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  1. The principle of stationary action is a cornerstone of modern physics, providing a powerful framework for investigating dynamical systems found in classical mechanics through to quantum field theory. However, ...

    Authors: Erik D. Fagerholm, W. M. C. Foulkes, Karl J. Friston, Rosalyn J. Moran and Robert Leech
    Citation: The Journal of Mathematical Neuroscience 2021 11:10
  2. We study pattern formation in a 2-population homogenized neural field model of the Hopfield type in one spatial dimension with periodic microstructure. The connectivity functions are periodically modulated in ...

    Authors: Karina Kolodina, John Wyller, Anna Oleynik and Mads Peter Sørensen
    Citation: The Journal of Mathematical Neuroscience 2021 11:9
  3. The neurons of the deep cerebellar nuclei (DCNn) represent the main functional link between the cerebellar cortex and the rest of the central nervous system. Therefore, understanding the electrophysiological p...

    Authors: Hugues Berry and Stéphane Genet
    Citation: The Journal of Mathematical Neuroscience 2021 11:7
  4. Decoding approaches provide a useful means of estimating the information contained in neuronal circuits. In this work, we analyze the expected classification error of a decoder based on Fisher linear discrimin...

    Authors: Matias Calderini and Jean-Philippe Thivierge
    Citation: The Journal of Mathematical Neuroscience 2021 11:6
  5. Memory and forgetting constitute two sides of the same coin, and although the first has been extensively investigated, the latter is often overlooked. A possible approach to better understand forgetting is to ...

    Authors: Antonios Georgiou, Mikhail Katkov and Misha Tsodyks
    Citation: The Journal of Mathematical Neuroscience 2021 11:4
  6. The reconstruction mechanisms built by the human auditory system during sound reconstruction are still a matter of debate. The purpose of this study is to propose a mathematical model of sound reconstruction b...

    Authors: Ugo Boscain, Dario Prandi, Ludovic Sacchelli and Giuseppina Turco
    Citation: The Journal of Mathematical Neuroscience 2021 11:2
  7. The brain is intrinsically organized into large-scale networks that constantly re-organize on multiple timescales, even when the brain is at rest. The timing of these dynamics is crucial for sensation, percept...

    Authors: Jennifer Creaser, Peter Ashwin, Claire Postlethwaite and Juliane Britz
    Citation: The Journal of Mathematical Neuroscience 2021 11:1
  8. A neural field models the large scale behaviour of large groups of neurons. We extend previous results for these models by including a diffusion term into the neural field, which models direct, electrical conn...

    Authors: Len Spek, Yuri A. Kuznetsov and Stephan A. van Gils
    Citation: The Journal of Mathematical Neuroscience 2020 10:21
  9. We provide theoretical conditions guaranteeing that a self-organizing map efficiently develops representations of the input space. The study relies on a neural field model of spatiotemporal activity in area 3b...

    Authors: Georgios Detorakis, Antoine Chaillet and Nicolas P. Rougier
    Citation: The Journal of Mathematical Neuroscience 2020 10:20
  10. Neural oscillations, including rhythms in the beta1 band (12–20 Hz), are important in various cognitive functions. Often neural networks receive rhythmic input at frequencies different from their natural frequ...

    Authors: Alexandros Gelastopoulos and Nancy J. Kopell
    Citation: The Journal of Mathematical Neuroscience 2020 10:19
  11. In this paper, we address the problem of the use of a human visual system (HVS) model to improve watermark invisibility. We propose a new color watermarking algorithm based on the minimization of the perceptio...

    Authors: Pascal Lefevre, David Alleysson and Philippe Carre
    Citation: The Journal of Mathematical Neuroscience 2020 10:17
  12. White matter pathways form a complex network of myelinated axons that regulate signal transmission in the nervous system and play a key role in behaviour and cognition. Recent evidence reveals that white matte...

    Authors: Seong Hyun Park and Jérémie Lefebvre
    Citation: The Journal of Mathematical Neuroscience 2020 10:16
  13. Morris–Lecar model is arguably the simplest dynamical model that retains both the slow–fast geometry of excitable phase portraits and the physiological interpretation of a conductance-based model. We augment t...

    Authors: Giuseppe Ilario Cirillo and Rodolphe Sepulchre
    Citation: The Journal of Mathematical Neuroscience 2020 10:13
  14. Binocular rivalry occurs when the two eyes are presented with incompatible stimuli and perception alternates between these two stimuli. This phenomenon has been investigated in two types of experiments: (1) Tr...

    Authors: Farzaneh Darki and James Rankin
    Citation: The Journal of Mathematical Neuroscience 2020 10:10
  15. Many biological and neural systems can be seen as networks of interacting periodic processes. Importantly, their functionality, i.e., whether these networks can perform their function or not, depends on the em...

    Authors: Christian Bick, Marc Goodfellow, Carlo R. Laing and Erik A. Martens
    Citation: The Journal of Mathematical Neuroscience 2020 10:9
  16. Following publication of the original article (Naud and Longtin in J Math Neurosci 9:3, 2019), the authors noticed a mistake in the first paragraph within “Altered propagation”.

    Authors: Richard Naud and André Longtin
    Citation: The Journal of Mathematical Neuroscience 2020 10:6

    The original article was published in The Journal of Mathematical Neuroscience 2019 9:3

  17. Coarse-graining microscopic models of biological neural networks to obtain mesoscopic models of neural activities is an essential step towards multi-scale models of the brain. Here, we extend a recent theory f...

