Multifractal and joint multifractal analysis of soil invertebrate fauna, altitude, and organic carbon

ABSTRACT The objectives of this study were to evaluate the degree of multifractality of the spatial distribution of altitude, organic carbon concentration, and invertebrate fauna diversity, and to characterize the degree of joint multifractal association among these variables. Soil sampling was performed every 20 m across a 2,540 m transect, with a total of 128 sampling points in a sugarcane area in Goiana municipality, Pernambuco State. For each sampling point, the altitude, organic carbon concentration, and macrofauna diversity (diversity indices and functional groups) were evaluated. Spatial distributions of altitude, organic carbon concentration, and macrofauna diversity were characterized by the generalized dimension spectrum (Dq) and singularity spectrums [f(α) versus α], which presented multifractal behavior with different degrees of heterogeneity in scales. Joint multifractal analysis was useful for revealing the relationships at multiple scales between the studied variables, as demonstrated by the non-detected associations using traditional statistical methods. To quantify the spatial variability of edaphic fauna based on the multiple scales and association sets in the joint dimension, the impact of agricultural production systems on biological diversity can be described. All of the studied variables displayed a multifractal behavior with greater or lower heterogeneity degree depending on the variable, with altitude and organic carbon being the most homogeneous attributes.

Multifractal Company Market: An Application to the Stock Market Indices

Using the multiscale normalized partition function, we exploit the multifractal analysis based on directly measurable shares of companies in the market. We present evidence that markets of competing firms are multifractal/multiscale. We verified this by (i) using our model that described the critical properties of the company market and (ii) analyzing a real company market defined by the S&P500 index. As the valuable reference case, we considered a four-group market model that skillfully reconstructs this index’s empirical data. We point out that a four-group company market organization is universal because it can perfectly describe the essential features of the spectrum of dimensions, regardless of the analyzed series of shares. The apparent differences from the empirical data appear only at the level of subtle effects.

A Multifractal Analysis and Machine Learning Based Intrusion Detection System with an Application in a UAS/RADAR System

The rapid development of Internet of Things (IoT) technology, together with mobile network technology, has created a never-before-seen world of interconnection, evoking research on how to make it vaster, faster, and safer. To support the ongoing fight against the malicious misuse of networks, in this paper we propose a novel algorithm called AMDES (unmanned aerial system multifractal analysis intrusion detection system) for spoofing attack detection. This novel algorithm is based on both wavelet leader multifractal analysis (WLM) and machine learning (ML) principles. In earlier research on unmanned aerial systems (UAS), intrusion detection systems (IDS) based on multifractal (MF) spectral analysis have been used to provide accurate MF spectrum estimations of network traffic. Such an estimation is then used to detect and characterize flooding anomalies that can be observed in an unmanned aerial vehicle (UAV) network. However, the previous contributions have lacked the consideration of other types of network intrusions commonly observed in UAS networks, such as the man in the middle attack (MITM). In this work, this promising methodology has been accommodated to detect a spoofing attack within a UAS. This methodology highlights a robust approach in terms of false positive performance in detecting intrusions in a UAS location reporting system.

Permutation Entropy of Weakly Noise-Affected Signals

We analyze the permutation entropy of deterministic chaotic signals affected by a weak observational noise. We investigate the scaling dependence of the entropy increase on both the noise amplitude and the window length used to encode the time series. In order to shed light on the scenario, we perform a multifractal analysis, which allows highlighting the emergence of many poorly populated symbolic sequences generated by the stochastic fluctuations. We finally make use of this information to reconstruct the noiseless permutation entropy. While this approach works quite well for Hénon and tent maps, it is much less effective in the case of hyperchaos. We argue about the underlying motivations.

Multifractal dimensions for projections of measures

In this paper, we calculate the multifractal Hausdorff and packing dimensions of Borel probability measures and study their behaviors under orthogonal projections. In particular, we try through these results to improve the main result of M. Dai in \cite{D} about the multifractal analysis of a measure of multifractal exact dimension.

Unstable entropies and dimension theory of partially hyperbolic systems

In this paper we define unstable topological entropy for any subsets (not necessarily compact or invariant) in partially hyperbolic systems as a Carathéodory–Pesin dimension characteristic, motivated by the work of Bowen and Pesin etc. We then establish some basic results in dimension theory for Bowen unstable topological entropy, including an entropy distribution principle and a variational principle in general setting. As applications of this new concept, we study unstable topological entropy of saturated sets and extend some results in Bowen (1973 Trans. Am. Math. Soc. 184 125–36); Pfister and Sullivan (2007 Ergod. Theor. Dynam. Syst. 27 929–56). Our results give new insights to the multifractal analysis for partially hyperbolic systems.

Application of Multifractal Analysis for Research of Structural Materials

Application of multifractal analysis for qualitative and quantitative description of structural materials is demonstrated. This makes it possible to evaluate the system’s characteristics of structures and to characterize the processes of self-organization in the materials. Formation of friction surface structures for aluminum alloys with Al2O3 and SiC additives in the scuffing mode is considered under comparable thermodynamic conditions. The addition of SiC, in comparison with Al2O3 , is less conducive to fragmentation and increase in the frequency of seizure and rupture processes. The addition of graphite into a composite material reinforced with SiC leads to increase in the degree of non-equilibrium of the thermodynamic conditions for the formation of the structures. Additional introduction of graphite further enhances the difference between materials with additions of Al2O3 and SiC, and this leads to the formation of the least ordered structures of the friction surface.