ISEP - LEMA - Laboratório de Engenharia Matemática
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O LEMA (Laboratório de Engenharia Matemática), constituído por 12 investigadores Doutorados e 4 Mestres em doutoramento, é um grupo de investigação associado ao Centro de Matemática da Universidade do Porto (CMUP), com o objectivo de promover e organizar actividades de investigação em áreas de Matemática Aplicada, das Ciências da Engenharia e da Engenharia Matemática.
Sendo um grupo multidisciplinar, o LEMA desenvolve actividades em domínios da Análise Numérica, dos Sistemas Dinâmicos e da Modelação e Análise de Dados, predominantemente, aplicadas à resolução de problemas nas áreas de especialização de Engenharia do ISEP.
Entre os objectivos do LEMA estão a organização de acções de formação, de seminários, de reuniões científicas e de estágios dirigidos a alunos.
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- Classification Performance of Multilayer Perceptrons with Different Risk FunctionalsPublication . Silva, Luís; Santos, Jorge; Marques de Sá, JoaquimIn the present paper we assess the performance of information-theoretic inspired risks functionals in multilayer perceptrons with reference to the two most popular ones, Mean Square Error and Cross-Entropy. The information-theoretic inspired risks, recently proposed, are: HS and HR2 are, respectively, the Shannon and quadratic Rényi entropies of the error; ZED is a risk reflecting the error density at zero errors; EXP is a generalized exponential risk, able to mimic a wide variety of risk functionals, including the information-thoeretic ones. The experiments were carried out with multilayer perceptrons on 35 public real-world datasets. All experiments were performed according to the same protocol. The statistical tests applied to the experimental results showed that the ubiquitous mean square error was the less interesting risk functional to be used by multilayer perceptrons. Namely, mean square error never achieved a significantly better classification performance than competing risks. Cross-entropy and EXP were the risks found by several tests to be significantly better than their competitors. Counts of significantly better and worse risks have also shown the usefulness of HS and HR2 for some datasets.
- E-local pseudovarietiesPublication . Moura, AnaGeneralizingapropertyofthepseudovarietyofallaperiodicsemi- groups observed by Tilson, we call E-local a pseudovariety V which satisfies the following property: for a finite semigroup, the subsemigroup generated by its idempotents belongs to V if and only if so do the subsemigroups generated by the idempotents in each of its regular D-classes. In this paper, we present sev- eral sufficient or necessary conditions for a pseudovariety to be E-local or for a pseudoidentity to define an E-local pseudovariety. We also determine several examples of the smallest E-local pseudovariety containing a given pseudovariety.
- Fuzzy modelling of prescribed burning effects on soil physical propertiesPublication . Carvalho, João P.; Meira Castro, Ana C.This paper presents the preliminary work of an approach where Fuzzy Boolean Nets (FBN) are being used to extract qualitative knowledge regarding the effect of prescribed fire burning on soil chemical physical properties. FBN were chosen due to the scarcity on available quantitative data.
- High-Content Analysis of Breast Cancer Using Single-Cell Deep Transfer LearningPublication . Kandaswamy, C.; Silva, L. M.; Alexandre, L. A.; Santos, Jorge M.High-content analysis has revolutionized cancer drug discovery by identifying substances that alter the phenotype of a cell, which prevents tumor growth and metastasis. The high-resolution biofluorescence images from assays allow precise quantitative measures enabling the distinction of small molecules of a host cell from a tumor. In this work, we are particularly interested in the application of deep neural networks (DNNs), a cutting-edge machine learning method, to the classification of compounds in chemical mechanisms of action (MOAs). Compound classification has been performed using image-based profiling methods sometimes combined with feature reduction methods such as principal component analysis or factor analysis. In this article, we map the input features of each cell to a particular MOA class without using any treatment-level profiles or feature reduction methods. To the best of our knowledge, this is the first application of DNN in this domain, leveraging single-cell information. Furthermore, we use deep transfer learning (DTL) to alleviate the intensive and computational demanding effort of searching the huge parameter's space of a DNN. Results show that using this approach, we obtain a 30% speedup and a 2% accuracy improvement.
- Idempotent-generated semigroups and pseudovarietiesPublication . Almeida, Jorge; Moura, AnaThe operator which constructs the pseudovariety generated by the idempotent-generated semigroups of a given pseudovariety is investigated. Several relevant examples of pseudovarieties generated by their idempotent- generated elements are given as well as some properties of this operator. Particular attention is paid to the pseudovarieties in {J, R, L, DA} concerning this operator and their generator ranks and idempotent-generator ranks.
- Interdisciplinary Team WorkPublication . Abreu, Stella; Caldeira, Amélia; Costa, Alexandra R.; Gomes, Tiago; Roque, Luis A.C.In this work, we describe an interdisciplinary teaching experiment involving three subjects of the scientific area of Mathematics and a fourth one in the area of Management. Using only one project, the students developed skills, in an integrated way, in the fields of the subjects involved. The structure of the project is described in detail. It is shown how the knowledge obtained in the different subjects is needed and how it connects together to answer the proposed challenges. We report the progress of the students’ work, the main difficulties and the skills developed during this process. We conclude with a reflection on the main problems and gains that may arise in projects of this kind.
