## Research Projects

Theoretical Basis for Opinion Dynamics

In this project, we investigate the use of Bayesian solutions as a basis for creating new models in Opinion Dynamics. By using subjective probabilities to model the opinions of the agents in an artificial society, we obtain a theoretical framework for proposing models for different circumstances. This provides a powerful tool for developing new descriptions as well as improving existing ones, with the additional benefit that the agents can be described as endowed with a bounded rationality (supported by grants from FAPESP and CNPq).This line of work has also allowed the modeling of emergence of extreme opinions. A very interesting application is the study of the circumstances that increase or decrease extreme opinions in a society. This has attracted some media attention (see the links in the Media section).

Articles:

- Martins, André C. R. (2008)Continuous
Opinions
and Discrete Actions in Opinion Dynamics Problems. International
Journal of Modern Physics C, v. 19, p. 617-624.

- Martins, André C. R. (2008) Mobility and social network effects on extremist opinions. Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, v. 78, p. 036104.
- Martins, André C. R. (2009) Bayesian updating rules in continuous opinion dynamics models. Journal of Statistical Mechanics. Theory and Experiment, v. 2009, p. P02017.
- Vicente, Renato; Martins, André C. R.; Caticha, Nestor (2009) Opinion dynamics of learning agents: does seeking consensus lead to disagreement?. Journal of Statistical Mechanics. Theory and Experiment, v. 2009, p. P03015.
- Martins, Andre C. R. (2009) A middle option for choices in the Continuous Opinions and Discrete Actions model, preprint arxiv:0904.1882
- Martins, Andre C. R.; Kuba, Cleber, D. (2009) The Importance of Disagreeing: Contrarians and Extremism in the CODA model, preprint arxiv:0901.2737

Social Effects on Science

The aim of this research is to investigate the consequences that social influences can have on the reliability of scientific knowledge. In order to better understand how different behaviors can influence or not the possibility that scientists will choose a better description, we use agent-based models as a tool to explore possible circumstances where a majority opinion in a scientific artificial society might not correspond to the best choice.

Articles:

- Martins, A. C. R. (2005) Deception and
Convergence of Opinions. JASSS, Journal of Artificial
Societies and
Social Simulation, Inglaterra, v. 8, n. 2, p. 3.

- Martins, A. C. R. (2008) Replication in the Deception and Convergence of Opinions Problem. JASSS, Journal of Artificial Societies and Social Simulation, v. 11, n.4, p. 8.
- Martins, A. C. R. (2009) Social Effects in Science: Modelling Agents for a Better Scientific Practice, preprint arxiv:0903.5127

Correlations in Financial Time Series

An important part of the correlation matrix for temporal series of many assets can be explained as noise. In order to model this effects, we are studying a statistical description that allows for a simple introduction of non-stationarity and that fits the eigenvalues of the correlation matrix reasonably well. This model has, as a limit case, a Random Matrix description of the problem, while preserving the existence of non-random eigenvalues.

Articles:

- Martins, A. C. R. (2007) Non-Stationary
Correlation Matrices and Noise. Physica. A, v. 379, p. 552-558.

- Martins, A. C. R. (2007) Random, but not so much: A parameterization for the returns and correlation matrix of financial time series. Physica. A, v. 383, p. 527-532.
- Rodrigues Neto, Camilo; Martins, A. C. R. (2009) Multifractality in the random parameter model for multivariate time series. Physica. A, p. 2198-2206

Diffusion
of Innovations

By using the techniques of Opinion Dynamics, we investigate how an
innovation will spread through a society of artificial agents. This has
interesting applications in the dissemination of new ideas as well as
the adoption of new products.

Articles:

- Martins, André C.R. ; Pereira, Carlos de B.; Vicente, Renato (2009) An opinion dynamics model for the diffusion of innovations.Physica. A, v. 388, p. 3225-3232.

Rationality and Heuristics - Normative Theories and Human Thinking

People do not obey to normative theories of rationality when making decisions. However, the observed behavior when dealing with uncertainty can be described as an approximation to a Bayesian inference. We aim to better understand the requirements for a rational behavior, from a Bayesian point of view and to understand what kinds of heuristics people use to make decisions when faced with uncertainty.

Articles:

- Martins, André C. R. (2005). Adaptive Probability Theory: Human Biases as an Adaptation, Cogprint preprint.
- Martins, André C.R. (2006) Probabilistic Biases as Bayesian Inference. Judgment And Decision Making, v. 1, n. 2, p. 108-117.

Starting Projects

Information Theory and Music

By applying techniques of Information Theory, we plan to develop new methods of musical analysis and make contributions to the problem of recomposing missing parts of musical works.

Citation Dynamics

Scientific citations are supposed to represent quality and to indicate who were the first scientists responsible for a given discovery. In this work, we propose models to explore the dynamics of how works get cited, with a special interest in the problem of earlier works that remain unknown for quite a while.