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作者： Martins, Natália Torres, Delfim F.M. Center for Research and Development in Mathematics and Applications Department of Mathematics University of Aveiro 3810-193 Aveiro Portugal

关键词： Difference equations

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Oscillatory Behaviour on a Non-autonomous Hybrid SIR-Model 1

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1st International Symposium on Molecular Logic and Computational Synthetic Biology, MLCSB 2018

作者： Rocha, Eugénio M. Center for Research and Development in Mathematics and Applications Department of Mathematics University of Aveiro Aveiro3810-193 Portugal

ISBN: (数字)9783030194321

ISBN: (纸本)9783030194314

We study the impact of some abstract agent intervention on the disease spread modelled by a SIR-model with linear growth infectivity. The intervention is meant to decrease the infectivity, which are activated by a threshold on the number of infected individuals. The coupled model is represented as a nonlinear non-autonomous hybrid system. Stability and reduction results are obtained using the notions of non-autonomous attractors, Bohl exponents, and dichotomy spectrum. Numerical examples are given where the number of infected individuals can oscillate around a equilibrium point or be a succession of bump functions, which are validated with a tool based on the notion of δ -complete decision procedures for solving satisfiability modulo theories problems over the real numbers and bounded δ -reachability. These findings seem to show that hybrid SIR-models are more flexible than standard models and generate a vast set of solution profiles. It also raises questions regarding the possibility of the agent intervention been somehow responsible for the shape and intensity of future outbreaks. © 2019, Springer Nature Switzerland AG.

关键词： Hybrid systems

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Spectral bounds for the k-regular induced subgraph problem 1

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International Conference on Matrix Analysis and its applications, MAT-TRIAD 2015

作者： Cardoso, Domingos Moreira Pinheiro, Sofia J. Center for Research and Development in Mathematics and Applications Department of Mathematics University of Aveiro Aveiro3810-193 Portugal

ISBN: (数字)9783319499840

ISBN: (纸本)9783319499826

Many optimization problems on graphs are reduced to the determination of a subset of vertices of maximum cardinality which induces a k-regular subgraph. For example, a maximum independent set, a maximum induced matching and a maximum clique is a maximum cardinality 0-regular, 1-regular and (ω(G) − 1)-regular induced subgraph, respectively, were ω(G) denotes the clique number of the graph G. The determination of the order of a k-regular induced subgraph of highest order is in general an NP-hard problem. This paper is devoted to the study of spectral upper bounds on the order of these subgraphs which are determined in polynomial time and in many cases are good approximations of the respective optimal solutions. The introduced upper bounds are deduced based on adjacency, Laplacian and signless Laplacian spectra. Some analytical comparisons between them are presented. Finally, all of the studied upper bounds are tested and compared through several computational experiments. © Springer International Publishing AG 2017.

关键词： Combinatorial optimization

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Comparison of Feature Selection Methods in Regression Modeling: A Simulation Study 23rd

Comparison of Feature Selection Methods in Regression Modeli...

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23rd International Conference on Computational Science and Its applications, ICCSA 2023

作者： Afreixo, Vera Cabral, Jorge Macedo, Pedro CIDMA – Center for Research and Development in Mathematics and Applications Department of Mathematics University of Aveiro Aveiro3810-193 Portugal

ISBN: (纸本)9783031371288

This simulation study explores the impact of different undesirable scenarios (e.g., collinearity, Simpson’s paradox, variable interaction, Freedman’s paradox) on feature selection and coefficients’ estimation using traditional methodologies, such as automatic selection (e.g., stepwise using Akaike information criterion and Bayesian information criterion) and penalized regression (e.g., least absolute shrinkage and selection operator (LASSO), elastic net, relaxed LASSO, adaptive LASSO, minimax concave penalty and smoothly clipped absolute deviation penalty, penalized regression with second-generation p-values). Specifically, we compare wrapper and embedded methods regarding the feature selection, coefficients’ estimation and models’ performance. Our results show that the choice of the methodology can affect the number and the type of selected features, as well as accuracy and precision of coefficients’ estimates. Furthermore, we find that the performance can also depend on the characteristics of the data. © 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Feature Selection

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Conditioned invariance and detectability subspaces in the behavioral approach

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IFAC-PapersOnLine 2017年第1期50卷 687-692页

作者： Pereira R. Rocha P. CIDMA Center for Research and Development in Mathematics and Applications Department of Mathematics University of Aveiro Aveiro Portugal SYSTEC Faculty of Engineering University of Porto Portugal

In this paper we extend the state space geometric notions of conditioned invariance and detectability subspaces to the behavioral framework. This is achieved based on the existing notions of behavioral tracking observer and of behavioral asymptotic observer introduced by Valcher, Willems, Trentelman and Trumph, combined with a notion of behavioral invariance introduced here. Moreover, we provide characterizations for the newly defined behavioral properties. © 2017

关键词： Behavior conditioned-invariance detectability invariance observer

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Optimal control strategies for reducing the number of active infected individuals with tuberculosis

Optimal control strategies for reducing the number of active...

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SIAM Conference on Control and Its applications 2013

作者： Rodrigues, Paula Silva, Cristiana J. Torres, Delfim F.M. Department of Mathematics Center of Mathematics and Applications New University of Lisbon Caparica2829-516 Portugal CIDMA - Center for Research and Development in Mathematics and Applications Department of Mathematics University of Aveiro Aveiro3810-193 Portugal

ISBN: (纸本)9781510813298

We propose and analyze an optimal control problem where the control system is a mathematical model for tuberculosis (TB) with different post-exposure interventions considered. We analyze the impact of transmission intensity on the control interventions and show that optimal control solutions reduce the number of active TB cases. © Copyright SIAM.

