• Research

    About Researches

    The Master's and Doctorate in Mathematical Modeling have multiple lines of academic, scientific and technological research, involving topics such as epidemiology, stochastic analysis, data science and statistics

Research Line

The Optimal Control Theory studies Optimization problems whose state variables are subject to differential equations (ordinary or partial) whose dynamics depend on a control variable, while Stochastic Optimization is focused on the study of optimization problems involving uncertainties modeled by a stochastic process. A stochastic optimization problem is usually formulated using conditional risk measures.

In this line of research, mathematical models and methods are studied with a focus on applications in problems of Finance, Economics and Actuarial Sciences. For applications in Finance and Economics, research projects are usually based on techniques involving Stochastic Calculation and/or Partial Differential Equations, whereas applications in Actuarial Sciences, such as Reserves calculation, tend to use statistical regression models or time series.

This line of research began worldwide with the development of Probability and the formal construction of the Brownian Movement in the early 20th century. This is probably one of the areas of mathematics with the most applications in the real world. From a theoretical point of view, we are interested in the study of Stochastic Differential Equations and the incorporation of path-dependence in several aspects of the theory.

In addition, another aspect of this line is the numerical resolution of differential equations, in particular random (RDEs) and stochastic (EDEs). The theory of EDEs and RDEs are themes, at the crossroads of differential equations and stochastic processes, with a wide variety of applications in the modeling of phenomena and practical situations in which the quantities of interest are subject to random disturbances. Since obtaining solutions to these equations is rarely possible, much attention is paid to the construction and study of approximation methods, with good qualitative properties, for their integration and simulation.

The objective of this line of research is the exploration and development of objects and research problems through methods originated from the statistical learning of machines (Machine Learning) and its applications in the analysis of structured and unstructured data. This range of empirical objects encompasses numerical, categorical and textual data, images, graphs, time series, among others. It also includes the development of algorithms, languages and methodologies for manipulating these complex databases, in tasks such as classification, regression, learning, identification of clusters, recommendation systems, optimization, extraction and representation of knowledge, modeling knowledge domains, data mining, text mining, visualization, sentiment analysis, high-dimensional data analysis, cryptography.

Mathematical epidemiology is an applied mathematics subject with more than a century of tradition, which incorporates ideas and methods from different branches of mathematics in the representation and analysis of its objects of study.    At EMAp, the Mathematical Epidemiology group studies how information on how communicable diseases can be treated from a quantitative point of view, differently from the classic statistical techniques well known in the medical field. In addition, the projects require a basic understanding of biological assumptions and the mathematical models that underlie infection models and the tools available today to extract biological information from these models.

In general, this line of research is divided into theoretical, methodological and applied aspects involving data analysis. In particular, EMAp researchers are interested in the following areas of Statistics: Estimation of time series in high dimension; Modeling of non-linear time series; Non-parametric tests; Monte Carlo simulation for Bayesian inference; Statistical inference for stochastic optimization problems averse to risk or neutral risk (central limit theorems, hypothesis tests, non-asymptotic confidence intervals); Nonparametric hypothesis testing using convex optimization techniques.

