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This period includes the peculiar time of the Covid-19 pandemic; therefore, we pay particular attention to this event and investigate how strong its impact on the structure and dynamics of the market was. Besides, the studied data covers a few other significant events like double bull and bear phases in 2019. We show that, throughout the considered interval, the exchange rate returns were multifractal with intermittent signatures of bifractality that can be associated with the most volatile periods of the market dynamics like a bull market onset in April 2019 and the Covid-19 outburst in March 2020. The topology of a minimal spanning tree representation of the market also used to alter during these events from a distributed type without any dominant node to a highly centralized type with a dominating hub of USDT. However, the MST topology during the pandemic differs in some details from other volatile periods.We investigate some relationships among the integral transform, the function space integral and the first variation of the partial derivative approach in the Banach algebra defined on the function space. We prove that the function space integral and the integral transform of the partial derivative in some Banach algebra can be expanded as the limit of a sequence of function space integrals.We construct a microscopic model to study discrete randomness in bistable systems coupled to an environment comprising many degrees of freedom. A quartic double well is bilinearly coupled to a finite number N of harmonic oscillators. Solving the time-reversal invariant Hamiltonian equations of motion numerically, we show that for N=1, the system exhibits a transition with increasing coupling strength from integrable to chaotic motion, following the Kolmogorov-Arnol'd-Moser (KAM) scenario. Raising N to values of the order of 10 and higher, the dynamics crosses over to a quasi-relaxation, approaching either one of the stable equilibria at the two minima of the potential. We corroborate the irreversibility of this relaxation on other characteristic timescales of the system by recording the time dependences of autocorrelation, partial entropy, and the frequency of jumps between the wells as functions of N and other parameters. Preparing the central system in the unstable equilibrium at the top of the barrier and the bath in a random initial state drawn from a Gaussian distribution, symmetric under spatial reflection, we demonstrate that the decision whether to relax into the left or the right well is determined reproducibly by residual asymmetries in the initial positions and momenta of the bath oscillators. This result reconciles the randomness and spontaneous symmetry breaking of the asymptotic state with the conservation of entropy under canonical transformations and the manifest symmetry of potential and initial condition of the bistable system.As the core technology of 5G mobile communication systems, massive multi-input multi-output (MIMO) can dramatically enhance the energy efficiency (EE), as well as the spectral efficiency (SE), which meets the requirements of new applications. Meanwhile, physical layer multicast technology has gradually become the focus of next-generation communication technology research due to its capacity to efficiently provide wireless transmission from point to multipoint. The availability of channel state information (CSI), to a large extent, determines the performance of massive MIMO. However, because obtaining the perfect instantaneous CSI in massive MIMO is quite challenging, it is reasonable and practical to design a massive MIMO multicast transmission strategy using statistical CSI. Epalrestat In this paper, in order to optimize the system resource efficiency (RE) to achieve EE-SE balance, the EE-SE trade-offs in the massive MIMO multicast transmission are investigated with statistical CSI. Firstly, we formulate the eigenvectors of the RE optimization multicast covariance matrices of different user terminals in closed form, which illustrates that in the massive MIMO downlink, optimal RE multicast precoding is supposed to be done in the beam domain. On the basis of this viewpoint, the optimal RE precoding design is simplified into a resource efficient power allocation problem. Via invoking the quadratic transform, we propose an iterative power allocation algorithm, which obtains an adjustable and reasonable EE-SE tradeoff. Numerical simulation results reveal the near-optimal performance and the effectiveness of our proposed statistical CSI-assisted RE maximization in massive MIMO.The evolution of modern automobiles to higher levels of connectivity and automatism has also increased the need to focus on the mitigation of potential cybersecurity risks. Researchers have proven in recent years that attacks on in-vehicle networks of automotive vehicles are possible and the research community has investigated various cybersecurity mitigation techniques and intrusion detection systems which can be adopted in the automotive sector. In comparison to conventional intrusion detection systems in large fixed networks and ICT infrastructures in general, in-vehicle systems have limited computing capabilities and other constraints related to data transfer and the management of cryptographic systems. In addition, it is important that attacks are detected in a short time-frame as cybersecurity attacks in vehicles can lead to safety hazards. This paper proposes an approach for intrusion detection of cybersecurity attacks in in-vehicle networks, which takes in consideration the constraints listed above. The approach is based on the application of an information entropy-based method based on a sliding window, which is quite efficient from time point of view, it does not require the implementation of complex cryptographic systems and it still provides a very high detection accuracy. Different entropy measures are used in the