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  1. Content type: Research

    Rapid action potential generation - spiking - and alternating intervals of spiking and quiescence - bursting - are two dynamic patterns commonly observed in neuronal activity. In computational models of neuron...

    Authors: John Burke, Mathieu Desroches, Anna M Barry, Tasso J Kaper and Mark A Kramer

    Citation: The Journal of Mathematical Neuroscience 2012 2:3

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  2. Content type: Research

    We study synaptic plasticity in a complex neuronal cell model where NMDA-spikes can arise in certain dendritic zones. In the context of reinforcement learning, two kinds of plasticity rules are derived, zone r...

    Authors: Mathieu Schiess, Robert Urbanczik and Walter Senn

    Citation: The Journal of Mathematical Neuroscience 2012 2:2

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  3. Content type: Research

    We describe a phenomenological model of seizure initiation, consisting of a bistable switch between stable fixed point and stable limit-cycle attractors. We determine a quasi-analytic formula for the exit time...

    Authors: Oscar Benjamin, Thomas HB Fitzgerald, Peter Ashwin, Krasimira Tsaneva-Atanasova, Fahmida Chowdhury, Mark P Richardson and John R Terry

    Citation: The Journal of Mathematical Neuroscience 2012 2:1

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  4. Content type: Research

    We introduce a test for robustness of heteroclinic cycles that appear in neural microcircuits modeled as coupled dynamical cells. Robust heteroclinic cycles (RHCs) can appear as robust attractors in Lotka-Volt...

    Authors: Peter Ashwin, Özkan Karabacak and Thomas Nowotny

    Citation: The Journal of Mathematical Neuroscience 2011 1:13

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  5. Content type: Research

    Pituitary cells of the anterior pituitary gland secrete hormones in response to patterns of electrical activity. Several types of pituitary cells produce short bursts of electrical activity which are more effe...

    Authors: Wondimu Teka, Joël Tabak, Theodore Vo, Martin Wechselberger and Richard Bertram

    Citation: The Journal of Mathematical Neuroscience 2011 1:12

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  6. Content type: Research

    We employ a Hodgkin-Huxley-type model of basolateral ionic currents in bullfrog saccular hair cells for studying the genesis of spontaneous voltage oscillations and their role in shaping the response of the ha...

    Authors: Alexander B Neiman, Kai Dierkes, Benjamin Lindner, Lijuan Han and Andrey L Shilnikov

    Citation: The Journal of Mathematical Neuroscience 2011 1:11

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  7. Content type: Research

    Dendritic spines are small protrusions on a neuronal dendrite that are the main locus of excitatory synaptic connections. Although their geometry is variable over time and along the dendrite, they typically co...

    Authors: David Holcman and Zeev Schuss

    Citation: The Journal of Mathematical Neuroscience 2011 1:10

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  8. Content type: Research

    A major obstacle in the analysis of many physiological models is the issue of model simplification. Various methods have been used for simplifying such models, with one common technique being to eliminate cert...

    Authors: Wenjun Zhang, Vivien Kirk, James Sneyd and Martin Wechselberger

    Citation: The Journal of Mathematical Neuroscience 2011 1:9

    Published on:

  9. Content type: Research

    Physical and physiological invariance laws, in particular time invariance and local symmetry, are at the outset of an abstract model. Harmonic analysis and Lie theory are the mathematical prerequisites for its...

    Authors: Hans Martin Reimann

    Citation: The Journal of Mathematical Neuroscience 2011 1:5

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  10. Content type: Research

    We consider the constrained optimization of excitatory synaptic input patterns to maximize spike generation in leaky integrate-and-fire (LIF) and theta model neurons. In the case of discrete input kicks with a...

    Authors: Jiaoyan Wang, Willie Costello and Jonathan E Rubin

    Citation: The Journal of Mathematical Neuroscience 2011 1:3

    Published on:

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