The Mathematical Principles of Scale Relativity Physics

Mazilu, Nicolae; Agop, Maricel; Merches, Ioan

doi:10.1201/9780429329050

Cited by 12 publications

(32 citation statements)

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“…This multifractal-type Schrödinger equation has differentiable solutions that come as a direct consequence of the multifractality of space. Such a result agrees with Berry's and Hall's phases, also similar findings obtained in the framework of usual quantum mechanics [31][32][33]. In the particular case of fractalization through a Markov-type stochasticization, i.e., for motions on Peano-type curves at Compton scale resolution:…”

Section: The Reconstruction Of Eeg Signals Through Scale Relativity Theorysupporting

confidence: 88%

“…Then let us observe that the same equation is also invariant with respect to the time and spatial coordinate transformations, which represent a group in itself (different than the multifractal-type Galilei group). These last transformations are, in the most general case of one-dimensional neural dynamics, a result of the multifractal-type SL(2R) group structure, but in two variables with three parameters, through the multifractal-type action [31,32]:…”

Section: The Reconstruction Of Eeg Signals Through Scale Relativity Theorymentioning

confidence: 99%

“…In accordance with the general mathematical procedures from [31,32], the neural dynamics may be described through a 2 × 2 matrix, with real elements. In a neural system, it is obvious that the problem revolves around a family of such matrices, each of them describing the dynamics of a neural system entity (structural unit).…”

Section: The Reconstruction Of Eeg Signals Through Scale Relativity Theorymentioning

confidence: 99%

“…It results that the matrix that generates the anharmonic curve [31,32] is a 2 × 2 matrix with real elements and can be written as:…”

Section: The Reconstruction Of Eeg Signals Through Scale Relativity Theorymentioning

confidence: 99%

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Novel Approach for EEG Signal Analysis in a Multifractal Paradigm of Motions. Epileptic and Eclamptic Seizures as Scale Transitions

Irimiciuc

Zală²,

Dimitriu

et al. 2021

Symmetry

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Two different operational procedures are proposed for evaluating and predicting the onset of epileptic and eclamptic seizures. The first procedure analyzes the electrical activity of the brain (EEG signals) using nonlinear dynamic methods (the time variations of the standard deviation, the variance, the skewness and the kurtosis; the evolution in time of the spatial–temporal entropy; the variations of the Lyapunov coefficients, etc.). The second operational procedure reconstructs any type of EEG signal through harmonic mappings from the usual space to the hyperbolic one using the time homographic invariance of a multifractal-type Schrödinger equation in the framework of the scale relativity theory (i.e., in a multifractal paradigm of motions). More precisely, the explicit differential descriptions of the brain activity in the form of 2 × 2 matrices with real elements disclose, through the in-phase coherences at various scale resolutions (i.e., as scale transitions), the multitude of brain neuronal dynamics, especially sequences of epileptic and eclamptic seizures. These two operational procedures are not mutually exclusive, but rather become complementary, offering valuable information concerning epileptic and eclamptic seizures. In such context, the prediction of epileptic and eclamptic seizures becomes fundamental for patients not responding to medical treatment and also presenting an increased rate of seizure recurrence.

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Section: The Reconstruction Of Eeg Signals Through Scale Relativity Theorysupporting

confidence: 88%

Section: The Reconstruction Of Eeg Signals Through Scale Relativity Theorymentioning

confidence: 99%

Section: The Reconstruction Of Eeg Signals Through Scale Relativity Theorymentioning

confidence: 99%

“…It results that the matrix that generates the anharmonic curve [31,32] is a 2 × 2 matrix with real elements and can be written as:…”

Section: The Reconstruction Of Eeg Signals Through Scale Relativity Theorymentioning

confidence: 99%

See 2 more Smart Citations

Novel Approach for EEG Signal Analysis in a Multifractal Paradigm of Motions. Epileptic and Eclamptic Seizures as Scale Transitions

Irimiciuc

Zală²,

Dimitriu

et al. 2021

Symmetry

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“…Now, new data regarding release dynamics, complementary to the class of solutions associated with Equation (1) (generated through initial and boundary conditions), can also be given on the base of the transformation groups (which leave invariant the Equation ( 1)) (Jaynes, 1973;Mazilu & Skyrmions, 2012;Merches & Agop, 2016;Agop & Paun, 2017). These transformation groups constitute, in the most general case of the one-dimensional drug release dynamics, a realization of the Lie group SL 2R ð Þ, through the action (Mazilu et al, 2020):…”

Section: Mathematical Modelmentioning

confidence: 99%

Theoretical model for the diclofenac release from PEGylated chitosan hydrogels

Ailincai

Agop

Marinaș³

et al. 2021

Drug Delivery

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Controlled drug delivery systems are of utmost importance for the improvement of drug bioavailability while limiting the side effects. For the improvement of their performances, drug release modeling is a significant tool for the further optimization of the drug delivery systems to cross the barrier to practical application. We report here on the modeling of the diclofenac sodium salt (DCF) release from a hydrogel matrix based on PEGylated chitosan in the context of Multifractal Theory of Motion, by means of a fundamental spinor set given by 2 Â 2 matrices with real elements, which can describe the drug-release dynamics at global and local scales. The drug delivery systems were prepared by in situ hydrogenation of PEGylated chitosan with citral in the presence of the DCF, by varying the hydrophilic/hydrophobic ratio of the components. They demonstrated a good dispersion of the drug into the matrix by forming matrix-drug entities which enabled a prolonged drug delivery behavior correlated with the hydrophilicity degree of the matrix. The application of the Multifractal Theory of Motion fitted very well on these findings, the fractality degree accurately describing the changes in hydrophilicity of the polymer. The validation of the model on this series of formulations encourages its further use for other systems, as an easy tool for estimating the drug release toward the design improvement. The present paper is a continuation of the work 'A theoretical mathematical model for assessing diclofenac release from chitosan-based formulations,' published in Drug Delivery Journal, 27(1), 2020, that focused on the consequences induced by the invariance groups of Multifractal Diffusion Equations in correlation with the drug release dynamics.

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From Special to General Relativity Through Complex Potential

Agop,

Irimiciuc

2024

Multifractal Theory of Motion

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The Mathematical Principles of Scale Relativity Physics

Cited by 12 publications

References 0 publications

Novel Approach for EEG Signal Analysis in a Multifractal Paradigm of Motions. Epileptic and Eclamptic Seizures as Scale Transitions

Novel Approach for EEG Signal Analysis in a Multifractal Paradigm of Motions. Epileptic and Eclamptic Seizures as Scale Transitions

Theoretical model for the diclofenac release from PEGylated chitosan hydrogels

From Special to General Relativity Through Complex Potential

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