  • SANTOS, S. S. ; TORRES, MATEO ; GALEANO, DIEGO ; SANCHEZ, M. M. ; CERNUZZI, LUCA ; ALBERTO PACCANARO . Machine Learning and Network Medicine approaches for Drug Repositioning for COVID-19. CELL, v. 3, p. 100396, 2021.
  • TORRES, MATEO ; YANG, HAIXUAN ; ROMERO, ALFONSO E. ; PACCANARO, ALBERTO . Protein function prediction for newly sequenced organisms. Nature Machine Intelligence, v. 7, p. 2522, 2021.
  • MCDONALD, J. TYSON ENGUITA, FRANCISCO JAVIER TAYLOR, DEANNE GRIFFIN, ROBERT J. PRIEBE, WALDEMAR EMMETT, MARK R. SAJADI, MOHAMMAD M. HARRIS, ANTHONY D. CLEMENT, JEAN DYBAS, JOSEPH M. AYKIN-BURNS, NUKHET GUARNIERI, JOSEPH W. SINGH, LARRY N. GRABHAM, PETER BAYLIN, STEPHEN B. YOUSEY, ALIZA PEARSON, ANDREA N. CORRY, PETER M. SARAVIA-BUTLER, AMANDA AUNINS, THOMAS R. SHARMA, SADHANA NAGPAL, PRASHANT MEYDAN, CEM FOOX, JONATHAN MOZSARY, CHRISTOPHER , et al. ; Role of miR-2392 in Driving SARS-CoV-2 Infection. Cell Reports, v. 1, p. 109839, 2021.
  • Cauã Roca Antunes, Alexandre Rademake rand Mara AbeL; A faster and less aggressive algorithm for correcting conservativity violations in ontology alignments; Applied Ontology   
  • SOTO SÁNCHEZ, JOSÉ EZEQUIEL ; WEYRICH, TIM ; MEDEIROS E SÁ, ASLA ; DE FIGUEIREDO, LUIZ HENRIQUE . An integer representation for periodic tilings of the plane by regular polygons. COMPUTERS & GRAPHICS-UK, 2021.
  • Luz, Paula M. ; Struchiner, Claudio J. ; KIM, SUN-YOUNG ; MINAMISAVA, RUTH ; ANDRADE, ANA LUCIA S. ; SANDERSON, COLIN ; RUSSELL, LOUISE B. ; TOSCANO, CRISTIANA M. . Modeling the cost-effectiveness of maternal acellular pertussis immunization (aP) in different socioeconomic settings: A dynamic transmission model of pertussis in three Brazilian states. VACCINE, v. 39, p. 125-136, 2021.
  • AMAKU, MARCOS ; COVAS, DIMAS TADEU ; BEZERRA COUTINHO, FRANCISCO ANTONIO ; AZEVEDO NETO, RAYMUNDO SOARES ; STRUCHINER, CLAUDIO ; WILDER-SMITH, ANNELIES ; Massad, Eduardo . Modelling the test, trace and quarantine strategy to control the COVID-19 epidemic in the state of São Paulo, Brazil. Infectious Disease Modelling, v. 6, p. 46-55, 2021.
  • SILVA, PAULO J. S. ; SAGASTIZÁBAL, CLAUDIA ; NONATO, LUÍS GUSTAVO ; Struchiner, Claudio José ; PEREIRA, TIAGO . Optimized delay of the second COVID-19 vaccine dose reduces ICU admissions. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, v. 118, p. e2104640118, 2021.
  • TORRES, THIAGO S. ; Luz, Paula M. ; COELHO, LARA E. ; JALIL, CRISTINA ; FALCO, GISELY G. ; SOUSA, LEONARDO P. ; JALIL, EMILIA ; BEZERRA, DANIEL R.B. ; CARDOSO, SANDRA W. ; HOAGLAND, BRENDA ; Struchiner, Claudio J. ; VELOSO, VALDILEA G. ; Grinsztejn, Beatriz . SARS-CoV-2 testing disparities across geographical regions from a large metropolitan area in Brazil: Results from a web-based survey among individuals interested in clinical trials for COVID-19 vaccines. Brazilian Journal of Infectious Diseases, v. 25, p. 101600, 2021.