- Lambert W functions in the analysis of nonlinear dynamics and bifurcations of a 2D γ-Ricker Population ModelPublication . Rocha, J. Leonel; Taha, Abdel-Kaddous; Abreu, StellaThe aim of this paper is to study the use of Lambert W functions in the analysis of nonlinear dynamics and bifurcations of a new two-dimensional 𝛾-Ricker population model. Through the use of such transcendental functions, it is possible to study the fixed points and the respective eigenvalues of this exponential diffeomorphism as analytical expressions. Consequently, the maximum number of fixed points is proved, depending on whether the Allee effect parameter 𝛾 is even or odd. In addition, the analysis of the bifurcation structure of this 𝛾-Ricker diffeomorphism, also taking into account the parity of the Allee effect parameter, demonstrates the results established using the Lambert W functions. Numerical studies are included to illustrate the theoretical results.
- A Mathematical Model for Supermarket Order PickingPublication . Costa e Silva, Eliana; Cruz, Manuel; Lopes, Isabel Cristina; Moura, AnaOrder picking consists in retrieving products from storage locations to sat- isfy independent orders from multiple customers. It is generally recognized as one of the most significant activities in a warehouse (Koster et al, 2007). In fact, order picking accounts up to 50% (Frazelle, 2001) or even 80% (Van den Berg, 1999) of the total warehouse operating costs. The critical issue in today’s business environ- ment is to simultaneously reduce the cost and increase the speed of order picking. In this paper, we address the order picking process in one of the Portuguese largest companies in the grocery business. This problem was proposed at the 92nd European Study Group with Industry (ESGI92). In this setting, each operator steers a trolley on the shop floor in order to select items for multiple customers. The objective is to improve their grocery e-commerce and bring it up to the level of the best inter- national practices. In particular, the company wants to improve the routing tasks in order to decrease distances. For this purpose, a mathematical model for a faster open shop picking was developed. In this paper, we describe the problem, our proposed solution as well as some preliminary results and conclusions.
- Numerical solution of a PDE system with non-linear steady state conditions that translates the air stripping pollutants removalPublication . Meira Castro, Ana C.; Matos, José; Gavina, A.This work deals with the numerical simulation of air stripping process for the pre-treatment of groundwater used in human consumption. The model established in steady state presents an exponential solution that is used, together with the Tau Method, to get a spectral approach of the solution of the system of partial differential equations associated to the model in transient state.
- Optimization process of polyester polymer mortars modified with recycled GFRP waste aggregates – application of factorial experiment design-Publication . Ribeiro, M. C. S.; Fiúza, António; Dinis, M. L.; Meira Castro, Ana C.; Silva, F.J.G.; Costa, C.; Ferreira, F.Glass fibre-reinforced plastics (GFRP), nowadays commonly used in the construction, transportation and automobile sectors, have been considered inherently difficult to recycle due to both: cross-linked nature of thermoset resins, which cannot be remolded, and complex composition of the composite itself, which includes glass fibres, matrix and different types of inorganic fillers. Presently, most of the GFRP waste is landfilled leading to negative environmental impacts and supplementary added costs. With an increasing awareness of environmental matters and the subsequent desire to save resources, recycling would convert an expensive waste disposal into a profitable reusable material. There are several methods to recycle GFR thermostable materials: (a) incineration, with partial energy recovery due to the heat generated during organic part combustion; (b) thermal and/or chemical recycling, such as solvolysis, pyrolisis and similar thermal decomposition processes, with glass fibre recovering; and (c) mechanical recycling or size reduction, in which the material is subjected to a milling process in order to obtain a specific grain size that makes the material suitable as reinforcement in new formulations. This last method has important advantages over the previous ones: there is no atmospheric pollution by gas emission, a much simpler equipment is required as compared with ovens necessary for thermal recycling processes, and does not require the use of chemical solvents with subsequent environmental impacts. In this study the effect of incorporation of recycled GFRP waste materials, obtained by means of milling processes, on mechanical behavior of polyester polymer mortars was assessed. For this purpose, different contents of recycled GFRP waste materials, with distinct size gradings, were incorporated into polyester polymer mortars as sand aggregates and filler replacements. The effect of GFRP waste treatment with silane coupling agent was also assessed. Design of experiments and data treatment were accomplish by means of factorial design and analysis of variance ANOVA. The use of factorial experiment design, instead of the one factor at-a-time method is efficient at allowing the evaluation of the effects and possible interactions of the different material factors involved. Experimental results were promising toward the recyclability of GFRP waste materials as polymer mortar aggregates, without significant loss of mechanical properties with regard to non-modified polymer mortars.