163 research outputs found
Outline of a novel architecture for cortical computation
In this paper a novel architecture for cortical computation has been
proposed. This architecture is composed of computing paths consisting of
neurons and synapses only. These paths have been decomposed into lateral,
longitudinal and vertical components. Cortical computation has then been
decomposed into lateral computation (LaC), longitudinal computation (LoC) and
vertical computation (VeC). It has been shown that various loop structures in
the cortical circuit play important roles in cortical computation as well as in
memory storage and retrieval, keeping in conformity with the molecular basis of
short and long term memory. A new learning scheme for the brain has also been
proposed and how it is implemented within the proposed architecture has been
explained. A number of mathematical results about the architecture have been
proposed, many of which without proof.Comment: 21 pages, four figure
A structural and a functional aspect of stable information processing by the brain
In this paper a model of neural circuit in the brain has been proposed which
is composed of cyclic sub-circuits. A big loop has been defined to be
consisting of a feed forward path from the sensory neurons to the highest
processing area of the brain and feed back paths from that region back up to
close to the same sensory neurons. It has been mathematically shown how some
smaller cycles can amplify signal. A big loop processes information by contrast
and amplify principle. It has been assumed that the spike train coming out of a
firing neuron encodes all the information produced by it as output. This
information over a period of time can be extracted by a Fourier transform. The
Fourier coefficients arranged in a vector form will uniquely represent the
neural spike train over a period of time. The information emanating out of all
the neurons in a given neural circuit over a period of time will be represented
by a collection of points in a multidimensional vector space. This cluster of
points represents the functional or behavioral form of the neural circuit. It
has been proposed that a particular cluster of vectors as the representation of
a new behavior is chosen by the brain interactively with respect to the memory
stored in that circuit and the synaptic plasticity of the circuit. It has been
proposed that in this situation a Coulomb force like expression governs the
dynamics of functioning of the circuit and stability of the system is reached
at the minimum of all the minima of a potential function derived from the force
like expression. The calculations have been done with respect to a pseudometric
defined in a multidimensional vector space.Comment: Sixteen pages, two figures. Accepted for publication in Cognitive
Neurodynamics (Springer
An FFT based measure of phase synchronization
In this paper phase of a signal has been viewed from a different angle.
According to this view a signal can have countably infinitely many phases, one
associated with each Fourier component. In other words each frequency has a
phase associated with it. It has been shown that if two signals are phase
synchronous then the difference between phases at a given component changes
very slowly across the subsequent components. This leads to an FFT based phase
synchronization measuring algorithm between any two signals. The algorithm does
not take any more time than the FFT itself. Mathematical motivations as well as
some results of implementation of the algorithm on artificially generated
signals and real EEG signals have been presented.Comment: 12 pages, 5 figures. Revised draft (substantial revision). Under
review in a journa
Differential Operator in Seizure Detection
Differential operators can detect significant changes in signals. This has
been utilized to enhance the contrast of the seizure signatures in depth EEG or
ECoG. We have actually taken normalized exponential of absolute value of single
or double derivative of epileptic ECoG. Variance operation has been performed
to automatically detect seizures. A novel method for determining the duration
of seizure has also been proposed. Since all operations take only linear time,
the whole method is extremely fast. Seven novel parameters have been introduced
whose patient specific thresholding brings down the rate of false detection to
a bare minimum. Results of implementation on the ECoG data of four epileptic
patients have been reported with an ROC curve analysis. High value of the area
under the ROC curve indicates excellent detection performance.Comment: 15 pages, 3 figures, two tables. Submitted to Computers in Biology
and Medicine (Elsevier
Fourier Uniformity: An Useful Tool for Analyzing EEG Signals with An Application to Source Localization
If two signals are phase synchronous then the respective Fourier component at
each spectral band should exhibit certain properties. In a pair of artificially
generated phase synchronous signals the phase difference at each frequency band
changes very slowly over the subsequent frequency bands. This has been called
Fourier uniformity in this paper and a measure of it has been proposed. An
usefulness of this measure has been outlined in the case of cortical source
localization of scalp EEG.Comment: Accepted for oral presententation in the International Joint
Conference of Neural Networks 2009, Atlanta, USA. It will not be included in
the proceedings for the author's inability to attend the conferenc
A Geometric Analysis of Time Series Leading to Information Encoding and a New Entropy Measure
A time series is uniquely represented by its geometric shape, which also
carries information. A time series can be modelled as the trajectory of a
particle moving in a force field with one degree of freedom. The force acting
on the particle shapes the trajectory of its motion, which is made up of
elementary shapes of infinitesimal neighborhoods of points in the trajectory.
It has been proved that an infinitesimal neighborhood of a point in a
continuous time series can have at least 29 different shapes or configurations.
