The Mathematical Characterization of the Complexity Matching during a Healing Circle Meditation.

The aim of the study is to evaluate the complexity matching between the HRVs of the group of Healers and the Healee during the various stages of the meditation protocol by employing a novel mathematical approach based on the H-rank algorithm. The complexity matching of heart rate variability is assessed before and during a heart-focused meditation in a close non-contact healing exercise. The experiment was conducted on a group of individuals (eight Healers and one Healee) throughout the various phases of the protocol over a ~75-minute period. The HRV signal for the cohort of individuals was recorded using high resolution HRV recorders with internal clocks for time synchronization. The Hankel transform (H-rank) approach was employed to reconstruct the real-world complex time series in order to measure the algebraic complexity of the heart rate variability and to assess the complexity matching between the reconstructed H-rank of the Healers and Healee during the different phases of the protocol. The integration of the embedding attractor technique was used to aid in the visualization of reconstructed H-rank in state space across the various phases. The findings demonstrate the changes in the degree of reconstructed H-rank (between the Healers and the Healee) during the heart-focused meditation healing phase by employing mathematically anticipated and validated algorithms. It is natural and thought-provoking to contemplate the mechanisms causing the complexity of the reconstructed H-rank to come closer; it can be explicitly stated that the purpose of the study is to communicate a clear idea that the H-rank algorithm is capable of registering subtle changes in the healing process, and that there was no intention of delving deep to uncover the mechanisms involved in the HRV matching. Therefore, the latter might be a distinct goal of future research.

A polarizable coarse-grained model for metal, metal oxide and composite metal/metal oxide nanoparticles and its applications.

We present a selected set of exemplifying applications of the novel polarizable coarse-grained model [see the first part] to various outstanding problems in the physics and chemistry of nanoparticles: electrostatic potential around silver and gold nanoparticles; spontaneous and external electric field-driven self-organization of gold and silver nanoparticle systems; and physisorption of carbon dioxide on titanium dioxide nanoparticles decorated with a gold catalyst. In the first application, the developed model has shown capabilities of predicting long-range potential with accuracy comparable to the tight-binding density functional theory methods. Furthermore, the electrostatic potential analysis in hot spot regions allowed us to identify twin defect lines in a silver nanostar as a promising candidate for an enhancer in surface-enhanced Raman spectroscopy. In the second application, the developed model has facilitated the elucidation of the microscopic mechanisms responsible for the self-organization of gold and silver nanoparticles. Analysis of Monte-Carlo simulations established that the self-organization process is driven by van der Waals interactions in the absence of an external electric field, and that it becomes gradually driven by electrostatic interactions in the presence of an external electric field with increasing strength of the external electric field. In the third application, the developed model combined with Monte-Carlo simulations has identified the dominant mechanism responsible for carbon dioxide transfer to the catalytic sites. Analysis of the obtained results indicates that surface diffusion is the dominant mechanism for the transport of carbon dioxide to the catalytic sites, and only in exceptional situations, direct physisorption becomes a competitive mechanism with the surface diffusion mechanism. These successful applications of the developed model indicate its wide range of applicability to various problems in the chemistry and physics of nanoparticles.

A polarizable coarse-grained model for metal, metal oxide and composite metal/metal oxide nanoparticles: development and implementation.

We present a polarizable coarse-grained model for metal, metal oxide, and composite metal/metal oxide nanoparticles with well-defined crystalline surfaces. The developed model uses a low-resolution polarizable "surface beads" representation of the nanoparticle's geometry and pairwise cross nanoparticle potential consisting of van der Waals and electrostatic interaction terms. The electrostatic interaction term of the cross nanoparticle potential incorporates a crucial physical aspect of electrostatic interaction into the metal and metal oxide systems, such as induced surface charges, making it possible to explore the nanoparticles' behavior in complex environments as well as investigate the interplay between electrostatic and van der Waals interactions in nanoparticle systems. The iterative stability, computational scaling, and performance of the presented model was tested on selected systems of gold, titanium dioxide, and composite gold/titanium dioxide nanoparticle systems. The model exhibits robust iterative stability and is able to converge the charge equilibration equation for fluctuating induced charges and dipoles within 10-60 "tug-tow" iterations in challenging situations, like crowded nanoparticle systems or nanoparticle systems in extreme external electric fields. The computation scaling of the presented model is semi-linear with respect to the number of nanoparticles in the system. It slightly varies depending on the size distribution of nanoparticles in a specific nanoparticle system. The computation cost of the model is significantly lower than that of conventional atomistic polarizable force field models and enables the treatment of large nanoparticle systems that are beyond the reach of currently existing atomistic force field models.

