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Canard solutions in neural mass models: consequences on critical regimes J. Math. Neurosc. (IF 2.3) Pub Date : 2021-09-16 Köksal Ersöz, Elif, Wendling, Fabrice
Mathematical models at multiple temporal and spatial scales can unveil the fundamental mechanisms of critical transitions in brain activities. Neural mass models (NMMs) consider the average temporal dynamics of interconnected neuronal subpopulations without explicitly representing the underlying cellular activity. The mesoscopic level offered by the neural mass formulation has been used to model e
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Canard solutions in neural mass models: consequences on critical regimes. J. Math. Neurosc. (IF 2.3) Pub Date : 2021-09-16 Elif Köksal Ersöz,Fabrice Wendling
Mathematical models at multiple temporal and spatial scales can unveil the fundamental mechanisms of critical transitions in brain activities. Neural mass models (NMMs) consider the average temporal dynamics of interconnected neuronal subpopulations without explicitly representing the underlying cellular activity. The mesoscopic level offered by the neural mass formulation has been used to model e
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Rendering neuronal state equations compatible with the principle of stationary action J. Math. Neurosc. (IF 2.3) Pub Date : 2021-08-12 Fagerholm, Erik D., Foulkes, W. M. C., Friston, Karl J., Moran, Rosalyn J., Leech, Robert
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, computational neuroscience, despite its heavy reliance on concepts in physics, is anomalous in this regard as its main equations of motion are not compatible with a Lagrangian formulation and
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Pattern formation in a 2-population homogenized neuronal network model J. Math. Neurosc. (IF 2.3) Pub Date : 2021-06-26 Karina Kolodina, John Wyller, Anna Oleynik, Mads Peter Sørensen
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 both the synaptic footprint and in the spatial scale. It is shown that the nonlocal synaptic interactions promote a finite band width instability. The stability method relies on a sequence of
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Auditory streaming emerges from fast excitation and slow delayed inhibition J. Math. Neurosc. (IF 2.3) Pub Date : 2021-05-03 Andrea Ferrario, James Rankin
In the auditory streaming paradigm, alternating sequences of pure tones can be perceived as a single galloping rhythm (integration) or as two sequences with separated low and high tones (segregation). Although studied for decades, the neural mechanisms underlining this perceptual grouping of sound remains a mystery. With the aim of identifying a plausible minimal neural circuit that captures this phenomenon
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A model of on/off transitions in neurons of the deep cerebellar nuclei: deciphering the underlying ionic mechanisms J. Math. Neurosc. (IF 2.3) Pub Date : 2021-04-01 Hugues Berry, Stéphane Genet
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 properties of DCNn is of fundamental importance to understand the overall functioning of the cerebellum. Experimental data suggest that DCNn can reversibly switch between two states: the firing
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Estimating Fisher discriminant error in a linear integrator model of neural population activity J. Math. Neurosc. (IF 2.3) Pub Date : 2021-02-19 Matias Calderini, Jean-Philippe Thivierge
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 discriminant analysis. We provide expressions that relate decoding error to the specific parameters of a population model that performs linear integration of sensory input. Results show conditions that
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M-current induced Bogdanov–Takens bifurcation and switching of neuron excitability class J. Math. Neurosc. (IF 2.3) Pub Date : 2021-02-15 Isam Al-Darabsah, Sue Ann Campbell
In this work, we consider a general conductance-based neuron model with the inclusion of the acetycholine sensitive, M-current. We study bifurcations in the parameter space consisting of the applied current $I_{app}$ , the maximal conductance of the M-current $g_{M}$ and the conductance of the leak current $g_{L}$ . We give precise conditions for the model that ensure the existence of a Bogdanov–Takens
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Retroactive interference model of forgetting J. Math. Neurosc. (IF 2.3) Pub Date : 2021-01-23 Antonios Georgiou, Mikhail Katkov, Misha Tsodyks
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 develop phenomenological models that implement its putative mechanisms in the most elementary way possible, and then experimentally test the theoretical predictions of these models. One such mechanism
