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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 o...
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, ...
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 ...
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...
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...
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...
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
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 ...
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 t...
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...
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...
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...
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...
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...
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...
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...
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...
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 ret...
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...
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 cha...
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 pe...
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...
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...
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 mo...
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 geometri...
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”.
The original article was published in The Journal of Mathematical Neuroscience 2019 9:3
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...
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...
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...
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 ...
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 ...
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...
Following publication of the original article [1], the authors noticed a mistake in the first paragraph within “Altered propagation”.
The original article was published in The Journal of Mathematical Neuroscience 2019 9:3
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
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 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...
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...
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...
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
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...
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...
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...
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 ...
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 wide...
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...
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 signi...
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...
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...
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 pr...
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...
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