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Introduction: Accurate prediction of tumor dynamics following Gamma Knife radiosurgery (GKRS) is critical for optimizing treatment strategies for patients with brain metastases (BMs). Traditional machine learning (ML) algorithms have been widely used for this purpose; however, recent advancements in deep learning, such as autoencoders, offer the potential to enhance predictive accuracy. This study aims to evaluate the efficacy of autoencoders compared to traditional ML models in predicting tumor progression or regression after GKRS. Objectives: The primary objective of this study is to assess whether integrating autoencoder-derived features into traditional ML models can improve their performance in predicting tumor dynamics three months post-GKRS in patients with brain metastases. Methods: This retrospective analysis utilized clinical data from 77 patients treated at the “Prof. Dr. Nicolae Oblu” Emergency Clinic Hospital-Iasi. Twelve variables, including socio-demographic, clinical, treatment, and radiosurgery-related factors, were considered. Tumor progression or regression within three months post-GKRS was the primary outcome, with 71 cases of regression and 6 cases of progression. Traditional ML models, such as Logistic Regression, Support Vector Machine (SVM), K-Nearest Neighbors (KNN), Extra Trees, Random Forest, and XGBoost, were trained and evaluated. The study further explored the impact of incorporating features derived from autoencoders, particularly focusing on the effect of compression in the bottleneck layer on model performance. Results: Traditional ML models achieved accuracy rates ranging from 0.91 (KNN) to 1.00 (Extra Trees). Integrating autoencoder-derived features generally enhanced model performance. Logistic Regression saw an accuracy increase from 0.91 to 0.94, and SVM improved from 0.85 to 0.96. XGBoost maintained consistent performance with an accuracy of 0.94 and an AUC of 0.98, regardless of the feature set used. These results demonstrate that hybrid models combining deep learning and traditional ML techniques can improve predictive accuracy. Conclusion: The study highlights the potential of hybrid models incorporating autoencoder-derived features to enhance the predictive accuracy and robustness of traditional ML models in forecasting tumor dynamics post-GKRS. These advancements could significantly contribute to personalized medicine, enabling more precise and individualized treatment planning based on refined predictive insights, ultimately improving patient outcomes.

Precision agriculture, together with remote sensing and vegetation indices, represents a modern correlation that maximizes efficiency and sustainability in farmland management, contributing to more efficient and responsible production. Remote sensing in agriculture is an important technology that uses data from sensors mounted on satellites, drones, and aircraft to monitor and evaluate agricultural land. Vegetation indices are needed in agricultural remote sensing and precision agriculture because they provide quantitative and objective information on agricultural crops contributing to more efficient, sustainable and cost-effective land management.

This study assesses the predictive performance of six machine learning models and a 1D Convolutional Neural Network (CNN) in forecasting tumor dynamics within three months following Gamma Knife radiosurgery (GKRS) in 77 brain metastasis (BM) patients. The analysis meticulously evaluates each model before and after hyperparameter tuning, utilizing accuracy, AUC, and other metrics derived from confusion matrices. The CNN model showcased notable performance with an accuracy of 98% and an AUC of 0.97, effectively complementing the broader model analysis. Initial findings highlighted that XGBoost significantly outperformed other models with an accuracy of 0.95 and an AUC of 0.95 before tuning. Post-tuning, the Support Vector Machine (SVM) demonstrated the most substantial improvement, achieving an accuracy of 0.98 and an AUC of 0.98. Conversely, XGBoost showed a decline in performance after tuning, indicating potential overfitting. The study also explores feature importance across models, noting that features like “control at one year”, “age of the patient”, and “beam-on time for volume V1 treated” were consistently influential across various models, albeit their impacts were interpreted differently depending on the model’s underlying mechanics. This comprehensive evaluation not only underscores the importance of model selection and hyperparameter tuning but also highlights the practical implications in medical diagnostic scenarios, where the accuracy of positive predictions can be crucial. Our research explores the effects of staged Gamma Knife radiosurgery (GKRS) on larger tumors, revealing no significant outcome differences across protocols. It uniquely considers the impact of beam-on time and fraction intervals on treatment efficacy. However, the investigation is limited by a small patient cohort and data from a single institution, suggesting the need for future multicenter research.

A unitary model of drug release dynamics is proposed, assuming that the polymer–drug system can be assimilated into a multifractal mathematical object. Then, we made a description of drug release dynamics that implies, via Scale Relativity Theory, the functionality of continuous and undifferentiable curves (fractal or multifractal curves), possibly leading to holographic-like behaviors. At such a conjuncture, the Schrödinger and Madelung multifractal scenarios become compatible: in the Schrödinger multifractal scenario, various modes of drug release can be “mimicked” (via period doubling, damped oscillations, modulated and “chaotic” regimes), while the Madelung multifractal scenario involves multifractal diffusion laws (Fickian and non-Fickian diffusions). In conclusion, we propose a unitary model for describing release dynamics in polymer–drug systems. In the model proposed, the polymer–drug dynamics can be described by employing the Scale Relativity Theory in the monofractal case or also in the multifractal one.

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.

This paper investigates the nonlinear dynamics of atmospheric aerosols during the transition from laminar to turbulent flows using the framework of Scale Relativity Theory. It is proposed that the transition from multifractal to non-multifractal scales (in the dynamics of the atmospheric aerosols) can be assimilated to the transition between laminar and turbulent states. These transitions are determined by the multifractal diffusion and deposition processes. The methodology used involves the application of the principle of scale covariance, which states that the laws of atmospheric physics remain invariant with respect to spatial and temporal transformations as well as scale transformations. Based on this principle, several conservation laws are constructed. In such context, the conservation law of the density of states associated with the multifractal-non-multifractal scale transition in a one-dimensional case is then considered. The model describes the non-linear behaviour of atmospheric aerosols undergoing diffusion and deposition processes. The theoretical approach was correlated using experimental data from a ceilometer and radar reflectivity factor data.

