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Carla Pinto

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José Tenreiro Machado

Instituto Politecnico do Porto

Giorgio Kaniadakis

SUNY: Stony Brook University

Stelios M . Potirakis

University of West Attica / Πανεπιστήμιο Δυτικής Αττικής

Georgia Tourassi

ISCTE - University Institute of Lisbon (ISCTE-IUL)

Second Bwanakare

Cardinal Stefan Wyszynski University in Warsaw

Chandrashekar Radhakrishnan

New York University Shanghai

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Papers by Carla Pinto

Power Law and Entropy Analysis of Catastrophic Phenomena

by José Tenreiro Machado and Carla Pinto

Catastrophic events, such as wars and terrorist attacks, tornadoes and hurricanes, earthquakes, t... more Catastrophic events, such as wars and terrorist attacks, tornadoes and hurricanes, earthquakes, tsunamis, floods and landslides, are always accompanied by a large number of casualties. The size distribution of these casualties has separately been shown to follow approximate power law (PL) distributions. In this paper, we analyze the statistical distributions of the number of victims of catastrophic phenomena, in particular, terrorism, and find double PL behavior. This means that the data sets are better approximated by two PLs instead of a single one. We plot the PL parameters, corresponding to several events, and observe an interesting pattern in the charts, where the lines that connect each pair of points defining the double PLs are almost parallel to each other. A complementary data analysis is performed by means of the computation of the entropy. The results reveal relationships hidden in the data that may trigger a future comprehensive explanation of this type of phenomena.

Power Law and Entropy Analysis of Catastrophic Phenomena

by José Tenreiro Machado, Carla Pinto, and Antonio Lopes

Catastrophic events, such as wars and terrorist attacks, tornadoes and hurricanes, earthquakes, t... more Catastrophic events, such as wars and terrorist attacks, tornadoes and hurricanes, earthquakes, tsunamis, floods and landslides, are always accompanied by a large number of casualties. The size distribution of these casualties has separately been shown to follow approximate power law (PL) distributions. In this paper, we analyze the statistical distributions of the number of victims of catastrophic phenomena, in particular, terrorism, and find double PL behavior. This means that the data sets are better approximated by two PLs instead of a single one. We plot the PL parameters, corresponding to several events, and observe an interesting pattern in the charts, where the lines that connect each pair of points defining the double PLs are almost parallel to each other. A complementary data analysis is performed by means of the computation of the entropy. The results reveal relationships hidden in the data that may trigger a future comprehensive explanation of this type of phenomena.

Sincronização de duas equações do tipo Hodgkin-Huxley

ABSTRACT

Curious phenomena in two coupled neurons

The symmetric coupled system is studied by Labouriau and Pinto using bifurcation theory. They fin... more

1. A New Architecture for the Central Pattern Generator of a Humanoid Robot

There has been a growing interest in the study of bipedal locomotion in the field of humanoid rob... more There has been a growing interest in the study of bipedal locomotion in the field of humanoid robotics. The study of how bipeds move also has the advantage of bringing new insights to the understanding of human locomotion. In this paper, we propose a new architecture for a neural-oscillator-based gait rhythm generator, also known as central pattern generator (CPG), using a network of six oscillators. We use symmetry to classify the periodic solutions produced by this CPG model and identify those solutions with known biped rhythms. We use the Matsuoka half-center oscillatory unit in the numerical simulations of the usual biped gaits.

$Research paper thumbnail of Bipedal locomotion: a fractional CPG for generating patterns$

Bipedal locomotion: a fractional CPG for generating patterns

Gait transition in a CPG model for bipeds

Central Pattern Generator for Legged Locomotion - a mathematical approach

This paper is a survey of the work done by Pinto and Golubitsky concerning two models of central ... more

Forced van der Pol oscillator of complex order

Summary. In this paper it is considered a complex order forced van der Pol oscillator. The comple... more

