Numerical Design of a Thread-Optimized Gripping System for Lap Joint Testing in a Split Hopkinson Apparatus.

Currently, few experimental methods exist that enable the mechanical characterization of adhesives under high strain rates. One such method is the Split Hopkinson Bar (SHB) test. The mechanical characterization of adhesives is performed using different specimen configurations, such as Single Lap Joint (SLJ) specimens. A gripping system, attached to the bars through threading, was conceived to enable the testing of SLJs. An optimization study for selecting the best thread was performed, analyzing the thread type, the nominal diameter, and the thread pitch. Afterwards, the gripping system geometry was numerically evaluated. The optimal threaded connection for the specimen consists of a trapezoidal thread with a 14 mm diameter and a 2 mm thread pitch. To validate the gripping system, the load-displacement (P-δ) curve of an SLJ, which was simulated as if it were tested on the SHB apparatus, was compared with an analogous curve from a validated drop-weight test numerical model.

LMI-Based Delayed Output Feedback Controller Design for a Class of Fractional-Order Neutral-Type Delay Systems Using Guaranteed Cost Control Approach.

In this research work, we deal with the stabilization of uncertain fractional-order neutral systems with delayed input. To tackle this problem, the guaranteed cost control method is considered. The purpose is to design a proportional-differential output feedback controller to obtain a satisfactory performance. The stability of the overall system is described in terms of matrix inequalities, and the corresponding analysis is performed in the perspective of Lyapunov's theory. Two application examples verify the analytic findings.

Fractional-Order Sensing and Control: Embedding the Nonlinear Dynamics of Robot Manipulators into the Multidimensional Scaling Method.

This paper studies the use of multidimensional scaling (MDS) to assess the performance of fractional-order variable structure controllers (VSCs). The test bed consisted of a revolute planar robotic manipulator. The fractional derivatives required by the VSC can be obtained either by adopting numerical real-time signal processing or by using adequate sensors exhibiting fractional dynamics. Integer (fractional) VCS and fractional (integer) sliding mode combinations with different design parameters were tested. Two performance indices based in the time and frequency domains were adopted to compare the system states. The MDS generated the loci of objects corresponding to the tested cases, and the patterns were interpreted as signatures of the system behavior. Numerical experiments illustrated the feasibility and effectiveness of the approach for assessing and visualizing VSC systems.

Entropy analysis of human death uncertainty.

Uncertainty about the time of death is part of one's life, and plays an important role in demographic and actuarial sciences. Entropy is a measure useful for characterizing complex systems. This paper analyses death uncertainty through the concept of entropy. For that purpose, the Shannon and the cumulative residual entropies are adopted. The first may be interpreted as an average information. The second was proposed more recently and is related to reliability measures such as the mean residual lifetime. Data collected from the Human Mortality Database and describing the evolution of 40 countries during several decades are studied using entropy measures. The emerging country and inter-country entropy patterns are used to characterize the dynamics of mortality. The locus of the two entropies gives a deeper insight into the dynamical evolution of the human mortality data series.

Uniform Manifold Approximation and Projection Analysis of Soccer Players.

In professional soccer, the choices made in forming a team lineup are crucial for achieving good results. Players are characterized by different skills and their relevance depends on the position that they occupy on the pitch. Experts can recognize similarities between players and their styles, but the procedures adopted are often subjective and prone to misclassification. The automatic recognition of players' styles based on their diversity of skills can help coaches and technical directors to prepare a team for a competition, to substitute injured players during a season, or to hire players to fill gaps created by teammates that leave. The paper adopts dimensionality reduction, clustering and computer visualization tools to compare soccer players based on a set of attributes. The players are characterized by numerical vectors embedding their particular skills and these objects are then compared by means of suitable distances. The intermediate data is processed to generate meaningful representations of the original dataset according to the (dis)similarities between the objects. The results show that the adoption of dimensionality reduction, clustering and visualization tools for processing complex datasets is a key modeling option with current computational resources.

Dynamical Analysis of the Dow Jones Index Using Dimensionality Reduction and Visualization.

Time-series generated by complex systems (CS) are often characterized by phenomena such as chaoticity, fractality and memory effects, which pose difficulties in their analysis. The paper explores the dynamics of multidimensional data generated by a CS. The Dow Jones Industrial Average (DJIA) index is selected as a test-bed. The DJIA time-series is normalized and segmented into several time window vectors. These vectors are treated as objects that characterize the DJIA dynamical behavior. The objects are then compared by means of different distances to generate proper inputs to dimensionality reduction and information visualization algorithms. These computational techniques produce meaningful representations of the original dataset according to the (dis)similarities between the objects. The time is displayed as a parametric variable and the non-locality can be visualized by the corresponding evolution of points and the formation of clusters. The generated portraits reveal a complex nature, which is further analyzed in terms of the emerging patterns. The results show that the adoption of dimensionality reduction and visualization tools for processing complex data is a key modeling option with the current computational resources.

Fractional-order modelling of epoxy resin.