This study aimed to investigate the behavior of chitosan/quaternized chitosan fibers in media mimicking wound exudates to understand their capacities as wound dressing. Fiber analysis of the fibers using dynamic vapor sorption proved their ability to adsorb moisture up to 60% and then to desorb it as a function of humidity, indicating their outstanding breathability. Dissolution analyses showed that quaternized chitosan leached from the fibers in water and PBS, whereas only small portions of chitosan were solubilized in water. In media containing lysozyme, the fibers degraded with a rate determined by their composition and pH, reaching a mass loss of up to 47% in media of physiologic pH. Notably, in media mimicking the wound exudate during healing, they adsorbed moisture even when their mass loss due to biodegradation was high, whereas they were completely degraded in the media of normal tissues, indicating bioabsorbable dressing capacities. A mathematical model was constructed, which characterized the degradation rate and morphology changes of chitosan/quaternized chitosan fibers through analyses of dynamics in scale space, using the Theory of Scale Relativity. The model was validated using experimental data, making it possible to generalize it to the degradation of other biopolymeric systems that address wound healing.

Background: The study investigated whether three deep-learning models, namely, the CNN_model (trained from scratch), the TL_model (transfer learning), and the FT_model (fine-tuning), could predict the early response of brain metastases (BM) to radiosurgery using a minimal pre-processing of the MRI images. The dataset consisted of 19 BM patients who underwent stereotactic-radiosurgery (SRS) within 3 months. The images used included axial fluid-attenuated inversion recovery (FLAIR) sequences and high-resolution contrast-enhanced T1-weighted (CE T1w) sequences from the tumor center. The patients were classified as responders (complete or partial response) or non-responders (stable or progressive disease). Methods: A total of 2320 images from the regression class and 874 from the progression class were randomly assigned to training, testing, and validation groups. The DL models were trained using the training-group images and labels, and the validation dataset was used to select the best model for classifying the evaluation images as showing regression or progression. Results: Among the 19 patients, 15 were classified as “responders” and 4 as “non-responders”. The CNN_model achieved good performance for both classes, showing high precision, recall, and F1-scores. The overall accuracy was 0.98, with an AUC of 0.989. The TL_model performed well in identifying the “progression” class, but could benefit from improved precision, while the “regression” class exhibited high precision, but lower recall. The overall accuracy of the TL_model was 0.92, and the AUC was 0.936. The FT_model showed high recall for “progression”, but low precision, and for the “regression” class, it exhibited a high precision, but lower recall. The overall accuracy for the FT_model was 0.83, with an AUC of 0.885. Conclusions: Among the three models analyzed, the CNN_model, trained from scratch, provided the most accurate predictions of SRS responses for unlearned BM images. This suggests that CNN models could potentially predict SRS prognoses from small datasets. However, further analysis is needed, especially in cases where class imbalances exist.

Using an analogy between the multi-fractal Schrödinger equation and the dumped oscillator equation through a special ansatz, Stoler-type coherences in the dynamics of physical systems are highlighted. Such a result implies a Ricatti-type gauge, a process that can be considered a calibration of the difference between the kinetic and potential energy of a Lagrangian, specified as a perfect square in generic coordinates.

Some possible correspondences between the Scale Relativity Theory and the Space–Time Theory can be established. Since both the multifractal Schrödinger equation from the Scale Relativity Theory and the General Relativity equations for a gravitational field with axial symmetry accept the same SL(2R)-type invariance, an Ernst-type potential (from General Relativity) and also a multi-fractal tensor (from Scale Relativity) are highlighted in the description of complex systems dynamics. In this way, a non-differentiable description of complex systems dynamics can become functional, even in the case of standard theories (General Relativity and Quantum Mechanics).

Dynamics in atmospheric structures are analyzed using the Scale Relativity Theory in Schrödinger-type and Madelung-type scenarios. In the Schrödinger-type scenario, the group invariances of the special linear group SL(2R)-type under Riccati-type gauges implies morphological atmospheric manifestations through frequency modulation, particularly through period doubling. In the Madelung-type scenario, the same group invariances type, manifested through harmonic mappings, implies the functionality of atmospheric mass conductions through mass superconducting-type by scale transition from nondifferentiable atmospheric dynamics to differentiable atmospheric dynamics. The compatibility of these two scenarios under the correlations of atmospheric morphologies-functionalities implies Stoler-type coherences of the atmospheric dynamics through the removal of atmospheric turbulence by means of laminar channels. Finally, these theories are successfully employed to analyze the vertical atmospheric dynamics of cases of insect swarms.

Two formulations based on diclofenac sodium salt encapsulated into a chitosan hydrogel were designed and prepared, and their drug release was investigated by combining in vitro results with mathematical modeling. To understand how the pattern of drug encapsulation impacted its release, the formulations were supramolecularly and morphologically characterized by scanning electron microscopy and polarized light microscopy, respectively. The mechanism of diclofenac release was assessed by using a mathematical model based on the multifractal theory of motion. Various drug-delivery mechanisms, such as Fickian- and non-Fickian-type diffusion, were shown to be fundamental mechanisms. More precisely, in a case of multifractal one-dimensional drug diffusion in a controlled-release polymer–drug system (i.e., in the form of a plane with a certain thickness), a solution that allowed the model’s validation through the obtained experimental data was established. The present research reveals possible new perspectives, for example in the prevention of intrauterine adhesions occurring through endometrial inflammation and other pathologies with an inflammatory mechanism background, such as periodontal diseases, and also therapeutic potential beyond the anti-inflammatory action of diclofenac as an anticancer agent, with a role in cell cycle regulation and apoptosis, using this type of drug-delivery system.

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 × 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.