Automatic Detection of Cracks on Concrete Surfaces in the Presence of Shadows.

Deep learning-based methods, especially convolutional neural networks, have been developed to automatically process the images of concrete surfaces for crack identification tasks. Although deep learning-based methods claim very high accuracy, they often ignore the complexity of the image collection process. Real-world images are often impacted by complex illumination conditions, shadows, the randomness of crack shapes and sizes, blemishes, and concrete spall. Published literature and available shadow databases are oriented towards images taken in laboratory conditions. In this paper, we explore the complexity of image classification for concrete crack detection in the presence of demanding illumination conditions. Challenges associated with the application of deep learning-based methods for detecting concrete cracks in the presence of shadows are elaborated on in this paper. Novel shadow augmentation techniques are developed to increase the accuracy of automatic detection of concrete cracks.

Color Recurrence Plots for Bearing Fault Diagnosis.

This paper presents bearing fault diagnosis using the image classification of different fault patterns. Feature extraction for image classification is carried out using a novel approach of Color recurrence plots, which is presented for the first time. Color recurrence plots are created using non-linear embedding of the vibration signals into delay coordinate space with variable time lags. Deep learning-based image classification is then performed by building the database of the extracted features of the bearing vibration signals in the form of Color recurrence plots. A Series of computational experiments are performed to compare the accuracy of bearing fault classification using Color recurrence plots. The standard bearing vibration dataset of Case Western Reserve University is used for those purposes. The paper demonstrates the efficacy and the accuracy of a new and unique approach of scalar time series extraction into two-dimensional Color recurrence plots for bearing fault diagnosis.

Information Hiding Based on Statistical Features of Self-Organizing Patterns.

A computational technique for the determination of optimal hiding conditions of a digital image in a self-organizing pattern is presented in this paper. Three statistical features of the developing pattern (the Wada index based on the weighted and truncated Shannon entropy, the mean of the brightness of the pattern, and the p-value of the Kolmogorov-Smirnov criterion for the normality testing of the distribution function) are used for that purpose. The transition from the small-scale chaos of the initial conditions to the large-scale chaos of the developed pattern is observed during the evolution of the self-organizing system. Computational experiments are performed with the stripe-type patterns, spot-type patterns, and unstable patterns. It appears that optimal image hiding conditions are secured when the Wada index stabilizes after the initial decline, the mean of the brightness of the pattern remains stable before dropping down significantly below the average, and the p-value indicates that the distribution becomes Gaussian.

A Data-Driven Damage Identification Framework Based on Transmissibility Function Datasets and One-Dimensional Convolutional Neural Networks: Verification on a Structural Health Monitoring Benchmark Structure.

Vibration-based data-driven structural damage identification methods have gained large popularity because of their independence of high-fidelity models of target systems. However, the effectiveness of existing methods is constrained by critical shortcomings. For example, the measured vibration responses may contain insufficient damage-sensitive features and suffer from high instability under the interference of random excitations. Moreover, the capability of conventional intelligent algorithms in damage feature extraction and noise influence suppression is limited. To address the above issues, a novel damage identification framework was established in this study by integrating massive datasets constructed by structural transmissibility functions (TFs) and a deep learning strategy based on one-dimensional convolutional neural networks (1D CNNs). The effectiveness and efficiency of the TF-1D CNN framework were verified using an American Society of Civil Engineers (ASCE) structural health monitoring benchmark structure, from which dynamic responses were captured, subject to white noise random excitations and a number of different damage scenarios. The damage identification accuracy of the framework was examined and compared with others by using different dataset types and intelligent algorithms. Specifically, compared with time series (TS) and fast Fourier transform (FFT)-based frequency-domain signals, the TF signals exhibited more significant damage-sensitive features and stronger stability under excitation interference. The utilization of 1D CNN, on the other hand, exhibited some unique advantages over other machine learning algorithms (e.g., traditional artificial neural networks (ANNs)), particularly in aspects of computation efficiency, generalization ability, and noise immunity when treating massive, high-dimensional datasets. The developed TF-1D CNN damage identification framework was demonstrated to have practical value in future applications.

