Distinction of Chaos from Randomness Is Not Possible from the Degree Distribution of the Visibility and Phase Space Reconstruction Graphs.

We investigate whether it is possible to distinguish chaotic time series from random time series using network theory. In this perspective, we selected four methods to generate graphs from time series: the natural, the horizontal, the limited penetrable horizontal visibility graph, and the phase space reconstruction method. These methods claim that the distinction of chaos from randomness is possible by studying the degree distribution of the generated graphs. We evaluated these methods by computing the results for chaotic time series from the 2D Torus Automorphisms, the chaotic Lorenz system, and a random sequence derived from the normal distribution. Although the results confirm previous studies, we found that the distinction of chaos from randomness is not generally possible in the context of the above methodologies.

The Impact of COVID-19 on Weak-Form Efficiency in Cryptocurrency and Forex Markets.

The COVID-19 pandemic has had an unprecedented impact on the global economy and financial markets. In this article, we explore the impact of the pandemic on the weak-form efficiency of the cryptocurrency and forex markets by conducting a comprehensive comparative analysis of the two markets. To estimate the weak-form of market efficiency, we utilize the asymmetric market deficiency measure (MDM) derived using the asymmetric multifractal detrended fluctuation analysis (A-MF-DFA) approach, along with fuzzy entropy, Tsallis entropy, and Fisher information. Initially, we analyze the temporal evolution of these four measures using overlapping sliding windows. Subsequently, we assess both the mean value and variance of the distribution for each measure and currency in two distinct time periods: before and during the pandemic. Our findings reveal distinct shifts in efficiency before and during the COVID-19 pandemic. Specifically, there was a clear increase in the weak-form inefficiency of traditional currencies during the pandemic. Among cryptocurrencies, BTC stands out for its behavior, which resembles that of traditional currencies. Moreover, our results underscore the significant impact of COVID-19 on weak-form market efficiency during both upward and downward market movements. These findings could be useful for investors, portfolio managers, and policy makers.

Investigating Dynamical Complexity and Fractal Characteristics of Bitcoin/US Dollar and Euro/US Dollar Exchange Rates around the COVID-19 Outbreak.

This article investigates the dynamical complexity and fractal characteristics changes of the Bitcoin/US dollar (BTC/USD) and Euro/US dollar (EUR/USD) returns in the period before and after the outbreak of the COVID-19 pandemic. More specifically, we applied the asymmetric multifractal detrended fluctuation analysis (A-MF-DFA) method to investigate the temporal evolution of the asymmetric multifractal spectrum parameters. In addition, we examined the temporal evolution of Fuzzy entropy, non-extensive Tsallis entropy, Shannon entropy, and Fisher information. Our research was motivated to contribute to the comprehension of the pandemic's impact and the possible changes it caused in two currencies that play a key role in the modern financial system. Our results revealed that for the overall trend both before and after the outbreak of the pandemic, the BTC/USD returns exhibited persistent behavior while the EUR/USD returns exhibited anti-persistent behavior. Additionally, after the outbreak of COVID-19, there was an increase in the degree of multifractality, a dominance of large fluctuations, as well as a sharp decrease of the complexity (i.e., increase of the order and information content and decrease of randomness) of both BTC/USD and EUR/USD returns. The World Health Organization (WHO) announcement, in which COVID-19 was declared a global pandemic, appears to have had a significant impact on the sudden change in complexity. Our findings can help both investors and risk managers, as well as policymakers, to formulate a comprehensive response to the occurrence of such external events.

On the Thermal Models for Resistive Random Access Memory Circuit Simulation.

