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Papers by Antonio Glaría
Clinical Physics and Physiological Measurement, 1983
... and A Murray A number of EEG analysis displays are already available. That of the CFM (Maynar... more ... and A Murray A number of EEG analysis displays are already available. That of the CFM (Maynard et a! 1969) measures the average amplitude of the rectified EEG taken from a specially selected frequency range, but contains no specific frequency information, Hjorth (1970 ...
Anaesthesia, 1986
Changes in the electroencephalograms of patients undergoing cardiac surgery with cardiopulmonary ... more Changes in the electroencephalograms of patients undergoing cardiac surgery with cardiopulmonary bypass were studied. A n analysis technique with a simple display of amplitude and frequency within the traditional bands was used. During the course qfan operation, there can be dramatic changes in frequency contribution with little or no change in overall EEG amplitude. Evaluation of the results shows that this technique clearly draws attention to periods of EEG change, and examples are given.
Electroencephalography and Clinical Neurophysiology, 1985
A single channel EEG recording was made in 25 patients undergoing cardiac surgery and analysed us... more A single channel EEG recording was made in 25 patients undergoing cardiac surgery and analysed using 5 different techniques--amplitude, cerebral function monitor, Fourier, Hjorth, and zero-crossing analyses. The results of the analyses were plotted as trend information on paper. These trends were studied for changes in the EEG during surgery. In the majority of cases changes were noted simultaneously by all 5 techniques. There were, however, some cases in which an amplitude-only technique showed no changes while frequency contributions were changing, and a frequency-only technique showed no changes while amplitudes were changing. The conclusion drawn is that major EEG changes are observed with any of the techniques studied, but that for improved sensitivity a technique analysing both frequency and amplitude information should be used.
Frontiers in Applied Mathematics and Statistics
Linear functional analysis historically founded by Fourier and Legendre played a significant role... more Linear functional analysis historically founded by Fourier and Legendre played a significant role to provide a unified vision of mathematical transformations between vector spaces. The possibility of extending this approach is explored when basis of vector spaces is built Tailored to the Problem Specificity (TPS) and not from the convenience or effectiveness of mathematical calculations. Standardized mathematical transformations, such as Fourier or polynomial transforms, could be extended toward TPS methods, on a basis, which properly encodes specific knowledge about a problem. Transition between methods is illustrated by comparing what happens in conventional Fourier transform with what happened during the development of Jewett Transform, reported in previous articles. The proper use of computational intelligence tools to perform Jewett Transform allowed complexity algorithm optimization, which encourages the search for a general TPS methodology.
Revista Ingeniería Biomédica, Jun 1, 2015
2013 27th International Conference on Advanced Information Networking and Applications Workshops, 2013
ABSTRACT The biological information coming from electro-physiologic signal sensors like ECG or mo... more ABSTRACT The biological information coming from electro-physiologic signal sensors like ECG or molecular signal devices like mass spectrometry has to be compressed for an efficient medical use by clinicians or to retain only the pertinent explanatory information about the mechanisms at the origin of the recorded signal for the researchers in life sciences. When the signal is periodic in time and/or space, classical compression processes like Fourier and wavelets transforms give good results concerning the compression rate, but bring in general no supplementary information about the interactions between elements of the living system producing the studied signal. Here, we define a new transform called dynalet based on Liénard differential equations susceptible to model the mechanism that is the source of the signal and we propose to apply this new technique to real signals like ECG, pulse activity and protein spectra in mass spectrometry.