    Authors: Valentin Schmutz, Wulfram Gerstner and Tilo Schwalger
    Citation: The Journal of Mathematical Neuroscience 2020 10:5
  18. Essential tremor manifests predominantly as a tremor of the upper limbs. One therapy option is high-frequency deep brain stimulation, which continuously delivers electrical stimulation to the ventral intermedi...

    Authors: Benoit Duchet, Gihan Weerasinghe, Hayriye Cagnan, Peter Brown, Christian Bick and Rafal Bogacz
    Citation: The Journal of Mathematical Neuroscience 2020 10:4
  19. The fruit fly’s natural visual environment is often characterized by light intensities ranging across several orders of magnitude and by rapidly varying contrast across space and time. Fruit fly photoreceptors...

    Authors: Aurel A. Lazar, Nikul H. Ukani and Yiyin Zhou
    Citation: The Journal of Mathematical Neuroscience 2020 10:3
  20. Recovering brain connectivity from tract tracing data is an important computational problem in the neurosciences. Mesoscopic connectome reconstruction was previously formulated as a structured matrix regressio...

    Authors: Patrick Kürschner, Sergey Dolgov, Kameron Decker Harris and Peter Benner
    Citation: The Journal of Mathematical Neuroscience 2019 9:9
  21. Following publication of the original article [1], the authors noticed a mistake in the first paragraph within “Altered propagation”.

    Authors: Richard Naud and André Longtin
    Citation: The Journal of Mathematical Neuroscience 2019 9:8

    The original article was published in The Journal of Mathematical Neuroscience 2019 9:3

  22. The emergent activity of biological systems can often be represented as low-dimensional, Langevin-type stochastic differential equations. In certain systems, however, large and abrupt events occur and violate ...

    Authors: Alexandre Melanson and André Longtin
    Citation: The Journal of Mathematical Neuroscience 2019 9:6
  23. Trigeminal neuralgia (TN) is a severe neuropathic pain, which has an electric shock-like characteristic. There are some common treatments for this pain such as medicine, microvascular decompression or radio fr...

    Authors: Mohammadreza Khodashenas, Golnaz Baghdadi and Farzad Towhidkhah
    Citation: The Journal of Mathematical Neuroscience 2019 9:4
  24. To establish and exploit novel biomarkers of demyelinating diseases requires a mechanistic understanding of axonal propagation. Here, we present a novel computational framework called the stochastic spike-diff...

    Authors: Richard Naud and André Longtin
    Citation: The Journal of Mathematical Neuroscience 2019 9:3

    The Correction to this article has been published in The Journal of Mathematical Neuroscience 2020 10:6

    The Correction to this article has been published in The Journal of Mathematical Neuroscience 2019 9:8

  25. Understanding nervous system function requires careful study of transient (non-equilibrium) neural response to rapidly changing, noisy input from the outside world. Such neural response results from dynamic in...

    Authors: Cheng Ly, Woodrow L. Shew and Andrea K. Barreiro
    Citation: The Journal of Mathematical Neuroscience 2019 9:2
  26. The ongoing acquisition of large and multifaceted data sets in neuroscience requires new mathematical tools for quantitatively grounding these experimental findings. Since 2015, the International Conference on...

    Authors: Zachary P. Kilpatrick, Julijana Gjorgjieva and Robert Rosenbaum
    Citation: The Journal of Mathematical Neuroscience 2019 9:1
  27. Theta (4–8 Hz) and gamma (30–80 Hz) rhythms in the brain are commonly associated with memory and learning (Kahana in J Neurosci 26:1669–1672, 2006; Quilichini et al. in J Neurosci 30:11128–11142, 2010). The preci...

    Authors: Yujia Zhou, Theodore Vo, Horacio G. Rotstein, Michelle M. McCarthy and Nancy Kopell
    Citation: The Journal of Mathematical Neuroscience 2018 8:13
  28. We review recent work on the theory and applications of stochastic hybrid systems in cellular neuroscience. A stochastic hybrid system or piecewise deterministic Markov process involves the coupling between a ...

    Authors: Paul C. Bressloff and James N. Maclaurin
    Citation: The Journal of Mathematical Neuroscience 2018 8:12
  29. We present the study of a minimal microcircuit controlling locomotion in two-day-old Xenopus tadpoles. During swimming, neurons in the spinal central pattern generator (CPG) generate anti-phase oscillations betwe...

    Authors: Andrea Ferrario, Robert Merrison-Hort, Stephen R. Soffe, Wen-Chang Li and Roman Borisyuk
    Citation: The Journal of Mathematical Neuroscience 2018 8:10
  30. Neurons in a micro-circuit connected by chemical synapses can have their connectivity affected by the prior activity of the cells. The number of synapses available for releasing neurotransmitter can be decreas...

    Authors: Elham Bayat Mokhtari, J. Josh Lawrence and Emily F. Stone
    Citation: The Journal of Mathematical Neuroscience 2018 8:7
  31. Many physiological phenomena have the property that some variables evolve much faster than others. For example, neuron models typically involve observable differences in time scales. The Hodgkin–Huxley model i...

    Authors: Cris R. Hasan, Bernd Krauskopf and Hinke M. Osinga
    Citation: The Journal of Mathematical Neuroscience 2018 8:5

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