292 research outputs found
On the spectra of certain integro-differential-delay problems with applications in neurodynamics
We investigate the spectrum of certain integro-differential-delay equations (IDDEs) which arise naturally within spatially distributed, nonlocal, pattern formation problems. Our approach is based on the reformulation of the relevant dispersion relations with the use of the Lambert function. As a particular application of this approach, we consider the case of the Amari delay neural field equation which describes the local activity of a population of neurons taking into consideration the finite propagation speed of the electric signal. We show that if the kernel appearing in this equation is symmetric around some point a= 0 or consists of a sum of such terms, then the relevant dispersion relation yields spectra with an infinite number of branches, as opposed to finite sets of eigenvalues considered in previous works. Also, in earlier works the focus has been on the most rightward part of the spectrum and the possibility of an instability driven pattern formation. Here, we numerically survey the structure of the entire spectra and argue that a detailed knowledge of this structure is important within neurodynamical applications. Indeed, the Amari IDDE acts as a filter with the ability to recognise and respond whenever it is excited in such a way so as to resonate with one of its rightward modes, thereby amplifying such inputs and dampening others. Finally, we discuss how these results can be generalised to the case of systems of IDDEs
Creativity and the Brain
Neurocognitive approach to higher cognitive functions that bridges the gap between psychological and neural level of description is introduced. Relevant facts about the brain, working memory and representation of symbols in the brain are summarized. Putative brain processes responsible for problem solving, intuition, skill learning and automatization are described. The role of non-dominant brain hemisphere in solving problems requiring insight is conjectured. Two factors seem to be essential for creativity: imagination constrained by experience, and filtering that selects most interesting solutions. Experiments with paired words association are analyzed in details and evidence for stochastic resonance effects is found. Brain activity in the process of invention of novel words is proposed as the simplest way to understand creativity using experimental and computational means. Perspectives on computational models of creativity are discussed
Effective Reduced Diffusion-Models: A Data Driven Approach to the Analysis of Neuronal Dynamics
We introduce in this paper a new method for reducing neurodynamical data to an effective diffusion equation, either experimentally or using simulations of biophysically detailed models. The dimensionality of the data is first reduced to the first principal component, and then fitted by the stationary solution of a mean-field-like one-dimensional Langevin equation, which describes the motion of a Brownian particle in a potential. The advantage of such description is that the stationary probability density of the dynamical variable can be easily derived. We applied this method to the analysis of cortical network dynamics during up and down states in an anesthetized animal. During deep anesthesia, intracellularly recorded up and down states transitions occurred with high regularity and could not be adequately described by a one-dimensional diffusion equation. Under lighter anesthesia, however, the distributions of the times spent in the up and down states were better fitted by such a model, suggesting a role for noise in determining the time spent in a particular state
Behaviourally meaningful representations from normalisation and context-guided denoising
Many existing independent component analysis algorithms include a preprocessing stage where the inputs are sphered. This amounts to normalising the data such that all correlations between the variables are removed. In this work, I show that sphering allows very weak contextual modulation to steer the development of meaningful features. Context-biased competition has been proposed as a model of covert attention and I propose that sphering-like normalisation also allows weaker top-down bias to guide attention
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