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On the potential role of lateral connectivity in retinal anticipation J. Math. Neurosc. (IF 2.3) Pub Date : 2021-01-09 Selma Souihel, Bruno Cessac
We analyse the potential effects of lateral connectivity (amacrine cells and gap junctions) on motion anticipation in the retina. Our main result is that lateral connectivity can—under conditions analysed in the paper—trigger a wave of activity enhancing the anticipation mechanism provided by local gain control (Berry et al. in Nature 398(6725):334–338, 1999; Chen et al. in J. Neurosci. 33(1):120–132
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A bio-inspired geometric model for sound reconstruction J. Math. Neurosc. (IF 2.3) Pub Date : 2021-01-04 Ugo Boscain, Dario Prandi, Ludovic Sacchelli, Giuseppina Turco
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 based on the functional architecture of the auditory cortex (A1). The model is inspired by the geometrical modelling of vision, which has undergone a great development in the last ten years. There
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Noisy network attractor models for transitions between EEG microstates J. Math. Neurosc. (IF 2.3) Pub Date : 2021-01-04 Jennifer Creaser, Peter Ashwin, Claire Postlethwaite, Juliane Britz
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, perception, cognition, and ultimately consciousness, but the underlying dynamics governing the constant reorganization and switching between networks are not yet well understood. Electroencephalogram
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Neural field models with transmission delays and diffusion J. Math. Neurosc. (IF 2.3) Pub Date : 2020-12-09 Len Spek, Yuri A. Kuznetsov, Stephan A. van Gils
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 connections. We extend known and prove new sun-star calculus results for delay equations to be able to include diffusion and explicitly characterise the essential spectrum. For a certain class of
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Stability analysis of a neural field self-organizing map J. Math. Neurosc. (IF 2.3) Pub Date : 2020-12-01 Georgios Detorakis, Antoine Chaillet, Nicolas P. Rougier
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 of the primary somatosensory cortex. We rely on Lyapunov’s theory for neural fields to derive theoretical conditions for stability. We verify the theoretical conditions by numerical experiments
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Interactions of multiple rhythms in a biophysical network of neurons J. Math. Neurosc. (IF 2.3) Pub Date : 2020-11-17 Alexandros Gelastopoulos, Nancy J. Kopell
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 frequency, but very little is known about how such input affects the network’s behavior. We use a simplified, yet biophysical, model of a beta1 rhythm that occurs in the parietal cortex, in order to
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Spatio-chromatic information available from different neural layers via Gaussianization J. Math. Neurosc. (IF 2.3) Pub Date : 2020-11-11 Jesús Malo
How much visual information about the retinal images can be extracted from the different layers of the visual pathway? This question depends on the complexity of the visual input, the set of transforms applied to this multivariate input, and the noise of the sensors in the considered layer. Separate subsystems (e.g. opponent channels, spatial filters, nonlinearities of the texture sensors) have been
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A new blind color watermarking based on a psychovisual model J. Math. Neurosc. (IF 2.3) Pub Date : 2020-10-23 Pascal Lefevre, David Alleysson, Philippe Carre
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 perception of color differences. This algorithm is based on a psychovisual model of the dynamics of cone photoreceptors. We used this model to determine the discrimination power of the human for a particular
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Synchronization and resilience in the Kuramoto white matter network model with adaptive state-dependent delays. J. Math. Neurosc. (IF 2.3) Pub Date : 2020-09-16 Seong Hyun Park,Jérémie Lefebvre
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 matter networks are adaptive and that myelin remodels itself in an activity-dependent way, during both developmental stages and later on through behaviour and learning. As a result, axonal conduction
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Attractor-state itinerancy in neural circuits with synaptic depression. J. Math. Neurosc. (IF 2.3) Pub Date : 2020-09-11 Bolun Chen,Paul Miller
Neural populations with strong excitatory recurrent connections can support bistable states in their mean firing rates. Multiple fixed points in a network of such bistable units can be used to model memory retrieval and pattern separation. The stability of fixed points may change on a slower timescale than that of the dynamics due to short-term synaptic depression, leading to transitions between quasi-stable
