The Cracking Behavior of Two Dental Composite Materials Validated through Multifractal Analyzes.

The aim of this in vitro study was to analyze, both experimentally and theoretically, the mechanical behavior of two types of composite materials used in restoring dental integrity. The samples of each composite resin, namely Filtek Supreme XT (3M ESPE, St. Paul, MN, USA) and Filtek Z250 (3M ESPE, St. Paul, MN, USA), were experimentally analyzed by determining their compressive strength and fracture behavior. The fractured fragments of the samples were subjected to surface evaluation by scanning electron microscopy. The compressive stress-compressive strain dependencies revealed stronger cracking of the Filtek Supreme XT composite than Filtek Z250 prior to fracture. Theoretically, the evaluation was made by means of holographic implementations of such types of composite materials. A Hooke-type equation in a differential form is presented, which links the proposed theoretical model with the experimentally obtained data.

Towards Multifractality through an Ernst-Type Potential in Complex Systems Dynamics.

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).

Coherences in the Dynamics of Physical Systems from a Multifractal Perspective of Motion.

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.

Drug-Loaded Polymeric Particulated Systems for Ophthalmic Drugs Release.

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.

Implications and Consequences of SL(2R) as Invariance Group in the Description of Complex Systems Dynamics from a Multifractal Perspective of Motion.

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.

Evaluating atrial fibrillations through strange attractors dynamics.

Nonlinear dynamics is nowadays widely employed in the study of biological phenomena. In such context, taking into account that abnormal heart rhythms display chaotic behaviours, in our opinion, the specific attractor dynamics can constitute a method for evaluating various cardiac afflictions. By using mathematical procedures specific to nonlinear dynamics we devise a new method for evaluating atrial fibrillations. Using data from ECG signals, we construct strange attractors corresponding to the phase space, specific to the analyzed signals. We show that their dynamics reflect abnormal heart rhythms. The skewness and kurtosis values are in accordance with pulse rate distributions from histograms of the analyzed signals. The Lyapunov exponent has positive values, close to zero for normal heart rhythm and with values over one order of magnitude higher in the case of fibrillation crises, highlighting a chaotic behavior for cardiac muscle dynamics. All the employed statistical parameters were calculated for a total of 5 cases (ECG signals) and statistical correlations were made using Python programming language. The presented results show that by applying nonlinear dynamics methods for analyzing the heart electrical activity we can obtain valuable information regarding fibrillation crises.

The Search for Atmospheric Laminar Channels: Experimental Results and Method Dissemination.

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.

A Theoretical Model for Release Dynamics of an Antifungal Agent Covalently Bonded to the Chitosan.

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.

The Role of Information in Managing Interactions from a Multifractal Perspective.

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".

Multifractality through Non-Markovian Stochastic Processes in the Scale Relativity Theory. Acute Arterial Occlusions as Scale Transitions.

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.

Toward Interactions through Information in a Multifractal Paradigm.

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.

New mechanisms of vesicles migration.

In multicellular organisms, both health and disease are defined by means of communication patterns involving the component cells. Despite the intricate networks of soluble mediators, cells are also programed to exchange complex messages pre-assembled as multimolecular cargo of membranous structures known as extracellular vesicles (EVs). Several biogenetic pathways produce EVs with different properties able to orchestrate neighboring cell reactions or to establish an environment ripe for spreading tumor cells. Such an effect is in fact an extension of similar physiological roles played by exosomes in guiding cell migration under nontumoral tissue remodeling and organogenesis. We start with a biological thought experiment equivalent to Bénard's experiment, involving a fluid layer of EVs adherent to an extracellular matrix, in a haptotactic gradient, then, we build and present the first Lorenz model for EVs migration. Using Galerkin's method of reducing a system of partial differential equations to a system of ordinary differential equations, a biological Lorenz system is developed. Such a physical frame distributing individual molecular or exosomal type cell-guiding cues in the extracellular matrix space could serve as a guide for tissue neoformation of the budding pattern in nontumoral or tumoral instances.

