" Nonlinear Signal Processing of Electroencephalogram .' Application in the Study of Neurodynamics. "

Interfacings of various subjects generate new field ofstudy and research that help in advancing human knowledge. One of the latest of such fields is Neurotechnology, which is an effective amalgamation of neuroscience, physics, biomedical engineering and computational methods. Neurotechnology provides a platform to interact physicist; neurologist and engineers to break methodology and terminology related barriers. Advancements in Computational capability, wider scope of applications in nonlinear dynamics and chaos in complex systems enhanced study of neurodynamics. However there is a need for an effective dialogue among physicists, neurologists and engineers. Application of computer based technology in the field of medicine through signal and image processing, creation of clinical databases for helping clinicians etc are widely acknowledged. Such synergic effects between widely separated disciplines may help in enhancing the effectiveness of existing diagnostic methods. One of the recent methods in this direction is analysis of electroencephalogram with the help of methods in nonlinear dynamics. This thesis is an effort to understand the functional aspects of human brain by studying electroencephalogram. The algorithms and other related methods developed in the present work can be interfaced with a digital EEG machine to unfold the information hidden in the signal. Ultimately this can be used as a diagnostic tool.

Contextual emergence of mental states from neurodynamics

The emergence of mental states from neural states by partitioning the neural phase space is analyzed in terms of symbolic dynamics. Well-defined mental states provide contexts inducing a criterion of structural stability for the neurodynamics that can be implemented by particular partitions. This leads to distinguished subshifts of finite type that are either cyclic or irreducible. Cyclic shifts correspond to asymptotically stable fixed points or limit tori whereas irreducible shifts are obtained from generating partitions of mixing hyperbolic systems. These stability criteria are applied to the discussion of neural correlates of consiousness, to the definition of macroscopic neural states, and to aspects of the symbol grounding problem. In particular, it is shown that compatible mental descriptions, topologically equivalent to the neurodynamical description, emerge if the partition of the neural phase space is generating. If this is not the case, mental descriptions are incompatible or complementary. Consequences of this result for an integration or unification of cognitive science or psychology, respectively, will be indicated.

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.

Financial time series analysis : Chaos and neurodynamics approach

This work aims at combining the Chaos theory postulates and Artificial Neural Networks classification and predictive capability, in the field of financial time series prediction. Chaos theory, provides valuable qualitative and quantitative tools to decide on the predictability of a chaotic system. Quantitative measurements based on Chaos theory, are used, to decide a-priori whether a time series, or a portion of a time series is predictable, while Chaos theory based qualitative tools are used to provide further observations and analysis on the predictability, in cases where measurements provide negative answers. Phase space reconstruction is achieved by time delay embedding resulting in multiple embedded vectors. The cognitive approach suggested, is inspired by the capability of some chartists to predict the direction of an index by looking at the price time series. Thus, in this work, the calculation of the embedding dimension and the separation, in Takens‘ embedding theorem for phase space reconstruction, is not limited to False Nearest Neighbor, Differential Entropy or other specific method, rather, this work is interested in all embedding dimensions and separations that are regarded as different ways of looking at a time series by different chartists, based on their expectations. Prior to the prediction, the embedded vectors of the phase space are classified with Fuzzy-ART, then, for each class a back propagation Neural Network is trained to predict the last element of each vector, whereas all previous elements of a vector are used as features.

Validación diagnóstica del test neural 1 para el síndrome de túnel del carpo

El objetivo de este estudio fue realizar una prueba de validez diagnostica del test neural 1 para el diagnóstico del Síndrome de Túnel del Carpo (STC) utilizando como prueba de referencia o de oro el test de conducción nerviosa. En este estudio participaron 115 sujetos, 230 manos con sospecha clínica de STC quienes fueron evaluados con el test de conducción nerviosa y el test neural 1. Se encontró una sensibilidad del 93.0% (IC 95%:88,21-96,79) y una especificidad del 6,67% (IC 95%:0,0-33,59), razón de verosimilitud positiva fue de 1,00 y razón de verosimilitud negativa de 1,05. Valor predictivo positivo de 86,9% y un valor predictivo negativo de 12,5%. Se concluye que el test neural 1 es una prueba clínica de alta sensibilidad y baja especificidad de gran utilidad para el monitoreo e identificación del STC. Es un procedimiento para el diagnóstico clínico de bajo costo que puede incluirse en los exámenes de rutina de los trabajadores como complemento a las pruebas clínicas sugeridas por las Gatiso para dar mayor precisión a la identificación temprana del STC. Se sugiere combinarla con otros test de mayor especificidad para ser aplicada en trabajadores en condiciones de riesgo o que presenten síntomas en miembros superiores y realizar otros estudios en donde participen sujetos sin diagnóstico clínico del STC.

Language processing with dynamic fields

We construct a mapping from complex recursive linguistic data structures to spherical wave functions using Smolensky's filler/role bindings and tensor product representations. Syntactic language processing is then described by the transient evolution of these spherical patterns whose amplitudes are governed by nonlinear order parameter equations. Implications of the model in terms of brain wave dynamics are indicated.

