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Activity Funded

Center for Computational and Stochastic Mathematics

Centro de Matemática Computacional e Estocástica

Reference
UIDB/04621/2020
Project Start Date
2020-01-01
Project End Date
2024-12-31
Principal Investigator
Funding Program
Concurso de avaliação no âmbito do Programa Plurianual de Financiamento de Unidades de I&D (2017/2018) - Financiamento Base

Abstract

10.2 Summary in English for general dissemination purposes CEMAT (Center for Computational and Stochastic Mathematics) is a R&D Unit of Instituto Superior Técnico, Universidade de Lisboa (IST-UL), committed to high quality interdisciplinary research, innovation and advanced education in computational and stochastic mathematics with focus on sciences (including life sciences) and engineering applications, and to active cooperation with industries. In the period 2018-2022, the research activities will be directed to reinforce the areas where the team is internationally recognized, namely: algebra and computing, appliedand numerical analysis, mathematical modeling in biomedicine, statistics and stochastic processes. More specifically, the objective is to deepen current research themes of identified significance and to extend the knowledge to new emergent interdisciplinary topics. CEMAT’s main goal is to be known internationally as a center of excellence for its impact in research, innovation, training and society outreach. The general research plan in each of the research areas is the following. ALGEBRA AND COMPUTING: Research will be devoted to two major fronts. Abstract Algebra: focusing on groups, semigroups, finite automata, and formal languages. Computation: the main topics deal with automated reasoning and development of computational tools on algebraic systems. This new computational machinery will be applied to obtain results on different algebras. APPLIED AND NUMERICAL ANALYSIS: Research will focus on theoretical and applied matters, enhancing the cooperation with engineers in developing numerical methods to solve direct and inverse problems. The training of MSc and PhD students will benefit from existing interactions with industries, to solve new challenging problems. MATHEMATICAL MODELING IN BIOMEDICINE: The main goal is the development and analysis of mathematical models and algorithms to simulate clinically relevant problems related with cardiovascular diseases, using personalized data. These activities will reinforce the longstanding collaboration with bioengineers and medical doctors and will contribute to develop new ones. STATISTICS AND STOCHASTIC PROCESSES: Research will be devoted to several topics, including: extreme value theory, multivariate analysis, quality control, robust statistics, stochastic and telecommunication networks, stochastic optimization, and time series. Work will be done in close connection with engineers and economists, and there will be a strong emphasis in producing codes to be implemented in widely used software packages such as the R statistical package. 10.3 Summary in English for evaluation CEMAT is committed to high quality interdisciplinary research, innovation and advanced education in computational and stochastic mathematics with focus on sciences (including life sciences) and engineering applications, and to active cooperation with industries. In the period 2018-2022 research activities will be directed to reinforce the areas where the team is internationally recognized, namely algebra and computing, applied and numerical analysis, mathematical modeling in biomedicine, statistics and stochastic processes. The main objective is to deepen current research themes and to extend the knowledge in new emergent interdisciplinary topics. CEMAT’s principal goal is to be known internationally as a center of excellence for its impact in research, innovation, training and society outreach. Key strategic actions for the next 5 years include: • Advanced training of PhD and MSc students; • Employment of talented PhD researchers under job contracts; • Increasing resources through applications for national and international projects; • Consolidation of the publication rate in peer-reviewed journals, engaging in high quality and impact; • Internationalization through participation in research networks, conferences, schools, workshops and seminars; • Dissemination and outreach activities directed to academic and non-academic audiences, including industrial users, to maximize the impact of CEMAT achievements. The general research plan in each of the research areas is the following. ALGEBRA AND COMPUTING: The aim is to work on Abstract and Computational Algebra. On Abstract Algebra, the topics to be studied include: (i) Transformation monoids (TMs) and their permutation groups of units, a theme that has caught the attention of top experts on both areas; (ii) Simplicial complexes with a Boolean representation arising from certain TMs; (iii) Various classes of semigroups: locally K-finite varieties of unary semigroups, pseudo-varieties and formations of finite semigroups; (iv) The profinite word problem in pseudo-varieties associated with star-free languages; (v) Characterization of classes of languages, not necessarily regular, by equations; (vi) Inverse subgroup theory: given a subgroup functor F and a group H, which groups satisfy G=F(H)? (vii) Constructions involving actions of monoids on idempotents to describe the structure of non-regular monoids. On Computational Algebra, a number of packages are planned, as well as re-writing Prover9, an automated theorem prover, to enable its maintenance at CEMAT. The computational tools obtained will be applied to produce results on several classes of algebras. APPLIED AND NUMERICAL ANALYSIS: Research will focus on theoretical and applied matters, enhancing the cooperation with engineers in developing numerical methods to solve direct and inverse challenging problems. It is essential to have a well-equipped computational lab (CEMAT-Lab) for the training of MSc and PhD students. Selected theoretical and applied research topics: i) New numerical methods for Neural Field Equations in several dimensions, to simulate the working memory; ii) Stiffness of the SDE process model in stochastic systems and its influence on filtering algorithms; iii) Volterra integral equations with memory effects and investigation on cordial equations; iv) Numerical methods for the solution of fractional differential equations with singularities in time at the origin; v) Boundary value problems in manifolds and extension of the MFS to the Navier-Stokes equations; vi) Inverse source and inverse obstacle problems with incomplete data. MATHEMATICAL MODELING IN BIOMEDICINE: The main goal is the development and the analysis of mathematical models and algorithms for the simulation of clinically relevant problems related with cardiovascular diseases, using personalized data. Work will progress in several directions: i) Derivation of realistic and comprehensive models of inflammation/coagulation using parameters obtained experimentally in fibrinogen-deficient mice (with IMM–Microvascular Biology and Inflammation group); ii) Development of reduced models of blood coagulation using techniques of asymptotic analysis; iii) Investigation of plaque growth and vascular nanomedicine distribution at various stages of atherosclerosis, and simulations in idealized and real geometries based on Isogeometric Analysis and FEM; iv) CFD study of hemodynamic factors on the initiation and progression of cerebral aneurysms incorporating experimental biomarkers (with Neurosurgery Dept., Univ. Coimbra Hospital); v) Hemodynamic studies on aortic malformations (with Pediatric Cardiology Dept., Sta Marta Hospital, Lisboa). STATISTICS AND STOCHASTIC PROCESSES: Research will be devoted to several topics: (i) Extreme Value Theory: univariate and spatial estimators; new estimators for dependence and extremes of Levy processes; applications to mortality modeling; (ii) Multivariate Analysis and Robust Statistics: detection of Internet traffic anomalies; variable selection methods based on information theory; regression models for functions with missing data; principal component geodesics in the spherical case; robustness of deep learning; (iii) Quality Control: ARL-unbiased versions of cumulative sum control charts for detection changes in count processes and traffic intensity of queueing systems; qualitative comparison of control charts performance; (iv) Stochastic Optimization: solution of investment and exit problems; applications to investment in green energy; (v) Stochastic Processes: modeling, sampling and estimation in digital social networks; modeling and analysis of intelligent transportation systems solutions in urban traffic signal control management; stochastic ordering of queuing networks; (vi) Time Series: new models of counts exhibiting long range dependence; clustering methodologies; multivariate binomial thinning operators and new models for multivariate integer-valued time series.

Institutions

Main Institutions

  • Universidade de Lisboa Centro de Matemática Computacional e Estocástica (ULisboa CEMAT)
  • Associação do Instituto Superior Técnico para a Investigação e Desenvolvimento (IST-ID)

Other Institutions

  • FCiênciasID Associação para a Investigação e Desenvolvimento de Ciências (Fciências.ID)

Funding 525.000,00 €

Fundação para a Ciência e a Tecnologia (FCT) - Portugal

525.000,00 €