Journal of Physics: Conference Series, 2007
Jewett Transform is not yet, it is being. First ideas on this metaphor are from 1980 while monito... more Jewett Transform is not yet, it is being. First ideas on this metaphor are from 1980 while monitoring cerebral function. It was conceived in contrast with Fourier Transform. Its application is limited to Auditory Brain Stem Responses. It uses a non-orthogonal physiologically rooted basis. Non-orthogonal basis has limited power in front of orthogonal basis: no analytical method exists to evaluate the corresponding transforms and numerical methods are required. In previous works, numerical methods were replaced for by trained artificial neural networks. Jewett transform was applied to increase the training set. Being a physiologically inspired basis, it promises better understanding of analysis of these evoked responses. It is envisioned that diverse new transforms, tailored to different problem specificity are to emerge. Considering the short temporal influence of Jewett components, it is stated that codifying temporal characteristics of Jewett components can be used to improve Jewett Transform. Previously used neural network was modified. Output vector codes are built up by grouping components instead of grouping parameters. This allows synaptic pruning in the artificial neural network. Only a fraction (0.49) of the previous network weights is used. Mean square error in fitting signal to model are acceptable (mean ε<0.3%, n= 600). Memorization is eliminated.
Journal of Engineering Research and Sciences, Apr 1, 2022
Currently, health disorders related to Blood Pressure (BP) fluctuations are within the most preva... more Currently, health disorders related to Blood Pressure (BP) fluctuations are within the most prevalent and of higher social and economic impact in the world. A continuous and routinary monitoring of the BP can contribute to the early identification of risk factors, and consequently, would help to prevent potential cardiovascular diseases. <br> <br> BP measurement methods based on the cuff are of widespread use today. The monitoring based on this technology is intrusive and cannot be made continuously, which is of fundamental importance to diagnose Hypertension accurately. Due to the discomfort, inconvenience and intrusiveness of the cuff-based measurements of BP most people undergo monitoring only when they present symptoms of cardiovascular problems and a high proportion of them do not complete the monitoring protocol. <br> <br> In order to provide a less intrusive technology for non-invasive and continuous BP monitoring, many researchers aimed to estimate th...
The main goal of this work is to study the initial technical feasibility of detecting physical st... more The main goal of this work is to study the initial technical feasibility of detecting physical stress caused by exercise associated with episodes of rising Blood Pressure (BP) by means of analyzing Pulse Wave (PW), in order to reduce intrusiveness resulting from the current use of non-invasive BP Monitors. Lead I Electrocardiogram (EKG) and right index finger and main toe Arterial Pulse Waves (PW) were recorded on healthy volunteers, Before and After Exercise (BAE). Trained Artificial Neural Networks (ANNs) were used for stress detection. A common training set was used for different ANN. PW Phase Planes BAE, vectorized and heartbeat segmented, were used as input vectors, while rest or stress condition BAE were used as target vectors. Pan-Tomkins algorithm was applied to EKG for PW segmentation. A digital polygraph was used to register the signals. Thirteen university students, 2 females and 11 males (24.3 ± 2.83 years old), participated as healthy volunteers. They usually carried ou...
Globalization and its emerging reality show the natural world collapsing and the social world bei... more Globalization and its emerging reality show the natural world collapsing and the social world being fractured and in turmoil. In this growing complexity, it is essential to advance in the research and study of human organizations, as adaptive, complex systems.
Modelling and Simulation in Engineering
We propose an efficient computational method to obtain the fractional derivative of a digital sig... more We propose an efficient computational method to obtain the fractional derivative of a digital signal. The proposal consists of a new interpretation of the Grünwald–Letnikov differintegral operator where we have introduced a finite Cauchy convolution with the Grünwald–Letnikov dynamic kernel. The method can be applied to any signal without knowing its analytical form. In the experiments, we have compared the proposed Grünwald–Letnikov computational fractional derivative method with the Riemman–Louville fractional derivative approach for two well-known functions. The simulations exhibit similar results for both methods; however, the Grünwald–Letnikov method outperforms the other approach in execution time. Finally, we show an application of how our proposal can be useful to find the fractional relationship between two well-known biomedical signals.