  • HALLAL, PEDRO C ; VICTORA, CESAR G ; SILVEIRA, MARIÂNGELA F ; BARROS, ALUÍSIO J D ; MENEZES, ANA M B ; HORTA, BERNARDO L ; Struchiner, Cláudio J ; HARTWIG, FERNANDO P ; VICTORA, GABRIEL D ; PELLANDA, LÚCIA C ; BURATTINI, MARCELO N ; DELLAGOSTIN, ODIR A ; BARROS, FERNANDO C . The challenge of conducting epidemiological research in times of pandemic and denialism: 1-year anniversary of the EPICOVID-19 project in Brazil. INTERNATIONAL JOURNAL OF EPIDEMIOLOGY, v. 50, p. 1049-1052, 2021.
  • MACEDO, LAYLLA RIBEIRO ; STRUCHINER, CLAUDIO JOSE ; MACIEL, Ethel Leonor Noia . Contexto de elaboração do Plano de Imunização contra COVID-19 no Brasil. Ciência & Saúde Coletiva, v. 26, p. 2859-2862, 2021.
  • HALLAL, PEDRO C. ; SILVEIRA, MARIANGELA F. ; MENEZES, ANA M. B. ; HORTA, BERNARDO L. ; BARROS, ALUÍSIO J. D. ; PELLANDA, LUCIA C. ; VICTORA, GABRIEL D. ; DELLAGOSTIN, ODIR A. ; Struchiner, Claudio J. ; BURATTINI, MARCELO N. ; MESENBURG, MARILIA A. ; JACQUES, NADEGE ; VIDALETTI, LUÍS PAULO ; AMBROS, EMANUELE L. ; BERLEZI, EVELISE M. ; SCHIRMER, HELENA ; RENNER, JANE D. P. ; COLLARES, KAUE ; IKEDA, MARIA LETÍCIA R. ; ARDENGHI, THIAGO M. ; DE GASPERI, PATRICIA ; HARTWIG, FERNANDO P. ; BARROS, FERNANDO C. ; VICTORA, CESAR G. . Slow Spread of SARS-CoV-2 in Southern Brazil Over a 6-Month Period: Report on 8 Sequential Statewide Serological Surveys Including 35611 Participants. AMERICAN JOURNAL OF PUBLIC HEALTH, v. 111, p. e1-e9, 2021.
  • MENEZES, ANA M. B. ; VICTORA, CESAR G. ; HARTWIG, FERNANDO P. ; SILVEIRA, MARIÂNGELA F. ; HORTA, BERNARDO L. ; BARROS, ALUÍSIO J. D. ; MESENBURG, MARILIA A. ; WEHRMEISTER, FERNANDO C. ; PELLANDA, LÚCIA C. ; DELLAGOSTIN, ODIR A. ; Struchiner, Cláudio J. ; BURATTINI, MARCELO N. ; BARROS, FERNANDO C. ; HALLAL, PEDRO C. . High prevalence of symptoms among Brazilian subjects with antibodies against SARS-CoV-2. Scientific Reports, v. 11, p. 13279, 2021.
  • BARROS, FERNANDO C ; HARTWIG, FERNANDO P ; BARROS, ALUÍSIO J D ; MENEZES, ANA M B ; HORTA, BERNARDO L ; Struchiner, Cláudio J ; VIDALETTI, LUIS PAULO ; SILVEIRA, MARIANGELA F ; MESENBURG, MARILIA A ; DELAGOSTIN, ODIR A ; HALLAL, PEDRO C ; VICTORA, CESAR G . COVID-19 and social distancing among children and adolescents in Brazil. REVISTA DE SAÚDE PÚBLICA (ONLINE), v. 55, p. 42, 2021.
  • SOUZA FILHO, BRENO AUGUSTO BORMANN DE ; STRUCHINER, CLÁUDIO JOSÉ . Uma proposta teórico-metodológica para elaboração de modelos teóricos. CADERNOS SAÚDE COLETIVA, v. 29, p. e1, 2021.
  • RODRIGUES, AMANDA ; Struchiner, Claudio J. ; COELHO, LARA E. ; VELOSO, VALDILEA G. ; Grinsztejn, Beatriz ; Luz, Paula M. . Late initiation of antiretroviral therapy: inequalities by educational level despite universal access to care and treatment. BMC PUBLIC HEALTH, v. 21, p. e1, 2021.
  • SANTOS, CLEBER VINICIUS BRITO DOS ; SEVÁ, ANAIÁ DA PAIXÃO ; WERNECK, GUILHERME LOUREIRO ; STRUCHINER, CLÁUDIO JOSÉ . Does deforestation drive visceral leishmaniasis transmission? A causal analysis. PROCEEDINGS OF THE ROYAL SOCIETY B-BIOLOGICAL SCIENCES, v. 288, p. 20211537, 2021.