The paper reports a new mathematical model for understanding the mechanism delivery from drug release systems. To do this, two drug release systems based on chitosan and diclofenac sodium salt as a drug model, were prepared by in situ hydrogelation in the presence of salicylaldehyde. The morphology of the systems was analyzed by scanning electron microscopy and polarized light microscopy and the drug release was in vitro investigated into a medium mimicking the in vivo environment. The drug release mechanism was firstly assessed by fitting the in vitro release data on five traditional mathematical model. In the context of pharmacokinetics behavioral analysis, a new mathematical procedure for describing drug release dynamics in polymer-drug complex systems was proposed. Assuming that the dynamics of polymer-drug system’s structural units take place on continuous and nondifferentiable curves (multifractal curves), it was showed that in a one-dimensional hydrodynamic formalism of multifractal variables the drug release mechanism is given through synchronous dynamics at a differentiable and non-differentiable scale resolutions.

Assimilating the atmosphere with multifractal entities, nonlinear behaviors in the framework of scale relativity theory regarding its hydrodynamic functionality are established at various scale resolutions. From this perspective, revealing a “hidden” symmetry of the specific multifractal force with the SL(2,R) group leads to synchronization of atmospheric entities on the basis of operational procedures (differential and integral Riemann-type geometries, harmonic mappings from Euclidian to hyperbolic space, variational principles, and others) that imply cellular self-structuring, laminar channels and singularities as turbulence generators. These behaviors can then be assimilated and compared with recent discoveries regarding laminar channels found in atmospheric turbulence through lidar data processing.

Cervical cancer represents a major health problem among females due to its increased mortality rate. The conventional therapies are very aggressive and unsatisfactory when it comes to survival rate, especially in terminal stages, which requires the development of new treatment alternatives. With the use of nanotechnology, various chemotherapeutic drugs can be transported via nanocarriers directly to cervical cancerous cells, thus skipping the hepatic first-pass effect and decreasing the rate of chemotherapy side effects. This review comprises various drug delivery systems that were applied in cervical cancer, such as lipid-based nanocarriers, polymeric and dendrimeric nanoparticles, carbon-based nanoparticles, metallic nanoparticles, inorganic nanoparticles, micellar nanocarriers, and protein and polysaccharide nanoparticles. Nanoparticles have a great therapeutic potential by increasing the pharmacological activity, drug solubility, and bioavailability. Through their mechanisms, they highly increase the toxicity in the targeted cervical tumor cells or tissues by linking to specific ligands. In addition, a nondifferentiable model is proposed through holographic implementation in the dynamics of drug delivery dynamics. As any hologram functions as a deep learning process, the artificial intelligence can be proposed as a new analyzing method in cervical cancer.

By operating with the Scale Relativity Theory by means of two scenarios (Schrӧdinger and Madelung-type scenarios) in the dynamics of complex systems, we can achieve a description of these complex systems through a holographic-type perspective. Then, a gauge invariance of the Riccati type becomes functional in complex-system dynamics, which implies several consequences: conservation laws (in particular, for dynamics, the kinetic momentum conservation law), simultaneity and synchronization among the structural units’ (belonging to a complex system) dynamics, and temporal patterns through harmonic mappings. Finally, an economic case analysis is highlighted.

The accurate determination of atmospheric temperature with telemetric platforms is an active issue, one that can also be tackled with the aid of multifractal theory to extract fundamental behaviors of the lower atmosphere, which can then be used to facilitate such determinations. Thus, in the framework of the scale relativity theory, PBL dynamics are analyzed through the aid of a multifractal hydrodynamic scenario. Considering the PBL as a complex system that is assimilated to mathematical objects of a multifractal type, its various dynamics work as a multifractal tunnel effect. Such a treatment allows one to define both a multifractal atmospheric transparency coefficient and a multifractal atmospheric reflectance coefficient. These products are then employed to create theoretical temperature profiles, which lead to correspondences with real results obtained by radiometer data (RPG-HATPRO radiometer), with favorable results. Such methods could be further used and refined in future applications to efficiently produce atmospheric temperature theoretical profiles.

In the first part of the current study, the effectiveness of the transversal cross-section reduction method for RC beams in marginal areas (by means of mechanical drilling) was validated. The said method “encourages” the formation of plastic hinges at the beam ends and, at the same time, allows for taking into account the bending stiffness of RC slabs, which is exerted upon the RC beams. In these conditions, the second part of the current research study (i.e., the current manuscript) highlights the real mode of reducing the lateral stiffness of the slabs upon the RC beams. These elements form a common body, together with the beam–column frame node. The same method as in the first part of the study—“weakening” the plates in the corner area through vertical drilling, without affecting the integrity of the reinforcing elements—was used. The analytical MR RC frame model, studied by means of the comparative method, highlights the efficiency of the transversal cross-section reduction method for RC slabs. Basically, the directing of the plastic deformations from the weakened slab areas towards the marginal areas of the reinforced concrete beams takes place. The beams rotate as far as the weakened slab areas allow its plastic deformation, thus being possible to observe the partial conservation effect of the beam–column frame joint. Furthermore, for the analytical model with the maximum number of vertical holes in the corner areas of the concrete plate, minimal plastic deformations are recorded for the marginal areas of the concrete columns. A partial conservation of the formation mechanism of the “beam-slab-frame node” common rigid block is also noted. Consequently, the dissipation of the seismic energy is made in a partially controlled and directed manner, in the “desired” areas, according to the “Strong Columns—Weak Beams” (SCWB) ductile mechanism of the lateral behavior to seismic actions for reinforced concrete frame structures. The mechanism is specified in current design norms for RC frame systems. The effectiveness of the method for reducing the transversal section of the RC plates in the corner areas by means of transversal drilling is highlighted and validated from the perspective of the local and global ductile seismic response of reinforced concrete frame structures. A significant reduction in the bending stiffness of the slabs upon the beams and a real development of the plastic hinges in the marginal areas of the beams (together with partial implications and plastic deformations) were observed.

