Percorrer por autor "Machado, J.A.Tenreiro"
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- Analysis and visualization of seismic data using mutual informationPublication . Machado, J.A.Tenreiro; Lopes, António M.Seismic data is difficult to analyze and classical mathematical tools reveal strong limitations in exposing hidden relationships between earthquakes. In this paper, we study earthquake phenomena in the perspective of complex systems. Global seismic data, covering the period from 1962 up to 2011 is analyzed. The events, characterized by their magnitude, geographic location and time of occurrence, are divided into groups, either according to the Flinn-Engdahl (F-E) seismic regions of Earth or using a rectangular grid based in latitude and longitude coordinates. Two methods of analysis are considered and compared in this study. In a first method, the distributions of magnitudes are approximated by Gutenberg-Richter (G-R) distributions and the parameters used to reveal the relationships among regions. In the second method, the mutual information is calculated and adopted as a measure of similarity between regions. In both cases, using clustering analysis, visualization maps are generated, providing an intuitive and useful representation of the complex relationships that are present among seismic data. Such relationships might not be perceived on classical geographic maps. Therefore, the generated charts are a valid alternative to other visualization tools, for understanding the global behavior of earthquakes.
- Analysis of Forest Fires by means of Pseudo Phase Plane and Multidimensional Scaling MethodsPublication . Machado, J.A.Tenreiro; Lopes, António M.Forest fires dynamics is often characterized by the absence of a characteristic length-scale, long range correlations in space and time, and long memory, which are features also associated with fractional order systems. In this paper a public domain forest fires catalogue, containing information of events for Portugal, covering the period from 1980 up to 2012, is tackled. The events are modelled as time series of Dirac impulses with amplitude proportional to the burnt area. The time series are viewed as the system output and are interpreted as a manifestation of the system dynamics. In the first phase we use the pseudo phase plane (PPP) technique to describe forest fires dynamics. In the second phase we use multidimensional scaling (MDS) visualization tools. The PPP allows the representation of forest fires dynamics in two-dimensional space, by taking time series representative of the phenomena. The MDS approach generates maps where objects that are perceived to be similar to each other are placed on the map forming clusters. The results are analysed in order to extract relationships among the data and to better understand forest fires behaviour.
- Analysis of Forest Fires by means of Pseudo Phase Plane and Multidimensional Scaling MethodsPublication . Machado, J.A.Tenreiro; Lopes, António M.Forest fires dynamics is often characterized by the absence of a characteristic length-scale, long range correlations in space and time, and long memory, which are features also associated with fractional order systems. In this paper a public domain forest fires catalogue, containing information of events for Portugal, covering the period from 1980 up to 2012, is tackled. The events are modelled as time series of Dirac impulses with amplitude proportional to the burnt area. The time series are viewed as the system output and are interpreted as a manifestation of the system dynamics. In the first phase we use the pseudo phase plane (PPP) technique to describe forest fires dynamics. In the second phase we use multidimensional scaling (MDS) visualization tools. The PPP allows the representation of forest fires dynamics in two-dimensional space, by taking time series representative of the phenomena. The MDS approach generates maps where objects that are perceived to be similar to each other are placed on the map forming clusters. The results are analysed in order to extract relationships among the data and to better understand forest fires behaviour.
- Analysis of global terrorism dynamics by means of entropy and state space portraitPublication . Lopes, António M.; Machado, J.A.Tenreiro; Mata, Maria EugéniaThis paper studies the global terrorism dynamics over the period 1970–2014. Data about terrorist events are analyzed by means of several mathematical tools, namely fractal dimension, entropy, state space portrait and multidimensional scaling, that reflect the dynamics in time and space. In a first phase, we consider worldwide events and we unveil the space–time characteristics exhibited by the global terrorism statistics. In a second phase, we group the events into eight geographic regions, and we analyze terrorism dynamics in a regional perspective. Finally, in a third phase, we adopt a complementary analysis of global terrorism based on multidimensional scaling and clustering techniques. The proposed methodology reveals to
- Application of Fractional Techniques in the Analysis of Forest FiresPublication . Lopes, António M.; Machado, J.A.TenreiroIn this paper we study the global behavior of forest fires (FFs) in the Continental United States for the period 1984–2013. The data are obtained from a public domain catalog maintained by the Monitoring Trends in Burn Severity project. First we adopt clustering analysis to reduce the information dimensionality. Then we adopt mathematical tools commonly used in the analysis of dynamical systems, namely fractal dimension, entropy and fractional Fourier transform. The fractional techniques unveil FF patterns embedded in the data.
