We apply symbolic dynamics techniques such as word statistics and measures of complexity to nonstationary noisy multivariate time series electroencephalograms (EEG) in order estimate event-related brain potentials (ERP). Their significance against surrogate data well between different experimental conditions is tested. These methods are validated by simulations using stochastic dynamical systems with time-dependent control parameters compared traditional ERP-analysis techniques. Continuous...

The emergence of mental states from neural by partitioning the phase space is analyzed in terms symbolic dynamics. Well-defined provide contexts inducing a criterion structural stability for neurodynamics that can be implemented particular partitions. This leads to distinguished subshifts finite type are either cyclic or irreducible. Cyclic shifts correspond asymptotically stable fixed points limit tori whereas irreducible obtained generating partitions mixing hyperbolic systems. These...

Inverse problems for dynamical system models of cognitive processes comprise the determination synaptic weight matrices or kernel functions neural networks neural/dynamic field models, respectively. We introduce dynamic modeling as a three tier top-down approach where are first described algorithms that operate on complex symbolic data structures. Second, expressions and operations represented by states transformations in abstract vector spaces. Third, prescribed trajectories through...

We propose an algorithm for the detection of recurrence domains complex dynamical systems from time series. Our approach exploits characteristic checkerboard texture exhibited in plots. In phase space, plots yield intersecting balls around sampling points that could be merged into cells a space partition. construct this partition by rewriting grammar applied to symbolic dynamics indices. A maximum entropy principle defines optimal size balls. The final application high-dimensional brain...

We consider several puzzles of bounded rationality. These include the Allais- and Ellsberg paradox, disjunction effect, related puzzles. argue that present account quantum cognition—taking probabilities rather than classical probabilities—can give a more systematic description these alternate treatments in traditional frameworks Unfortunately, probabilistic treatment does not always provide deeper understanding true explanation One reason is approaches introduce additional parameters which...

Metastability refers to the fact that state of a dynamical system spends large amount time in restricted region its available phase space before transition takes place, bringing into another from where it might recur previous one. beim Graben and Hutt (2013) suggested use recurrence plot (RP) technique introduced by Eckmann et al. (1987) for segmentation system's trajectories metastable states using grammars. Here, we apply this structure analysis (RSA) first resting-state brain dynamics...

Abstract The first goal of this work is to study the solvability neural field equation (known as ‘Amari equation’) which an integro‐differential in m + 1 dimensions. In particular, we show existence global solutions for smooth activation functions f with values [0, 1] and L kernels w via Banach fixpoint theorem. We note that setting much more general than most related studies, e.g. Ermentrout McLeod ( Proceedings Royal Society Edinburgh 1993; 123A :461–478). For a Heaviside‐type function ,...

We study inverse problems in neural field theory, i.e., the construction of synaptic weight kernels yielding a prescribed dynamics. address issues existence, uniqueness, and stability solutions to problem for Amari equation as special case, prove that these are generally ill-posed. In order construct problem, we first recast into linear perceptron an infinite-dimensional Banach or Hilbert space. second step, sets biorthogonal function systems allowing approximation by generalized Hebbian...

EDITORIAL article Front. Comput. Neurosci., 17 November 2014 Volume 8 - | https://doi.org/10.3389/fncom.2014.00149

We investigate the effect of symbolic encoding applied to times series consisting some deterministic signal and additive noise, as well time given by a with randomly distributed initial conditions model event-related brain potentials. introduce an estimator signal-to-noise ratio (SNR) system means averages running complexity measures such Shannon Rényi entropies, prove its asymptotical equivalence linear SNR in case entropies symbol distributions. A improvement factor is defined, exhibiting...

According to Kant’ss (1724‐1804) philosophical aesthetics, laid down in his Critique of the Power Judgement (1790), Beauty is “subjective purposefulness”, reflected by “harmony cognitive faculties”, which are “understanding” and “imagination”. On one hand, understanding refers mental capability find regularities sensory manifolds, while imagination intuition, phantasy, creativity mind, on other hand. Inspired reinforcement learning theory Schmid-huber, I present a neural network analogy for...

More than thirty years ago, Amari and colleagues proposed a statistical framework for identifying structurally stable macrostates of neural networks from observations their microstates. We compare stochastic stability criterion with deterministic based on the ergodic theory dynamical systems, recently scheme contextual emergence applied to particular inter-level relations in neuroscience. Stochastic criteria rely macro-level contexts, which make them sensitive differences between different...

Recurrent temporal dynamics is a phenomenon observed frequently in high-dimensional complex systems and its detection challenging task. Recurrence quantification analysis utilizing recurrence plots may extract such dynamics, however it still encounters an unsolved pertinent problem: the optimal selection of distance thresholds for estimating structure dynamical systems. The present work proposes stochastic Markov model recurrent that allows analytical derivation criterion threshold. goodness...

Quasistationarity is ubiquitous in complex dynamical systems. In brain dynamics there ample evidence that event-related potentials reflect such quasistationary states. order to detect them from time series, several segmentation techniques have been proposed. this study we elaborate a recent approach for detecting states as recurrence domains by means of analysis and subsequent symbolisation methods. As result, are obtained partition cells can be further aligned unified different...

Metastable attractors and heteroclinic orbits are present in the dynamics of various complex systems. Although their occurrence is well-known, identification modeling a challenging task. The work reviews briefly literature proposes novel combination experimental data by dynamical This applies recurrence structure analysis permitting derivation an optimal symbolic representation metastable states transitions. To derive sequences conditions, introduces Hausdorff clustering algorithm for...