72 research outputs found
On the Electrodynamics of Neural Networks
We present a microscopic approach for the coupling of cortical activity, as resulting from proper dipole currents of pyramidal neurons, to the electromagnetic field in extracellular fluid in presence of diffusion and Ohmic conduction. Starting from a full-fledged three-compartment model of a single pyramidal neuron, including shunting and dendritic propagation, we derive an observation model for dendritic dipole currents in extracellular space and thereby for the dendritic field potential that contributes to the local field potential of a neural population. Under reasonable simplifications, we then derive a leaky integrate-and-fire model for the dynamics of a neural network, which facilitates comparison with existing neural network and observation models. In particular, we compare our results with a related model by means of numerical simulations. Performing a continuum limit, neural activity becomes represented by a neural field equation, while an observation model for electric field potentials is obtained from the interaction of cortical dipole currents with charge density in non-resistive extracellular space as described by the Nernst-Planck equation. Our work consistently satisfies the widespread dipole assumption discussed in the neuroscientific literature
Finding needles in haystacks: Symbolic resonance analysis of event-related potentials unveils different processing demands
Previous ERP studies have found an N400–P600 pattern in sentences in which the number of arguments does not match the number of arguments that the verb can take. In the present study, we elaborate on this question by investigating whether the case of the mismatching object argument in German (accusative/direct object versus dative/indirect object) affects processing differently. In general, both types of mismatches elicited a biphasic N400–P600 response in the ERP. However, traditional voltage average analysis was unable to reveal differences between the two mismatching conditions, that is, between a mismatching accusative versus dative. Therefore, we employed a recently developed method on ERP data analysis, the symbolic resonance analysis (SRA), where EEG epochs are symbolically encoded in sequences of three symbols depending on a given parameter, the encoding threshold. We found a larger proportion of threshold crossing events with negative polarity in the N400 time window for a mismatching dative argument compared to a mismatching accusative argument. By contrast, the proportion of threshold crossing events with positive polarity was smaller for dative in the P600 time window. We argue that this difference is due to the phenomenon of “free dative” in German. This result also shows that the SRA provides a useful tool for revealing ERP differences that cannot be discovered using the traditional voltage average analysis
Turing Computation with Recurrent Artifcial Neural Networks
We improve the results by Siegelmann & Sontag (1995) by providing a novel and
parsimonious constructive mapping between Turing Machines and Recurrent
Artificial Neural Networks, based on recent developments of Nonlinear Dynamical
Automata. The architecture of the resulting R-ANNs is simple and elegant,
stemming from its transparent relation with the underlying NDAs. These
characteristics yield promise for developments in machine learning methods and
symbolic computation with continuous time dynamical systems. A framework is
provided to directly program the R-ANNs from Turing Machine descriptions, in
absence of network training. At the same time, the network can potentially be
trained to perform algorithmic tasks, with exciting possibilities in the
integration of approaches akin to Google DeepMind's Neural Turing Machines.Comment: 11 pages, 3 figure
A modular architecture for transparent computation in recurrent neural networks
publisher: Elsevier articletitle: A modular architecture for transparent computation in recurrent neural networks journaltitle: Neural Networks articlelink: http://dx.doi.org/10.1016/j.neunet.2016.09.001 content_type: article copyright: © 2016 Elsevier Ltd. All rights reserved
Topographic voltage and coherence mapping of brain potentials by means of the symbolic resonance analysis
We apply the recently developed symbolic resonance analysis to electroencephalographic measurements of event-related brain potentials (ERPs) in a language processing experiment by using a three-symbol static encoding with varying thresholds for analyzing the ERP epochs, followed by a spin-flip transformation as a nonlinear filter. We compute an estimator of the signal-to-noise ratio (SNR) for the symbolic dynamics measuring the coherence of threshold-crossing events. Hence, we utilize the inherent noise of the EEG for sweeping the underlying ERP components beyond the encoding thresholds. Plotting the SNR computed within the time window of a particular ERP component (the N400) against the encoding thresholds, we find different resonance curves for the experimental conditions. The maximal differences of the SNR lead to the estimation of optimal encoding thresholds. We show that topographic brain maps of the optimal threshold voltages and of their associated coherence differences are able to dissociate the underlying physiological processes, while corresponding maps gained from the customary voltage averaging technique are unable to do so
Geometric representations for minimalist grammars
We reformulate minimalist grammars as partial functions on term algebras for
strings and trees. Using filler/role bindings and tensor product
representations, we construct homomorphisms for these data structures into
geometric vector spaces. We prove that the structure-building functions as well
as simple processors for minimalist languages can be realized by piecewise
linear operators in representation space. We also propose harmony, i.e. the
distance of an intermediate processing step from the final well-formed state in
representation space, as a measure of processing complexity. Finally, we
illustrate our findings by means of two particular arithmetic and fractal
representations.Comment: 43 pages, 4 figure
Network theory approach for data evaluation in the dynamic force spectroscopy of biomolecular interactions
Investigations of molecular bonds between single molecules and molecular
complexes by the dynamic force spectroscopy are subject to large fluctuations
at nanoscale and possible other aspecific binding, which mask the experimental
output. Big efforts are devoted to develop methods for effective selection of
the relevant experimental data, before taking the quantitative analysis of bond
parameters. Here we present a methodology which is based on the application of
graph theory. The force-distance curves corresponding to repeated pulling
events are mapped onto their correlation network (mathematical graph). On these
graphs the groups of similar curves appear as topological modules, which are
identified using the spectral analysis of graphs. We demonstrate the approach
by analyzing a large ensemble of the force-distance curves measured on:
ssDNA-ssDNA, peptide-RNA (system from HIV1), and peptide-Au surface. Within our
data sets the methodology systematically separates subgroups of curves which
are related to different intermolecular interactions and to spatial
arrangements in which the molecules are brought together and/or pulling speeds.
This demonstrates the sensitivity of the method to the spatial degrees of
freedom, suggesting potential applications in the case of large molecular
complexes and situations with multiple binding sites
Complementarity in classical dynamical systems
The concept of complementarity, originally defined for non-commuting
observables of quantum systems with states of non-vanishing dispersion, is
extended to classical dynamical systems with a partitioned phase space.
Interpreting partitions in terms of ensembles of epistemic states (symbols)
with corresponding classical observables, it is shown that such observables are
complementary to each other with respect to particular partitions unless those
partitions are generating. This explains why symbolic descriptions based on an
\emph{ad hoc} partition of an underlying phase space description should
generally be expected to be incompatible. Related approaches with different
background and different objectives are discussed.Comment: 18 pages, no figure
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