FCT: CMA - Artigos em revista internacional com arbitragem científica
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- An Innovative Approach to Estimate Infection by COVID-19Publication . Oliveira, Manuela; Garção, Eugénio; Grilo, Luís M.; Mexia, João T.; CMA - Centro de Matemática e AplicaçõesGiven that individuals in a certain population are different (among other things they have a different immune system), it is possible that some are infected with the known virus COVID-19 and are asymptomatic and therefore not diagnosed with the disease. Thus, estimates of the number of infected and dead with COVID-19 may not correspond to reality. This study seeks to indicate a procedure to estimate the number of individuals in the infected population that are asymptomatic (not diagnosed, but possible transmitters of the disease), based on the number of infected individuals (already diagnosed). We showed how with data available (numbers of symptomatic, symptomatic in the hospital and deceased) on the evolution of the pandemic in five regions of mainland Portugal it is possible to estimate the number of asymptomatic and immune individuals in the population.
- A family of optimal weighted conjugate-gradient-type methods for strictly convex quadratic minimizationPublication . Oviedo, Harry; Andreani, Roberto; Raydan, Marcos; CMA - Centro de Matemática e Aplicações; Springer NetherlandsWe introduce a family of weighted conjugate-gradient-type methods, for strictly convex quadratic functions, whose parameters are determined by a minimization model based on a convex combination of the objective function and its gradient norm. This family includes the classical linear conjugate gradient method and the recently published delayed weighted gradient method as the extreme cases of the convex combination. The inner cases produce a merit function that offers a compromise between function-value reduction and stationarity which is convenient for real applications. We show that each one of the infinitely many members of the family exhibits q-linear convergence to the unique solution. Moreover, each one of them enjoys finite termination and an optimality property related to the combined merit function. In particular, we prove that if the n × n Hessian of the quadratic function has p < n different eigenvalues, then each member of the family obtains the unique global minimizer in exactly p iterations. Numerical results are presented that demonstrate that the proposed family is promising and exhibits a fast convergence behavior which motivates the use of preconditioning strategies, as well as its extension to the numerical solution of general unconstrained optimization problems.
- Optimizing Vehicle Replacement in Sustainable Urban Freight Transportation Subject to Presence of Regulatory MeasuresPublication . Ahani, Parisa; Arantes, Amílcar; Garmanjani, Rohollah; Melo, Sandra; CMA - Centro de Matemática e Aplicações; Molecular Diversity Preservation International (MDPI)Since the 1990s, studies and pilot tests have been conducted to reduce traffic, accidents, and pollution due to urban freight transport (UFT). These ended up in several policies, regulations, and restrictions for UFT, such as low emission zones, delivery time windows, and vehicle size and weight restrictions. However, issues in UFT under regulatory measures still persist. This study introduces an optimization framework for deriving an optimal combination of various types of vehicles with different capacities for vehicle replacement with UFT. This framework allows an understanding of how an urban freight company with a limited budget efficiently satisfies its freight demand within an urban area in the presence of regulatory measures by urban administrators. The introduced formulation, which is mixed-integer linear programming, will assist the operator in choosing the best investment strategy for introducing new vehicles of certain types and sizes, for operation in different zones, into its fleet while gaining economic benefits and having a positive impact on the liveability of the urban area. Furthermore, an elasticity analysis is performed to consider the effects of specific uncertain parameters on the total cost. The numerical results show that the share of electric vehicles in the fleet increases, and they are more competitive than diesel vehicles.
- The associative-commutative spectrum of a binary operationPublication . Huang, Jia; Lehtonen, Erkko; CMA - Centro de Matemática e Aplicações; Elsevier Science B.V., IncWe initiate the study of a quantitative measure for the failure of a binary operation to be commutative and associative. We call this measure the associative-commutative spectrum as it extends the associative spectrum (also known as the subassociativity type), which measures the nonassociativity of a binary operation. In fact, the associative-commutative spectrum (resp. associative spectrum) is the cardinality of the operad with (resp. without) permutations obtained naturally from a groupoid (a set with a binary operation). In this paper we provide some general results on the associative-commutative spectrum, precisely determine this measure for certain binary operations, and propose some problems for future study.
- Consistency of Decision in Finite and Numerable Multinomial ModelsPublication . Akoto, Isaac; Mexia, João T.; CMA - Centro de Matemática e Aplicações; MDPI - Multidisciplinary Digital Publishing InstituteThe multinomial distribution is often used in modeling categorical data because it describes the probability of a random observation being assigned to one of several mutually exclusive categories. Given a finite or numerable multinomial model (Formula presented.) whose decision is indexed by a parameter (Formula presented.) and having a cost (Formula presented.) depending on (Formula presented.) and on (Formula presented.), we show that, under general conditions, the probability of taking the least cost decision tends to 1 when n tends to ∞, i.e., we showed that the cost decision is consistent, representing a Statistical Decision Theory approach to the concept of consistency, which is not much considered in the literature. Thus, under these conditions, we have consistency in the decision making. The key result is that the estimator (Formula presented.) with components (Formula presented.), where (Formula presented.) is the number of times we obtain the ith result when we have a sample of size n, is a consistent estimator of (Formula presented.). This result holds both for finite and numerable models. By this result, we were able to incorporate a more general form for consistency for the cost function of a multinomial model.
