Discrete mean square approximation applied to error calculation in biomolecules and brownian motion

Advanced research frontiers are extended from biophysics relations on the Earth upto the discovering any type of alive matter within the whole space. Microorganisms’ motion within the molecular biology processes integrates variety of microorgnisms functions. In continuation of our Brownian motion phenomena research, we consistently build molecular-microorganisms structures hierarchy. We recognize everywhere biomimetic similarities between the particles in alive and nonalive matter. The research data are based on real experiments, without external energy impulses. So, we develop the analysis, inspired by fractal nature Brownian motion, as recognized joint parameter between particles in alive and nonalive biophysical systems. This is also in line with advance trends in hybrid submicroelectronic integrations. The important innovation in this paper is that we introduced approximation of trajectory and error calculations, using discrete mean square approximation, what cumulatively provide much more precise biophysical systems parameters. By this paper, we continue to generate new knowledge in direction to get complex relations between the particles clusters in biophysical systems condensed matter.

Variation Trends of Fractal Dimension in Epileptic EEG Signals

Epileptic diseases take EEG as an important basis for clinical judgment, and fractal algorithms were often used to analyze electroencephalography (EEG) signals. However, the variation trends of fractal dimension (D) were opposite in the literature, i.e., both D decreasing and increasing were reported in previous studies during seizure status relative to the normal status, undermining the feasibility of fractal algorithms for EEG analysis to detect epileptic seizures. In this study, two algorithms with high accuracy in the D calculation, Higuchi and roughness scaling extraction (RSE), were used to study D variation of EEG signals with seizures. It was found that the denoising operation had an important influence on D variation trend. Moreover, the D variation obtained by RSE algorithm was larger than that by Higuchi algorithm, because the non-fractal nature of EEG signals during normal status could be detected and quantified by RSE algorithm. The above findings in this study could be promising to make more understandings of the nonlinear nature and scaling behaviors of EEG signals.

The fractal nature analysis by applying grain formations of SAC305/OSP Cu and SAC305-0.05Ni/OSP Cu solder joints for microelectronic packaging

The electronic packaging and systems are very important topics as the limitation of miniaturization approaches in semiconductor industry. Regarding the optimal materials microstructure for these applications, we studied different alloys such as Sn-3.0Ag-0.5Cu (wt.%)/organic solderability preservative (SAC305/OSP) Cu and SAC305–0.05Ni/OSP Cu solder joints. We implemented the fractal dimension characterization and microstructure morphology reconstruction. This is the first time that we applied fractals on such alloys. The morphology reconstruction is important for predicting and designing the optimal microstructure for the advanced desirable properties these alloys. These analyzed parameters are important for the hand-held devices and systems especially for the exploitation. The fractal reconstruction was applied on the prepared microstructures with five different magnifications. The results confirmed successful application of fractals in this area of materials science considering the grains and shapes reconstructions.

Forensic science and fractal nature analysis

Forensic photography, also referred to as crime scene photography, is an activity that records the initial appearance of the crime scene and physical evidence in order to provide a permanent record for the court. Nowadays, we cannot imagine a crime scene investigation without photographic evidence. Crime or accident scene photographs can often be reanalyzed in cold cases or when the images need to be enlarged to show critical details. Fractals are rough or fragmented geometric shapes that can be subdivided into parts, each of which is a reduced copy of the whole. Fractal dimension (FD) is an important fractal geometry feature. There are many applications of fractals in various forensic fields, including image processing, image analysis, texture segmentation, shape classification, and identifying the image features such as roughness and smoothness of an image. Fractal analysis is applicable in forensic archeology and paleontology, as well. The damaged image can be reviewed, analyzed, and reconstructed by fractal nature analysis.