This paper describes epoxy resins by means of electrical impedance spectroscopy (EIS) and the mathematical tool of fractional calculus (FC). Two stages are considered: first, the EIS is used for testing the samples and, second, the measured data are approximated using integer and fractional order models. The FC-based modelling describes the epoxy resins using a small number of parameters that reflect their main characteristics. The EIS data gathered for the epoxies samples are compared with those of different adhesives and sealants by means of a hierarchical clustering algorithm that unravels the relationships between the distinct materials. This article is part of the theme issue 'Advanced materials modelling via fractional calculus: challenges and perspectives'.

Rare and extreme events: the case of COVID-19 pandemic.

Complex systems have characteristics that give rise to the emergence of rare and extreme events. This paper addresses an example of such type of crisis, namely the spread of the new Coronavirus disease 2019 (COVID-19). The study deals with the statistical comparison and visualization of country-based real-data for the period December 31, 2019, up to April 12, 2020, and does not intend to address the medical treatment of the disease. Two distinct approaches are considered, the description of the number of infected people across time by means of heuristic models fitting the real-world data, and the comparison of countries based on hierarchical clustering and multidimensional scaling. The computational and mathematical modeling lead to the emergence of patterns, highlighting similarities and differences between the countries, pointing toward the main characteristics of the complex dynamics.

A Review of Fractional Order Entropies.

Fractional calculus (FC) is the area of calculus that generalizes the operations of differentiation and integration. FC operators are non-local and capture the history of dynamical effects present in many natural and artificial phenomena. Entropy is a measure of uncertainty, diversity and randomness often adopted for characterizing complex dynamical systems. Stemming from the synergies between the two areas, this paper reviews the concept of entropy in the framework of FC. Several new entropy definitions have been proposed in recent decades, expanding the scope of applicability of this seminal tool. However, FC is not yet well disseminated in the community of entropy. Therefore, new definitions based on FC can generalize both concepts in the theoretical and applied points of view. The time to come will prove to what extend the new formulations will be useful.

Entropy Analysis of Soccer Dynamics.

This paper adopts the information and fractional calculus tools for studying the dynamics of a national soccer league. A soccer league season is treated as a complex system (CS) with a state observable at discrete time instants, that is, at the time of rounds. The CS state, consisting of the goals scored by the teams, is processed by means of different tools, namely entropy, mutual information and Jensen-Shannon divergence. The CS behavior is visualized in 3-D maps generated by multidimensional scaling. The points on the maps represent rounds and their relative positioning allows for a direct interpretation of the results.

Complexity Analysis of Escher's Art.

Art is the output of a complex system based on the human spirit and driven by several inputs that embed social, cultural, economic and technological aspects of a given epoch. A solid quantitative analysis of art poses considerable difficulties and reaching assertive conclusions is a formidable challenge. In this paper, we adopt complexity indices, dimensionality-reduction and visualization techniques for studying the evolution of Escher's art. Grayscale versions of 457 artworks are analyzed by means of complexity indices and represented using the multidimensional scaling technique. The results are correlated with the distinct periods of Escher's artistic production. The time evolution of the complexity and the emergent patterns demonstrate the effectiveness of the approach for a quantitative characterization of art.

On the Complexity Analysis and Visualization of Musical Information.

This paper considers several distinct mathematical and computational tools, namely complexity, dimensionality-reduction, clustering, and visualization techniques, for characterizing music. Digital representations of musical works of four artists are analyzed by means of distinct indices and visualized using the multidimensional scaling technique. The results are then correlated with the artists' musical production. The patterns found in the data demonstrate the effectiveness of the approach for assessing the complexity of musical information.

Structure-Guided Functional Annotation of the Influenza A Virus NS1 Protein Reveals Dynamic Evolution of the p85ß-Binding Site during Circulation in Humans.