Resistive Random Access Memories (RRAMs) are based on resistive switching (RS) operation and exhibit a set of technological features that make them ideal candidates for applications related to non-volatile memories, neuromorphic computing and hardware cryptography. For the full industrial development of these devices different simulation tools and compact models are needed in order to allow computer-aided design, both at the device and circuit levels. Most of the different RRAM models presented so far in the literature deal with temperature effects since the physical mechanisms behind RS are thermally activated; therefore, an exhaustive description of these effects is essential. As far as we know, no revision papers on thermal models have been published yet; and that is why we deal with this issue here. Using the heat equation as the starting point, we describe the details of its numerical solution for a conventional RRAM structure and, later on, present models of different complexity to integrate thermal effects in complete compact models that account for the kinetics of the chemical reactions behind resistive switching and the current calculation. In particular, we have accounted for different conductive filament geometries, operation regimes, filament lateral heat losses, the use of several temperatures to characterize each conductive filament, among other issues. A 3D numerical solution of the heat equation within a complete RRAM simulator was also taken into account. A general memristor model is also formulated accounting for temperature as one of the state variables to describe electron device operation. In addition, to widen the view from different perspectives, we deal with a thermal model contextualized within the quantum point contact formalism. In this manner, the temperature can be accounted for the description of quantum effects in the RRAM charge transport mechanisms. Finally, the thermometry of conducting filaments and the corresponding models considering different dielectric materials are tackled in depth.

Stochastic Computing Emulation of Memristor Cellular Nonlinear Networks.

Cellular Nonlinear Networks (CNN) are a concept introduced in 1988 by Leon Chua and Lin Yang as a bio-inspired architecture capable of massively parallel computation. Since then, CNN have been enhanced by incorporating designs that incorporate memristors to profit from their processing and memory capabilities. In addition, Stochastic Computing (SC) can be used to optimize the quantity of required processing elements; thus it provides a lightweight approximate computing framework, quite accurate and effective, however. In this work, we propose utilization of SC in designing and implementing a memristor-based CNN. As a proof of the proposed concept, an example of application is presented. This application combines Matlab and a FPGA in order to create the CNN. The implemented CNN was then used to perform three different real-time applications on a 512 × 512 gray-scale and a 768 × 512 color image: storage of the image, edge detection, and image sharpening. It has to be pointed out that the same CNN was used for the three different tasks, with the sole change of some programmable parameters. Results show an excellent capability with significant accompanying advantages, such as the low number of needed elements further allowing for a low cost FPGA-based system implementation, something confirming the system's capacity for real time operation.

A Universal Physics-Based Model Describing COVID-19 Dynamics in Europe.

The self-organizing mechanism is a universal approach that is widely followed in nature. In this work, a novel self-organizing model describing diffusion over a lattice is introduced. Simulation results for the model's active lattice sites demonstrate an evolution curve that is very close to those describing the evolution of infected European populations by COVID-19. The model was further examined against real data regarding the COVID-19 epidemic for seven European countries (with a total population of 290 million) during the periods in which social distancing measures were imposed, namely Italy and Spain, which had an enormous spread of the disease; the successful case of Greece; and four central European countries: France, Belgium, Germany and the Netherlands. The value of the proposed model lies in its simplicity and in the fact that it is based on a universal natural mechanism, which through the presentation of an equivalent dynamical system apparently documents and provides a better understanding of the dynamical process behind viral epidemic spreads in general-even pandemics, such as in the case of COVID-19-further allowing us to come closer to controlling such situations. Finally, this model allowed the study of dynamical characteristics such as the memory effect, through the autocorrelation function, in the studied epidemiological dynamical systems.

Analysis of rattleback chaotic oscillations.

Rattleback is a canoe-shaped object, already known from ancient times, exhibiting a nontrivial rotational behaviour. Although its shape looks symmetric, its kinematic behaviour seems to be asymmetric. When spun in one direction it normally rotates, but when it is spun in the other direction it stops rotating and oscillates until it finally starts rotating in the other direction. It has already been reported that those oscillations demonstrate chaotic characteristics. In this paper, rattleback's chaotic dynamics are studied by applying Kane's model for different sets of (experimentally decided) parameters, which correspond to three different experimental prototypes made of wax, gypsum, and lead-solder. The emerging chaotic behaviour in all three cases has been studied and evaluated by the related time-series analysis and the calculation of the strange attractors' invariant parameters.