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Coarse-grained event tree analysis for quantifying Hodgkin-Huxley neuronal network dynamics

Yi Sun, Aaditya V. Rangan, Douglas Zhou, David Cai
2011 Journal of Computational Neuroscience  
We present an event tree analysis of studying the dynamics of the Hodgkin-Huxley (HH) neuronal networks.  ...  We demonstrate that for even small differences in inputs, some dynamical regimes of HH networks contain sufficiently higher order statistics as reflected in event chains within the event tree analysis.  ...  We thank two anonymous referees for helpful comments on the manuscript.  ... 
doi:10.1007/s10827-011-0339-7 pmid:21597895 fatcat:isdqwtlv7reibow2ofpax3cbje

Generative Models of Brain Dynamics – A review [article]

Mahta Ramezanian Panahi, Germán Abrevaya, Jean-Christophe Gagnon-Audet, Vikram Voleti, Irina Rish, Guillaume Dumas
2021 arXiv   pre-print
for the analysis of neuroscientific data.  ...  The principled design and discovery of biologically- and physically-informed models of neuronal dynamics has been advancing since the mid-twentieth century.  ...  Guillaume Dumas is funded by the Institute for Data Valorization (IVADO), Montréal and the Fonds de recherche du Québec (FRQ).  ... 
arXiv:2112.12147v2 fatcat:gg2njt2ks5gudk7ewxype2zvni

A perspective on bridging scales and design of models using low-dimensional manifolds and data-driven model inference

Jesper Tegnér, Hector Zenil, Narsis A. Kiani, Gordon Ball, David Gomez-Cabrero
2016 Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences  
The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.  ...  .: Hjärnfonden, ERC Consolidator, Torsten Söderberg Foundation, Stockholm County Council, Swedish Excellence Center for e-Science and Swedish Research Council (3R program MH and project grant NT).  ...  thousands of nonlinear Hodgkin-Huxley equations.  ... 
doi:10.1098/rsta.2016.0144 pmid:27698038 pmcid:PMC5052728 fatcat:2k2fznroazauxf4il5m7dludby

Variability of collective dynamics in random tree networks of strongly coupled stochastic excitable elements

Ali Khaledi-Nasab, Justus A. Kromer, Lutz Schimansky-Geier, Alexander B. Neiman
2018 Physical review. E  
Using Hodgkin-Huxley type nodal elements, such a setup serves as a model for sensory neurons with branched myelinated distal terminals.  ...  We study the collective dynamics of strongly diffusively coupled excitable elements on small random tree networks. Stochastic external inputs are applied to the leaves causing large spiking events.  ...  Just for his valuable comments and suggestions and D.F. Russell for discussions which inspired this work.  ... 
doi:10.1103/physreve.98.052303 fatcat:gqvbrizbdbcvbon6hrjlcbfehq

Towards dynamical network biomarkers in neuromodulation of episodic migraine

Markus Dahlem, Sebastian Rode, Arne May, Naoya Fujiwara, Yoshito Hirata, Kazuyuki Aihara, Jürgen Kurths
2013 Translational Neuroscience  
Then, we propose a strategy to employ the new theoretical concept of dynamical network biomarkers (DNB) in episodic manifestations of chronic disorders.  ...  In particular, as a first example, we introduce the use of computational models in migraine and illustrate on the basis of this example the potential of DNB as early-warning signals for neuromodulation  ...  Likewise, a coarse-graining in time from individual spiking to rate or activitybased dynamics in simulated cell populations is needed for the relevant time scales in migraine.  ... 
doi:10.2478/s13380-013-0127-0 pmid:24288590 pmcid:PMC3840387 fatcat:crtsag623vcmhpomfl4252j4r4

Variability of collective dynamics in random tree networks of strongly-coupled stochastic excitable elements [article]

Ali Khaledi-Nasab, Justus Kromer, Lutz Schimansky-Geier, Alexander Neiman
2018 bioRxiv   pre-print
Using Hodgkin-Huxley type nodal elements, such a setup serves as a model for sensory neurons with branched myelinated distal terminals.  ...  We study the collective dynamics of strongly diffusively coupled excitable elements on small random tree networks. Stochastic external inputs are applied to the leaves causing large spiking events.  ...  Just for his valuable comments and suggestions and D.F. Russell for discussions which inspired this work.  ... 
doi:10.1101/382911 fatcat:mypcjio6brbrjdwkhljz5cmeqe

Computational models of epileptiform activity

Fabrice Wendling, Pascal Benquet, Fabrice Bartolomei, Viktor Jirsa
2016 Journal of Neuroscience Methods  
occurring outside seizures like, for instance, interictal spikes or high-frequency oscillations in partial epilepsies.  ...  status epilepticus )*(+,$%-./'$0-,( Epileptiform activity refers to brain activity recorded during epileptic phenomena that cover not only the seizure episodes but also the plethora of abnormal transient events  ...  Raineteau for providing the hippocampal slice confocal image in Figure 1 .  ... 
doi:10.1016/j.jneumeth.2015.03.027 pmid:25843066 fatcat:altbj3ga5faj7dzlqla2pixwpq

Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience

Peter Ashwin, Stephen Coombes, Rachel Nicks
2016 Journal of Mathematical Neuroscience  
practical framework for further successful applications of mathematics to understanding network dynamics in neuroscience.  ...  There are also surprises in the dynamical complexity of the attractors that can robustly appear - for example, heteroclinic network attractors.  ...  We thank Kyle Wedgwood for providing Fig. 11 .  ... 
doi:10.1186/s13408-015-0033-6 pmid:26739133 pmcid:PMC4703605 fatcat:m2sisazz2ndqvb76b23kivib7m

