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.

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.

The recovery of global stock markets indices after impacts due to pandemics.

The COVID-19 brings back the debate about the impact of disease outbreaks in economies and financial markets. The error correction terms (ECT) and cointegration processing tools have been applied in studies for identifying possible transmission mechanisms between distinct time series. This paper adopts the vector error correction model (VECM) to investigate the dynamic coupling between the pandemics (e.g., the COVID-19, EBOLA, MERS and SARS) and the evolution of key stocks exchange indices (e.g., Dow-Jones, S&P 500, EuroStoxx, DAX, CAC, Nikkei, HSI, Kospi, S&P ASX, Nifty and Ibov). The results show that the shocks caused by the diseases significantly affected the markets. Nonetheless, except for the COVID-19, the stock exchange indices reveal a sustained and fast recovering when an identical length time window of 79 days is analyzed. In addition, our findings contribute to point a higher volatility for all financial indices during the COVID-19, a strong impact over the Ibov-Brazil and its poor recover when compared to the other indices.

On multistep tumor growth models of fractional variable-order.

Fractional mathematical oncology is a research topic that applies non-integer order calculus to tackle cancer problems such as tumor growth analysis or its optimal treatment. This work proposes a multistep exponential model with a fractional variable-order representing the evolution history of a tumor. Model parameters are tuned according to variable fractional order profiles while assessing their capability of fitting a clinical time series. The results point to the superiority of the proposed model in describing the experimental data, thus providing new perspectives for modeling tumor growth.