Bifurcation scenario of a network of two coupled rings of cells

We study the bifurcation scenario appearing in systems of two coupled rings of cells with Z3 × Z5... more We study the bifurcation scenario appearing in systems of two coupled rings of cells with Z3 × Z5 exact symmetry, and Z3 interior symmetry. This study was motivated by previous work by Antoneli, Dias and Pinto, on two rings of cells coupled through a 'buffer' cell, with Z3 × Z5 and D3 × D5 exact and interior symmetry groups. There, quasi-periodic behavior was found through a sequence of Hopf bifurcations. We questioned if an analogous mechanism could explain the appearance of quasi-periodic motion in the examples considered here. Surprisingly, we observe periodic and quasi-periodic states appearing also through Hopf bifurcations. We compute the relevant states numerically.

Effects of treatment, vertical transmission, and condom use in a mathematical model for HIV dynamics

In this paper we propose a mathematical model for HIV/AIDS dynamics, that includes treatment, ver... more In this paper we propose a mathematical model for HIV/AIDS dynamics, that includes treatment, vertical transmission and condom use. The population is divided in two groups, the ones that use condom, and the ones that don’t. We simulate the model for distinct values of the recruiment rate of susceptibles that don’t use condom, p2, of movement rate of infectious, d , and of the contact rate betweem susceptibles and infected individuals that don’t use condom, b11. We observe that for increasing values of p2, the proportion of susceptibles that don’t use condom increases, and the proportions of treated and AIDS individuals decrease. For increasing values of d , the proportions of infected individuals decrease, which in turn increases the treated and infected with AIDS individuals. Finally, increasing b11 leads to the decrease of susceptible and infected individuals that don’t use condom, and an increase in the proportion of treated individuals. Future work will focus on the study of the...

Bifurcations In Symmetrically Coupled

This paper studies the bifurcation of two Hodgkin-Huxley equations coupled symmetrically in the f... more This paper studies the bifurcation of two Hodgkin-Huxley equations coupled symmetrically in the first variable as follows: CHH = # # # # # # # # # # # # # # # # # # # # # # # # # # # dv = f(v,y) 2 (v u) dy j =#(# j (v) y j ) # j (v) du = f(u, z) 2 (u v) dz j =#(# j (u) z j ) # j (u) where f is the expression for the dynamics of the electric potential, I is the stimulus intensity, # j and # j give the dynamics for the ionic channels and # is the temperature compensating factor, in a Hodgkin-Huxley system, with the parameters of [9] (see also [11], [13] for notation)

Effects of Treatment, Awareness and Condom Use in a Coinfection Model for Hiv and HCV in MSM

Journal of Biological Systems, 2015

ABSTRACT We develop a new a coinfection model for hepatitis C virus (HCV) and the human immunodef... more ABSTRACT We develop a new a coinfection model for hepatitis C virus (HCV) and the human immunodeficiency virus (HIV). We consider treatment for both diseases, screening, unawareness and awareness of HIV infection, and the use of condoms. We study the local stability of the disease-free equilibria for the full model and for the two submodels (HCV only and HIV only submodels). We sketch bifurcation diagrams for different parameters, such as the probabilities that a contact will result in a HIV or an HCV infection. We present numerical simulations of the full model where the HIV, HCV and double endemic equilibria can be observed. We also show numerically the qualitative changes of the dynamical behavior of the full model for variation of relevant parameters. We extrapolate the results from the model for actual measures that could be implemented in order to reduce the number of infected individuals.

A Delay Mathematical Model for HIV Dynamics in HIV-Specific Helper Cells

Springer Proceedings in Mathematics & Statistics, 2014

Probability and statistics: selected problems

ABSTRACT Probability and Statistics—Selected Problems is a unique book for senior undergraduate a... more ABSTRACT Probability and Statistics—Selected Problems is a unique book for senior undergraduate and graduate students to fast review basic materials in Probability and Statistics. Descriptive statistics are presented first, and probability is reviewed secondly. Discrete and continuous distributions are presented. Sample and estimation with hypothesis testing are presented in the last two chapters. The solutions for proposed excises are listed for readers to references. Fundamentals in Probability and Statistics Worked examples Proposed exercises Solutions for proposed exercises

