Related papers: Cortical Dynamics of Neural-Connectivity Fields
The incorporation of appropriate inductive bias plays a critical role in learning dynamics from data. A growing body of work has been exploring ways to enforce energy conservation in the learned dynamics by encoding Lagrangian or…
Many mathematical models of synaptic plasticity have been proposed to explain the diversity of plasticity phenomena observed in biological organisms. These models range from simple interpretations of Hebb's postulate, which suggests that…
In this paper we first recall the definition of geometical model of the visual cortex, focusing in particular on the geometrical properties of horizontal cortical connectivity. Then we recognize that histograms of edges - co-occurrences are…
An inhomogeneous anisotropic physical model of the brain cortex is presented that predicts the emergence of non--evanescent (weakly damped) wave--like modes propagating in the thin cortex layers transverse to both the mean neural fiber…
In this review, we examine computational models that explore the role of neural oscillations in speech perception, spanning from early auditory processing to higher cognitive stages. We focus on models that use rhythmic brain activities,…
There is enormous interest -- both mathematically and in diverse applications -- in understanding the dynamics of coupled oscillator networks. The real-world motivation of such networks arises from studies of the brain, the heart, ecology,…
Advancing our knowledge of how the brain processes information remains a key challenge in neuroscience. This thesis combines three different approaches to the study of the dynamics of neural networks and their encoding representations: a…
At functional scales, cortical behavior results from the complex interplay of a large number of excitable cells operating in noisy environments. Such systems resist to mathematical analysis, and computational neurosciences have largely…
We are offering a particular interpretation (well within the range of experimentally and theoretically accepted notions) of neural connectivity and dynamics and discuss it as the data-and-process architecture of the visual system. In this…
Understanding how receptive fields emerge and organize within brain networks and how neural dynamics couple with stimuli space is fundamental to neuroscience. Models often rely on fine-tuning connectivity to match empirical data, which may…
Nonlinear dynamical modeling of interaction between automatic and conscious processes in the human brain is considered in terms of the quaternion fields. The interaction is due, particularly, to the nonlinear firing rate of neurons.…
We introduce and study a new model of interacting neural networks, incorporating the spatial dimension (e.g. position of neurons across the cortex) and some learning processes. The dynamic of each neural network is described via the elapsed…
Neurobiological theories of spatial cognition developed with respect to recording data from relatively small and/or simplistic environments compared to animals' natural habitats. It has been unclear how to extend theoretical models to large…
Recent experiments have highlighted how collective dynamics in networks of brain regions affect behavior and cognitive function. In this paper we show that a simple, homogeneous system of densely connected oscillators representing the…
Spatiotemporal flows of neural activity, such as traveling waves, have been observed throughout the brain since the earliest recordings; yet there is still little consensus on their functional role. Recent experiments and models have linked…
Biological cells in soft materials can be modeled as anisotropic force contraction dipoles. The corresponding elastic interaction potentials are long-ranged ($\sim 1/r^3$ with distance $r$) and depend sensitively on elastic constants,…
Neural field theory is used to quantitatively analyze the two-dimensional spatiotemporal correlation properties of gamma-band (30 -- 70 Hz) oscillations evoked by stimuli arriving at the primary visual cortex (V1), and modulated by patchy…
Motivated by the formation of ring-like filament structures in the cortex of plant and animal cells, we study the dynamics of a two-dimensional layer of cytoskeletal filaments and motor proteins near a surface by a general continuum theory.…
Spontaneous oscillations measured by Local field potentials (LFPs), electroencephalograms and magnetoencephalograms exhibits variety of oscillations spanning frequency band ($1-100$ Hz) in animals and humans. Both instantaneous power and…
Helical structures like alpha helices, DNA, and microtubules have profound importance in biology. It has been suggested that these periodic arrangements of constituent units could support collective excitations similarly to crystalline…