  • MASINI, R. ; MEDEIROS, M. C. ; MENDES, EDUARDO F. . Machine learning advances for time series forecasting. Journal Of Economic Surveys, 2021.                                                                                                                                                   
  • MASINI, R. ; MEDEIROS, MARCELO C. ; MENDES, EDUARDO F. . Regularized Estimation of High-Dimensional Vector AutoRegressions with Weakly Dependent Innovations,. Journal of Time Series Analysis (Online), 2022.
  • LAPORTA, GABRIEL Z. ; ILACQUA, ROBERTO C. ; BERGO, EDUARDO S. ; CHAVES, LEONARDO S. M. ; RODOVALHO, SHEILA R. ; MORESCO, GILBERTO G. ; FIGUEIRA, ELDER A. G. ; Massad, Eduardo ; DE OLIVEIRA, TATIANE M. P. ; BICKERSMITH, SARA A. ; CONN, JAN E. ; SALLUM, MARIA ANICE M. . Malaria transmission in landscapes with varying deforestation levels and timelines in the Amazon: a longitudinal spatiotemporal study. Scientific Reports, v. 11, p. 6477, 2021.
  • Amaku, Marcos ; COVAS, DIMAS TADEU ; Coutinho, Francisco Antonio Bezerra ; Azevedo, Raymundo Soares ; Massad, Eduardo . Modelling the impact of contact tracing of symptomatic individuals on the COVID-19 epidemic. Clinics, v. 76, p. e2639, 2021.
  • OLIVEIRA, TATIANE M. P. ; LAPORTA, GABRIEL Z. ; BERGO, EDUARDO S. ; CHAVES, LEONARDO SUVEGES MOREIRA ; ANTUNES, JOSÉ LEOPOLDO F. ; BICKERSMITH, SARA A. ; CONN, JAN E. ; Massad, Eduardo ; SALLUM, MARIA ANICE MUREB . Vector role and human biting activity of Anophelinae mosquitoes in different landscapes in the Brazilian Amazon. Parasites & Vectors, v. 14, p. 236, 2021.
  • CLANCY, INDIA L. ; JONES, ROBERT T. ; POWER, GRACE M. ; LOGAN, JAMES G. ; IRIART, JORGE ALBERTO BERNSTEIN ; Massad, Eduardo ; KINSMAN, JOHN . Public health messages on arboviruses transmitted by Aedes aegypti in Brazil. BMC PUBLIC HEALTH, v. 21, p. 1362, 2021.
  • AMAKU, M. ; COUTINHO, F. A. ; ÉBOLI, O. ; MASSAD, E. . Some problems with the use of the Dirac delta function I: What is the value of ∫0∞δ(x)dx?. REVISTA BRASILEIRA DE ENSINO DE FÍSICA (ONLINE), v. 43, p. e20210132-1, 2021. 
  • Amaku, Marcos ; COUTINHO, FRANCISCO A. B. ; ÉBOLI, OSCAR J. P. ; Massad, Eduardo . Some Problems with the Dirac Delta Function: Divergent Series in Physics. BRAZILIAN JOURNAL OF PHYSICS, v. 51, p. 1324-1332, 2021.
  • ALBANI, VINICIUS V.L. ; LORIA, JENNIFER ; Massad, Eduardo ; ZUBELLI, JORGE P. . The Impact of COVID-19 Vaccination Delay: A Data-Driven Modelling Analysis for Chicago and New York City. VACCINE, v. X, p. X-X, 2021.
  • AMAKU, M. ; COVAS, DIMAS TADEU ; Coutinho, Francisco Antonio Bezerra ; Azevedo, Raymundo Soares ; MASSAD, E. . Modelling the impact of delaying vaccination against SARS-CoV-2 assuming unlimited vaccine supply. Theoretical Biology and Medical Modelling, v. 18, p. 14, 2021.
  • ALBANI, VINICIUS ; LORIA, JENNIFER ; Massad, Eduardo ; ZUBELLI, JORGE . COVID-19 underreporting and its impact on vaccination strategies. BMC INFECTIOUS DISEASES, v. 21, p. 1111, 2021.