In the last few decades, a series of earthquakes were recorded which pointed out several deficiencies regarding the ductile seismic response of MR RC frame structures. Thus, the research problem centres around the failure mechanisms registered by the structures, which differ from the general notions of seismic response commonly found in current design standards and norms regarding seismic actions. In these conditions, in the present paper—by using comparative methods—the analytical validation of the solution of plastic hinge concentration and seismic energy dissipation in the marginal beam areas is proposed. Therefore, the RC beam sections were reduced (weakened) in the marginal areas which exhibit a plastic deformation potential, as well as in the corner areas of concrete slabs with vertical rectangular holes. The significant outcomes of this research imply the partial “guiding” of plastic hinges in the zones adjacent to beam ends. Furthermore, a reduction of both the negative effects of horizontal rigidization of the beams and the cracking and plastic deformation effects of beam-column frame joints was observed. With these technical implications, a complex mechanism of plastic deformation of MR RC frame models is registered in which all lateral elements (including RC columns) participate in the dissipation of seismic energy, without the occurrence of the “weak storey” mechanism for any of the analytical RC frame models. Furthermore, it is possible to observe the partial formation of the global plastic mechanism “Strong Columns—Weak Beams” (SCWB) for some of the structural models. Finally, the analytically studied innovative element regarding the improvement of the seismic response of pure MR RC frame structures is successfully validated.

Drug delivery to the anterior or posterior segments of the eye is a major challenge due to the protection barriers and removal mechanisms associated with the unique anatomical and physiological nature of the ocular system. The paper presents the preparation and characterization of drug-loaded polymeric particulated systems based on pre-emulsion coated with biodegradable polymers. Low molecular weight biopolymers (chitosan, sodium hyaluronate and heparin sodium) were selected due to their ability to attach polymer chains to the surface of the growing system. The particulated systems with dimensions of 190–270 nm and a zeta potential varying from −37 mV to +24 mV depending on the biopolymer charges have been obtained. Current studies show that particles release drugs (dexamethasone/pilocarpine/bevacizumab) in a safe and effective manner, maintaining therapeutic concentration for a longer period of time. An extensive modeling study was performed in order to evaluate the drug release profile from the prepared systems. In a multifractal paradigm of motion, nonlinear behaviors of a drug delivery system are analyzed in the fractal theory of motion, in order to correlate the drug structure with polymer. Then, the functionality of a SL(2R) type “hidden symmetry” implies, through a Riccati type gauge, different “synchronization modes” (period doubling, damped oscillations, quasi-periodicity and intermittency) during the drug release process. Among these, a special mode of Kink type, better reflects the empirical data. The fractal study indicated more complex interactions between the angiogenesis inhibitor Bevacizumab and polymeric structure.

Endometriosis is considered a serious public health issue because of the large number of females affected by this illness. Chronic pain management in patients with endometriosis demands new strategies to increase the life quality of these patients. The development of drug delivery systems represents a new approach in pain treatment among endometriosis patients. Diclofenac sodium, one of the most utilized nonsteroidal anti-inflammatory drugs (NSAID), has its own limitations when being used in formulas such as oral, parental, or local applications. In this paper, a series of four drug release formulations based on chitosan, 2-hydroxy-5-nitrobenzaldehyde, and diclofenac sodium salt were prepared in view of the investigation of the drug release ability. The formulations were analyzed from a morphological and supramolecular point of view by scanning electron microscopy and polarized light microscopy. The in vitro drug release ability was investigated by mimicking a physiologic environment. A mathematical model, using the fractal paradigm of motion, is utilized to explain the behaviors of the drug delivery system presented in this paper. These results suggest a great potential of the proposed drug delivery system, based on chitosan and 2-hydroxy-5-nitrobenzaldehyde to improve the diclofenac sodium salt bioavailability, and it may represent a future treatment formula for endometriosis pain.

In this manuscript, multifractal theories of motion based on scale relativity theory are considered in the description of atmospheric dynamics. It is shown that these theories have the potential to highlight nondimensional mass conduction laws that describe the propagation of atmospheric entities. Then, using special operational procedures and harmonic mappings, these equations can be rewritten and simplified for their plotting and analysis to be performed. The inhomogeneity of these conduction phenomena is analyzed, and it is found that it can fluctuate and increase at certain fractal dimensions, leading to the conclusion that certain atmospheric structures and phenomena of either atmospheric transmission or stability can be explained by atmospheric fractal dimension inversions. Finally, this hypothesis is verified using ceilometer data throughout the atmospheric profiles.

This paper aims to present a multifractal approach of the turbulent atmosphere, by proposing that it can be considered a complex system whose structural units support dynamics on continuous but non-differentiable multifractal curves. Implementing the theoretical framework of multifractality through non-differentiable functions in the form of scale relativity theory with arbitrary and constant fractal dimension, the minimal vortex of an instance of turbulent flow is considered. The results of this assumption lead to an equation that describes the minimal vortex itself, and the velocity fields that compose it, the vortex and turbulent energy dissipation derived from the vortex being plotted and studied. With its structure mathematically described, while employing a classical dynamical turbulence model and relations between turbulent energy dissipation and the minimal vortex, relations are then extrapolated to allow for the solving of multiple turbulent parameters using the inner and outer length scales of the turbulent flow. These equations are then solved as altitude profiles with the necessary length scales obtained from processing lidar data. Finally, profiles are taken periodically and assembled into timeseries, in order to exemplify the method and to compare the results with known literature.

The main aim of the paper was to simulate the drug release by a multifractal theoretical model, as a valuable method to assess the drug release mechanism. To do this, drug delivery films were prepared by mixing poly(vinyl alcohol boric acid) (PVAB) and diclofenac (DCF) sodium salt drug in different mass ratios from 90/10 to 70/30, in order to obtain drug delivery systems with different releasing rates. The different drug content of the three systems was confirmed by energy-dispersive spectroscopy (EDAX) analysis, and the encapsulation particularities were investigated by scanning electron microscopy (SEM), atomic force microscopy (AFM), and polarized optical microscopy (POM) techniques. The ability of the PVAB matrix to anchor the DCF was assessed by Fourier transform infrared (FTIR) spectroscopy. The in vitro release of the diclofenac sodium salt from the formulations was investigated in biomimetic conditions (pH=7.4 and 37°C) by UV-Vis spectroscopy, measuring the absorbance of the drug at 275 nm and fitting the results on a previously drawn calibration curve. An estimation of the drug release kinetics was performed by fitting three traditional mathematical models on experimental release data. Further, the drug delivery was simulated by the fractal theory of motion, in which the release dynamics of the polymer-drug complex system is described through various Riccati-type “regimes.” To explain such dynamics involved multifractal self-modulation in the form of period doubling, quasiperiodicity, intermittency, etc., as well as multifractal self-modulation of network type. Standard release dynamics were explained by multifractal behaviors of temporary kink type. The good correlation between the traditional mathematical models and the new proposed theoretical model demonstrated the validity of the multifractal model for the investigation of the drug release.