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Geometry of color perception. Part 2: perceived colors from real quantum states and Hering's rebit. J. Math. Neurosc. (IF 2.3) Pub Date : 2020-09-09 M Berthier
Inspired by the pioneer work of H.L. Resnikoff, which is described in full detail in the first part of this two-part paper, we give a quantum description of the space $\mathcal{P}$ of perceived colors. We show that $\mathcal{P}$ is the effect space of a rebit, a real quantum qubit, whose state space is isometric to Klein’s hyperbolic disk. This chromatic state space of perceived colors can be represented
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The geometry of rest-spike bistability. J. Math. Neurosc. (IF 2.3) Pub Date : 2020-09-04 Giuseppe Ilario Cirillo,Rodolphe Sepulchre
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 this model with one slow inward current to capture the additional property of bistability between a resting state and a spiking limit cycle for a range of input current. The resulting dynamical
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Neurally plausible mechanisms for learning selective and invariant representations. J. Math. Neurosc. (IF 2.3) Pub Date : 2020-08-18 Fabio Anselmi,Ankit Patel,Lorenzo Rosasco
Coding for visual stimuli in the ventral stream is known to be invariant to object identity preserving nuisance transformations. Indeed, much recent theoretical and experimental work suggests that the main challenge for the visual cortex is to build up such nuisance invariant representations. Recently, artificial convolutional networks have succeeded in both learning such invariant properties and,
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A sub-Riemannian model of the visual cortex with frequency and phase. J. Math. Neurosc. (IF 2.3) Pub Date : 2020-07-29 E Baspinar,A Sarti,G Citti
In this paper, we present a novel model of the primary visual cortex (V1) based on orientation, frequency, and phase selective behavior of V1 simple cells. We start from the first-level mechanisms of visual perception, receptive profiles. The model interprets V1 as a fiber bundle over the two-dimensional retinal plane by introducing orientation, frequency, and phase as intrinsic variables. Each receptive
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Methods to assess binocular rivalry with periodic stimuli. J. Math. Neurosc. (IF 2.3) Pub Date : 2020-06-15 Farzaneh Darki,James Rankin
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) Traditional experiments where the stimulus is fixed, (2) eye-swap experiments in which the stimulus periodically swaps between eyes many times per second (Logothetis et al. in Nature 380(6575):621–624
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Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review. J. Math. Neurosc. (IF 2.3) Pub Date : 2020-05-27 Christian Bick,Marc Goodfellow,Carlo R Laing,Erik A Martens
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 emerging collective dynamics of the network. Synchrony of oscillations is one of the most prominent examples of such collective behavior and has been associated both with function and dysfunction
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Spatially extended balanced networks without translationally invariant connectivity. J. Math. Neurosc. (IF 2.3) Pub Date : 2020-05-13 Christopher Ebsch,Robert Rosenbaum
Networks of neurons in the cerebral cortex exhibit a balance between excitation (positive input current) and inhibition (negative input current). Balanced network theory provides a parsimonious mathematical model of this excitatory-inhibitory balance using randomly connected networks of model neurons in which balance is realized as a stable fixed point of network dynamics in the limit of large network
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Geometry of color perception. Part 1: structures and metrics of a homogeneous color space. J. Math. Neurosc. (IF 2.3) Pub Date : 2020-05-12 Edoardo Provenzi
This is the first half of a two-part paper dealing with the geometry of color perception. Here we analyze in detail the seminal 1974 work by H.L. Resnikoff, who showed that there are only two possible geometric structures and Riemannian metrics on the perceived color space $\mathcal{P} $ compatible with the set of Schrödinger’s axioms completed with the hypothesis of homogeneity. We recast Resnikoff’s
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Correction to: Linking demyelination to compound action potential dispersion with a spike-diffuse-spike approach. J. Math. Neurosc. (IF 2.3) Pub Date : 2020-04-20 Richard Naud,André Longtin
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”.
