Investigation on Non-Segmentation Based Algorithms for Microvasculature Quantification in OCTA Images

Optical Coherence Tomography Angiography (OCTA) is an imaging modality that provides threedimensional information of the retinal microvasculature and therefore promises early diagnosis and sufficient monitoring in ophthalmology. However, there is considerable variability between experts analysing this data. Measures for quantitative assessment of the vasculature need to be developed and established, such as fractal dimension. Fractal dimension can be used to assess the complexity of vessels and has been shown to be independently associated with neovascularization, a symptom of diseases such as diabetic retinopathy. This investigation assessed the performance of three fractal dimension algorithms: Box Counting Dimension (BCD), Information Dimension (ID), and Differential Box Counting (DBC). Two of those, BCD and ID, rely on previous vessel segmentation. Assessment of the added value or disturbance regarding the segmentation step is a second aim of this study. The investigation was performed on a data set composed of 9 in vivo human eyes. Since there is no ground truth available, the performance of the methods in differentiating the Superficial Vascular Complex (SVC) and Deep Vascular Complex (DVC) layers apart and the consistency of measurements of the same layer at different time-points were tested. The performance parameters were the ICC and the Mann- Whitney U tests. The three applied methods were suitable to tell the different layers apart and showed consistent values applied in the same slab. Within the consistency test, the non-segmentation-based method, DBC, was found to be less accurate, expressed in a lower ICC value, compared to its segmentation-based counterparts. This result is thought to be due to the DBC’s higher sensitivity when compared to the other methods. This higher sensitivity might help detect changes in the microvasculature, like neovascularization, but is also more likely prone to noise and artefacts.

An Analysis of COVID-19 in Europe Based on Fractal Dimension and Meteorological Data

The present paper proposes a fractal analysis of the Covid-19 dynamics in 45 European countries. We introduce a new idea of using the box-counting dimension of the epidemiologic curves as a means of classifying the Covid-19 pandemic in the countries taken into consideration. The classification can be a useful tool in deciding upon the quality and accuracy of the data available. We also investigated the reproduction rate, which proves to have significant fractal features, thus enabling another perspective on this epidemic characteristic. Moreover, we studied the correlation between two meteorological parameters: global radiation and daily mean temperature and two Covid-19 indicators: daily new cases and reproduction rate. The fractal dimension differences between the analysed time series graphs could represent a preliminary analysis criterion, increasing research efficiency. Daily global radiation was found to be stronger linked with Covid-19 new cases than air temperature (with a greater correlation coefficient -0.386, as compared with -0.318), and consequently it is recommended as the first-choice meteorological variable for prediction models.

Dimension estimates for iterated function systems and repellers. Part II

This is the second part of our study on the dimension theory of $C^1$ iterated function systems (IFSs) and repellers on $\mathbb {R}^d$ . In the first part [D.-J. Feng and K. Simon. Dimension estimates for $C^1$ iterated function systems and repellers. Part I. Preprint, 2020, arXiv:2007.15320], we proved that the upper box-counting dimension of the attractor of every $C^1$ IFS on ${\Bbb R}^d$ is bounded above by its singularity dimension, and the upper packing dimension of every ergodic invariant measure associated with this IFS is bounded above by its Lyapunov dimension. Here we introduce a generalized transversality condition (GTC) for parameterized families of $C^1$ IFSs, and show that if the GTC is satisfied, then the dimensions of the IFS attractor and of the ergodic invariant measures are given by these upper bounds for almost every (in an appropriate sense) parameter. Moreover, we verify the GTC for some parameterized families of $C^1$ IFSs on ${\Bbb R}^d$ .

Quantitative Analysis of Protein Evolution: The Phylogeny of Osteopontin

The phylogenetic analysis of proteins conventionally relies on the evaluation of amino acid sequences or coding sequences. Individual amino acids have measurable features that allow the translation from strings of letters (amino acids or bases) into strings of numbers (physico-chemical properties). When the letters are converted to measurable properties, such numerical strings can be evaluated quantitatively with various tools of complex systems research. We build on our prior phylogenetic analysis of the cytokine Osteopontin to validate the quantitative approach toward the study of protein evolution. Phylogenetic trees constructed from the number strings differentiate among all sequences. In pairwise comparisons, autocorrelation, average mutual information and box counting dimension yield one number each for the overall relatedness between sequences. We also find that bivariate wavelet analysis distinguishes hypermutable regions from conserved regions of the protein. The investigation of protein evolution via quantitative study of the physico-chemical characteristics pertaining to the amino acid building blocks broadens the spectrum of applicable research tools, accounts for mutation as well as selection, gives assess to multiple vistas depending on the property evaluated, discriminates more accurately among sequences, and renders the analysis more quantitative than utilizing strings of letters as starting points.