Machine learning is a branch of artificial intelligence that allows computer systems to learn directly from examples, data, and experience. Statistical modeling is more about finding connections between variables and consequently the impact of these relationships, while also catering for prediction. It should be clear that these two methodologies are different in terms of their purpose, despite the fact that they use similar means to get there. The evaluation of the machine learning algorithm uses a set of tests to validate its accuracy. Although, for a statistical model, the analysis of regression parameters by confidence intervals, significance tests and other tests can be used to assess the legitimacy of the model. To demonstrate the applications and usefulness of this theory, an experimental study was conducted on zebrafish exposed to mycotoxin. Methods: Patulin (70 µg/L) and kojic acid (100 mg/L, 204 mg/L, and 284 mg/L) were administered by immersion to zebrafish once daily for a period of 7 days before the behavior testing. The following behavioral tests were performed: a novel tank test (NTT) (to assess the explorative behavior and anxiety); and a Y-maze test (which measures the spontaneous explorative behavior). Behavioral tests were performed on separate days. For the behavior tests, the statistical analysis was performed using ANOVA variation analysis (two-way ANOVA). All results are expressed as the mean ± standard error of the mean. The values of the general index F for which p < 0.05 were considered statistically significant. Results: Y-maze—patulin exposure led to an intensification of the locomotor activity and an increased traveled distance and number of arm entries. By increasing the spontaneous alternation between the aquarium’s arms, patulin has shown a stimulating effect on spatial memory. In the case of zebrafish exposed to 100 mg/L kojic acid, the traveled distance was shorter by 27% than the distance attained by those in the control group. The higher doses of kojic acid (204 mg/L and 284 mg/L) led to an increased locomotor activity, distance traveled, number of arm entries, and the spontaneous alternation. The increase in spontaneous alternation demonstrates that 204 mg/L and 284 mg/L kojic acid doses had a stimulating effect on spatial memory. Novel tank test—compared to the control group, the traveled distance of the patulin-exposed fish is slightly reduced. Compared to the control group, the traveled distance of the kojic acid-exposed fish is reduced, due to a shorter mobile time (by 25–27% in the case of fish exposed to 204 mg/L and 284 mg/L kojic acid). Patulin and kojic acid exhibit toxic effects on zebrafish liver, kidney, and myocardium and leads to severe alteration. We continued the analysis by trying some machine learning algorithms on the classification problems in the case of the two behavioral tests MAZE and NTT, after which we concluded that the results were better in the case of the NTT test relative to the MAZE test and that the use of decision tree algorithms leads to amazing results, knowing that their hierarchical structure allows them to learn signals from both classes. Conclusions: The groups exposed to patulin and kojic acid show histological changes in the liver, kidneys, and myocardial muscle tissue. The novel tank test, which assesses exploratory behavior, has been shown to be conclusive in the behavioral analysis of fish that have been given toxins, demonstrating that the intoxicated fish had a decreased explorative behavior and increased anxiety. We were able to detect a machine learning algorithm in the category of decision trees, which can be trained to classify the behavior of fish that were given a toxin in the category of those used in the experiment, only by analyzing the characteristic features of the NTT Behavior Test.

In the present paper, correlations between multifractality and stochasticity in atmospheric dynamics are investigated. Starting with two descriptions of atmospheric scenarios, one based on scale relativity theory and another based on stochastic theory, correspondences between parameters and variables belonging to both scenarios are found. In such a context, by replacing an atmospheric conservative passive additive with a non-differentiable component of the atmospheric multifractal velocity, stochastic evolution equations are found for this component, which reveal the multifractal variational transport coefficient and the multifractal molecular diffusion coefficient, along with the multifractal inhomogeneity variation. Furthermore, equations which describe a multifractal Reynolds number and singularity spectrum are also found. Finally, these theoretical results are validated through remote sensing data obtained with the aid of a ceilometer platform.

Possible implications and consequences of using SL(2R) as invariance groups in the description at any scale resolution of the dynamics of any complex system are analyzed. From this perspective and based on Jaynes’ remark (any circumstance left unspecified in the description of any complex system dynamics has the concrete expression in the existence of an invariance group), in the present paper one specifies such unspecified circumstances that result directly from the consideration of the canonical formalism induced by the SL(2R) as invariance group. It follows that both the Hamiltonian function and the Guassian distribution acquire the status of invariant group functions, the parameters that define the Hamiltonian acquire statistical significances based on a principle of maximizing informational energy, the class of statistical hypotheses specific to Gaussians of the same average acts as transitivity manifolds of the group (transitivity manifolds which can be correlated with the multifractal-non-multifractal scale transitions), joint invariant functions induced through SL(2R) groups isomorphism (the SL(2R) variables group, and the SL(2R) parameters group, etc.). For an ensemble of oscillators of the same frequency, the unspecified circumstances return to the ignorance of the amplitude and phase of each of the oscillators, which forces the recourse to a statistical ensemble traversed by the transformations of the Barbilian-type group. Finally, the model is validated based on numerical simulations and experimental results that refer to transient phenomena in ablation plasmas. The novelty of our model resides in the fact that fractalization through stochasticization is imposed through group invariance, situation in which the group’s transitivity manifolds can be correlated with the scale resolution.

