Book of Abstractsiiiwcdanm2016.yolasite.com/resources/BOOK of ABSTRACTS.pdf · Distance sampling using the minimum description length principle Fernando Ceia 1,2 and Russell Alpizar-Jara

Program Committee

Cristina Dias - Instituto Politécnico de Portalegre, Portugal

João Miranda - Instituto Politécnico de Portalegre, Portugal

Adelaide Proença - Instituto Politécnico de Portalegre, Portugal

Carla Santos - Instituto Politécnico de Beja, Portugal

Luís Grilo - Instituto Politécnico de Tomar, Portugal

Fernando Carapau - Universidade de Évora, Portugal

Portalegre, Portugal

i

Title:

III Workshop on Computational Data Analysis and Numerical Methods- Book of abstracts

(suporte eletrónico)

Publisher:

Instituto Politécnico de Portalegre

Praça do Município, 7300 Portalegre

Editors:

Carla Santos, Cristina Dias, Fernando Carapau e Luís Grilo

Copyright © 2016 left to the authors of individual papers

All rights reserved

ISBN: 978-989-8806-13-0

ii

WELCOME TO THE WCDANM 2016

Dear Participants, Colleagues and Friends,

it is a great honour and a privilege to give you all our warmest welcome to the third Annual Workshop of

Computational Data Analysis and Numerical Methods (III WCDANM).

This Workshop is being held at the beautiful campus of Instituto Politécnico de Portalegre, located in the city of

Portalegre, Portugal. The host institution, has been fully committed on this challenge from the beginning, and

we do hope that the final result exceed expectations for participants, sponsors and organizers. We wish to thank

specially to them, as this event could not be possible without any of these essential parts.

The support from sponsors, the availability and contributions from Invited speakers, the high scientific level of

oral and poster presentations from participants and, at the end, curious, active and interested assistants, will

contribute to the success of the meeting. From the organizing committee we want also to thank them for their

continuous help and implication in the effort. Finally, our gratitude to the members of the scientific and

organizing committees that have been working together hard to yield a balanced, wide-scoped and interesting

programme. Special thanks to the Local Chair Cristina Dias (Instituto Politécnico de Portalegre), Carla Santos

(Instituto Politécnico de Beja) and Fernando Carapau (Universidade de Évora), who have been in charge of many

tasks, and have fulfilled a brilliant labour.

As in previous meetings, Computational Data Analysis and Numerical Methods will be approached by recognized

experts in specific fields. The CDANM Workshop series is unique in that it brings together researchers from all

over the country who use Data analysis and Numerical methods in their research with particular interest in

applications.

We hope that you enjoy the Workshop and find it intellectually stimulating. We wish that it could provide an

opportunity for the “mathematical” community to work together and to plan new initiatives.

We are very happy you have joined us in Portalegre and hope you have a memorable time!

Portalegre, November 18th, 2016.

Luís Miguel Grilo

Chair of the WCDANM Instituto Politécnico de Tomar

iii

Committees Scientific Committee

Amílcar Oliveira - Universidade Aberta, Portugal


Célia Nunes - Universidade da Beira Interior, Portugal


Dário Ferreira - Universidade da Beira Interior, Portugal


Filomena Teodoro - Escola Naval, Portugal



Manuel Branco - Universidade de Évora

Sandra Ferreira - Universidade da Beira Interior, Portugal

Teresa Oliveira - Universidade Aberta, Portugal

Program Committee



Adelaide Proença - Instituto Politécnico de Portalegre, Portugal




Sponsored by

iv

SCIENTIFIC PROGRAM 10h00 - 10h30 Registration and Icebreak

10h30m Opening Ceremony Room: Anfiteatro E1

11h00 - 12h30 Parallel Sessions M1 and M2

Parallel Session M1 Chair: Luis Grilo (I.P. Tomar & CMA - FCT/UNL, Portugal) Room Anfiteatro E1

Fernando Ceia and Russell Alpizar-Jara Distance sampling using the minimum description length principle

Amilcar Oliveira and Teresa A. Oliveira p-Charts and np-Charts for Attribute Control based on Life Distributions