Dynamical principles in neuroscience

Mikhail I. Rabinovich, Pablo Varona, Allen I. Selverston, Henry D. I. Abarbanel
2006 Reviews of Modern Physics  
Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: ͑i͒ Even the simplest neural network, with only a few neurons and synaptic connections, has an enormous number  ...  connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. ͑v͒ Since nervous systems are able to organize behavior based on sensory  ...  shown in Fig. 9͑a͒ but using Hodgkin-Huxley spikingbursting neuron models.  ... 
doi:10.1103/revmodphys.78.1213 fatcat:koqrqbdcefeyzf43jx77don24a

Stochastic Resonance and Finite Resolution in a Network of Leaky Integrate-and-Fire Neurons [chapter]

Nhamo Mtetwa, Leslie S. Smith, Amir Hussain
2002 Lecture Notes in Computer Science  
There are two primary classes of FPGA architectures: coarse-grained, and fine-grained. Coarse-grained architectures consist of fairly large but powerful configurable logic blocks.  ...  The system of equations proposed by Hodgkin and Huxley is rather complicated (Maass and Bishop, 1999) . For this reason, several simplifications of the Hodgkin-Huxley equations have been proposed.  ...  . (^+ w 2)(4 r + w 2) (^+ w 2) ( 4 r + u ; 2) (A.14) I 4 +^2 ~ ^ -^ + 7 2 +^ -^ -(^+ a ; 2)2(^ + a;2)2 The Fourier transform G(cj) for V(t) is given by: Z7rT*\r Ta ' fc=l *=1 Therefore: Let & ki = e **  ... 
doi:10.1007/3-540-46084-5_20 fatcat:skn4oukeqzg4vnbkslu7ysu3qi

The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs

WR Softky, C Koch
1993 Journal of Neuroscience  
of spiking typical of a Hodgkin-Huxley-like system.  ...  The instantaneous response r(t) was taken directly from the PSTH of the cell for all m stimuli, coarse-graining t to bins 20 msec wide (indexed by i= 0, 20, 40 msec).  ... 
doi:10.1523/jneurosci.13-01-00334.1993 pmid:8423479 fatcat:p7i6v5g3ebexxfihqekw2q7iqe

25th Annual Computational Neuroscience Meeting: CNS-2016

Tatyana O. Sharpee, Alain Destexhe, Mitsuo Kawato, Vladislav Sekulić, Frances K. Skinner, Daniel K. Wójcik, Chaitanya Chintaluri, Dorottya Cserpán, Zoltán Somogyvári, Jae Kyoung Kim, Zachary P. Kilpatrick, Matthew R. Bennett (+597 others)
2016 BMC Neuroscience  
These results outline a framework for categorizing neuronal types based on their functional properties.  ...  I will discuss theoretical results that point to functional advantages of splitting neural populations into subtypes, both in feedforward and recurrent networks.  ...  The funders had no role in study design, data collection and analysis, the decision to publish, or the preparation of the manuscript.  ... 
doi:10.1186/s12868-016-0283-6 pmid:27534393 pmcid:PMC5001212 fatcat:bt45etzj2bbolfcxlxo7hlv6ju

Metastable dynamics of neural circuits and networks [article]

Braden A.W. Brinkman, Han Yan, Arianna Maffei, Il Memming Park, Alfredo Fontanini, Jin Wang, Giancarlo La Camera
2021 arXiv   pre-print
Cortical neurons emit seemingly erratic trains of action potentials, or "spikes", and neural network dynamics emerge from the coordinated spiking activity within neural circuits.  ...  These approaches include: (i) a theoretical framework based on non-equilibrium statistical physics for network dynamics; (ii) statistical approaches to extract information about metastable states from  ...  Acknowledgments The authors wish to thank Tianshu Li for preparing Figure 1 .  ... 
arXiv:2110.03025v2 fatcat:fzzryumjjrc2royxs22uf2ylxu

A Brief History of Simulation Neuroscience

Xue Fan, Henry Markram
2019 Frontiers in Neuroinformatics  
We show how industrialization of neuroscience and the resulting large disconnected datasets are generating demand for integrative neuroscience, how the scale of neuronal and connectivity maps is driving  ...  cells are connected to each other, and how the seemingly infinite networks they form give rise to the vast diversity of brain functions.  ...  Almost 80 years ago, the first intracellular recording of individual neurons was achieved in the squid giant axon with glass microelectrodes (Hodgkin and Huxley, 1939) .  ... 
doi:10.3389/fninf.2019.00032 pmid:31133838 pmcid:PMC6513977 fatcat:omyrnds7kngjlk4mm4gg5t7gqa

Beyond mean field theory: statistical field theory for neural networks

Michael A Buice, Carson C Chow
2013 Journal of Statistical Mechanics: Theory and Experiment  
Mean field theories have been a stalwart for studying the dynamics of networks of coupled neurons. They are convenient because they are relatively simple and possible to analyze.  ...  However, classical mean field theory neglects the effects of fluctuations and correlations due to single neuron effects.  ...  , say those described by a set of Hodgkin-Huxley neurons.  ... 
doi:10.1088/1742-5468/2013/03/p03003 pmid:25243014 pmcid:PMC4169078 fatcat:m6vgzazz7zadpl5emkql6t4qrq
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