Proceedings of the 10th International Joint Conference on Biomedical Engineering Systems and Technologies, 2017
Electroencephalography and clinical neurophysiology, 1990
The EEGs of 9 infants and 9 adults undergoing cardiac surgery were analysed during 2 different te... more The EEGs of 9 infants and 9 adults undergoing cardiac surgery were analysed during 2 different temperature ranges. Variance analysis showed that there were very significant interactions between age and temperature effects (P less than 0.01) and between temperature and specific frequency bands (P less than 0.005). These interactions were studied further and the greatest changes were discovered in the infant group when the temperature fell from the upper to the lower hypothermic range: low delta activity increased significantly while those of alpha and theta fell significantly. The significant quantitative differences found in this study agree with qualitative observations from other reports.
2010 IEEE 24th International Conference on Advanced Information Networking and Applications Workshops, 2010
A methodological proposal to estimate a Tailored to the Problem Specificity mathematical transfor... more A methodological proposal to estimate a Tailored to the Problem Specificity mathematical transformation is developed. To begin, Linear Analysis is briefly visited because of its significant role providing a unified vision of mathematical transformations. Thereafter it is explored the possibilities of extending this approach when basis of vector spaces are built tailored to the specific knowledge on a problem; not only from the convenience or effectiveness of mathematical calculations. Basis becomes not necessarily orthogonal neither linear. Standardized Mathematical Transformations such as Fourier or polynomial Transforms, could be extended, towards these new transformations. This was previously done to model Auditory Brainstem Responses using Jewett Transform. The proper use of Computational Intelligence tools was critical in this extension. It allowed important Complexity Algorithm optimization, which encourages the search for generalizing the methodology. In previous works, Artificial Neural Networks trained with backpropagation performed Jewett Transform. Mean Square Error in fitting Auditory Brainstem Responses to a model built using this transform are acceptable (mean ε< 0.3%, n= 600). The complexity of the best trained neural network algorithm was reduced to evaluate 100 inner products on 65 dimension vectors, 20 inner products on 100 dimension vectors and to calculate 120 sigmoid functions. Finally, using the trained Artificial Neural Network to estimate the Transform was thousands of times faster than using numerical gradient descent methods. (Abstract)
Articles by Antonio Glaría
I. Artificial Neural Networks (ANN) are complex adaptive systems [1] used in nonlinear data model... more I. Artificial Neural Networks (ANN) are complex adaptive systems [1] used in nonlinear data modeling; inference is their emergent phenomena; trained ANN can be Universal Approximators in vector spaces [2]. ANN can estimate Tailored to the Problem Specificity (TPS) Mathematical Transforms. II. Jean Baptiste Joseph Fourier working on heat propagation found that periodic functions, either "continuous or discontinuous, can be expanded in a series of sinusoids " *3+. The series can model most of periodic functions. Legendre "méthode des moindres carrés" is used to evaluate the series coefficients. III. Fourier series evolved, since 1822 up to date, schematically, in a six stage process [4]. Constant during this process; new bases definition, Linear Combination (LC) of base elements spans Vector space and Legendre "méthode des moindres carrés" used to estimate coefficients. Fourier Series give rise to Fourier Transform. Euler relation allows rewriting sinusoids as imaginary exponentials and harmonic coefficients become a continuous function. The series is a particular case of the Transform. Fourier transform is systematically generalized to Linear Transforms [5]. New orthogonal bases, such as polynomials, replace for imaginary exponentials. Fourier transform is a particular case of Linear Transform. New limited time duration orthogonal bases, ondelettes, are defined and Wavelet Transform is established [6]. A painless methodology allowing non orthogonal bases in Linear and Wavelet Transforms is developed and Frames Transforms are defined [7]. In 2007 Dynalet Transform [8] is defined to characterize periodic biological signals generated within homeostatic systems. New bases are the solutions of van der Pol oscillators. These bases replace for the permanent and damped circular dynamics used by Fourier and Wavelet transforms. Finally Linear or Wavelet evolved to TPS Transforms *9+. New "physiologically plausible" bases are intended to represent actual generators of biological phenomena. Bases for TPS transform can be parameterized and be either orthogonal or non orthogonal. Trained ANN are used to estimate TPS transforms. IV. Three study cases on TPS applications. (1) Modeling Average Auditory Brainstem Responses using TPS Jewett Transform [10]. Time delayed second order overdamped functions are new basis [10], defining a transform consisting of five coefficients and fifteen parameters. (2) Using TPS methodology to estimate Dynalet Transform [8]. Hamiltonian and Potential function evaluation is conventionally used to estimate Dynalet transform [8]. TPS method uses analog computing techniques to solve van der Pol equation. Dynalet defines one coefficient and three parameters per harmonic. (3) Modeling Haemodynamic Response Function in functional Magnetic Resonance Imaging (fMRI) using TPS Glover Transform [13]. Relaxation Glover equation elements [13] are new bases, defining one coefficient and four parameters. Last two transforms are currently being developed. V. It is claimed that TPS bases, being "physiologically plausible", increases interpretability. On another hand, the use of trained ANN decreases Algorithm Complexity.
