Diante da pandemia de coronavírus, pesquisadores das várias áreas do conhecimento na Universidade de São Paulo sentiram-se desafiados a direcionar suas linhas de pesquisa para novas investigações com o objetivo de auxiliar a sociedade a conter o avanço da doença. Conheça aqui as várias ações do IME-USP para ajudar no combate à pandemia.

Predicting the spatial-temporal dynamics of the COVID19 pandemic considering mobile geolocation data
Pedro S. Peixoto, Sérgio M. Oliva Filho, Cláudia M. Peixoto (IME-USP)

Mobile geolocation data is a valuable asset in the detection of movement patterns of a population, notably in a pandemic situation as with COVID19. The population movement patterns are a key input in the design of models that predict the spatial spreading of infectious diseases.

The main goal of this project is to develop a metapopulation model with spatial coupling between cities of Brazil, that may allow a rapid assessment of risk which can trigger mitigation strategies. The model is intended to capture both early stages of the epidemic, providing early warning, and also capturing the later stages of the epidemic, providing inputs for longer-term planning, relevant, for example, for strategic economic planning. Hence, the study is intended to help public administrators in action plans and resources allocation, whilst also providing a study on how mobile geolocation data may be employed in epidemic models.

The mobility data is based on millions of anonymized mobile visits data in Brazil, obtained from collaborations with companies that develop geolocation services for mobile applications. The main challenges to be dealt with are: (i) the big-data processing, which requires heavy use of scientific computing; (ii) careful parameters estimation from best-of-knowledge available COVID19 data, requiring optimization and statistics experience; (iii) mathematical modeling and analysis of the proposed model, which go beyond classic local metapopulation models available in the literature; (iv) development of communication material for the general public and public administration offices, which is key to ensure that the main results of this research reach those that can need it. Given the complexity of the project, it is to be developed as a joint collaboration effort, with the main team based in São Paulo State, within USP, UNESP, and UFABC.

Simulando epidemias no R
Alexandre Galvão Patriota (IME-USP)

O objetivo da pesquisa é entender como as epidemias ocorrem por meio de simulações. Alguns cenários são considerados em uma população clusterizada. Os códigos estão disponíveis no github.

Fabio Kon (IME-USP) e Alessandro Santiago dos Santos (IPT)

Numa iniciativa de pesquisa e desenvolvimento tecnológico para cidades inteligentes, a plataforma InterSCity foi concebida para coletar, armazenar, processar e visualizar dados sobre cidades utilizando ferramentas avançadas de software livre, computação de alto desempenho e ciência de dados.

Previsões para o número de casos confirmados e de óbitos por covid-19 utilizando métodos de análise de séries temporais
Pedro A. Morettin, Airlane P. Alencar, Francisco Marcelo M. Rocha, Chang Chiann e Clelia Toloi (IME-USP)

O objetivo da pesquisa é aplicar e avaliar metodologias de séries temporais para a previsão do número diário de casos confirmados e de óbitos por covid-19 utilizando os dados oficiais disponibilizados no Painel coronavírus do Ministério da Saúde. Diversas metodologias serão avaliadas como modelos ARIMA, modelos espaço de estados, modelos não lineares com correlação serial e modelos utilizando ondaletas.

Detecção de pontos de mudança na curva de contágios do novo coronavírus e predição de curto prazo
Florencia Leonardi (IME-USP)

O objetivo da pesquisa é ajustar um modelo estatístico aos dados de casos reportados de sars-cov2, disponíveis em bases de dados públicas, para detectar mudanças na dinâmica deste processo e predizer no curto prazo o número de novos casos. A análise está sendo empregada às séries de casos reportados em diferentes países da América Latina, estados e cidades brasileiras.

# Computational Applied Mathematics

##### Computer Graphics
Study of techniques of mathematical and computational modeling aiming the realistic simulation of natural phenomena through computer graphics. Currently, we focus on some applications in Biology.

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##### Numerical Methods and Computational Fluid Mechanics
Development of numerical methods for partial differential equations of fluid mechanics and applications, specially in multiphase flows and problems related to numerical weather and climate prediction.