Linear algebra: selected problems

ABSTRACT Linear Algebra—Selected Problems is a unique book for senior undergraduate and graduate ... more ABSTRACT Linear Algebra—Selected Problems is a unique book for senior undergraduate and graduate students to fast review basic materials in Linear Algebra. Vector spaces are presented first, and linear transformations are reviewed secondly. Matrices and Linear systems are presented. Determinants and Basic geometry are presented in the last two chapters. The solutions for proposed excises are listed for readers to references. Fundamentals in Linear Algebra Worked examples Proposed exercises Solutions for proposed exercises

Two coupled neurons

2006 IEEE International Conference on Computational Cybernetics, ICCC, 2006

Page 1. TWO COUPLED NEURONS CARLA MAPINTO, ISABEL S. LABOURIAU ABSTRACT. We review the dynamical ... more

Fractional Model for Malaria Disease

Volume 7B: 9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, 2013

We study a fractional model for malaria transmission under control strategies. We consider the in... more We study a fractional model for malaria transmission under control strategies. We consider the integer order model proposed by in and modify it to become a fractional order model. We study numerically the model for variation of the values of the fractional derivative and of the parameter that models personal protection, b. From observation of the figures we conclude that as b is increased from 0 to 1 there is a corresponding decrease in the number of infectious humans and infectious mosquitoes, for all values of α. This means that this result is invariant for variation of fractional derivative, in the values tested. These results are in agreement with those obtained in [15] for α = 1.0 and suggest that our fractional model is epidemiologically wellposed.

Self-Similarity in World Economy ⋆

Self-similarity is a property of complex networks, commonly observed in many distinct areas of sc... more Self-similarity is a property of complex networks, commonly observed in many distinct areas of science. Many real networks are said to be scale-free since they show a power law behavior. In this paper, we focus in self-similarity of economical phenomena. For that purpose we analyze data and their corresponding statistical properties. We approximate data by trendlines, whose parameters are unequivocally related with each type of phenomenon.

Complex order van der Pol oscillator

Nonlinear Dynamics, 2011

In this paper it is considered a complex order van der Pol oscillator. The complex derivative D α... more In this paper it is considered a complex order van der Pol oscillator. The complex derivative D α±jβ , 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.

Power Law and Entropy Analysis of Catastrophic Phenomena

by José Tenreiro Machado and Carla Pinto

Catastrophic events, such as wars and terrorist attacks, tornadoes and hurricanes, earthquakes, t... more Catastrophic events, such as wars and terrorist attacks, tornadoes and hurricanes, earthquakes, tsunamis, floods and landslides, are always accompanied by a large number of casualties. The size distribution of these casualties has separately been shown to follow approximate power law (PL) distributions. In this paper, we analyze the statistical distributions of the number of victims of catastrophic phenomena, in particular, terrorism, and find double PL behavior. This means that the data sets are better approximated by two PLs instead of a single one. We plot the PL parameters, corresponding to several events, and observe an interesting pattern in the charts, where the lines that connect each pair of points defining the double PLs are almost parallel to each other. A complementary data analysis is performed by means of the computation of the entropy. The results reveal relationships hidden in the data that may trigger a future comprehensive explanation of this type of phenomena.

Power Law and Entropy Analysis of Catastrophic Phenomena

by José Tenreiro Machado, Carla Pinto, and Antonio Lopes

Catastrophic events, such as wars and terrorist attacks, tornadoes and hurricanes, earthquakes, t... more Catastrophic events, such as wars and terrorist attacks, tornadoes and hurricanes, earthquakes, tsunamis, floods and landslides, are always accompanied by a large number of casualties. The size distribution of these casualties has separately been shown to follow approximate power law (PL) distributions. In this paper, we analyze the statistical distributions of the number of victims of catastrophic phenomena, in particular, terrorism, and find double PL behavior. This means that the data sets are better approximated by two PLs instead of a single one. We plot the PL parameters, corresponding to several events, and observe an interesting pattern in the charts, where the lines that connect each pair of points defining the double PLs are almost parallel to each other. A complementary data analysis is performed by means of the computation of the entropy. The results reveal relationships hidden in the data that may trigger a future comprehensive explanation of this type of phenomena.