Immunotherapy represents a promising strategy for the treatment of cancer, which functions via the reprogramming and activation of antitumor immunity. However, adverse events resulting from immunotherapy that are related to the low specificity of tumor cell-targeting represent a limitation of immunotherapy’s efficacy. The potential of nanotechnologies is represented by the possibilities of immunotherapeutical agents being carried by nanoparticles with various material types, shapes, sizes, coated ligands, associated loading methods, hydrophilicities, elasticities, and biocompatibilities. In this review, the principal types of nanovectors (nanopharmaceutics and bioinspired nanoparticles) are summarized along with the shortcomings in nanoparticle delivery and the main factors that modulate efficacy (the EPR effect, protein coronas, and microbiota). The mechanisms by which nanovectors can target cancer cells, the tumor immune microenvironment (TIME), and the peripheral immune system are also presented. A possible mathematical model for the cellular communication mechanisms related to exosomes as nanocarriers is proposed.

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.

In this paper, a practical application of theoretical developments found in our previous works is explored in relation to atmospheric lidar data. Multifractal structures, previously named “laminar channels”, have been identified in atmospheric profiles—these exhibit cellular and self-structuring properties, and are spatially ordered across the atmospheric profile. Furthermore, these structures have been connected to the spontaneous emergence of turbulent behavior in the calm atmospheric flow. Calculating the location and occurrence of these channels can help identify features of atmospheric evolution, such as the development of the planetary boundary layer (PBL). Employing this theoretical background to atmospheric lidar data, attempts are made to confirm this suggestion and extract information about atmospheric structure and evolution by analyzing turbulent vortex scale dynamics and scale-corresponding Lyapunov exponents that form the basis of identifying the laminar channels in atmospheric lidar profiles. A parameter named “scale laminarity index” is then introduced, which quantifies the relation between vortex scale and chaoticity throughout the profile. Finally, the algorithmic methods employed in this study are described and distributed for future use.

The pulsed laser deposition process is a complex one, encompassing a wide range of physical phenomena that act at different time scales, ranging from laser absorption to melting, plasma formation, and thin film deposition. In the past 15 years, there has been an exponential increase in theoretical models for different aspects of laser ablation phenomena, especially laser-produced plasmas. Among these. new types of models based on multifractal physics have been proposed. The models aim to describe the various dynamics reported for laser-produced plasmas in both the multifractal-type Schrodinger representation and in the multifractal-type hydrodynamic representation. The two approaches are complementary, as the Schrodinger representation uses operation procedures (invariance groups, variational principles, harmonic maps, etc.) while the hydrodynamic representation translates the dynamics of the laser-produced plasma into fluid motion of a multifractal type. The aim of this review is to report on the wide range of dynamics that can be discussed within the framework of a multifractal approach to plasma dynamics.

Assimilating a complex fluid with a fractal object, non-differentiable behaviors in its dynamics are analyzed. Complex fluid dynamics in the form of hydrodynamic-type fractal regimes imply “holographic implementations” through velocity fields at non-differentiable scale resolution, via fractal solitons, fractal solitons–fractal kinks, and fractal minimal vortices. Complex fluid dynamics in the form of Schrödinger type fractal regimes imply “holographic implementations”, through the formalism of Airy functions of fractal type. Then, the in-phase coherence of the dynamics of the complex fluid structural units induces various operational procedures in the description of such dynamics: special cubics with SL(2R)-type group invariance, special differential geometry of Riemann type associated to such cubics, special apolar transport of cubics, special harmonic mapping principle, etc. In such a manner, a possible scenario toward chaos (a period-doubling scenario), without concluding in chaos (nonmanifest chaos), can be mimed.

In this paper, developments are made towards simulating complex atmospheric behavior using turbulent energy cascade staging models developed through scale relativity theories. Such theoretical considerations imply gauges that describe atmospheric parameters as multifractal functions undertaking scale symmetry breaking at each stage of the turbulent energy cascade. It is found that gauges of higher complexity (in this case, a Riccati-type gauge) can exhibit more complex behavior accordingly, such as both dilation and contraction, but properly parameterizing the solutions formed by these gauges in terms of turbulent staging can be challenging given the multiple constants and parameters. However, it is found that a logistic-type approximation of the multifractal equations of motion that describe turbulent atmospheric entities can be coupled with a model produced by a simpler gauge, and this combination can reveal instances of laminar, or otherwise non-chaotic, behavior in a given turbulent flow at certain scales. Employing the theory with elastic lidar data, quasi-laminar behavior is found in the vicinity of the planetary boundary layer height, and laminar channels are revealed throughout an atmospheric column—these might be used to reveal complex vertical transport behavior in the atmospheric column.

The mathematical concept of minimal atomicity is extended to fractal minimal atomicity, based on the nondifferentiability of the motion curves of physical system entities on a fractal manifold. For this purpose, firstly, different results concerning minimal atomicity from the mathematical procedure of the Quantum Measure Theory and also several physical implications are obtained. Further, an inverse method with respect to the common developments concerning the minimal atomicity concept has been used, showing that Quantum Mechanics is identified as a particular case of Fractal Mechanics at a given scale resolution. More precisely, for fractality through Markov type stochastic processes, i.e., fractalization through stochasticization, the standard Schrödinger equation is identified with the geodesics of a fractal space for motions of the physical system entities on nondifferentiable curves on fractal dimension two at Compton scale resolution. In the one-dimensional stationary case of the fractal Schrödinger type geodesics, a special symmetry induced by the homographic group in Barbilian’s form “makes possible the synchronicity” of all entities of a given physical system. The integral and differential properties of this group under the restriction of defining a parallelism of directions in Levi-Civita’s sense impose correspondences with the “dynamics” of the hyperbolic plane so that harmonic mappings between the ordinary flat space and the hyperbolic one generate (by means of a variational principle) a priori probabilities in Jaynes’ sense. The explicitation of such situation specifies the fact that the hydrodynamical variant of a Fractal Mechanics is more easily approached and, from this, the fact that Quantum Measure Theory can be a particular case of a possible Fractal Measure Theory.

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.