关键词： Optimal control systems

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PLAY2ESCAPE - A DIGITAL ESCAPE ROOM IN MATH CLASSES FOR UNDERGRADUATE TOURISM STUDENTS - CASE STUDY 18

PLAY2ESCAPE - A DIGITAL ESCAPE ROOM IN MATH CLASSES FOR UNDE...

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18th International Conference on e-Learning and Digital Learning, ELDL 2024 and 12th International Conference on Sustainability, Technology and Education, STE 2024, Part of the 18th Multi Conference on Computer Science and Information Systems 2024, MCCSIS 2024

作者： Pais, Sónia Sousa, Ana Elisa Lopes, Maria Sofia CIDMA - Center for Research and Development in Mathematics and Applications University of Aveiro Portugal CITUR - Centre for Tourism Research Development and Innovation Polytechnic of Leiria Portugal

ISBN: (纸本)9789898704573

The younger generation, particularly those born in the late 20th and early 21st centuries known as "Generation Z," are deeply integrated with technologies in their daily live. Developing a better understanding of how such technologies influence learning is important to pedagogical approaches designed to co-opt technological applications in novel strategies for teaching and self-learning. Educational technology offers numerous advantages, including: enhancing students' learning experiences, increasing motivation and ultimately, improving student performance. Recognising these advantages, an educational resource was developed, where students explore their problem-solving skill in digital escape room. This paper presents a case study of first-year undergraduate students from a Portuguese higher education institution using a math-related digital escape room intended to increase students' interest and motivation. The aim of the study is to assess how the escape rooms contributes to student motivation, interest and the consolidation of learning. Assessment of students’ perception was based on a quantitative survey and on the results of an evaluation test. Our findings suggest that Escape Room represent an effective educational approach that increases student interest and helps consolidate learning. © 2024 e-Learning and Digital Learning. All Rights Reserved.

关键词： Contrastive Learning

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A Sturm-Liouville equation on the crossroads of continuous and discrete hypercomplex analysis

A Sturm-Liouville equation on the crossroads of continuous a...

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作者： Cação, Isabel Falcão, M. Irene Malonek, Helmuth R. Tomaz, Graça University of Aveiro Center for Research and Development in Mathematics and Applications Aveiro Portugal University of Minho Centre of Mathematics Braga Portugal Polytechnic of Guarda Research Unit for Inland Development Guarda Portugal

The paper studies discrete structural properties of polynomials that play an important role in the theory of spherical harmonics in any dimensions. These polynomials have their origin in the research on problems of harmonic analysis by means of generalized holomorphic (monogenic) functions of hypercomplex analysis. The Sturm-Liouville equation that occurs in this context supplements the knowledge about generalized Vietoris number sequences (Formula presented.), first encountered as a special sequence (corresponding to (Formula presented.)) by Vietoris in connection with positivity of trigonometric sums. Using methods of the calculus of holonomic differential equations, we obtain a general recurrence relation for (Formula presented.), and we derive an exponential generating function of (Formula presented.) expressed by Kummer's confluent hypergeometric function. © 2021 John Wiley & Sons, Ltd.

关键词： Polynomials

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The q-symmetric variational calculus

The q-symmetric variational calculus

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作者： Brito Da Cruz, Artur M.C. Martins, Natália Escola Superior de Tecnologia de Setúbal Estefanilha 2910-761 Setúbal Portugal Center for Research and Development in Mathematics and Applications University of Aveiro 3810-193 Aveiro Portugal Center for Research and Development in Mathematics and Applications Department of Mathematics University of Aveiro 3810-193 Aveiro Portugal

We bring a new approach to the study of quantum calculus and introduce the q-symmetric variational calculus. We prove a necessary optimality condition of Euler-Lagrange type and a sufficient optimality condition for symmetric quantum variational problems. The results are illustrated with an example. © 2012 Elsevier Ltd. All rights reserved.

关键词： Variational techniques

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When Games get in the way: Gamification Approach for Teaching Maths – A Case Study With Undergraduate Tourism Students 18

When Games get in the way: Gamification Approach for Teachin...

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18th European Conference on Games Based Learning, ECGBL 2024

作者： Pais, Sónia Hall, Andreia CIDMA Center for Research and Development in Mathematics and Applications University of Aveiro Aveiro Portugal CITUR – Centre for Tourism Research Development and Innovation Polytechnic Institute of Leiria Leiria Portugal

ISBN: (纸本)9781917204194

Planning more dynamic and motivating lessons for students is the goal of any teacher, especially maths teachers, a subject where the lack of interest and motivation to learn is so evident and a major concern. Several studies highlight the positive impact of the adoption of gamification strategies in teaching/learning, both in student motivation and in the development of soft skills (teamwork, creativity, decision-making, leadership, communication, and critical thinking). Game-based learning thus promotes students' interest and involves them in this process. In this sense, one of the authors of this study chose to use several (non-digital) games to support the teaching-learning process in her classes. The games used were developed by the authors and have been thoroughly designed to address specific maths topics. The games took various forms, including card games, board games and other hands-on activities. The participants in the study are first-year undergraduate students from a Portuguese higher education institution and encompassed the course of "Quantitative Methods". The aim of the study is to investigate students’ perceptions of the use of gamification in the maths teaching-learning process. To gather information about students’ insights on the use of games in math classes a quantitative survey was conducted. Similar studies have shown that higher education students are usually receptive to the use of games, finding it useful to increase their motivation and consider game-based learning can positively impact learning. Our findings are in line with those studies. © 2024 Dechema e.V.. All rights reserved.

关键词： Students

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