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Mesoscopic population equations for spiking neural networks with synaptic short-term plasticity J. Math. Neurosc. (IF 2.3) Pub Date : 2020-04-06 Valentin Schmutz, Wulfram Gerstner, Tilo Schwalger
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 for mesoscopic population dynamics with static synapses to the case of dynamic synapses exhibiting short-term plasticity (STP). The extended theory offers an approximate mean-field dynamics for
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Phase-dependence of response curves to deep brain stimulation and their relationship: from essential tremor patient data to a Wilson-Cowan model. J. Math. Neurosc. (IF 2.3) Pub Date : 2020-03-30 Benoit Duchet,Gihan Weerasinghe,Hayriye Cagnan,Peter Brown,Christian Bick,Rafal Bogacz
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 intermediate nucleus of the thalamus at about 130 Hz. Constant stimulation can lead to side effects, it is therefore desirable to find ways to stimulate less while maintaining clinical efficacy. One strategy
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Sparse identification of contrast gain control in the fruit fly photoreceptor and amacrine cell layer. J. Math. Neurosc. (IF 2.3) Pub Date : 2020-02-12 Aurel A Lazar,Nikul H Ukani,Yiyin Zhou
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 robustly transduce and, in conjunction with amacrine cells, process visual scenes and provide the resulting signal to downstream targets. Here, we model the first step of visual processing in
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The hyperbolic model for edge and texture detection in the primary visual cortex. J. Math. Neurosc. (IF 2.3) Pub Date : 2020-01-30 Pascal Chossat
The modeling of neural fields in the visual cortex involves geometrical structures which describe in mathematical formalism the functional architecture of this cortical area. The case of contour detection and orientation tuning has been extensively studied and has become a paradigm for the mathematical analysis of image processing by the brain. Ten years ago an attempt was made to extend these models
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Exact solutions to cable equations in branching neurons with tapering dendrites. J. Math. Neurosc. (IF 2.3) Pub Date : 2020-01-28 Lu Yihe,Yulia Timofeeva
Neurons are biological cells with uniquely complex dendritic morphologies that are not present in other cell types. Electrical signals in a neuron with branching dendrites can be studied by cable theory which provides a general mathematical modelling framework of spatio-temporal voltage dynamics. Typically such models need to be solved numerically unless the cell membrane is modelled either by passive
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Greedy low-rank algorithm for spatial connectome regression. J. Math. Neurosc. (IF 2.3) Pub Date : 2019-11-14 Patrick Kürschner,Sergey Dolgov,Kameron Decker Harris,Peter Benner
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 regression problem (Harris et al. in Neural Information Processing Systems, 2016), but existing techniques do not scale to the whole-brain setting. The corresponding matrix equation is challenging to solve
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Stochastic Network Models in Neuroscience: A Festschrift for Jack Cowan. Introduction to the Special Issue. J. Math. Neurosc. (IF 2.3) Pub Date : 2016-04-05 Paul C Bressloff,Bard Ermentrout,Olivier Faugeras,Peter J Thomas
Jack Cowan's remarkable career has spanned, and molded, the development of neuroscience as a quantitative and mathematical discipline combining deep theoretical contributions, rigorous mathematical work and groundbreaking biological insights. The Banff International Research Station hosted a workshop in his honor, on Stochastic Network Models of Neocortex, July 17-24, 2014. This accompanying Festschrift
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Neural Field Models with Threshold Noise. J. Math. Neurosc. (IF 2.3) Pub Date : 2016-03-05 Rüdiger Thul,Stephen Coombes,Carlo R Laing
The original neural field model of Wilson and Cowan is often interpreted as the averaged behaviour of a network of switch like neural elements with a distribution of switch thresholds, giving rise to the classic sigmoidal population firing-rate function so prevalent in large scale neuronal modelling. In this paper we explore the effects of such threshold noise without recourse to averaging and show