The aim of the study was to create a mathematical model useful for monitoring the release of bioactive aldehydes covalently bonded to the chitosan by reversible imine linkage, considered as a polymer–drug system. For this purpose, two hydrogels were prepared by the acid condensation reaction of chitosan with the antifungal 2-formyl-phenyl-boronic acid and their particularities; influencing the release of the antifungal aldehyde by shifting the imination equilibrium to the reagents was considered, i.e., the supramolecular nature of the hydrogels was highlighted by polarized light microscopy, while scanning electron microscopy showed their microporous morphology. Furthermore, the in vitro fungicidal activity was investigated on two fungal strains and the in vitro release curves of the antifungal aldehyde triggered by the pH stimulus were drawn. The theoretical model was developed starting from the hypothesis that the imine-chitosan system, both structurally and functionally, can be assimilated, from a mathematical point of view, with a multifractal object, and its dynamics were analyzed in the framework of the Scale Relativity Theory. Thus, through Riccati-type gauges, two synchronous dynamics, one in the scale space, associated with the fungicidal activity, and the other in the usual space, associated with the antifungal aldehyde release, become operational. Their synchronicity, reducible to the isomorphism of two SL(2R)-type groups, implies, by means of its joint invariant functions, bioactive aldehyde compound release dynamics in the form of “kink–antikink pairs” dynamics of a multifractal type. Finally, the theoretical model was validated through the experimental data.

In the framework of the Multifractal Theory of Motion, which is expressed by means of the multifractal hydrodynamic model, complex system dynamics are explained through uniform and non-uniform flow regimes of multifractal fluids. Thus, in the case of the uniform flow regime of the multifractal fluid, the dynamics’ description is “supported” only by the differentiable component of the velocity field, the non-differentiable component being null. In the case of the non-uniform flow regime of the multifractal fluid, the dynamics’ description is “supported” by both components of the velocity field, their ratio specifying correlations through homographic transformations. Since these transformations imply metric geometries explained, for example, by means of Killing–Cartan metrics of the SL(2R)-type algebra, of the set of 2 × 2 matrices with real elements, and because these metrics can be “produced” as Cayleyan metrics of absolute geometries, the dynamics’ description is reducible, based on a minimal principle, to harmonic mappings from the usual space to the hyperbolic space. Such a conjecture highlights not only various scenarios of dynamics’ evolution but also the types of interactions “responsible” for these scenarios. Since these types of interactions become fundamental in the self-structuring processes of polymeric-type materials, finally, the theoretical model is calibrated based on the author’s empirical data, which refer to controlled drug release applications.

By assimilating biological systems, both structural and functional, into multifractal objects, their behavior can be described in the framework of the scale relativity theory, in any of its forms (standard form in Nottale’s sense and/or the form of the multifractal theory of motion). By operating in the context of the multifractal theory of motion, based on multifractalization through non-Markovian stochastic processes, the main results of Nottale’s theory can be generalized (specific momentum conservation laws, both at differentiable and non-differentiable resolution scales, specific momentum conservation law associated with the differentiable–non-differentiable scale transition, etc.). In such a context, all results are explicated through analyzing biological processes, such as acute arterial occlusions as scale transitions. Thus, we show through a biophysical multifractal model that the blocking of the lumen of a healthy artery can happen as a result of the “stopping effect” associated with the differentiable-non-differentiable scale transition. We consider that blood entities move on continuous but non-differentiable (multifractal) curves. We determine the biophysical parameters that characterize the blood flow as a Bingham-type rheological fluid through a normal arterial structure assimilated with a horizontal “pipe” with circular symmetry. Our model has been validated based on experimental clinical data.

Two distinct operational procedures are proposed for diagnosis and tracking of heart disease evolution (in particular atrial fibrillations). The first procedure, based on the application of non-linear dynamic methods (strange attractors, skewness, kurtosis, histograms, Lyapunov exponent, etc.) analyzes the electrical activity of the heart (electrocardiogram signals). The second procedure, based on multifractalization through Markovian and non-Markovian-type stochasticizations in the framework of the scale relativity theory, reconstructs any type of EKG signal by means of harmonic mappings from the usual space to the hyperbolic one. These mappings mime various scale transitions by differential geometries, in Riemann spaces with symmetries of SL(2R)-type. Then, the two operational procedures are not mutually exclusive, but rather become complementary, through their finality, which is gaining valuable information concerning fibrillation crises. As such, the author’s proposed method could be used for developing new models for medical diagnosis and evolution tracking of heart diseases (patterns dynamics, signal reconstruction, etc.).

This paper shall present a multifractal interpretation of turbulent atmospheric entities, considering them a complex system whose dynamics are manifested on continuous yet non-differentiable multifractal curves. By bringing forth theoretical considerations regarding multifractal structures through non-differentiable functions in the form of an adaptation of scale relativity theory, the minimal vortex of an instance of turbulent flow is considered. In this manner, the spontaneous breaking of scale invariance becomes a mechanism for atmospheric turbulence generation. This then leads to a general equation for the non-differentiable vortex itself, with its component velocity fields, and to a vortex turbulent energy dissipation—all of which are plotted and studied. Once the structure of the non-differentiable multifractal structure is mathematically described, an improved phenomenological turbulence model and relations between turbulent energy dissipation and the minimal vortex are employed together, exemplifying the codependency of such models. Using turbulent medium wave propagation theory, certain relations are then extrapolated which allow the obtaining of the inner and outer length scales of the turbulent flow using lidar data. Finally, these altitude profiles are compiled and assembled into timeseries to exemplify the theory and to compare the results with known literature. This model is a generalization of our recent results published under the title “On a Multifractal Approach of Turbulent Atmosphere Dynamics”.

In the framework of the multifractal hydrodynamic model, the correlations informational entropy–cross-entropy manages attractive and repulsive interactions through a multifractal specific potential. The classical dynamics associated with them imply Hubble-type effects, Galilei-type effects, and dependences of interaction constants with multifractal degrees at various scale resolutions, while the insertion of the relativistic amendments in the same dynamics imply multifractal transformations of a generalized Lorentz-type, multifractal metrics invariant to these transformations, and an estimation of the dimension of the multifractal Universe. In such a context, some correspondences with standard cosmologies are analyzed. Since the same types of interactions can also be obtained as harmonics mapping between the usual space and the hyperbolic plane, two measures with uniform and non-uniform temporal flows become functional, temporal measures analogous with Milne’s temporal measures in a more general manner. This work furthers the analysis published recently by our group in “Towards Interactions through Information in a Multifractal Paradigm”.