Image Entropy for the Identification of Chimera States of Spatiotemporal Divergence in Complex Coupled Maps of Matrices.

Complex networks of coupled maps of matrices (NCMM) are investigated in this paper. It is shown that a NCMM can evolve into two different steady states-the quiet state or the state of divergence. It appears that chimera states of spatiotemporal divergence do exist in the regions around the boundary lines separating these two steady states. It is demonstrated that digital image entropy can be used as an effective measure for the visualization of these regions of chimera states in different networks (regular, feed-forward, random, and small-world NCMM).

Permutation Entropy Based on Non-Uniform Embedding.

A novel visualization scheme for permutation entropy is presented in this paper. The proposed scheme is based on non-uniform attractor embedding of the investigated time series. A single digital image of permutation entropy is produced by averaging all possible plain projections of the permutation entropy measure in the multi-dimensional delay coordinate space. Computational experiments with artificially-generated and real-world time series are used to demonstrate the advantages of the proposed visualization scheme.

Applicability of time-averaged holography for micro-electro-mechanical system performing non-linear oscillations.

Optical investigation of movable microsystem components using time-averaged holography is investigated in this paper. It is shown that even a harmonic excitation of a non-linear microsystem may result in an unpredictable chaotic motion. Analytical results between parameters of the chaotic oscillations and the formation of time-averaged fringes provide a deeper insight into computational and experimental interpretation of time-averaged MEMS holograms.

Early Diagnosis of Problems Related to the Self-Organization of the Cardiovascular System Based on the Interplay between RR and JT Cardiac Intervals.

The dynamics of the collapse of complexity observable in the performance of the cardiovascular system during the stress test is investigated in this paper. For this purpose, the interplay between the RR and JT cardiac intervals is measured and assessed for each participant. This case study involves a modest sample size of eight individuals with normal and elevated blood pressure. Although it is anticipated that the interaction between the RR and JT intervals is rather complex during the stress test, the existence of interpretable time delays between those cardiac intervals is demonstrated using the time delayed patterns algorithm. The assessment of the cardiovascular mobilization taking place during the stress test is also an integral part of this study. The velocity of adaptation index Ad and the newly formulated modified adaptation index Ar (computed only for the recovery phase) are used to quantify the healthy mobilization of the cardiovascular system for each participant. The time frequency analysis of the difference signal between the RR and JT intervals is used to quantify the collapse of complexity around the load termination point. Finally, a semi-gauge indication tool is constructed to assess the overall goodness of the self-organization of the cardiovascular system during the stress test.

Validation of noninvasive MOEMS-assisted measurement system based on CCD sensor for radial pulse analysis.

Examination of wrist radial pulse is a noninvasive diagnostic method, which occupies a very important position in Traditional Chinese Medicine. It is based on manual palpation and therefore relies largely on the practitioner's subjective technical skills and judgment. Consequently, it lacks reliability and consistency, which limits practical applications in clinical medicine. Thus, quantifiable characterization of the wrist pulse diagnosis method is a prerequisite for its further development and widespread use. This paper reports application of a noninvasive CCD sensor-based hybrid measurement system for radial pulse signal analysis. First, artery wall deformations caused by the blood flow are calibrated with a laser triangulation displacement sensor, following by the measurement of the deformations with projection moiré method. Different input pressures and fluids of various viscosities are used in the assembled artificial blood flow system in order to test the performance of laser triangulation technique with detection sensitivity enhancement through microfabricated retroreflective optical element placed on a synthetic vascular graft. Subsequently, the applicability of double-exposure whole-field projection moiré technique for registration of blood flow pulses is considered: a computational model and representative example are provided, followed by in vitro experiment performed on a vascular graft with artificial skin atop, which validates the suitability of the technique for characterization of skin surface deformations caused by the radial pulsation.