Predicting Tumor Dynamics Post-Staged GKRS: Machine Learning Models in Brain Metastases Prognosis.

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 Holographic-Type Model in the Description of Polymer-Drug Delivery Processes.

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.

Theoretical and Experimental Designs on Several Mechanical Properties of Cu-Al-Zn Shape Memory Alloys Used in the Processing Industry.

By assimilating shape memory alloys with mathematical multifractal-type objects, a theoretical model based on Scale Relativity Theory in the form of The Multifractal Theory of Motion, in order to explain the mechanical behavior of such material, is proposed. The model is validated by analyzing the mechanical behavior of Cu-Al-Zn shape memory alloy with various chemical compositions. More precisely, the multifractal tunnel effect can "mime" the mechanical hysteresis of such a material, a situation in which a direct correspondence for several mechanical properties of Cu-Al-Zn is highlighted (the chemical composition can be correlated with the shapes of the curves controlled through the multifractality degree, while the areas delimited by the same curves can be correlated with the multifractal specific potential, as a measure of the mechanical memory degree).

Drug Release from Nanoparticles (Polymeric Nanocapsules and Liposomes) Mimed through a Multifractal Tunnelling-Type Effect.

The present study analyzes (theoretically and experimentally) a drug release process from nanoparticles (polymeric nanocapsules and liposomes). This process is functionalized on the surface with an aptamer. These types of drug release processes can also be included in cream-type formulations. The obtained cream ensures the active targeting of tumor epithelial cells, in the case of skin cancer, because it can be easily administered to the skin by spreading, thus avoiding side effects caused by the toxicity of the drug to healthy cells, increasing both patient compliance and the effectiveness of the treatment. The process of obtaining these formulations is a simple one, easy to use and highly reproductible. The theoretical model, based on the multifractal tunnel effect within the Scale Relativity Theory, considers the system as a complex one. In this model, complexity is replaced with system multifractality, quantified in physical quantities as multifractal dimensions and multifractal functions. The main advantage of this approach consists in the fact that it allows us to obtain information on system behavior at a microscopic level and to evaluate microscopic characteristics of the system, such as intrinsic transparences of the drug molecules, multifractal constants as indicators of the system's complexity, the frequency of interactions within the system and the energy ratio between potential barrier energy and the energy of drug molecules.

AI Evaluation of Imaging Factors in the Evolution of Stage-Treated Metastases Using Gamma Knife.

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.

Theoretical and Experimental Aspects of Sodium Diclofenac Salt Release from Chitosan-Based Hydrogels and Possible Applications.

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.

Theoretical-Experimental Approach of Chitosan/Quaternized Chitosan Nanofibers' Behavior in Wound Exudate Media.

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.

Langmuir Probe Perturbations during In Situ Monitoring of Pulsed Laser Deposition Plasmas.

The recent advancements in pulsed laser deposition (PLD) control via plasma diagnostics techniques have been positive and raised questions on the limitation of some techniques, such as the Langmuir probe (LP). The particularities of laser-produced plasma can lead to incorrect interpretation of collected electrical signal. In this paper, we explored the limitations of LP as a technique for in situ PLD control by performing investigations on several metallic plasmas, expanding in various Ar atmosphere conditions. Sub-microsecond modulation was seen in the reconstructed IV characteristics attributed to non-equilibrium dynamics of the ejected charges. A perturbative regime was recorded for Ar pressures higher than 2 Pa, where ionic bursts were observed in the electron saturation region. This perturbation was identified as a plasma fireball. A non-linear multifractal model was developed here to explore these new regimes of the LP. The strange attractors characterizing each fireball were reconstructed, and their evolution with the Ar pressure is discussed. Both short- and long-time non-linear behavior were correlated via probe bias, and the pressure effect on the strange attractor's defining the fireball-like behavior was investigated. A good correlation was noticed between the simulated data and experimental findings.