Sincronização de duas equações do tipo Hodgkin-Huxley

ABSTRACT

Curious phenomena in two coupled neurons

The symmetric coupled system is studied by Labouriau and Pinto using bifurcation theory. They fin... more

1. A New Architecture for the Central Pattern Generator of a Humanoid Robot

There has been a growing interest in the study of bipedal locomotion in the field of humanoid rob... more There has been a growing interest in the study of bipedal locomotion in the field of humanoid robotics. The study of how bipeds move also has the advantage of bringing new insights to the understanding of human locomotion. In this paper, we propose a new architecture for a neural-oscillator-based gait rhythm generator, also known as central pattern generator (CPG), using a network of six oscillators. We use symmetry to classify the periodic solutions produced by this CPG model and identify those solutions with known biped rhythms. We use the Matsuoka half-center oscillatory unit in the numerical simulations of the usual biped gaits.

$Research paper thumbnail of Bipedal locomotion: a fractional CPG for generating patterns$

Bipedal locomotion: a fractional CPG for generating patterns

Gait transition in a CPG model for bipeds

Central Pattern Generator for Legged Locomotion - a mathematical approach

This paper is a survey of the work done by Pinto and Golubitsky concerning two models of central ... more

Forced van der Pol oscillator of complex order

Summary. In this paper it is considered a complex order forced van der Pol oscillator. The comple... more

Bifurcation scenario of a network of two coupled rings of cells

We study the bifurcation scenario appearing in systems of two coupled rings of cells with Z3 × Z5... more We study the bifurcation scenario appearing in systems of two coupled rings of cells with Z3 × Z5 exact symmetry, and Z3 interior symmetry. This study was motivated by previous work by Antoneli, Dias and Pinto, on two rings of cells coupled through a 'buffer' cell, with Z3 × Z5 and D3 × D5 exact and interior symmetry groups. There, quasi-periodic behavior was found through a sequence of Hopf bifurcations. We questioned if an analogous mechanism could explain the appearance of quasi-periodic motion in the examples considered here. Surprisingly, we observe periodic and quasi-periodic states appearing also through Hopf bifurcations. We compute the relevant states numerically.

Effects of treatment, vertical transmission, and condom use in a mathematical model for HIV dynamics

In this paper we propose a mathematical model for HIV/AIDS dynamics, that includes treatment, ver... more In this paper we propose a mathematical model for HIV/AIDS dynamics, that includes treatment, vertical transmission and condom use. The population is divided in two groups, the ones that use condom, and the ones that don’t. We simulate the model for distinct values of the recruiment rate of susceptibles that don’t use condom, p2, of movement rate of infectious, d , and of the contact rate betweem susceptibles and infected individuals that don’t use condom, b11. We observe that for increasing values of p2, the proportion of susceptibles that don’t use condom increases, and the proportions of treated and AIDS individuals decrease. For increasing values of d , the proportions of infected individuals decrease, which in turn increases the treated and infected with AIDS individuals. Finally, increasing b11 leads to the decrease of susceptible and infected individuals that don’t use condom, and an increase in the proportion of treated individuals. Future work will focus on the study of the...

Bifurcations In Symmetrically Coupled

This paper studies the bifurcation of two Hodgkin-Huxley equations coupled symmetrically in the f... more This paper studies the bifurcation of two Hodgkin-Huxley equations coupled symmetrically in the first variable as follows: CHH = # # # # # # # # # # # # # # # # # # # # # # # # # # # dv = f(v,y) 2 (v u) dy j =#(# j (v) y j ) # j (v) du = f(u, z) 2 (u v) dz j =#(# j (u) z j ) # j (u) where f is the expression for the dynamics of the electric potential, I is the stimulus intensity, # j and # j give the dynamics for the ionic channels and # is the temperature compensating factor, in a Hodgkin-Huxley system, with the parameters of [9] (see also [11], [13] for notation)