Rational characterization of virulence and host-adaptive markers in the multifunctional influenza A virus NS1 protein is hindered by a lack of comprehensive knowledge about NS1-host protein protein interfaces. Here, we surveyed the impact of amino acid variation in NS1 at its structurally defined binding site for host p85ß, a regulator of phosphoinositide 3-kinase (PI3K) signaling. Structure-guided alanine scanning of all viral residues at this interface defined 10 positions contributing to the interaction, with residues 89, 95, 98, 133, 145, and 162 being the most important. A bioinformatic study of >24,000 publicly available NS1 sequences derived from viruses infecting different hosts highlighted several prevalent amino acid variants at the p85ß interface that either enhanced (I95) or weakened (N135, T145, L161, Y161, S164) p85ß binding. Interestingly, analysis of viruses circulating in humans since the 1918 pandemic revealed the temporal acquisition of functionally relevant variants at this interface. I95 (which enhanced p85ß binding) quickly became prevalent in the 1940s and experimentally conferred a fitness advantage to a recombinant 1930s-based H1N1 virus in human lung epithelial cells. Surprisingly, H1N1 and H3N2 viruses recently acquired T145 or N135, respectively, which diminished p85ß binding but apparently not the overall fitness in the human population. Evolutionary analyses revealed covariation of the NS1-p85ß binding phenotype in humans with functional changes at multiple residues in other viral proteins, suggesting an unexplored compensatory or synergistic interplay between phenotypes in vivo Overall, our data provide a resource to understand the consequences of the NS1-p85ß binding spectrum of different influenza viruses and highlight the dynamic evolution of this property in viruses circulating in humans.IMPORTANCE In humans, influenza A viruses are responsible for causing seasonal epidemics and occasional pandemics. These viruses also circulate and evolve in other animal species, creating a reservoir from which novel viruses with distinct properties can emerge. The viral nonstructural protein NS1 is an important host range determinant and virulence factor that exhibits strain-specific interactions with several host factors, although few have been characterized extensively. In the study described here, we comprehensively surveyed the impact of natural and unnatural NS1 variations on the binding of NS1 to host p85ß, a subunit of phosphoinositide 3-kinase that regulates intracellular metabolism and contributes to virus replication and virulence. We define the p85ß-binding site on NS1 and provide a predictive resource to assess this ability of NS1 in viruses from different hosts. Strikingly, we uncover a spectrum of p85ß binding by different NS1 proteins and reveal that viruses evolving in humans have undergone dynamic changes in this NS1 function over the last century.

Complexity Analysis of Global Temperature Time Series.

Climate has complex dynamics due to the plethora of phenomena underlying its evolution. These characteristics pose challenges to conducting solid quantitative analysis and reaching assertive conclusions. In this paper, the global temperature time series (TTS) is viewed as a manifestation of the climate evolution, and its complexity is calculated by means of four different indices, namely the Lempel-Ziv complexity, sample entropy, signal harmonics power ratio, and fractal dimension. In the first phase, the monthly mean TTS is pre-processed by means of empirical mode decomposition, and the TTS trend is calculated. In the second phase, the complexity of the detrended signals is estimated. The four indices capture distinct features of the TTS dynamics in a 4-dim space. Hierarchical clustering is adopted for dimensional reduction and visualization in the 2-dim space. The results show that TTS complexity exhibits space-time variability, suggesting the presence of distinct climate forcing processes in both dimensions. Numerical examples with real-world data demonstrate the effectiveness of the approach.

Design and implementation of grid multi-scroll fractional-order chaotic attractors.

This paper proposes a novel approach for generating multi-scroll chaotic attractors in multi-directions for fractional-order (FO) systems. The stair nonlinear function series and the saturated nonlinear function are combined to extend equilibrium points with index 2 in a new FO linear system. With the help of stability theory of FO systems, stability of its equilibrium points is analyzed, and the chaotic behaviors are validated through phase portraits, Lyapunov exponents, and Poincaré section. Choosing the order 0.96 as an example, a circuit for generating 2-D grid multiscroll chaotic attractors is designed, and 2-D 9 × 9 grid FO attractors are observed at most. Numerical simulations and circuit experimental results show that the method is feasible and the designed circuit is correct.

Precise tracking control via iterative learning for one-sided Lipschitz Caputo fractional-order systems.

This paper investigates iterative learning control for Caputo fractional-order systems with one-sided Lipschitz nonlinearity. Both open- and closed-loop P-type learning algorithms are proposed to achieve perfect tracking for the desired trajectory, and their convergence conditions are established. It is shown that the algorithms can make the output tracking error converge to zero along the iteration axis. A simulation example illustrates the application of the theoretical findings, and shows the effectiveness of the proposed approach.

Disturbance observer-based delayed robust feedback control design for a class of uncertain variable fractional-order systems: Order-dependent and delay-dependent stability.

This work addresses the stabilization of variable fractional-order (VFO) neutral-type systems with structure perturbations and unknown disturbance signals using the feedback control approach. The goal is to design disturbance-observer-based delayed state- and output-feedback controllers to achieve robust stability of such VFO systems. The proposed controller consists of two parts, namely a primary controller based on the linear feedback technique, and an auxiliary controller based on the disturbance observer. A disturbance observer is developed to estimate the disturbance signal, which is generated by an exogenous system. Based on matrix inequalities, order-dependent and delay-dependent conditions are formulated via FO Lyapunov theory that guarantee the robust stability of the closed-loop system. Simulations verify the main results.

Improved Parameter Identification for Lithium-Ion Batteries Based on Complex-Order Beetle Swarm Optimization Algorithm.

With the aim of increasing the model accuracy of lithium-ion batteries (LIBs), this paper presents a complex-order beetle swarm optimization (CBSO) method, which employs complex-order (CO) operator concepts and mutation into the traditional beetle swarm optimization (BSO). Firstly, a fractional-order equivalent circuit model of LIBs is established based on electrochemical impedance spectroscopy (EIS). Secondly, the CBSO is used for model parameters' identification, and the model accuracy is verified by simulation experiments. The root-mean-square error (RMSE) and maximum absolute error (MAE) optimization metrics show that the model accuracy with CBSO is superior when compared with the fractional-order BSO.