Frontiers in Applied Mathematics and Statistics, 2022
Linear functional analysis historically founded by Fourier and Legendre played a significant role... more Linear functional analysis historically founded by Fourier and Legendre played a significant role to provide a unified vision of mathematical transformations between vector spaces. The possibility of extending this approach is explored when basis of vector spaces is built Tailored to the Problem Specificity (TPS) and not from the convenience or effectiveness of mathematical calculations. Standardized mathematical transformations, such as Fourier or polynomial transforms, could be extended toward TPS methods, on a basis, which properly encodes specific knowledge about a problem. Transition between methods is illustrated by comparing what happens in conventional Fourier transform with what happened during the development of Jewett Transform, reported in previous articles. The proper use of computational intelligence tools to perform Jewett Transform allowed complexity algorithm optimization, which encourages the search for a general TPS methodology.
Clinical Physics and Physiological Measurement, 1983
... and A Murray A number of EEG analysis displays are already available. That of the CFM (Maynar... more ... and A Murray A number of EEG analysis displays are already available. That of the CFM (Maynard et a! 1969) measures the average amplitude of the rectified EEG taken from a specially selected frequency range, but contains no specific frequency information, Hjorth (1970 ...
Anaesthesia, 1986
Changes in the electroencephalograms of patients undergoing cardiac surgery with cardiopulmonary ... more Changes in the electroencephalograms of patients undergoing cardiac surgery with cardiopulmonary bypass were studied. A n analysis technique with a simple display of amplitude and frequency within the traditional bands was used. During the course qfan operation, there can be dramatic changes in frequency contribution with little or no change in overall EEG amplitude. Evaluation of the results shows that this technique clearly draws attention to periods of EEG change, and examples are given.
Electroencephalography and Clinical Neurophysiology, 1985
A single channel EEG recording was made in 25 patients undergoing cardiac surgery and analysed us... more A single channel EEG recording was made in 25 patients undergoing cardiac surgery and analysed using 5 different techniques--amplitude, cerebral function monitor, Fourier, Hjorth, and zero-crossing analyses. The results of the analyses were plotted as trend information on paper. These trends were studied for changes in the EEG during surgery. In the majority of cases changes were noted simultaneously by all 5 techniques. There were, however, some cases in which an amplitude-only technique showed no changes while frequency contributions were changing, and a frequency-only technique showed no changes while amplitudes were changing. The conclusion drawn is that major EEG changes are observed with any of the techniques studied, but that for improved sensitivity a technique analysing both frequency and amplitude information should be used.