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Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience. J. Math. Neurosc. (IF 2.3) Pub Date : 2016-01-08 Peter Ashwin,Stephen Coombes,Rachel Nicks
The tools of weakly coupled phase oscillator theory have had a profound impact on the neuroscience community, providing insight into a variety of network behaviours ranging from central pattern generation to synchronisation, as well as predicting novel network states such as chimeras. However, there are many instances where this theory is expected to break down, say in the presence of strong coupling
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Wilson-Cowan Equations for Neocortical Dynamics. J. Math. Neurosc. (IF 2.3) Pub Date : 2016-01-04 Jack D Cowan,Jeremy Neuman,Wim van Drongelen
In 1972-1973 Wilson and Cowan introduced a mathematical model of the population dynamics of synaptically coupled excitatory and inhibitory neurons in the neocortex. The model dealt only with the mean numbers of activated and quiescent excitatory and inhibitory neurons, and said nothing about fluctuations and correlations of such activity. However, in 1997 Ohira and Cowan, and then in 2007-2009 Buice
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Correction to: Linking demyelination to compound action potential dispersion with a spike-diffuse-spike approach. J. Math. Neurosc. (IF 2.3) Pub Date : 2019-08-22 Richard Naud,André Longtin
Following publication of the original article [1], the authors noticed a mistake in the first paragraph within “Altered propagation”.
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The uncoupling limit of identical Hopf bifurcations with an application to perceptual bistability. J. Math. Neurosc. (IF 2.3) Pub Date : 2019-08-05 Alberto Pérez-Cervera,Peter Ashwin,Gemma Huguet,Tere M Seara,James Rankin
We study the dynamics arising when two identical oscillators are coupled near a Hopf bifurcation where we assume a parameter ϵ uncouples the system at $\epsilon =0$ . Using a normal form for $N=2$ identical systems undergoing Hopf bifurcation, we explore the dynamical properties. Matching the normal form coefficients to a coupled Wilson–Cowan oscillator network gives an understanding of different types
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Data-driven inference for stationary jump-diffusion processes with application to membrane voltage fluctuations in pyramidal neurons. J. Math. Neurosc. (IF 2.3) Pub Date : 2019-07-26 Alexandre Melanson,André Longtin
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 the assumptions of this approach. We address this situation here by providing a novel method that reconstructs a jump-diffusion stochastic process based solely on the statistics of the original
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Drift-diffusion models for multiple-alternative forced-choice decision making. J. Math. Neurosc. (IF 2.3) Pub Date : 2019-07-03 Alex Roxin
The canonical computational model for the cognitive process underlying two-alternative forced-choice decision making is the so-called drift–diffusion model (DDM). In this model, a decision variable keeps track of the integrated difference in sensory evidence for two competing alternatives. Here I extend the notion of a drift–diffusion process to multiple alternatives. The competition between n alternatives
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A modified Hodgkin-Huxley model to show the effect of motor cortex stimulation on the trigeminal neuralgia network. J. Math. Neurosc. (IF 2.3) Pub Date : 2019-05-31 Mohammadreza Khodashenas,Golnaz Baghdadi,Farzad Towhidkhah
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 frequency. In this regard, transcranial direct current stimulation (tDCS) is another therapeutic method to reduce pain, which has been recently attracting the therapists’ attention. The positive
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Linking demyelination to compound action potential dispersion with a spike-diffuse-spike approach. J. Math. Neurosc. (IF 2.3) Pub Date : 2019-05-30 Richard Naud,André Longtin
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-diffuse-spike (SSDS) model for assessing the effects of demyelination on axonal transmission. It models transmission through nodal and internodal compartments with two types of operations: a stochastic