So information can be encoded in it in at least 29 different ways. A 3-point
neighborhood (the smallest) in a discrete time series can have precisely 13
different shapes or configurations. In other words, a discrete time series can
be expressed as a string of 13 symbols. Across diverse real as well as
simulated data sets it has been observed that 6 of them occur more frequently
and the remaining 7 occur less frequently. Based on frequency distribution of
13 configurations or 13 different ways of information encoding a novel entropy
measure, called semantic entropy (E), has been defined. Following notion of
power in Newtonian mechanics of the moving particle whose trajectory is the
time series, a notion of information power (P) has been introduced for time
series. E/P turned out to be an important indicator of synchronous behaviour of
time series as observed in epileptic EEG signals.Comment: 29 pages, 12 figure
A Mathematical Model of Tripartite Synapse: Astrocyte Induced Synaptic Plasticity
In this paper we present a biologically detailed mathematical model of
tripartite synapses, where astrocytes modulate short-term synaptic plasticity.
The model consists of a pre-synaptic bouton, a post-synaptic dendritic
spine-head, a synaptic cleft and a peri-synaptic astrocyte controlling Ca2+
dynamics inside the synaptic bouton. This in turn controls glutamate release
dynamics in the cleft. As a consequence of this, glutamate concentration in the
cleft has been modeled, in which glutamate reuptake by astrocytes has also been
incorporated. Finally, dendritic spine-head dynamics has been modeled. As an
application, this model clearly shows synaptic potentiation in the hippocampal
region, i.e., astrocyte Ca2+ mediates synaptic plasticity, which is in
conformity with the majority of the recent findings (Perea & Araque, 2007;
Henneberger et al., 2010; Navarrete et al., 2012).Comment: 42 pages, 14 figures, Journal of Biological Physics (to appear
Behavioral response to strong aversive stimuli: A neurodynamical model
In this paper a theoretical model of functioning of a neural circuit during a
behavioral response has been proposed. A neural circuit can be thought of as a
directed multigraph whose each vertex is a neuron and each edge is a synapse.
It has been assumed in this paper that the behavior of such circuits is
manifested through the collective behavior of neurons belonging to that
circuit. Behavioral information of each neuron is contained in the coefficients
of the fast Fourier transform (FFT) over the output spike train. Those
coefficients form a vector in a multidimensional vector space. Behavioral
dynamics of a neuronal network in response to strong aversive stimuli has been
studied in a vector space in which a suitable pseudometric has been defined.
The neurodynamical model of network behavior has been formulated in terms of
existing memory, synaptic plasticity and feelings. The model has an analogy in
classical electrostatics, by which the notion of force and potential energy has
been introduced. Since the model takes input from each neuron in a network and
produces a behavior as the output, it would be extremely difficult or may even
be impossible to implement. But with the help of the model a possible
explanation for an hitherto unexplained neurological observation in human brain
has been offered. The model is compatible with a recent model of sequential
behavioral dynamics. The model is based on electrophysiology, but its relevance
to hemodynamics has been outlined.Comment: Submitted to journa
A Novel Matrix Representation of Discrete Biomedical Signals
In this work we propose a novel symmetric square matrix representation of one
or more digital signals of finite equal length. For appropriate window length
and sliding paradigm this matrix contains useful information about the signals
in a two dimensional image form. Then this representation can be treated either
as an algebraic matrix or as a geometric image. We have shown applications of
both on human multichannel intracranial electroencephalogram (iEEG). In the
first application we have shown that for certain patients the highest
eigenvalue of the matrix obtained from the epileptic focal channels goes up
during a seizure. The focus of this paper is on an application of the second
concept, by which we have come up with an automatic seizure detection algorithm
on a publicly available benchmark data. Except for delay in detection in all
other aspects the new algorithm outperformed the detection performance based on
a support vector machine based algorithm. We have also indicated how this
sparse random matrix representation of brain electrical signals can encode the
activities of the brain
Comparison of feature extraction and dimensionality reduction methods for single channel extracellular spike sorting
Spikes in the membrane electrical potentials of neurons play a major role in
the functioning of nervous systems of animals. Obtaining the spikes from
different neurons has been a challenging problem for decades. Several schemes
have been proposed for spike sorting to isolate the spikes of individual
neurons from electrical recordings in extracellular media. However, there is
much scope for improvement in the accuracies obtained using the prevailing
methods of spike sorting. To determine more effective spike sorting strategies
using well known methods, we compared different types of signal features and
techniques for dimensionality reduction in feature space. We tried to determine
an optimum or near optimum feature extraction and dimensionality reduction
methods and an optimum or near optimum number of features for spike sorting. We
assessed relative performance of well known methods on simulated recordings
specially designed for development and benchmarking of spike sorting schemes,
with varying number of spike classes and the well established method of
-means clustering of selected features. We found that almost all well known
methods performed quite well. Nevertheless, from spike waveforms of 64 samples,
sampled at 24 kHz, using principal component analysis (PCA) to select around 46
to 55 features led to the better spike sorting performance than most other
methods (Wilcoxon signed rank sum test, ).Comment: 12 pages, 2 figure
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