Frontiers in Applied Mathematics and Statistics
Linear functional analysis historically founded by Fourier and Legendre played a significant role... more Linear functional analysis historically founded by Fourier and Legendre played a significant role to provide a unified vision of mathematical transformations between vector spaces. The possibility of extending this approach is explored when basis of vector spaces is built Tailored to the Problem Specificity (TPS) and not from the convenience or effectiveness of mathematical calculations. Standardized mathematical transformations, such as Fourier or polynomial transforms, could be extended toward TPS methods, on a basis, which properly encodes specific knowledge about a problem. Transition between methods is illustrated by comparing what happens in conventional Fourier transform with what happened during the development of Jewett Transform, reported in previous articles. The proper use of computational intelligence tools to perform Jewett Transform allowed complexity algorithm optimization, which encourages the search for a general TPS methodology.
Revista Ingeniería Biomédica, Jun 1, 2015
2013 27th International Conference on Advanced Information Networking and Applications Workshops, 2013
ABSTRACT The biological information coming from electro-physiologic signal sensors like ECG or mo... more ABSTRACT The biological information coming from electro-physiologic signal sensors like ECG or molecular signal devices like mass spectrometry has to be compressed for an efficient medical use by clinicians or to retain only the pertinent explanatory information about the mechanisms at the origin of the recorded signal for the researchers in life sciences. When the signal is periodic in time and/or space, classical compression processes like Fourier and wavelets transforms give good results concerning the compression rate, but bring in general no supplementary information about the interactions between elements of the living system producing the studied signal. Here, we define a new transform called dynalet based on Liénard differential equations susceptible to model the mechanism that is the source of the signal and we propose to apply this new technique to real signals like ECG, pulse activity and protein spectra in mass spectrometry.
Journal of Physics: Conference Series, 2007
Jewett Transform is not yet, it is being. First ideas on this metaphor are from 1980 while monito... more Jewett Transform is not yet, it is being. First ideas on this metaphor are from 1980 while monitoring cerebral function. It was conceived in contrast with Fourier Transform. Its application is limited to Auditory Brain Stem Responses. It uses a non-orthogonal physiologically rooted basis. Non-orthogonal basis has limited power in front of orthogonal basis: no analytical method exists to evaluate the corresponding transforms and numerical methods are required. In previous works, numerical methods were replaced for by trained artificial neural networks. Jewett transform was applied to increase the training set. Being a physiologically inspired basis, it promises better understanding of analysis of these evoked responses. It is envisioned that diverse new transforms, tailored to different problem specificity are to emerge. Considering the short temporal influence of Jewett components, it is stated that codifying temporal characteristics of Jewett components can be used to improve Jewett Transform. Previously used neural network was modified. Output vector codes are built up by grouping components instead of grouping parameters. This allows synaptic pruning in the artificial neural network. Only a fraction (0.49) of the previous network weights is used. Mean square error in fitting signal to model are acceptable (mean ε<0.3%, n= 600). Memorization is eliminated.
Journal of Engineering Research and Sciences, Apr 1, 2022
Currently, health disorders related to Blood Pressure (BP) fluctuations are within the most preva... more Currently, health disorders related to Blood Pressure (BP) fluctuations are within the most prevalent and of higher social and economic impact in the world. A continuous and routinary monitoring of the BP can contribute to the early identification of risk factors, and consequently, would help to prevent potential cardiovascular diseases. <br> <br> BP measurement methods based on the cuff are of widespread use today. The monitoring based on this technology is intrusive and cannot be made continuously, which is of fundamental importance to diagnose Hypertension accurately. Due to the discomfort, inconvenience and intrusiveness of the cuff-based measurements of BP most people undergo monitoring only when they present symptoms of cardiovascular problems and a high proportion of them do not complete the monitoring protocol. <br> <br> In order to provide a less intrusive technology for non-invasive and continuous BP monitoring, many researchers aimed to estimate th...