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Efficient calculation of heterogeneous non-equilibrium statistics in coupled firing-rate models. J. Math. Neurosc. (IF 2.3) Pub Date : 2019-05-09 Cheng Ly,Woodrow L Shew,Andrea K Barreiro
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 interactions among multiple, heterogeneous brain regions. Realistic modeling of these large networks requires enormous computational resources, especially when high-dimensional parameter spaces
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Special Issue from the 2017 International Conference on Mathematical Neuroscience. J. Math. Neurosc. (IF 2.3) Pub Date : 2019-01-07 Zachary P Kilpatrick,Julijana Gjorgjieva,Robert Rosenbaum
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 Mathematical Neuroscience (ICMNS) has provided a forum for researchers to discuss current mathematical innovations emerging in neuroscience. This special issue assembles current research and
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M-Current Expands the Range of Gamma Frequency Inputs to Which a Neuronal Target Entrains. J. Math. Neurosc. (IF 2.3) Pub Date : 2018-12-05 Yujia Zhou,Theodore Vo,Horacio G Rotstein,Michelle M McCarthy,Nancy Kopell
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 precision of co-firing between neurons and incoming inputs is critical in these cognitive functions. We consider an inhibitory neuron model with M-current under forcing from gamma pulses and a sinusoidal
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Stochastic Hybrid Systems in Cellular Neuroscience. J. Math. Neurosc. (IF 2.3) Pub Date : 2018-08-22 Paul C Bressloff,James N Maclaurin
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 piecewise deterministic differential equation and a time-homogeneous Markov chain on some discrete space. The latter typically represents some random switching process. We begin by summarizing
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Data Assimilation Methods for Neuronal State and Parameter Estimation. J. Math. Neurosc. (IF 2.3) Pub Date : 2018-08-09 Matthew J Moye,Casey O Diekman
This tutorial illustrates the use of data assimilation algorithms to estimate unobserved variables and unknown parameters of conductance-based neuronal models. Modern data assimilation (DA) techniques are widely used in climate science and weather prediction, but have only recently begun to be applied in neuroscience. The two main classes of DA techniques are sequential methods and variational methods
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Bifurcations of Limit Cycles in a Reduced Model of the Xenopus Tadpole Central Pattern Generator. J. Math. Neurosc. (IF 2.3) Pub Date : 2018-07-18 Andrea Ferrario,Robert Merrison-Hort,Stephen R Soffe,Wen-Chang Li,Roman Borisyuk
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 between left and right half-centres. Experimental recordings show that the same CPG neurons can also generate transient bouts of long-lasting in-phase oscillations between left-right centres. These
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What Is Required for Neuronal Calcium Waves? A Numerical Parameter Study. J. Math. Neurosc. (IF 2.3) Pub Date : 2018-07-13 Markus Breit,Gillian Queisser
Neuronal calcium signals propagating by simple diffusion and reaction with mobile and stationary buffers are limited to cellular microdomains. The distance intracellular calcium signals can travel may be significantly increased by means of calcium-induced calcium release from internal calcium stores, notably the endoplasmic reticulum. The organelle, which can be thought of as a cell-within-a-cell,
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Investigating the Correlation-Firing Rate Relationship in Heterogeneous Recurrent Networks. J. Math. Neurosc. (IF 2.3) Pub Date : 2018-06-06 Andrea K Barreiro,Cheng Ly
The structure of spiking activity in cortical networks has important implications for how the brain ultimately codes sensory signals. However, our understanding of how network and intrinsic cellular mechanisms affect spiking is still incomplete. In particular, whether cell pairs in a neural network show a positive (or no) relationship between pairwise spike count correlation and average firing rate
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Effect of Neuromodulation of Short-term Plasticity on Information Processing in Hippocampal Interneuron Synapses. J. Math. Neurosc. (IF 2.3) Pub Date : 2018-05-29 Elham Bayat Mokhtari,J Josh Lawrence,Emily F Stone