Fractal and Convolutional Analysis for Deep Atmospheric Turbulence Using Machine Learning

Atmospheric turbulence studies indicate the presence of self-similar scaling structures over a range of scales from the inertial outer scale to the dissipative inner scale. A measure of this self-similar structure has been obtained by computing the fractal dimension of images visualizing the turbulence using the widely used box-counting method. If applied blindly, the box-counting method can lead to misleading results in which the edges of the scaling range, corresponding to the upper and lower length scales referred to above are incorporated in an incorrect way. Furthermore, certain structures arising in turbulent flows that are not self-similar can deliver spurious contributions to the box-counting dimension. An appropriately trained Convolutional Neural Network can take account of both the above features in an appropriate way, using as inputs more detailed information than just the number of boxes covering the putative fractal set. To give a particular example, how the shape of clusters of covering boxes covering the object changes with box size could be analyzed. We will create a data set of decaying isotropic turbulence scenarios for atmospheric turbulence using Large-Eddy Simulations (LES) and analyze characteristic structures arising from these. These could include contours of velocity magnitude, as well as of levels of a passive scalar introduced into the simulated flows. We will then identify features of the structures that can be used to train the networks to obtain the most appropriate fractal dimension describing the scaling range, even when this range is of limited extent, down to a minimum of one order of magnitude.

Investigation of Adsorption Characteristics and Influencing Factors for Diesel Engine Exhaust Particles

The adsorption process of diesel exhaust particles has a great influence on the particles. A single-cylinder diesel exhaust particle collection system was established to collect particle samples with different adsorption environment conditions, and the adsorption capacity of the samples was analyzed and characterized by an isothermal adsorption test; the change patterns of particle characteristics were investigated by the scanning electron microscope and thermogravimetric analyzer, correlation analysis of the factors influencing the adsorption process was performed. The results show that the particles have adsorption capacity and belong to the type of multilayer adsorption on porous media; the pore diameter is continuously distributed in the range of 8–80 nm with multiple peaks, which is the category of mesoporous and macroporous; the adsorption capacity of the sample particles increase with the increase of engine speed. Compared with the particles at the inlet of the exhaust pipe, the box-counting dimension (DB) of particles at the outlet increased, the content of water and soluble organic fraction (SOF) increased, the activation energy (E) decreased. Among the parameters affecting the adsorption process, the increase of hydrocarbons concentration contribute to the increase of particle adsorption and E reduction; the increase of the average temperature of the exhaust pipe inhibit the increase of the DB, and the increase of the temperature difference between the inlet and outlet facilitate the adsorption of water and SOF by the particles; the decrease of the adsorption time is one of the main reasons for the slowdown of the increase in DB; the average pore diameter had the greatest positive correlation with the amount of variation in the DB; the increase in specific surface area and pore volume of the sample particles was the dominant cause of the increase in adsorption capacity as well as the decrease in E.

Application of Fractal Dimension of Terrestrial Laser Point Cloud in Classification of Independent Trees

Tree precise classification and identification of forest species is a core issue of forestry resource monitoring and ecological effect assessment. In this paper, an independent tree species classification method based on fractal features of terrestrial laser point cloud is proposed. Firstly, the terrestrial laser point cloud data of an independent tree is preprocessed to obtain terrestrial point clouds of independent tree canopy. Secondly, the multi-scale box-counting dimension calculation algorithm of independent tree canopy dense terrestrial laser point cloud is proposed. Furthermore, a robust box-counting algorithm is proposed to improve the stability and accuracy of fractal dimension expression of independent tree point cloud, which implementing gross error elimination based on Random Sample Consensus. Finally, the fractal dimension of a dense terrestrial laser point cloud of independent trees is used to classify different types of independent tree species. Experiments on nine independent trees of three types show that the fractal dimension can be stabilized under large density variations, proving that the fractal features of terrestrial laser point cloud can stably express tree species characteristics, and can be used for accurate classification and recognition of forest species.

Complex systems analysis informs on the spread of COVID-19

Objectives The non-linear progression of new infection numbers in a pandemic poses challenges to the evaluation of its management. The tools of complex systems research may aid in attaining information that would be difficult to extract with other means. Methods To study the COVID-19 pandemic, we utilize the reported new cases per day for the globe, nine countries and six US states through October 2020. Fourier and univariate wavelet analyses inform on periodicity and extent of change. Results Evaluating time-lagged data sets of various lag lengths, we find that the autocorrelation function, average mutual information and box counting dimension represent good quantitative readouts for the progression of new infections. Bivariate wavelet analysis and return plots give indications of containment vs. exacerbation. Homogeneity or heterogeneity in the population response, uptick vs. suppression, and worsening or improving trends are discernible, in part by plotting various time lags in three dimensions. Conclusions The analysis of epidemic or pandemic progression with the techniques available for observed (noisy) complex data can extract important characteristics and aid decision making in the public health response.