Additive Manufactured Strain Sensor Using Stereolithography Method with Photopolymer Material.

As a result of the developments in additive manufacturing (AM) technology, 3D printing is transforming from a method used only in rapid prototyping to a technique used to produce large-scale equipment. This study presents the fabrication and experimental studies of a 3D-printed strain sensor that can be used directly in soft applications. Photopolymer-based conductive and flexible ultraviolet (UV) resin materials are used in the fabrication of the sensor. A Stereolithography (SLA)-based printer is preferred for 3D fabrication. The bottom base of the sensor, which consists of two parts, is produced from flexible UV resin, while the channels that should be conductive are produced from conductive UV resin. In total, a strain sensor with a thickness of 2 mm was produced. Experimental studies were carried out under loading and unloading conditions to observe the hysteresis effect of the sensor. The results showed a close linear relationship between the strain sensor and the measured resistance value. In addition, tensile test specimens were produced to observe the behavior of conductive and non-conductive materials. The tensile strength values obtained from the test results will provide information about the sensor placement. In addition, the flexible structure of the strain sensor will ensure its usability in many soft applications.

Clocking convergence to a stable limit cycle of a periodically driven nonlinear pendulum.

Convergence to a stable limit cycle of a periodically driven nonlinear pendulum is analyzed in this paper. The concept of the H-rank of a scalar sequence is used for the assessment of transient processes of the system. The circle map is used to illustrate the complex structure of the manifold of non-asymptotic convergence to a fixed point. It is demonstrated that the manifold of non-asymptotic convergence to a stable limit cycle also exists in the stroboscopic representation of the transient data of the periodically driven nonlinear pendulum. A simple method based on a short external impulse is proposed for the control of transient processes when the transition time to stable limit cycles must be minimized.

Pinning Impulsive Synchronization of Stochastic Delayed Neural Networks via Uniformly Stable Function.

This article investigates the synchronization of stochastic delayed neural networks under pinning impulsive control, where a small fraction of nodes are selected as the pinned nodes at each impulsive moment. By proposing a uniformly stable function as a new tool, some novel mean square decay results are presented to analyze the error system obtained from the leader and the considered neural networks. For the divergent error system without impulsive effects, the impulsive gains of pinning impulsive controller can admit destabilizing impulse and the number of destabilizing impulse may be infinite. However, if the error system without impulsive effects is convergent, to achieve the synchronization of the stochastic neural networks, the growth exponent of the product of impulsive gains can not exceed some positive constant. It is shown that the obtained results increase the flexibility of the impulsive gains compared with the existing results. Finally, a numerical example is given to illustrate the practicality of synchronization criteria.

Detection of Atrial Fibrillation Episodes based on 3D Algebraic Relationships between Cardiac Intervals.

In this study, the notion of perfect matrices of Lagrange differences is employed to detect atrial fibrillation episodes based on three ECG parameters (JT interval, QRS interval, RR interval). The case study comprised 8 healthy individuals and 7 unhealthy individuals, and the mean and standard deviation of age was 65.84 ± 1.4 years, height was 1.75 ± 0.12 m, and weight was 79.4 ± 0.9 kg. Initially, it was demonstrated that the sensitivity of algebraic relationships between cardiac intervals increases when the dimension of the perfect matrices of Lagrange differences is extended from two to three. The baseline dataset was established using statistical algorithms for classification by means of the developed decision support system. The classification helps to determine whether the new incoming candidate has indications of atrial fibrillation or not. The application of probability distribution graphs and semi-gauge indicator techniques aided in visualizing the categorization of the new candidates. Though the study's data are limited, this work provides a strong foundation for (1) validating the sensitivity of the perfect matrices of Lagrange differences, (2) establishing a robust baseline dataset for supervised classification, and (3) classifying new incoming candidates within the classification framework. From a clinical standpoint, the developed approach assists in the early detection of atrial fibrillation in an individual.

The Complexity of the Arterial Blood Pressure Regulation during the Stress Test.

