No Laboratório de Modelagem em Sistemas Complexos (LMSC), estudamos, por meio de modelos teóricos e computacionais, sistemas que apresentam muitos elementos de base (unidades) que podem interagir entre si. Estes sistemas podem apresentar uma transição entre dois comportamentos. De um lado, um comportamento pode ser descrito apenas pelo conhecimento das características de um único elemento de base. De outro lado, o outro comportamento necessita de ingredientes adicionais para sua descrição, como a interação entre as unidades. Esta transição, dada por um valor crítico da interação, pode acontecer nos chamados sistemas complexos ou em sistemas desordenados. Por meio de técnicas da Física Estatística e Computacional, estudamos tanto os sistemas complexos como os meios desordenados. Acreditamos que nessas transições os sistemas naturais mais complicados são estáveis e apresentam regime ótimo de funcionamento.

In the Laboratory of Complex Systems Modeling (LMSC), through theoretical and computational models, we study systems that have many basic elements (units) that can interact with each other. These systems can provide a transition between two behaviors. On the one hand, a behavior can be described only by knowledge of the characteristics of a single base element. On the other hand, the other behavior requires additional ingredients to its description, as the interaction between units. This transition, given by a critical value of interaction, can happen in so-called complex systems or in disordered systems. Using techniques of Statistical and Computational Physics we study both complex systems and disordered media. We believe that at these transitions, complicated natural systems are stable and have optimal operation.

In complex systems, the collective behavior can be complicated and quite different from the behavior of individual units.

The interaction between the units can extend in time scales and/or long-range space, thus not presenting a characteristic scale (allowing predictability).

We study some subjects, such systems:

(A) biological (model growth and population dynamics etc.);

(B) social (development cooperation, psychophysics, opinion formation, epidemiological models, etc..) nd

(C) economic (neuro models, decision-making etc.).

We use graph theory (complex networks), non-extensive statistical mechanics, game theory and techniques of statistical physics for theoretical modeling of the systems considered. We also use computational agent modeling and Monte Carlo simulation.

We also study disordered systems. The disorder of a material medium is represented by the fluctuations of some characteristics of their magnitudes. It plays the role of breaking the translation symmetry of a homogeneous substrate. This can take a given system to present different behavior when disturbed by waves or particles (spread / location). In the last century, such systems were almost exclusively treated in the theory of transport. This theory disregards the phase coherence between waves or correlations in the movement of particles. However, in recent decades, experimental observations (weak localization of waves) showed that new physical systems (mesoscopic, for example) exhibit behaviors that cannot be explained by the theory of traditional transport. These systems, which may be conventional, as in the optical paths have to particles or closed to interference waves. The interesting point is that the paths closed or interference is not destroyed by the process of averaging over the disorder. The spread of particles can take place by walking with memory that can be deterministic or stochastic. For waves, the spread is through the scattering of waves by impurities of the medium. In the case of waves, we consider the scattering of waves by magnetic centers, with special emphasis on meta-materials.

We are also interested in the applications of our results to day-to-day problems. Examples of such applications are the development of algorithms:

(i) the computer recognition of image textures that are significant for the analysis of medical images, for example;

(ii) data encryption (transmission security and data storage);

(iii) optimization problems and

(iv) inverse problems and cryptanalysis.

The LMSC is part of:

(i) National Institute of Science and Technology in Complex Systems, coordinated by Constantino Tsallis;

(ii) research group CNPq Statistical Physics and Computer Science, coordinated by José Roberto Felicio and the Drugowich

(iii) Support Center for Research in Medical Physics, coordinated by Oswaldo Baffa Filho.

Our research has been supported by the aid

(i) Project Universal CNPq;

(ii) Regular Support, FAPESP;

(iii) INCT-SC, CNPq;

(iv) Pro-Sul/CNPq

(v) PRP/USP (Projeto 1).

In 2009, with the support of CNPq, we held the I School and Conference on Computer Modeling. Also in 2009, the article Is it Possible to compare outside researchers with different scientific interests?, Published in Scientometrics, 68, 179-189 (2006), was awarded the CAPES / Thomson Reuters Scientific Productivity and Impact, how best to work and Bibliometrics Scientometrics the past five years. This work illustrates how methods of statistical physics can be applied to various fields of knowledge, in this case scientometrics. 

Propagação e Localização de Ondas e Partículas em Meios Desordenados e Sistemas Complexos

O maior objetivo deste projeto de pesquisa é a compreensão dos diversos aspectos de transições da fase localizada (não-ergódica) à estendida (ergódica) na difusão de ondas ou partículas em meios desordenados. Estes sistemas podem estar em- ou fora-do-equilíbrio e em sistemas  complexos. 

Crescimento de tumores e seu tratamento usando modelos da dinâmica de populações

 A compreensão da auto-organização celular durante o processo de crescimento é de extrema importância na medicina e na biologia. As curvas de crescimento de organismos, tumores e outros sistemas biológicos são descritas por variáveis como volume, massa, comprimento ou número de células em função do tempo. Esse crescimento é bem ajustado por curvas sigmoidais (em forma de S). A compreensão da dinâmica de crescimento ao longo do curso clínico da doença pode levar a protocolos de tratamento mais eficientes. Uma abordagem comum nesses estudos é não considerar a localização espacial de cada indivíduo (células). Assume-se que há uma mistura homogênea e que os indivíduos podem se encontrar com a mesma probabilidade. Nesse caso a evolução do sistema pode ser descrita matematicamente por equações diferenciais. Uma outra abordagem comum nestes estudos é considerar os coeficientes das equações diferenciais como funções deterministas. No entanto, estudos com sistemas reais mostram que ambas as abordagens mencionados acima não descrevem corretamente o crescimento desses sistemas. Neste projeto de pesquisa, propomos uma nova abordagem em modelos de crescimento de tumores. Para tanto, utilizaremos uma função generalizada de crescimento e acrescentaremos a ela um termo de difusão. Além disso propomos considerar os coeficientes dessa função como variáveis estocásticas. Esperamos com essas modifiações obter uma descrição mais precisa do crescimento de tumores e, consequentemente, aumentar o poder preditivo dos modelos para gerar protocolos de tratamento mais eficientes.

Propagation and Localization of Waves and Particles in Disordered Media and Complex Systems

The major objective of this research project is the understanding of various aspects of transitions from localized (non-ergodic) to extended (ergodic) phases in the diffusion of waves or particles in disordered media. These systems can be in-or out-of-balance and complex systems. 

Tumor growth and treatment using population dynamics models

The understanding of self-organization during the cell growth process is of utmost importance in medicine and biology. The growth curve of organisms, tumors and other biological systems are described by variables such as size, weight, length and number of cells as function of time. This growth is well fitted by sigmoidal curves (S-shaped). Understanding the dynamics of growth throughout the clinical course of disease can lead to more efficient treatment protocols. A common approach in these studies is not to consider the spatial location of each individual (cell). It is assumed that there is a homogeneous mixture and that individuals can meet each other with the same probability. In this case the evolution of the system can be mathematically described by differential equations. Another common approach in these studies is to consider the coefficients of differential equations as deterministic functions. However, studies of actual systems show that both approaches mentioned above do not correctly describe the growth of these systems. In this research project, we propose a new approach in models of tumor growth. To do so, we will use a generalized function of growth and will add to it a diffusion term. In addition we propose to consider the coefficients of this function as stochastic variables. We expect these changes we will obtain a more accurate description of tumors growth and thereby increase the predictive power of models to generate more effective treatment protocols.