Interpolation Methods Applied on Biomolecules and Condensed Matter Brownian Motion

Biophysical and condensed matter systems connection is of great importance nowadays due to the need for a new approach in microelectronic biodevices, biocomputers or biochips advanced development. Considering that the living and nonliving systems’ submicroparticles are identical, we can establish the biunivocally correspondent relation between these two particle systems, as a biomimetic correlation based on Brownian motion fractal nature similarities, as the integrative property. In our research, we used the experimental results of bacterial motion under the influence of energetic impulses, like music, and also some biomolecule motion data. Our goal is to define the relation between biophysical and physical particle systems, by introducing mathematical analytical forms and applying Brownian motion fractal nature characterization and fractal interpolation. This work is an advanced research in the field of new solutions for high-level microelectronic integrations, which include submicrobiosystems like part of even organic microelectronic considerations, together with some physical systems of particles in solid-state solutions as a nonorganic part. Our research is based on Brownian motion minimal joint properties within the integrated biophysical systems in the wholeness of nature.

SIX FRACTAL CODES OF LIFE FROM BIOATOMS ATOMIC MASS TO CHROMOSOMES NUMERICAL STANDING WAVES: THREE BREAKTHOUGHS IN ASTROBIOLOGY, CANCERS AND ARTIFICIAL INTELLIGENCE

The discovery of a simple numerical formula for the projection of all the atomic mass of life-sustaining CONHSP bioatoms leads to the emergence of a set of Nested CODES unifying all the biological, genetic and genomic components by unifying them from bioatoms up to 'to whole genomes. In particular, we demonstrate the existence of a digital meta-code common to the three languages ​​of biology that are RNA, DNA and amino acid sequences. Through this meta-code, genomic and proteomic images appear almost analogous and correlated. The analysis of the textures of these images then reveals a binary code as well as an undulatory code whose analysis on the human genome makes it possible to predict the alternating bands constituting the cariotypes of the chromosomes. The application of these codes to perspectives in astrobiology and the emergence of binary codes and regions of local stability (voting process), whose fractal nature we demonstrate, is illustrated. The fundamental discovery described here will undoubtedly one day constitute a new biomathematic approach to the emergence of living things.

Topological properties of Sierpinski network and its application

Background: Sierpinski graphs S(n,k) are largely studied because of their fractal nature with applications in topology, chemistry, mathematics of Tower of Hanoi, and computer sciences. Applications of molecular structure descriptors are a standard procedure that are used to correlate the biological activity of molecules with their chemical structures and thus can be helpful in the field of pharmacology. Objective: The aim of this article is to establish analytically closed computing formulae for eccentricity-based descriptors of Sierpinski networks and their regularizations. These computing formulae are useful to determine a large number of properties like thermodynamic properties, physicochemical properties, chemical and biological activity of chemical graphs. Methods: At first, vertex sets have been partitioned on the basis of their degrees, eccentricities, and frequencies of occurrence. Then these partitions are used to compute the eccentricity-based indices with the aid of some combinatorics. Results: The total eccentric index and eccentric-connectivity index have been computed. We also compute some eccentricity-based Zagreb indices of the Sierpinski networks. Moreover, a comparison has also been presented in the form of graphs. Conclusion: These computations will help the readers to estimate the thermodynamic properties, physicochemical properties of chemical structures, which are of fractal nature and can not be dealt with easily. A 3D graphical representation is also presented to understand the dynamics of the aforementioned topological descriptors.

An Extended Correlation Dimension of Complex Networks

Fractal and self-similarity are important characteristics of complex networks. The correlation dimension is one of the measures implemented to characterize the fractal nature of unweighted structures, but it has not been extended to weighted networks. In this paper, the correlation dimension is extended to the weighted networks. The proposed method uses edge-weights accumulation to obtain scale distances. It can be used not only for weighted networks but also for unweighted networks. We selected six weighted networks, including two synthetic fractal networks and four real-world networks, to validate it. The results show that the proposed method was effective for the fractal scaling analysis of weighted complex networks. Meanwhile, this method was used to analyze the fractal properties of the Newman–Watts (NW) unweighted small-world networks. Compared with other fractal dimensions, the correlation dimension is more suitable for the quantitative analysis of small-world effects.