  • Massad, E.; AMAKU, M. ; COVAS, DIMAS TADEU ; Lopez, Luis Fernandez ; Coutinho, F.A.B. . Estimating the effects of reopening of schools on the course of the epidemic of COVID-19. EPIDEMIOLOGY AND INFECTION, v. X, p. 1-11, 2021
  • DE LA CRUZ, H.. Steady-state density preserving method for stochastic mechanical systems. European Physical Journal Plus, v. 136, p. 799-812, 2021.
  • GARCIA-ZANABRIA, GERMAIN ; RAIMUNDO, M. M. ; Poco, J. ; NERY, MARCELO ; SILVA, CLAUDIO T. ; NONATO, LUIS G. CriPAV: Street-Level Crime Patterns Analysis and Visualization. IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, 2021.
  • CARVALHO, LUIZ MAX; IBRAHIM, JOSEPH G. . On the normalized power prior. STATISTICS IN MEDICINE, v. 1, p. sim.9124, 2021.
  • LANA, RAQUEL MARTINS ; FREITAS, LAÍS PICININI ; CODEÇO, CLÁUDIA TORRES ; PACHECO, ANTÔNIO GUILHERME ; CARVALHO, LUIZ MAX FAGUNDES DE ; VILLELA, DANIEL ANTUNES MACIEL ; COELHO, FLÁVIO CODEÇO ; CRUZ, OSWALDO GONÇALVES ; NIQUINI, ROBERTA PEREIRA ; PORTO, VICTOR BERTOLLO GOMES ; GAVA, CAROLINE ; GOMES, MARCELO FERREIRA DA COSTA ; BASTOS, LEONARDO SOARES . Identificação de grupos prioritários para a vacinação contra COVID-19 no Brasil. CADERNOS DE SAÚDE PÚBLICA, v. 37, p. e00049821-e00049821, 2021.
  • Aronna, Maria Soledad; BONNANS, J. FRÉDÉRIC ; KRÖNER, AXEL . State Constrained Control-Affine Parabolic Problems II: Second Order Sufficient Optimality Conditions. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, v. 59, p. 1628-1655, 2021.
  • ARONNA, M. SOLEDAD; GUGLIELMI, R. ; MOSCHEN, L. M. . A model for COVID-19 with isolation, quarantine and testing as control measures. Epidemics, v. 1, p. 1-16, 2021.
  • SOLEDAD ARONNA, MARIA; TRÖLTZSCH, FREDI . First and second order optimality conditions for the control of Fokker-Planck equations. ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, v. 1, p. 1, 2021.
  • CHAVES, JULIO C. ; A.H.B. da Silva, Moacyr ; Evsukoff, Alexandre G. . Gravity Model Parameter Variation during a Long-Term Study using Mobile Phone Data in the Rio de Janeiro Metropolitan Area. CASE STUDIES ON TRANSPORT POLICY, v. 1, p. 20-30, 2021.
  • DE SOUZA, MARCOS ; SOUZA, RENATO ROCHA . Mapeamento de conhecimento científico: modelagem de tópicos das teses e dissertações do Programa de Pós-Graduação em Ciência da Informação da UFMG. EM QUESTÃO, v. 27, p. 228-250, 2021.
  • ABGAZ, Y. ; SOUZA, RENATO ROCHA ; DORN, A. ; METHUKU, Japesh ; KOCH, Gerda . A Methodology for Semantic Enrichment of Cultural Heritage Images Using Artificial Intelligence Technologies. JOURNAL OF IMAGING, v. 7, p. 1-22, 2021.
  • AREFIDAMGHANI, REZA ; Behling, Roger ; BELLO-CRUZ, YUNIER ; IUSEM, ALFREDO N. ; SANTOS, LUIZ-RAFAEL . The circumcentered-reflection method achieves better rates than alternating projections. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, v. 79, p. 507-530, 2021.
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Mathematical and Computational Models for Optimizing Strategies for Reducing the Levels of Violence with Victims in Brazil