Luis M. Grilo Exploratory factor analysis in burnout state

M. Filomena Teodoro, Mariana A. P. Andrade, Eliana Costa e Silva and Ana Borges Modeling electricity prices

Parallel Session M2 Chair: Teresa Oliveira (Univ.Aberta, Portugal) Room Sala E2

Carlos Ramos Animal movement: symbolic dynamics and topological classification

Sandra Nunes An Introduction to Item Response Theory

Ana Nata and Natália Bebiano Numerical range of a linear pencil

Teresa Oliveira Topics on Problem-Based Learning in e-Learning

12h30 - 14h00 Lunch

14h00 - 15h00 Parallel Sessions T1 and T2

Parallel Session T1 Chair: Fernando Carapau (Univ. Évora & CIMA- UÉvora, Portugal) Room Anfiteatro E1

Santiago Vila A modified Levenberg-Marquardt method to estimate the radius of convergence of a power series

Fernando Carapau and Paulo Correia A new one-dimensional model for blood flow based on Cosserat theory

Luis Bandeira and Pablo Pedregal Quasiconvexity and Rank-One Convexity of Polynomials

Manuel Branco and J. C. Rosales On the enumeration of the set of elementary numerical semigroups with fixed multiplicity, Frobenius number or genus

Parallel Session T2 Chair: Cristina Dias (I.P. Portalegre & CMA - FCT/UNL, Portugal) Room Sala E2

João Miranda Mathematics for European Research and Education: Some Challenging Trends?

Carla Santos, Célia Nunes, Cristina Dias and João T. Mexia Obtaining COBS from the extension of a balanced mixed model

Cristina Dias, Carla Santos, João Miranda, and João T. Mexia Study of the Relative Relevances associated to a strongly first eingenvalue

Célia Nunes, Gilberto Capistrano, Anacleto Mário, Dário Ferreira, Sandra S. Ferreira and João T. Mexia Occurrences of failures in ANOVA

15h00 - 15h45 Coffee Break

16h00 – SOCIAL PROGRAM - Visit to the Museu da Tapeçaria de Portalegre, Guy

v

Abstracts

vi

Table of Contents

Distance sampling using the minimum description length principle 1

Fernando Ceia and Russell Alpizar-Jara

p-Charts and np-Charts for Attribute Control based on Life Distributions 2

Amílcar Oliveira and Teresa A. Oliveira

Exploratory factor analysis in burnout state 3

Luís M. Grilo

Modeling electricity prices 4

M. Filomena Teodoro, Mariana A. P. Andrade, Eliana Costa e Silva and

Ana Borges

Animal movement: symbolic dynamics and topological classification 5

Carlos Ramos

An Introduction to Item Response Theory 6

Sandra Nunes, Teresa Oliveira and Amílcar Oliveira

Numerical range of a linear pencil 8

Ana Nata and Natália Bebiano

Topics on Problem-Based Learning in e-Learning 9

Teresa Oliveira

A modified Levenberg-Marquardt method to estimate the radius of

convergence of a power series 11

Santiago Vila

A new one-dimensional model for blood ow based on Cosserat theory 12

Fernando Carapau and Paulo Correia

Quasiconvexity and Rank-One Convexity of Polynomials 13

Luís Bandeira and Pablo Pedregal

On the enumeration of the set of elementary numerical semigroups with fixed multiplicity,

Frobenius number or genus 14

Manuel B. Branco and J. C. Rosales

Mathematics for European Research and Education: Some Challenging Trends? 16

João Miranda and Cristina Dias

Obtaining COBS from the extension of a balanced mixed model 17

Carla Santos, Célia Nunes, Cristina Dias and João T. Mexia

Study of the Relative Relevances associated to a strongly first eingenvalue 18

Cristina Dias, Carla Santos, João Miranda, and João T. Mexia

Occurrences of failures in ANOVA 19

Célia Nunes, Gilberto Capistrano, Anacleto Mário, Dário Ferreira, Sandra

S.Ferreira and João T. Mexia

Distance sampling using the minimum description

length principle

Fernando Ceia1,2 and Russell Alpizar-Jara3,4

1Escola Basica Jose Regio Portalegre, [email protected] de Investigacao em Matematica e Aplicacoes, Instituto de Investigacao e

Formacao Avancada, Universidade de Evora3Departamento de Matematica, Escola de Ciencias e Tecnologia, Universidade de Evora,

[email protected] de Investigacao em Matematica e Aplicacoes, Instituto de Investigacao e

Formacao Avancada, Universidade de Evora

Abstract

Population density estimation in distance sampling requires fitting a probabilitydensity function denoted by f(y|θ), where y represents the perpendicular(ou radial) dis-tance from a detected animal (or object) to a transect line (or point), and θ representsthe vector parameter indexing this family of probability density functions. Currently,the most popular approach to estimate f(·), is based on a semi–parametric methodol-ogy proposed by [1]. The main idea is to find the maximum likelihood estimator for θusing a parametric functional form combined with a series expansion. We present an al-ternative approach based on the Minimum Description Length principle (MDL)[2], andits application to estimate a density function through a histogram [3]. This method-ology no longer need to assume an a priori parametric function to fit our data andvariable class intervals are also allowed, optimizing the number of class intervals andcompressing the available information at most.