- Bipedal Locomotion: A Fractional CPG for Generating PatternsPublication . Pinto, Carla M.A.; Machado, J.A.TenreiroThere has been an increase interest in the study of animal locomotion. Many models for the generation of locomotion patterns of different animals, such as centipedes, millipedes, quadrupeds, hexapods, bipeds, have been proposed. The main goal is the understanding of the neural bases that are behind animal locomotion. In vertebrates, goal-directed locomotion is a complex task, involving the central pattern generators located somewhere in the spinal cord, the brainstem command systems for locomotion, the control systems for steering and control of body orientation, and the neural structures responsible for the selection of motor primitives. In this paper, we focus in the neural networks that send signals to the muscle groups in each joint, the so-called central pattern generators (CPGs). We consider a fractional version of a CPG model for locomotion in bipeds. A fractional derivative) Dα f (x), with α non-integer, is a generalization of the concept of an integer derivative, where α = 1 The integer CPG model has been proposed by Golubitsky, Stewart, Buono and Collins, and studied later by Pinto and Golubitsky. It is a four cells model, where each cell is modelled by a system of ordinary differential equations. The coupling between the cells allows two independent permutations, and, as so, the system has D2 symmetry. We consider 0 < α ≤ 1 and we compute, for each value of α, the amplitude and the period of the periodic solutions identified with two legs' patterns in bipeds. We find the amplitude and the period increase as α varies from zero up to one.
- Can power laws help us understand gene and proteome information?Publication . Costa, António Cardoso; Machado, J.A.Tenreiro; Quelhas, DulceProteins are biochemical entities consisting of one or more blocks typically folded in a 3D pattern. Each block (a polypeptide) is a single linear sequence of amino acids that are biochemically bonded together. The amino acid sequence in a protein is defined by the sequence of a gene or several genes encoded in the DNA-based genetic code. This genetic code typically uses twenty amino acids, but in certain organisms the genetic code can also include two other amino acids. After linking the amino acids during protein synthesis, each amino acid becomes a residue in a protein, which is then chemically modified, ultimately changing and defining the protein function. In this study, the authors analyze the amino acid sequence using alignment-free methods, aiming to identify structural patterns in sets of proteins and in the proteome, without any other previous assumptions. The paper starts by analyzing amino acid sequence data by means of histograms using fixed length amino acid words (tuples). After creating the initial relative frequency histograms, they are transformed and processed in order to generate quantitative results for information extraction and graphical visualization. Selected samples from two reference datasets are used, and results reveal that the proposed method is able to generate relevant outputs in accordance with current scientific knowledge in domains like protein sequence/proteome analysis.
- Casualties distribution in human and natural hazardsPublication . Pinto, Carla M.A.; Lopes, A.Mendes; Machado, J.A.TenreiroCatastrophic events, such as wars and terrorist attacks, big tornadoes and hurricanes, huge earthquakes, tsunamis, floods, and landslides, are always accompanied by a large number of casualties. The size distribution of these casualties have separately been shown to follow approximate power law (PL) distributions. In this paper, we analyze the number of victims of catastrophic phenomena, in particular, terrorism, and find double PL behavior. This means that the data set is better approximated by two PLs instead of one. We have plotted the two PL parameters corresponding to all terrorist events occurred in every year, from 1980 to 2010. We observe an interesting pattern in the chart, where the lines, that connect each pair of points defining the double PLs, are roughly aligned to each other.
- Complex order biped rhythmsPublication . Pinto, Carla M.A.; Machado, J.A.TenreiroAnimal locomotion is a complex process, involving the central pattern generators (neural networks, located in the spinal cord, that produce rhythmic patterns), the brainstem command systems, the steering and posture control systems and the top layer structures that decide which motor primitive is activated at a given time. Pinto and Golubitsky studied an integer CPG model for legs rhythms in bipeds. It is a four-coupled identical oscillators' network with dihedral symmetry. This paper considers a new complex order central pattern generator (CPG) model for locomotion in bipeds. A complex derivative Dα±jβ, with α, β ∈ ℜ+, j = √-1, is a generalization of the concept of an integer derivative, where α = 1, β = 0. Parameter regions where periodic solutions, identified with legs' rhythms in bipeds, occur, are analyzed. Also observed is the variation of the amplitude and period of periodic solutions with the complex order derivative.
- Complex order van der Pol oscillatorPublication . Pinto, Carla M.A.; Machado, J.A.TenreiroIn this paper a complex-order van der Pol oscillator is considered. The complex derivative Dα±ȷβ , with α,β∈R + is a generalization of the concept of integer derivative, where α=1, β=0. By applying the concept of complex derivative, we obtain a high-dimensional parameter space. Amplitude and period values of the periodic solutions of the two versions of the complex-order van der Pol oscillator are studied for variation of these parameters. Fourier transforms of the periodic solutions of the two oscillators are also analyzed.