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 decreased by repetitive activation through depletion of readily releasable neurotransmitter (NT), or increased through facilitation, where the probability of release of NT is increased by prior activation
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Analysis of an Attractor Neural Network's Response to Conflicting External Inputs. J. Math. Neurosc. (IF 2.3) Pub Date : 2018-05-16 Kathryn Hedrick,Kechen Zhang
The theory of attractor neural networks has been influential in our understanding of the neural processes underlying spatial, declarative, and episodic memory. Many theoretical studies focus on the inherent properties of an attractor, such as its structure and capacity. Relatively little is known about how an attractor neural network responds to external inputs, which often carry conflicting information
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Saddle Slow Manifolds and Canard Orbits in [Formula: see text] and Application to the Full Hodgkin-Huxley Model. J. Math. Neurosc. (IF 2.3) Pub Date : 2018-04-19 Cris R Hasan,Bernd Krauskopf,Hinke M Osinga
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 is well known for explaining the ionic mechanism that generates the action potential in the squid giant axon. Rubin and Wechselberger (Biol. Cybern. 97:5–32, 2007) nondimensionalized this model
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The Dynamics of Networks of Identical Theta Neurons. J. Math. Neurosc. (IF 2.3) Pub Date : 2018-02-05 Carlo R Laing
We consider finite and infinite all-to-all coupled networks of identical theta neurons. Two types of synaptic interactions are investigated: instantaneous and delayed (via first-order synaptic processing). Extensive use is made of the Watanabe/Strogatz (WS) ansatz for reducing the dimension of networks of identical sinusoidally-coupled oscillators. As well as the degeneracy associated with the constants
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Kernel Reconstruction for Delayed Neural Field Equations. J. Math. Neurosc. (IF 2.3) Pub Date : 2018-02-05 Jehan Alswaihli,Roland Potthast,Ingo Bojak,Douglas Saddy,Axel Hutt
Understanding the neural field activity for realistic living systems is a challenging task in contemporary neuroscience. Neural fields have been studied and developed theoretically and numerically with considerable success over the past four decades. However, to make effective use of such models, we need to identify their constituents in practical systems. This includes the determination of model parameters
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Sparse Functional Identification of Complex Cells from Spike Times and the Decoding of Visual Stimuli. J. Math. Neurosc. (IF 2.3) Pub Date : 2018-01-18 Aurel A Lazar,Nikul H Ukani,Yiyin Zhou
We investigate the sparse functional identification of complex cells and the decoding of spatio-temporal visual stimuli encoded by an ensemble of complex cells. The reconstruction algorithm is formulated as a rank minimization problem that significantly reduces the number of sampling measurements (spikes) required for decoding. We also establish the duality between sparse decoding and functional identification
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Robust Exponential Memory in Hopfield Networks. J. Math. Neurosc. (IF 2.3) Pub Date : 2018-01-16 Christopher J Hillar,Ngoc M Tran
The Hopfield recurrent neural network is a classical auto-associative model of memory, in which collections of symmetrically coupled McCulloch–Pitts binary neurons interact to perform emergent computation. Although previous researchers have explored the potential of this network to solve combinatorial optimization problems or store reoccurring activity patterns as attractors of its deterministic dynamics
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A Rate-Reduced Neuron Model for Complex Spiking Behavior. J. Math. Neurosc. (IF 2.3) Pub Date : 2017-12-11 Koen Dijkstra,Yuri A Kuznetsov,Michel J A M van Putten,Stephan A van Gils
We present a simple rate-reduced neuron model that captures a wide range of complex, biologically plausible, and physiologically relevant spiking behavior. This includes spike-frequency adaptation, postinhibitory rebound, phasic spiking and accommodation, first-spike latency, and inhibition-induced spiking. Furthermore, the model can mimic different neuronal filter properties. It can be used to extend