Coordinator: Eduardo Massad (FGV EMAp)

Resumo: Este projeto de pesquisa tem como objetivo desenvolver metodologias, modelos matemáticos e ferramentas de ciência de dados para auxiliar órgãos de segurança pública na análise de padrões de crimes no Brasil, visando aumentar a eficiência das polícias e a criação de políticas públicas voltadas para prevenção e controle de atividades criminais. Especificamente, o projeto tem como principais objetivos: 1) Criar uma sistemática para mapear, categorizar e integrar dados públicos e privados relacionados a eventos criminais, criando assim uma base para o desenvolvimento de políticas de segurança, auxiliando ainda na gestão da ordem pública e a redução dos níveis de violência; 2) Criar ferramentas para acessar, integrar e analisar os dados, desenvolvendo metodologias capazes de revelar padrões de atividades criminosas a partir de conjuntos de dados variados. Tais ferramentas possibilitarão uma melhor compreensão de como características urbanas e sociais impactam na taxa e no tipo de crime; 3) Construção de modelos matemáticos com capacidade descritiva e preditiva de otimização de estratégias de redução dos níveis de violência e todas as suas vertentes; O projeto será executado em duas cidades do Brasil: São Paulo e Rio de Janeiro. Para mais detalhes, clique aqui.

Abstract: Violence, understood in its broad sense, can be defined as “aggression by external causes”. In general, there are essentially two types of violence: intentional (crimes) and unintentional (accidents). This division has support in the concepts proposed by Flamínio Favero of “criminal” and “accidental”. For purposes of legal liability, these categories are classified as “intentional” and “negligent”. The study “Global Burden of Disease 2016”, published in volume 390, pp. 1083-1464, of the magazine The Lancet, calculated the total number of yearly deaths by violence in the world at 4.6 million, of the 1.5 million due to traffic accidents, 1.8 million due to unintentional injuries, 1.2 million by interpersonal violence, and 162 thousand due to natural disasters. The same study calculated the 20 number of disability-adjusted life-years (DALYs) due to the various forms of violence in the world as 255 million, of the 78 million by traffic accidents, 107 million caused by unintentional injuries, 59 million by interpersonal violence, and 11 million by natural disasters. In absolute numbers, Brazil occupies second place in the world in deaths caused by interpersonal violence and twelfth in deaths normalized per 100 thousand inhabitants. The economic impacts of violence in Brazil still need to be estimated with some degree of precision, and this study will supply rational bases for reliable economic calculation. Besides this, it will provide support for possible alteration of Brazil’s Penal Code and Code of Criminal Sentencing. Therefore, the present project intends to construct databases, as well as optimize and integrate existing databases, to store and recover data of interest for formulating public policies. Mathematical optimization models will be constructed for strategies to reduce the levels of violence in Brazil, as well as its costs in terms of lives lost and economic performance. The project will count on the participation of the Center for Data Science of New York University (USA), University of Coimbra (Portugal), University of Derby (United Kingdom), York University (Canada), and the Department of Legal Medicine of the University of São Paulo (USP).

Colaborators: Jorge Poco (FGV EMAp), Moacyr Alvim Horta Barbosa da Silva (FGV EMAp), Silvia Martorano Raimundo (USP), Raphael Ximenes (Pós-doutorando, University Health Network, UHN, Canadá), Luis Gustavo Nonato (USP-ICMC), David Greenhalgh ((University of Strathchlyde, UK), Kyle Treiber (University of Cambridge, UK)

Financier: Programa Institucional de Internacionalização – CAPES –PrInt e Rede de Pesquisa e Conhecimento Aplicado da FGV.