evaluation Shannon Entropy, Renyi Entropy, Sample Entropy, Approximate Entropy, Permutation Entropy, Dispersion and Fuzzy Entropy. This paper evaluates the impact of the different hyperparameters present in the definition of entropy measures on a very large public data set of CAN-bus traffic with millions of CAN-bus messages with four different types of attacks Denial of Service, Fuzzy Attack and two spoofing attacks related to RPM and Gear information. The sliding window approach in combination with entropy measures can detect attacks in a time-efficient way and with great accuracy for specific choices of the hyperparameters and entropy measures.It is known that in pathological conditions, physiological systems develop changes in the multiscale properties of physiological signals. However, in real life, little is known about how changes in the function of one of the two coupled physiological systems induce changes in function of the other one, especially on their multiscale behavior. Hence, in this work we aimed to examine the complexity of cardio-respiratory coupled systems control using multiscale entropy (MSE) analysis of cardiac intervals MSE (RR), respiratory time series MSE (Resp), and synchrony of these rhythms by cross multiscale entropy (CMSE) analysis, in the heart failure (HF) patients and healthy subjects. We analyzed 20 min of synchronously recorded RR intervals and respiratory signal during relaxation in the supine position in 42 heart failure patients and 14 control healthy subjects. Heart failure group was divided into three subgroups, according to the RR interval time series characteristics (atrial fibrillation (HFAF), sinus rhythm (HFSin), and sinus rhythm with ventricular extrasystoles (HFVES)). Compared with healthy control subjects, alterations in respiratory signal properties were observed in patients from the HFSin and HFVES groups. Further, mean MSE curves of RR intervals and respiratory signal were not statistically different only in the HFSin group (p = 0.43). The level of synchrony between these time series was significantly higher in HFSin and HFVES patients than in control subjects and HFAF patients (p less then 0.01). In conclusion, depending on the specific pathologies, primary alterations in the regularity of cardiac rhythm resulted in changes in the regularity of the respiratory rhythm, as well as in the level of their asynchrony.In this study, a new approach to basis of intelligent systems and machine learning algorithms is introduced for solving singular multi-pantograph differential equations (SMDEs). For the first time, a type-2 fuzzy logic based approach is formulated to find an approximated solution. The rules of the suggested type-2 fuzzy logic system (T2-FLS) are optimized by the square root cubature Kalman filter (SCKF) such that the proposed fineness function to be minimized. Furthermore, the stability and boundedness of the estimation error is proved by novel approach on basis of Lyapunov theorem. The accuracy and robustness of the suggested algorithm is verified by several statistical examinations. It is shown that the suggested method results in an accurate solution with rapid convergence and a lower computational cost.Accurate blood smear quantification with various blood cell samples is of great clinical importance. The conventional manual process of blood smear quantification is quite time consuming and is prone to errors. Therefore, this paper presents automatic detection of the most frequently occurring condition in human blood-microcytic hyperchromic anemia-which is the cause of various life-threatening diseases. This task has been done with segmentation of blood contents, i.e., Red Blood Cells (RBCs), White Blood Cells (WBCs), and platelets, in the first step. Then, the most influential features like geometric shape descriptors, Gray Level Co-occurrence Matrix (GLCM), Gray Level Run Length Matrix (GLRLM), and Gabor features (mean squared energy and mean amplitude) are extracted from each of the RBCs. To discriminate the cells as hypochromic microcytes among other RBC classes, scanning is done at angles (0∘, 45∘, 90∘, and 135∘). To achieve high-level accuracy, Adaptive Synthetic (AdaSyn) sampling for imbalance learning is used to balance the datasets and locality sensitive discriminant analysis (LSDA) technique is used for feature reduction. Finally, upon using these features, classification of blood cells is done using the multilayer perceptual model and random forest learning algorithms. Performance in terms of accuracy was 96%, which is better than the performance of existing techniques. The final outcome of this work may be useful in the efforts to produce a cost-effective screening scheme that could make inexpensive screening for blood smear analysis available globally, thus providing early detection of these diseases.To eliminate the influence of white noise in partial discharge (PD) detection, we propose a novel method based on complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) and approximate entropy (ApEn). By introducing adaptive noise into the decomposition process, CEEMDAN can effectively separate the original signal into different intrinsic mode functions (IMFs) with distinctive frequency scales. Afterward, the approximate entropy value of each IMF is calculated to eliminate noisy IMFs. Then, correlation coefficient analysis is employed to select useful IMFs that represent dominant PD features. Finally, real IMFs are extracted for PD signal reconstruction. On the basis of EEMD, CEEMDAN can further improve reconstruction accuracy and reduce iteration numbers to solve mode mixing problems. The results on both simulated and on-site PD signals show that the proposed method can be effectively employed for noise suppression and successfully extract PD pulses. The fusion algorithm combines the CEEMDAN algorithm and the ApEn algorithm with their respective advantages and has a better de-noising effect than EMD and EEMD.