Effects of Treatment, Awareness and Condom Use in a Coinfection Model for Hiv and HCV in MSM

Journal of Biological Systems, 2015

ABSTRACT We develop a new a coinfection model for hepatitis C virus (HCV) and the human immunodef... more ABSTRACT We develop a new a coinfection model for hepatitis C virus (HCV) and the human immunodeficiency virus (HIV). We consider treatment for both diseases, screening, unawareness and awareness of HIV infection, and the use of condoms. We study the local stability of the disease-free equilibria for the full model and for the two submodels (HCV only and HIV only submodels). We sketch bifurcation diagrams for different parameters, such as the probabilities that a contact will result in a HIV or an HCV infection. We present numerical simulations of the full model where the HIV, HCV and double endemic equilibria can be observed. We also show numerically the qualitative changes of the dynamical behavior of the full model for variation of relevant parameters. We extrapolate the results from the model for actual measures that could be implemented in order to reduce the number of infected individuals.

A Delay Mathematical Model for HIV Dynamics in HIV-Specific Helper Cells

Springer Proceedings in Mathematics & Statistics, 2014

Probability and statistics: selected problems

ABSTRACT Probability and Statistics—Selected Problems is a unique book for senior undergraduate a... more ABSTRACT Probability and Statistics—Selected Problems is a unique book for senior undergraduate and graduate students to fast review basic materials in Probability and Statistics. Descriptive statistics are presented first, and probability is reviewed secondly. Discrete and continuous distributions are presented. Sample and estimation with hypothesis testing are presented in the last two chapters. The solutions for proposed excises are listed for readers to references. Fundamentals in Probability and Statistics Worked examples Proposed exercises Solutions for proposed exercises

Linear algebra: selected problems

ABSTRACT Linear Algebra—Selected Problems is a unique book for senior undergraduate and graduate ... more ABSTRACT Linear Algebra—Selected Problems is a unique book for senior undergraduate and graduate students to fast review basic materials in Linear Algebra. Vector spaces are presented first, and linear transformations are reviewed secondly. Matrices and Linear systems are presented. Determinants and Basic geometry are presented in the last two chapters. The solutions for proposed excises are listed for readers to references. Fundamentals in Linear Algebra Worked examples Proposed exercises Solutions for proposed exercises

Two coupled neurons

2006 IEEE International Conference on Computational Cybernetics, ICCC, 2006

Page 1. TWO COUPLED NEURONS CARLA MAPINTO, ISABEL S. LABOURIAU ABSTRACT. We review the dynamical ... more

Fractional Model for Malaria Disease

Volume 7B: 9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, 2013

We study a fractional model for malaria transmission under control strategies. We consider the in... more We study a fractional model for malaria transmission under control strategies. We consider the integer order model proposed by in and modify it to become a fractional order model. We study numerically the model for variation of the values of the fractional derivative and of the parameter that models personal protection, b. From observation of the figures we conclude that as b is increased from 0 to 1 there is a corresponding decrease in the number of infectious humans and infectious mosquitoes, for all values of α. This means that this result is invariant for variation of fractional derivative, in the values tested. These results are in agreement with those obtained in [15] for α = 1.0 and suggest that our fractional model is epidemiologically wellposed.

Self-Similarity in World Economy ⋆

Self-similarity is a property of complex networks, commonly observed in many distinct areas of sc... more Self-similarity is a property of complex networks, commonly observed in many distinct areas of science. Many real networks are said to be scale-free since they show a power law behavior. In this paper, we focus in self-similarity of economical phenomena. For that purpose we analyze data and their corresponding statistical properties. We approximate data by trendlines, whose parameters are unequivocally related with each type of phenomenon.

Complex order van der Pol oscillator

Nonlinear Dynamics, 2011

In this paper it is considered a complex order van der Pol oscillator. The complex derivative D α... more In this paper it is considered a complex order van der Pol oscillator. The complex derivative D α±jβ , 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.