference, Occam's Razor, and Statistical Mechanics on the Space of Probability Distributions", Balasubramanian 1997 https://doi.org/10.1162/neco.1997.9.2.349
• "Statistical mechanics of neocortical interactions Large-scale EEG influences on molecular processes", Ingber 2016 https://doi.org/10.1016/j.jtbi.2016.02.003
• "Statistical Mechanics of Nervous Nets", J.D. Cowan https://doi.org/10.1007/978-3-642-87596-0_17
• "Stochastic sensitivity analysis of noise-indueced suppression of firing and giant variability of spiking in a Hodgkin-Huxley neuron model", Bashkirtseva, Neiman, & Ryashko 2015 https://doi.org/10.1103/PhysRevE.91.052920
• "A structured scaffold underlies activity in the hippocampus", Mulders, Yim, Lee, Lee, Thibaud, Taillefumier, & Fiete 2021 https://doi.org/10.1101/2021.11.20.469406
• "Synaptic bouton properties are tuned to best fit the prevailing firing pattern", Knodel, Geiger, Ge, Bucher, Grillo, Wittum, Schuster, & Queisser 2014 https://doi.org/10.3389/fncom.2014.00101
• "Synchronization and suppression of chaos in non-locally coupled map lattices", Szmoski, Pinto, van Kan, Batista 2009 https://doi.org/10.1007/s12043-009-0175-8
• "Synchronization-based computation through networks of coupled oscillators", Malagarriga, García-Vellisca, Villa, Buldú, García-Ojalvo, & Pons 2015 https://doi.org/10.3389/fncom.2015.00097
• "Taking Cognition Seriously: A generalised physics of cognition", Taylor, Tran, & Nicolau 2021 https://doi.org/10.1007/978-3-030-92163-7_19
• "The Temporal Rich Club Phenomenon", Pedreschi, Battaglia, & Barrat 2021 https://doi.org/10.1038/s41567-022-01634-8
• "Temporal Sequence Learning, Prediction, and Control - A Review of different models and their relation to biological mechanisms", Wörgötter & Porr 2005 https://doi.org/10.1162/0899766053011555
• "A theory joint attractor dynamics in the hippocampus and the entorhinal cortex accounts for artificial remapping and grid cell field-to-field variability", Agmon & Burak 2020 https://doi.org/10.7554/eLife.56894
• "Topological and phenomenological classification of bursting oscillations", Bertram, Butte, Kiemel, & Sherman, 1995 https://doi.org/10.1007/BF02460633
• "Topological Model of Neural Information Networks", Marcolli 2021 https://doi.org/10.1007/978-3-030-80209-7_67
• "The Topology of the Brain and Visual Perception", Zeeman 1962
• "Theta functions and optimal lattices for a grid cells model", Bétermin 2021 https://doi.org/10.1137/20M1376431
• "The Time Course of Perceptual Choice: The Leaky, Competing Accumulator Model", Usher & McClelland, 2001 https://doi.org/10.1037/0033-295X.108.3.550
• "Topological Schemas of Memory Spaces", Babichev & Dabaghian 2021 https://doi.org/10.3389/fncom.2018.00027
• "The topology of the directed clique complex as a network invariant", Masulli & Villa YEAR 2016 https://doi.org/10.1186/s40064-016-2022-y
• "Translational Diffusion in Lipid Membranes byond the Saffman-Delbrück Approximation", Petrov & Schwille 2007 https://doi.org/10.1529/biophysj.107.126565
• "Transient Chaotic Dimensionality Expansion by Recurrent Networks", Keup, Kühn, Dahmen, & Helias 2021 https://doi.org/10.1103/PhysRevX.11.021064
• "Transition between Tonic Spiking and Bursting in a Neuron Model via the Blue-Sky Catastrophe", Shilnikov & Cymbalyuk 2005 https://doi.org/10.1103/PhysRevLett.94.048101
• "Two’s company, three (or more) is a simplex: Algebraic-topological tools for understanding higher-order structure in neural data", Giusti, Ghrist, Bassett 2016 https://doi.org/10.1007/s10827-016-0608-6
• "An Unfolding Theory Approach to Bursting in Fast-Slow Systems", Golubitsky, Josić, & Kaper, 2001 https://www.asc.ohio-state.edu/golubitsky.4/reprintweb-0.5/output/papers/bursting12.pdf
• "Unsupervised learning for robust working memory", Gu & Lim 2022 https://doi.org/10.1371/journal.pcbi.1009083
• "Waves and Oscillations in Model Neuronal Networks", Curtu 2003 http://d-scholarship.pitt.edu/8159/1/CurtuRodica2003.pdf
• "What can a single neuron compute?", Agüera y Arcas, Fairhall, & Bialek 2000 https://proceedings.neurips.cc/paper/2000/file/a19acd7d2689207f9047f8cb01357370-Paper.pdf
• "What Can Topology Tell Us About the Neural Code?", Curto 2016 http://dx.doi.org/10.1090/bull/1554
• "What makes it possible to learn probability distributions in the natural world?", Bialek, Palmer, Schwab 2021 https://doi.org/10.48550/arXiv.2008.12279
• "Why do networks have inhibitory/negative connections?", Wang, Powell, Geisa, Bridgeford, Vogelstein 2022 https://doi.org/10.48550/arXiv.2208.03211