Traffic microsimulation models use the movement of individual driver-vehicle-units (DVUs) and their interactions, which allows a detailed estimation of the traffic noise using Common Noise Assessment Methods (CNOSSOS). The Dynamic Traffic Noise Assessment (DTNA) methodology is applied to real traffic situations, then compared to on-field noise levels from measurement campaigns. This makes it possible to determine the influence of certain local traffic factors on the evaluation of noise. The pattern of distribution of vehicles along the avenue is related to the logic of traffic light control. The analysis of the inter-cycles noise variability during the simulation and measurement time shows no influence from local factors on the prediction of the dynamic traffic noise assessment tool based on CNOSSOS. A multifractal approach of acoustic waves propagation and the source behaviors in the traffic area are implemented. The novelty of the approach also comes from the multifractal model’s freedom which allows the simulation, through the fractality degree, of various behaviors of the acoustic waves. The mathematical backbone of the model is developed on Cayley–Klein-type absolute geometries, implying harmonic mappings between the usual space and the Lobacevsky plane in a Poincaré metric. The isomorphism of two groups of SL(2R) type showcases joint invariant functions that allow associations of pulsations–velocities manifolds type.

In a multifractal paradigm of motion, Shannon’s information functionality of a minimization principle induces multifractal–type Newtonian behaviors. The analysis of these behaviors through motion geodesics shows the fact that the center of the Newtonian-type multifractal force is different from the center of the multifractal trajectory. The measure of this difference is given by the eccentricity, which depends on the initial conditions. In such a context, the eccentricities’ geometry becomes, through the Cayley–Klein metric principle, the Lobachevsky plane geometry. Then, harmonic mappings between the usual space and the Lobachevsky plane in a Poincaré metric can become operational, a situation in which the Ernst potential of general relativity acquires a classical nature. Moreover, the Newtonian-type multifractal dynamics, perceived and described in a multifractal paradigm of motion, becomes a local manifestation of the gravitational field of general relativity.

In a multifractal paradigm of motion, nonlinear behavior of transient periodic plasmas, such as Schrodinger and hydrodynamic-type regimes, at various scale resolutions are represented. In a stationary case of Schrodinger-type regimes, the functionality of “hidden symmetry” of the group SL (2R) is implied though Riccati–Gauge different “synchronization modes” among period plasmas’ structural units. These modes, expressed in the form of period doubling, damped oscillations, quasi-periodicity, intermittences, etc., mimic the various non-linear behaviors of the transient plasma dynamics similar to chaos transitions scenarios. In the hydrodynamic regime, the non-Newtonian behavior of the transient plasma dynamics can be corelated with the viscous tension tensor of the multifractal type. The predictions given by our theoretical model are confronted with experimental data depicting electronic and ionic oscillatory dynamics seen by implementing the Langmuir probe technique on transient plasmas generated by ns-laser ablation of nickel and manganese targets.

In the motion fractal theory, the scale relativity dynamics of any complex system are described through various Schrödinger or hydrodynamic type fractal “regimes”. In the one dimensional stationary case of Schrödinger type fractal “regimes”, synchronizations of complex system entities implies a joint invariant function with the simultaneous action of two isomorphic groups of the S L ( 2 R ) type as solutions of Stoka type equations. Among these joint invariant functions, Gaussians become in the Jeans’s sense, probability density (i.e., stochasticity) whenever the information on the complex system analyzed is fragmentary. In the two-dimensional case of hydrodynamic type fractal “regimes” at a non-differentiable scale, the soliton and soliton-kink of fractal type of the velocity field generate the minimal vortex of fractal type that becomes the source of all turbulences in the complex systems dynamics. Some correlations of our model to experimental data were also achieved.

The dynamics of a transient plasma generated by laser ablation on a Mg target was investigated by means of the Langmuir probe method and fractal analysis. The empirical data showcased the presence of an oscillatory behavior at short expansion times (

The optimization of the pulsed laser deposition process was attempted here for the generation of hydroxyapatite thin films. The deposition process was monitored with an ICCD (Intensified Coupled Charged Device) fast gated camera and a high-resolution spectrometer. The global dynamics of the laser produced plasma showed a self-structuring into three components with different composition and kinetics. The optical emission spectroscopy revealed the formation of a stoichiometric plasma and proved that the segregation in the kinetic energy of the plasma structure is also reflected by the individual energies of the ejected particles. Atomic Force Microscopy was also implemented to investigate the properties and the quality of the deposited film. The presence of micrometric clusters was seen at a high laser fluence deposition with in-situ ICCD imaging. We developed a fractal model based on Schrödinger type functionalities. The model can cover the distribution of the excited states in the laser produced plasma. Moreover, we proved that SL(2R) invariance can facilitate plasma substructures synchronization through a self-modulation in amplitude.

The properties of pulsed laser deposited of Ni60Ti40 shape memory thin films generated in various deposition conditions were investigated. In-situ plasma monitoring was implemented by means of space- and time-resolved optical emission spectroscopy, and ICCD fast camera imaging. Structural and chemical analyses were performed on the thin films using SEM, AFM, EDS, and XRD equipment. The deposition parameters influence on the chemical composition of the thin films was investigated. The peeled layer presented on DSC a solid-state transformation in a different transformation domain compared to the target properties. A fractal model was used to describe the dynamics of laser produced plasma through various non-differentiable functionalities. Through hydrodynamic type regimes, space-time homographic transformations were correlated with the global dynamics of the ablation plasmas. Spatial simultaneity of homographic transformation through a special SL(2R) invariance implies the description of plasma dynamics through Riccati type equations, establishing correlations with the optical emission spectroscopy measurements.