Scale Transitions as Foundations of Physics

Mazilu, Nicolae; Agop, Maricel; Merches, Ioan

doi:10.1142/12151

Cited by 11 publications

(33 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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“…In the following, any complex system can be assimilated with a multifractal object. Then, since in the framework of scale relativity theory [6][7][8][9], the dynamics of complex system entities are described through continuous and non-differentiable curves (multifractal curves), the motion equation (with geodesics equation status) becomes (for detail see [6][7][8][9]):…”

Section: Motion Equationmentioning

confidence: 99%

Assessment of Complex System Dynamics via Harmonic Mapping in a Multifractal Paradigm

et al. 2021

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In the present paper, nonlinear behaviors of complex system dynamics from a multifractal perspective of motion are analyzed. In the framework of scale relativity theory, by analyzing the dynamics of complex system entities based on continuous but non-differentiable curves (multifractal curves), both the Schrödinger and Madelung scenarios on the holographic implementations of dynamics are functional and complementary. In the Madelung scenario, the holographic implementation of dynamics (i.e., free of any external or internal constraints) has some important consequences explicated by means of various operational procedures. The selected procedures involve synchronous modes through SL (2R) transformation group based on a hidden symmetry, coherence domains through Riemann manifold embedded with a Poincaré metric based on a parallel transport of direction (in a Levi Civita sense). Other procedures used here relate to the stationary-non-stationary dynamics transition through harmonic mapping from the usual space to the hyperbolic one manifested as cellular and channel type self-structuring. Finally, the Madelung scenario on the holographic implementations of dynamics are discussed with respect to laser-produced plasma dynamics.

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Multi-fractal modeling of curcumin release mechanism from polymeric nanomicelles

et al. 2022

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The physicochemical properties of “smart” or stimuli-sensitive amphiphilic copolymers can be modeled as a function of their environment. In special, pH-sensitive copolymers have practical applications in the biomedical field as drug delivery systems. Interactions between the structural units of any polymer-drug system imply mutual constraints at various scale resolutions and the nonlinearity is accepted as one of the most fundamental properties. The release kinetics, as a function of pH, of a model active principle, i.e., Curcumin, from nanomicelles obtained from amphiphilic pH-sensitive poly(2-vinylpyridine)-b-poly(ethylene oxide) (P2VP-b-PEO) tailor-made diblock copolymers was firstly studied by using the Rietger-Peppas equation. The value of the exponential coefficient, n, is around 0.5, generally suggesting a diffusion process, slightly disturbed in some cases. Moreover, the evaluation of the polymer-drug system’s nonstationary dynamics was caried out through harmonic mapping from the usual space to the hyperbolic one. The kinetic model we developed, based on fractal theory, fits very well with the experimental data obtained for the release of Curcumin from the amphiphilic copolymer micelles in which it was encapsulated. This model is a variant of the classical kinetic models based on the formal kinetics of the process.

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Scale Transitions as Foundations of Physics

Cited by 11 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

Assessment of Complex System Dynamics via Harmonic Mapping in a Multifractal Paradigm

Multi-fractal modeling of curcumin release mechanism from polymeric nanomicelles

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