The main goal of this work is to study the initial technical feasibility of detecting physical st... more The main goal of this work is to study the initial technical feasibility of detecting physical stress caused by exercise associated with episodes of rising Blood Pressure (BP) by means of analyzing Pulse Wave (PW), in order to reduce intrusiveness resulting from the current use of non-invasive BP Monitors. Lead I Electrocardiogram (EKG) and right index finger and main toe Arterial Pulse Waves (PW) were recorded on healthy volunteers, Before and After Exercise (BAE). Trained Artificial Neural Networks (ANNs) were used for stress detection. A common training set was used for different ANN. PW Phase Planes BAE, vectorized and heartbeat segmented, were used as input vectors, while rest or stress condition BAE were used as target vectors. Pan-Tomkins algorithm was applied to EKG for PW segmentation. A digital polygraph was used to register the signals. Thirteen university students, 2 females and 11 males (24.3 ± 2.83 years old), participated as healthy volunteers. They usually carried ou...
Globalization and its emerging reality show the natural world collapsing and the social world bei... more Globalization and its emerging reality show the natural world collapsing and the social world being fractured and in turmoil. In this growing complexity, it is essential to advance in the research and study of human organizations, as adaptive, complex systems.
Modelling and Simulation in Engineering
We propose an efficient computational method to obtain the fractional derivative of a digital sig... more We propose an efficient computational method to obtain the fractional derivative of a digital signal. The proposal consists of a new interpretation of the Grünwald–Letnikov differintegral operator where we have introduced a finite Cauchy convolution with the Grünwald–Letnikov dynamic kernel. The method can be applied to any signal without knowing its analytical form. In the experiments, we have compared the proposed Grünwald–Letnikov computational fractional derivative method with the Riemman–Louville fractional derivative approach for two well-known functions. The simulations exhibit similar results for both methods; however, the Grünwald–Letnikov method outperforms the other approach in execution time. Finally, we show an application of how our proposal can be useful to find the fractional relationship between two well-known biomedical signals.
Proceedings of the 10th International Joint Conference on Biomedical Engineering Systems and Technologies, 2017
Electroencephalography and clinical neurophysiology, 1990
The EEGs of 9 infants and 9 adults undergoing cardiac surgery were analysed during 2 different te... more The EEGs of 9 infants and 9 adults undergoing cardiac surgery were analysed during 2 different temperature ranges. Variance analysis showed that there were very significant interactions between age and temperature effects (P less than 0.01) and between temperature and specific frequency bands (P less than 0.005). These interactions were studied further and the greatest changes were discovered in the infant group when the temperature fell from the upper to the lower hypothermic range: low delta activity increased significantly while those of alpha and theta fell significantly. The significant quantitative differences found in this study agree with qualitative observations from other reports.
2010 IEEE 24th International Conference on Advanced Information Networking and Applications Workshops, 2010
A methodological proposal to estimate a Tailored to the Problem Specificity mathematical transfor... more A methodological proposal to estimate a Tailored to the Problem Specificity mathematical transformation is developed. To begin, Linear Analysis is briefly visited because of its significant role providing a unified vision of mathematical transformations. Thereafter it is explored the possibilities of extending this approach when basis of vector spaces are built tailored to the specific knowledge on a problem; not only from the convenience or effectiveness of mathematical calculations. Basis becomes not necessarily orthogonal neither linear. Standardized Mathematical Transformations such as Fourier or polynomial Transforms, could be extended, towards these new transformations. This was previously done to model Auditory Brainstem Responses using Jewett Transform. The proper use of Computational Intelligence tools was critical in this extension. It allowed important Complexity Algorithm optimization, which encourages the search for generalizing the methodology. In previous works, Artificial Neural Networks trained with backpropagation performed Jewett Transform. Mean Square Error in fitting Auditory Brainstem Responses to a model built using this transform are acceptable (mean ε< 0.3%, n= 600). The complexity of the best trained neural network algorithm was reduced to evaluate 100 inner products on 65 dimension vectors, 20 inner products on 100 dimension vectors and to calculate 120 sigmoid functions. Finally, using the trained Artificial Neural Network to estimate the Transform was thousands of times faster than using numerical gradient descent methods. (Abstract)