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##### Numerical Methods and Optimization
Optimization is the area of study that deals with the problem of finding values for variables that, among all values that satisfy a given constraint, minimize (or maximize) an objective function. We are interested in the nonlinear optimization problem with real variables, where we study analytical properties fulfilled by the solutions, in particular, the ones that can be used to guide an iterative process to solve the problem. The group also works in the area of shape optimization, where the variable is the geometry, or shape, of subsets of Rn, and which is in particular concerned with partial differential equations constraints. Optimization is a cross-disciplinary field which relies on mathematical tools from different disciplines such as differential geometry, topology, optimal control, numerical analysis and applied linear algebra. The interests of this research group ranges from theoretical problems to computational implementation and applications in real problems in Physics, Chemistry, Statistics, Economics, Engineering and Industrial Mathematics. The group has a fruitful collaboration with the Department of Computer Science from IME-USP.

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# Differential Equations and Applications

##### Dynamics of Evolution Equations
We consider fundamental aspects of the qualitative behavior of infinite dimensional dynamical systems, derived from partial differential equations or from functional equations. These systems play an important role in the mathematical modeling of natural phenomena related to several areas, as Physics, Biology, Chemistry, Economics, Engineering and Ecology.

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##### Dynamics of Hamiltonian Systems
To study the Hamiltonian dynamics of mechanical systems with emphasis on applications to celestial mechanics and to the motion of solid bodies inside fluids. To analyze the dynamical consequences of forces that dissipate energy.

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##### Geometric Mechanics and Control Theory
Study of problems of geometric mechanics, celestial mechanics and of Control theory.

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##### Geometric Theory from PDEs and several complex variables
Tmain purpose of the project is to continue the work undertaking by the research team of Projeto Temático 2003/12206-0 in the fields of Linear Partial Differential Equations and Multidimensional Complex Analysis as well as to increase our activities on supervision of graduate students research work in these areas. The main topics to be studied are: (a) Local, semi-global and global solvability for linear differential operators and involutive systems of complex vector fields; (b) Regularity properties of the solutions: $C^\infty$, analytic and Gevrey hypoellipticity; (c) General properties of the approximate solutions to involutive systems of complex vector fields; (d) The theory of Hardy spaces for solutions of non-elliptic vectohe r fields; (e) The extension of the F. and M. Riesz and Rudin-Carleson theorems to complex vector fields.

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##### Non-Linear Partial Differential Equations
Studies of stability of stationary waves.

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##### Qualitative Theory of Differential Equations and Applications
The main topics studied are smooth or non-smooth vector fields, implicit differential equations, and reversible vector fields. From the geometrical point of view, for differential equations the special curves in surfaces (main curvature lines, asymptotic lines, Darboux curves) and other questions that relate dynamics and geometry are studied. For vector fields, the proposed general lines in the Thom-Smale program are studied: determination of boundary cycle quotas, global phenomena (periodic connections and orbits), singular perturbation, asymptotic behavior, dynamics and bifurcations. In summary, the aim is to study techniques from the Qualitative Theory of Ordinary Differential Equations and apply them to Differential Geometry and to problems of different areas such as control theory, physics, biology, engineering, etc.

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# Dynamical Systems

##### Dynamics and Geometry in Low Dimensions
The modern theory of dynamical systems began with the work of Poincaré in the early twentieth century and since then has grown and matured, becoming an important and active area of mathematics, with several sub-areas. The main research themes of this group are: Dynamics in dimension 2 (dynamics of homeomorphisms and diffeomorphisms of the torus, topological dynamics on surfaces, Hénon maps); Teichmüller theory and its connections with dynamics and geometry in low dimensions; Endomorphisms of the interval, critical circle maps, renormalization and parameter space; Pseudo-holomorphic curves and symplectic dynamics; Complex dynamics in dimensions 1 and 2. The group has a fruitful collaboration with the Department of Mathematics from IME-USP. For more information, access the group website

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##### Ergodic Theory: Ergodic Optimization and Thermodynamic Formalism
The focus of the Ergodic Theory is the study of invariant measures for a dynamic or group actions. Besides being one of the main branches of the theory of dynamical systems, the results produced are used as a tool and are important to researchers from several other areas from both pure and applied mathematics: probabilists, specialists in rigorous statistical mechanics, in symbolic dynamics, in amenable groups and others. The most frequent research lines are Ergodic Optimization and Thermodynamic Formalism. More specifically: the study of maximizing measures, Gibbs and equilibrium measures, grounds states and phase transitions.