Unifying syntactic theory and sentence processing difficulty through a connectionist minimalist parser

Syntactic theory provides a rich array of representational assumptions about linguistic knowledge and processes. Such detailed and independently motivated constraints on grammatical knowledge ought to play a role in sentence comprehension. However most grammar-based explanations of processing difficulty in the literature have attempted to use grammatical representations and processes per se to explain processing difficulty. They did not take into account that the description of higher cognition in mind and brain encompasses two levels: on the one hand, at the macrolevel, symbolic computation is performed, and on the other hand, at the microlevel, computation is achieved through processes within a dynamical system. One critical question is therefore how linguistic theory and dynamical systems can be unified to provide an explanation for processing effects. Here, we present such a unification for a particular account to syntactic theory: namely a parser for Stabler's Minimalist Grammars, in the framework of Smolensky's Integrated Connectionist/Symbolic architectures. In simulations we demonstrate that the connectionist minimalist parser produces predictions which mirror global empirical findings from psycholinguistic research.

Towards dynamical system models of language-related brain potentials

Event-related brain potentials (ERP) are important neural correlates of cognitive processes. In the domain of language processing, the N400 and P600 reflect lexical-semantic integration and syntactic processing problems, respectively. We suggest an interpretation of these markers in terms of dynamical system theory and present two nonlinear dynamical models for syntactic computations where different processing strategies correspond to functionally different regions in the system's phase space.

Single tap identification for fast BCI control

One of the major aims of BCI research is devoted to achieving faster and more efficient control of external devices. The identification of individual tap events in a motor imagery BCI is therefore a desirable goal. EEG is recorded from subjects performing and imagining finger taps with their left and right hands. A Differential Evolution based feature selection wrapper is used in order to identify optimal features in the spatial and frequency domains for tap identification. Channel-frequency band combinations are found which allow differentiation of tap vs. no-tap control conditions for executed and imagined taps. Left vs. right hand taps may also be differentiated with features found in this manner. A sliding time window is then used to accurately identify individual taps in the executed tap and imagined tap conditions. Highly statistically significant classification accuracies are achieved with time windows of 0.5 s and more allowing taps to be identified on a single trial basis.

Population based models of cortical drug response: insights from anaesthesia

A great explanatory gap lies between the molecular pharmacology of psychoactive agents and the neurophysiological changes they induce, as recorded by neuroimaging modalities. Causally relating the cellular actions of psychoactive compounds to their influence on population activity is experimentally challenging. Recent developments in the dynamical modelling of neural tissue have attempted to span this explanatory gap between microscopic targets and their macroscopic neurophysiological effects via a range of biologically plausible dynamical models of cortical tissue. Such theoretical models allow exploration of neural dynamics, in particular their modification by drug action. The ability to theoretically bridge scales is due to a biologically plausible averaging of cortical tissue properties. In the resulting macroscopic neural field, individual neurons need not be explicitly represented (as in neural networks). The following paper aims to provide a non-technical introduction to the mean field population modelling of drug action and its recent successes in modelling anaesthesia.

Strain and excursion of the sciatic, tibial, and plantar nerves during a modified straight leg raising test

A modified straight leg raising (SLR) in which ankle dorsiflexion is performed before hip flexion has been suggested to diagnose distal neuropathies such as tarsal tunnel syndrome. This study evaluates the clinical hypothesis that strain in the nerves around the ankle and foot caused by ankle dorsiflexion can be further increased with hip flexion. Linear displacement transducers were inserted into the sciatic, tibial, and plantar nerves and plantar fascia of eight embalmed cadavers to measure strain during the modified SLR. Nerve excursion was measured with a digital calliper. Ankle dorsiflexion resulted in a significant strain and distal. excursion of the tibial nerve. With the ankle in dorsiflexion, the proximal excursion and tension increase in the sciatic nerve associated with hip flexion were transmitted distally along the nerve from the hip to beyond the ankle. As hip flexion had an impact on the nerves around the ankle and foot but not on the plantar fascia, the modified SLR may be a useful test to differentially diagnose plantar heel pain. Although the modified SLR caused the greatest increase in nerve strain nearest the moving joint, mechanical forces acting on peripheral nerves are transmitted well beyond the moving joint. (c) 2006 Orthopaedic Research Society.

Description and training of neural network dynamics

Attractor properties of a popular discrete-time neural network model are illustrated through numerical simulations. The most complex dynamics is found to occur within particular ranges of parameters controlling the symmetry and magnitude of the weight matrix. A small network model is observed to produce fixed points, limit cycles, mode-locking, the Ruelle-Takens route to chaos, and the period-doubling route to chaos. Training algorithms for tuning this dynamical behaviour are discussed. Training can be an easy or difficult task, depending whether the problem requires the use of temporal information distributed over long time intervals. Such problems require training algorithms which can handle hidden nodes. The most prominent of these algorithms, back propagation through time, solves the temporal credit assignment problem in a way which can work only if the relevant information is distributed locally in time. The Moving Targets algorithm works for the more general case, but is computationally intensive, and prone to local minima.

A representation of representation applied to a discussion of variable binding

States or state sequences in neural network models are made to represent concepts from applications. This paper motivates, introduces and discusses a formalism for denoting such representations; a representation for representations. The formalism is illustrated by using it to discuss the representation of variable binding and inference abstractly, and then to present four specific representations. One of these is an apparently novel hybrid of phasic and tensor-product representations which retains the desirable properties of each.