I. Artificial Neural Networks (ANN) are complex adaptive systems [1] used in nonlinear data model... more I. Artificial Neural Networks (ANN) are complex adaptive systems [1] used in nonlinear data modeling; inference is their emergent phenomena; trained ANN can be Universal Approximators in vector spaces [2]. ANN can estimate Tailored to the Problem Specificity (TPS) Mathematical Transforms. II. Jean Baptiste Joseph Fourier working on heat propagation found that periodic functions, either "continuous or discontinuous, can be expanded in a series of sinusoids " *3+. The series can model most of periodic functions. Legendre "méthode des moindres carrés" is used to evaluate the series coefficients. III. Fourier series evolved, since 1822 up to date, schematically, in a six stage process [4]. Constant during this process; new bases definition, Linear Combination (LC) of base elements spans Vector space and Legendre "méthode des moindres carrés" used to estimate coefficients. Fourier Series give rise to Fourier Transform. Euler relation allows rewriting sinusoids as imaginary exponentials and harmonic coefficients become a continuous function. The series is a particular case of the Transform. Fourier transform is systematically generalized to Linear Transforms [5]. New orthogonal bases, such as polynomials, replace for imaginary exponentials. Fourier transform is a particular case of Linear Transform. New limited time duration orthogonal bases, ondelettes, are defined and Wavelet Transform is established [6]. A painless methodology allowing non orthogonal bases in Linear and Wavelet Transforms is developed and Frames Transforms are defined [7]. In 2007 Dynalet Transform [8] is defined to characterize periodic biological signals generated within homeostatic systems. New bases are the solutions of van der Pol oscillators. These bases replace for the permanent and damped circular dynamics used by Fourier and Wavelet transforms. Finally Linear or Wavelet evolved to TPS Transforms *9+. New "physiologically plausible" bases are intended to represent actual generators of biological phenomena. Bases for TPS transform can be parameterized and be either orthogonal or non orthogonal. Trained ANN are used to estimate TPS transforms. IV. Three study cases on TPS applications. (1) Modeling Average Auditory Brainstem Responses using TPS Jewett Transform [10]. Time delayed second order overdamped functions are new basis [10], defining a transform consisting of five coefficients and fifteen parameters. (2) Using TPS methodology to estimate Dynalet Transform [8]. Hamiltonian and Potential function evaluation is conventionally used to estimate Dynalet transform [8]. TPS method uses analog computing techniques to solve van der Pol equation. Dynalet defines one coefficient and three parameters per harmonic. (3) Modeling Haemodynamic Response Function in functional Magnetic Resonance Imaging (fMRI) using TPS Glover Transform [13]. Relaxation Glover equation elements [13] are new bases, defining one coefficient and four parameters. Last two transforms are currently being developed. V. It is claimed that TPS bases, being "physiologically plausible", increases interpretability. On another hand, the use of trained ANN decreases Algorithm Complexity.
Frontiers in Applied Mathematics and Statistics, 2022
Linear functional analysis historically founded by Fourier and Legendre played a significant role... more Linear functional analysis historically founded by Fourier and Legendre played a significant role to provide a unified vision of mathematical transformations between vector spaces. The possibility of extending this approach is explored when basis of vector spaces is built Tailored to the Problem Specificity (TPS) and not from the convenience or effectiveness of mathematical calculations. Standardized mathematical transformations, such as Fourier or polynomial transforms, could be extended toward TPS methods, on a basis, which properly encodes specific knowledge about a problem. Transition between methods is illustrated by comparing what happens in conventional Fourier transform with what happened during the development of Jewett Transform, reported in previous articles. The proper use of computational intelligence tools to perform Jewett Transform allowed complexity algorithm optimization, which encourages the search for a general TPS methodology.