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# Mathematical Modeling and Applications

##### Bayesian Statistics, Stochastic Optimization and Sparse Systems
Full Bayesian Significance Test (FBST) is a new statistical procedure to access the likelihood of precise hypothesis. This procedure solve several problems from similar frequentist statistical methods, as p-values, or from orthodox bayesian statistics, like bayesian factors.

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##### Mathematical Models Applied to Epidemiology
The principal aim of this project is the study of local and global human mobility and their influence on the spreading of contagious diseases. The spatial dynamics and choice of parameters should take into account the seasonal variations. The risks of contamination and epidemiological thresholds shall also be evaluated. Stochastic modeling is adequate for mobility. Due to difficulties in obtaining sufficient data, Monte Carlo techniques will be use to generate data for initial tests.

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##### Mathematical Models for Social Systems
We consider mathematical models as an aid in the interpretation of empirical evidence in social systems. We are interested specifically in the emergence and sustaining of altruism in large scale in human societies; in relations between cognitive limitations, social structure and opinion dynamics; and opinion dynamics under imitation processes, adaption, self-references and reputation effects. We employ analytic and simulation techniques from statistical mechanics of disordered systems, as well as frameworks from evolutionary games theory and complex networks. Rigorous results do not constitute our main focus, but are quite desirable whenever possible. This project is part of the Center for Natural and Artificial Information Processing Systems, CNAIPS-USP, which receives financial support from our University.

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##### Mathematical Models in Genetics
Algebraic model for the genetic code. Mathematical modeling of gene expression.

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# Mathematical Physics

##### Classical and Quantum Field Theory
Development of a general formalism (Lagrangian and Hamiltonian), symmetries and conservation laws, Geometric models (general relativity, caliber theories, ...)

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##### Rigorous Statistical Mechanics: Classical and Quantum
Rigorous study of short and long-range models of statistical mechanics, such as the Ising type models, in the classic case, as well as the Hubbard and BCS types, in the quantum case. The primary objective is to produce theorems to get a better understanding of them. In general, we are looking for results about the behavior of the correlations, the description of the DLR states in the classical case and the KMS states in the quantum case, the existence or not of phase transitions, the characterization of the ground states, the properties of the pressure, among others. The mathematical tools used are probability, graph theory and combinatorics, functional analysis, C*-algebras and von Neumann algebras, convex analysis, measure theory, ergodic theory, etc.

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# Analysis and Dynamical Systems

##### Dynamical Systems
Dynamical Systems at IME-USP
Seminários de Sistemas Dinâmicos-IME-USP

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# Logic, Set Theory, General Topology and Combinatorics

##### Combinatorics
Teoria da Computação, Combinatória e Otimização

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##### Logic, Set Theory, General Topology

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Assistant Professor

##### Algorithms, Combinatorial Optimization, and Theory of Computation
Research in a broad spectrum of combinatorial optimization problems and its applications, with particular focus on complexity issues, design and analysis of efficient exact and approximation algorithms, use of polyhedral approaches, and other techniques. Research topics include semidefinite optimization, probabilistic methods, network design, routing, packing, as well as game theoretical problems.

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##### Bioinformatics
To study the application of mathematical and computing techniques for the generation and management of information in the Biology and Biotechnology areas.

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##### Combinatorics and Graph Theory
Research in discrete and computational geometry, matroid theory, probabilistic methods and random combinatorial structures, graphs and hypergraphs (structural properties, extremal problems, coloring, decomposition, and others).

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##### Computational Musicology
To develop research related to the following issues: the processing of sound signals, acoustic simulation in music environments and listening rooms, automatic analysis of musical signals, sound synthesis and interactive performance in the context of electroacoustic music.

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##### Computer Vision
To research the range of methods and techniques through which computer systems may be able to interact with and respond to images and to model learning processes in their many manifestations.

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##### Cryptography and Data Security
To develop efficient (and demonstrably secure) algorithms and protocols based on issues such as integer factorization, discrete logarithm calculation, calculation of bilinear pairing, etc.

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##### Logic, Artificial Intelligence, and Formal Methods
To develop artificial intelligence techniques and study their applications in Computer Science as well as in other areas.

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##### Software Systems
To develop software systems, especially the distributed ones, the concurrent ones and the ones for storage and retrieval of data; study the evaluation and the definition of technologies that facilitate their construction, maintenance and evolution.

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