- Online Lifetime Prediction for Lithium-Ion Batteries with Cycle-by-Cycle Updates, Variance Reduction, and Model EnsemblingPublication . Strange, Calum; Ibraheem, Rasheed; dos Reis, Gonçalo; CMA - Centro de Matemática e Aplicações; MDPI - Multidisciplinary Digital Publishing InstituteLithium-ion batteries have found applications in many parts of our daily lives. Predicting their remaining useful life (RUL) is thus essential for management and prognostics. Most approaches look at early life prediction of RUL in the context of designing charging profiles or optimising cell design. While critical, said approaches are not directly applicable to the regular testing of cells used in applications. This article focuses on a class of models called ‘one-cycle’ models which are suitable for this task and characterized by versatility (in terms of online prediction frameworks and model combinations), prediction from limited input, and cells’ history independence. Our contribution is fourfold. First, we show the wider deployability of the so-called one-cycle model for a different type of battery data, thus confirming its wider scope of use. Second, reflecting on how prediction models can be leveraged within battery management cloud solutions, we propose a universal Exponential-smoothing (e-forgetting) mechanism that leverages cycle-to-cycle prediction updates to reduce prediction variance. Third, we use this new model as a second-life assessment tool by proposing a knee region classifier. Last, using model ensembling, we build a “model of models”. We show that it outperforms each underpinning model (from in-cycle variability, cycle-to-cycle variability, and empirical models). This ‘ensembling’ strategy allows coupling explainable and black-box methods, thus giving the user extra control over the final model.
- The Use of Generalized Means in the Estimation of the Weibull Tail CoefficientPublication . Caeiro, Frederico; Henriques-Rodrigues, Lígia; Gomes, M. Ivette; CMA - Centro de Matemática e Aplicações; WileyDue to the specificity of the Weibull tail coefficient, most of the estimators available in the literature are based on the log excesses and are consequently quite similar to the estimators used for the estimation of a positive extreme value index. The interesting performance of estimators based on generalized means leads us to base the estimation of the Weibull tail coefficient on the power mean-of-order-p. Consistency and asymptotic normality of the estimators under study are put forward. Their performance for finite samples is illustrated through a Monte Carlo simulation. It is always possible to find a negative value of p (contrarily to what happens with the mean-of-order-p estimator for the extreme value index), such that, for adequate values of the threshold, there is a reduction in both bias and root mean square error.
- Regression-type analysis for multivariate extreme valuesPublication . de Carvalho, Miguel; Kumukova, Alina; dos Reis, Gonçalo; CMA - Centro de Matemática e Aplicações; SpringerThis paper devises a regression-type model for the situation where both the response and covariates are extreme. The proposed approach is designed for the setting where the response and covariates are modeled as multivariate extreme values, and thus contrarily to standard regression methods it takes into account the key fact that the limiting distribution of suitably standardized componentwise maxima is an extreme value copula. An important target in the proposed framework is the regression manifold, which consists of a family of regression lines obeying the latter asymptotic result. To learn about the proposed model from data, we employ a Bernstein polynomial prior on the space of angular densities which leads to an induced prior on the space of regression manifolds. Numerical studies suggest a good performance of the proposed methods, and a finance real-data illustration reveals interesting aspects on the conditional risk of extreme losses in two leading international stock markets.
- A flexible split‐step scheme for solving McKean‐Vlasov stochastic differential equationsPublication . Chen, Xingyuan; dos Reis, Gonçalo; CMA - Centro de Matemática e Aplicações; ElsevierWe present an implicit Split-Step explicit Euler type Method (dubbed SSM) for the simulation of McKean-Vlasov Stochastic Differential Equations (MV-SDEs) with drifts of superlinear growth in space, Lipschitz in measure and non-constant Lipschitz diffusion coefficient. The scheme is designed to leverage the structure induced by the interacting particle approximation system, including parallel implementation and the solvability of the implicit equation. The scheme attains the classical 1/2 root mean square error (rMSE) convergence rate in stepsize and closes the gap left by [1] regarding efficient implicit methods and their convergence rate for this class of McKean-Vlasov SDEs. A sufficient condition for mean-square contractivity of the scheme is presented. Several numerical examples are presented, including a comparative analysis to other known algorithms for this class (Taming and Adaptive time-stepping) across parallel and non-parallel implementations.
- Review - "knees" in Lithium-Ion Battery Aging TrajectoriesPublication . Attia, Peter M.; Bills, Alexander; Brosa Planella, Ferran; Dechent, Philipp; dos Reis, Gonçalo; Dubarry, Matthieu; Gasper, Paul; Gilchrist, Richard; Greenbank, Samuel; Howey, David; Liu, Ouyang; Khoo, Edwin; Preger, Yuliya; Soni, Abhishek; Sripad, Shashank; Stefanopoulou, Anna G.; Sulzer, Valentin; CMA - Centro de Matemática e Aplicações; Electrochemical Society IncLithium-ion batteries can last many years but sometimes exhibit rapid, nonlinear degradation that severely limits battery lifetime. In this work, we review prior work on "knees"in lithium-ion battery aging trajectories. We first review definitions for knees and three classes of "internal state trajectories"(termed snowball, hidden, and threshold trajectories) that can cause a knee. We then discuss six knee "pathways", including lithium plating, electrode saturation, resistance growth, electrolyte and additive depletion, percolation-limited connectivity, and mechanical deformation - some of which have internal state trajectories with signals that are electrochemically undetectable. We also identify key design and usage sensitivities for knees. Finally, we discuss challenges and opportunities for knee modeling and prediction. Our findings illustrate the complexity and subtlety of lithium-ion battery degradation and can aid both academic and industrial efforts to improve battery lifetime.