On the separation of particle flow during pulse laser deposition of heterogeneous materials - A multi-fractal approach

Statistical Analysis and Machine Learning Used in the Case of Two Behavioral Tests Applied in Zebrafish Exposed to Mycotoxins

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.

Multifractal Model for Transient Phenomena Analysis in Laser Produced Plasmas

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.

A theoretical mathematical model for assessing diclofenac release from chitosan-based formulations

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.

Non-Linear Behaviors of Transient Periodic Plasma Dynamics in a Multifractal Paradigm

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.

A Theoretical Multifractal Model for Assessing Urea Release from Chitosan Based Formulations

This paper reports the calibration of a theoretical multifractal model based on empirical data on the urea release from a series of soil conditioner systems. To do this, a series of formulations was prepared by in situ hydrogelation of chitosan with salicylaldehyde in the presence of different urea amounts. The formulations were morphologically characterized by scanning electron microscopy and polarized light microscopy. The in vitro urea release was investigated in an environmentally simulated medium. The release data were fitted on five different mathematical models, Korsmeyer–Peppas, Zero order, First order, Higuchi and Hixson–Crowell, which allowed the establishment of a mechanism of urea release. Furthermore, a multifractal model, used for the fertilizer release for the first time, was calibrated using these empirical data. The resulting fit was in good agreement with the experimental data, validating the multifractal theoretical model.

Towards Stochasticity through Joint Invariant Functions of Two Isomorphic Lie Algebras of SL(2R) Type

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.

Investigations of Transient Plasma Generated by Laser Ablation of Hydroxyapatite during the Pulsed Laser Deposition Process

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.

In-Situ Plasma Monitoring during the Pulsed Laser Deposition of Ni60Ti40 Thin Films

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.

Investigations of Laser Produced Plasmas Generated by Laser Ablation on Geomaterials. Experimental and Theoretical Aspects

Several surface investigation techniques, such as X-ray diffraction (XRD), EDX, and optical microscopy, were employed in order to describe the mineral contents in several geomaterials. Space and time resolved optical emission spectroscopy was implemented to analyze the plasma generated by the laser–geomaterial interaction. The values of the plasma parameters (velocity and temperature) were discussed with respect to the nature of the minerals composing the geomaterials and the morphological structure of the samples. Correlations were found between the excitation temperatures of the atomic and ionic species of the plasmas and the presence of calcite in the samples. A mathematical model was built to describe the dynamics in ablation plasma using various mathematical operational procedures: multi structuring of the ablation plasma by means of the fractal analysis and synchronizations of the ablation plasma entities through SL (2R) type group invariance and in a particular case, through self-modulation in the form of Stoler type transformations. Since Stoler type transformations are implied in general, in the charge creation and annihilation processes, then the SL (2R) type group invariance become fundamental in the description of ablation plasma dynamics.

Lorenz Type Behaviors in the Dynamics of Laser Produced Plasma

An innovative theoretical model is developed on the backbone of a classical Lorenz system. A mathematical representation of a differential Lorenz system is transposed into a fractal space and reduced to an integral form. In such a conjecture, the Lorenz variables will operate simultaneously on two manifolds, generating two transformation groups, one corresponding to the space coordinates transformation and another one to the scale resolution transformation. Since these groups are isomorphs various types isometries become functional. The Lorenz system was further adapted to describe the dynamics of ejected particles as a result of laser matter interaction in a fractal paradigm. The simulations were focused on the dynamics of charged particles, and showcase the presence of current oscillations, a heterogenous velocity distribution and multi-structuring at different interaction scales. The theoretical predictions were compared with the experimental data acquired with noninvasive diagnostic techniques. The experimental data confirm the multi-structure scenario and the oscillatory behavior predicted by the mathematical model.