In this study, two categories of persons with normal and high ABP are subjected to the bicycle stress test (9 persons with normal ABP and 10 persons with high ABP). All persons are physically active men but not professional sportsmen. The mean and the standard deviation of age is 41.11 ± 10.21 years; height 178.88 ± 0.071 m; weight 80.53 ± 10.01 kg; body mass index 25.10 ± 2.06 kg/m2. Machine learning algorithms are employed to build a set of rules for the classification of the performance during the stress test. The heart rate, the JT interval, and the blood pressure readings are observed during the load and the recovery phases of the exercise. Although it is obvious that the two groups of persons will behave differently throughout the bicycle stress test, with this novel study, we are able to detect subtle variations in the rate at which these changes occur. This paper proves that these differences are measurable and substantial to detect subtle differences in the self-organization of the human cardiovascular system. It is shown that the data collected during the load phase of the stress test plays a more significant role than the data collected during the recovery phase. The data collected from the two groups of persons are approximated by Gaussian distribution. The introduced classification algorithm based on the statistical analysis and the triangle coordinate system helps to determine whether the reaction of the cardiovascular system of a new candidate is more pronounced by an increased heart rate or an increased blood pressure during the stress test. The developed approach produces valuable information about the self-organization of human cardiovascular system during a physical exercise.

Antibacterial Activity of Silver and Gold Particles Formed on Titania Thin Films.

Metal-based nanoparticles with antimicrobial activity are gaining a lot of attention in recent years due to the increased antibiotics resistance. The development and the pathogenesis of oral diseases are usually associated with the formation of bacteria biofilms on the surfaces; therefore, it is crucial to investigate the materials and their properties that would reduce bacterial attachment and biofilm formation. This work provides a systematic investigation of the physical-chemical properties and the antibacterial activity of TiO2 thin films decorated by Ag and Au nanoparticles (NP) against Veillonella parvula and Neisseria sicca species associated with oral diseases. TiO2 thin films were formed using reactive magnetron sputtering by obtaining as-deposited amorphous and crystalline TiO2 thin films after annealing. Au and Ag NP were formed using a two-step process: magnetron sputtering of thin metal films and solid-state dewetting. The surface properties and crystallographic nature of TiO2/NP structures were investigated by SEM, XPS, XRD, and optical microscopy. It was found that the higher thickness of Au and Ag thin films results in the formation of the enlarged NPs and increased distance between them, influencing the antibacterial activity of the formed structures. TiO2 surface with AgNP exhibited higher antibacterial efficiency than Au nanostructured titania surfaces and effectively reduced the concentration of the bacteria. The process of the observation and identification of the presence of bacteria using the deep learning technique was realized.

Visualization of Complex Processes in Cardiovascular System during Electrical Auricular Vagus Nerve Stimulation.

The analysis of human physiological systems from the point of view of complex systems theory remains a very ambitious task. The complexity of the problem often encourages the use of innovative mathematical methods analyzing the processes that take place in space and time. The main goal of this paper is to visualize the cardiovascular system during auricular vagus nerve stimulation (aVNS) using the matrix differences to evaluate the dynamic signal interfaces by cointegrating the initial signal data into the matrices during each case. Algebraic relationships between RR/JT and JT/QRS cardiac intervals are used not only to track the cardiovascular changes during aVNS but also to characterize individual features of the person during the transit through the therapy. This paper presents the computational techniques that can visualize the complex dynamical processes taking place in the cardiovascular system using the electrical aVNS therapy. Four healthy volunteers participated in two verum and two placebo experiments. We discovered that the body's reaction to the stimulation was very different in each of the cases, but the presented techniques opened new possibilities for a novel interpretation of the dynamics of the cardiovascular system.

Higher order solitary solutions to the meta-model of diffusively coupled Lotka-Volterra systems.

A meta-model of diffusively coupled Lotka-Volterra systems used to model various biomedical phenomena is considered in this paper. Necessary and sufficient conditions for the existence of nth order solitary solutions are derived via a modified inverse balancing technique. It is shown that as the highest possible solitary solution order n is increased, the number of nonzero solution parameter values remains constant for solitary solutions of order n > 3 . Analytical and computational experiments are used to illustrate the obtained results.