Keywords: detectability function, distance sampling, normalized likelihood, stochasticcomplexity.

References

[1] Buckland, S. T. (1992). Maximum likelihood fitting of the Hermite and simple polyno-mials densities. Applied Statistics, 41, 241–266.

[2] Rissanen, J. (1978). Modeling by shortest data description. Automatica 14, 465–471.

[3] Kontkanen, P. and Myllymaki, P. (2006). Information–Theoretically Optimal HistogramDensity Estimation. Helsinki Institute for Information Technology. 10 p.

1

p-Charts and np-Charts for Attribute Control based on

Life Distributions

Amılcar Oliveira1,2 and Teresa A. Oliveira3,4

1Universidade Aberta, [email protected] of Statistics and Applications of University of Lisbon

3Universidade Aberta, [email protected] of Statistics and Applications of University of Lisbon

Abstract

In this talk we introduce charts for attribute control considering (i) the number ofdefective items, named np-charts; (ii) means of the proportion (p) of defective items,named p-charts. np-charts are preferable to the charts for proportion (p) of defectiveitems, when the sample size (n) remains constant for all of subgroups. The benefitsof using np-charts over p-charts are an easier interpretation and the fact that no cal-culation is required for each sample result. We provide an update for np-charts andsome recent ideas on the topic based on life distributions. When the sample size (n) isconstant, charts for attribute control related to the number (np) of defective items, area good alternative to the p-charts. An update for p-charts and some recent ideas onthe topic are provided considering life distributions. Implementations in the R softwareare discussed using examples.

Keywords: life distributions, p-charts, np-charts.

References

[1] Birnbaum, Z.W. and Saunders, S.C. (1969) A new family of life distributions, Journalof Applied Probability, 6, 319–327.

[2] Davis, D.J. (1952) An analysis of some failure data, Journal of American StatisticalAssociation, 47, 113–150.

[3] Efron, B. and Tibshirani, R.J. (1993) An Introduction to the Bootstrap, Chapman andHall, New York.

[4] Leiva, V., Soto, G., Cabrera, E. and Cabrera, G. (2011) New control charts based onthe Birnbaum-Saunders distribution and their implementation, Colombian Journal ofStatistics, 34, 147–176.

[5] Marshall, A.W. and Olkin, I. (2007) Life Distributions, Springer, New York.

[6] Montgomery, D.C. (2005) Introduction to Statistical Quality Control, Wiley, New York.

[7] Team (2014) R: A language and environment for statistical computing, R Foundationfor Statistical Computing, Vienna, Austria, available at URL www.R-project.org.

[8] Scrucca, L. (2004) qcc: an R package for quality control charting and statistical processcontrol, R Journal, 4, 11–17.

2

Exploratory factor analysis in burnout state

Luıs M. Grilo1,2

1Unidade Departamental de Matematica e Fısica, Instituto Politecnico de Tomar,[email protected]

2Centro de Matematica e Aplicacoes (CMA), Faculdade de Ciencias e Tecnologia daUniversidade Nova de Lisboa (FCT/UNL), Portugal

Abstract

Occupational burnout is characterized by excessive and continued psychologicalstress that affects some people in the workplace, leading them to feel emotionally andphysically exhausted. This state is also characterized by lack of enthusiasm/energy,motivation, engagement, and may have a dimension of frustration or cynicism, leadingto a reduction of effectiveness in labour. These symptoms, which have been growing inglobal terms, may occur in workers in any sector of activity (such as health, educationand services). Based on a sample obtained using a survey (internationally validated),applied to thousands of workers of a Portuguese business sector, we statistically analysesome ordinal variables in Likert scale, considering psychosocial dimension with epidemi-ological evidence for health. In particular, the relational structure of the variables isevaluated through exploratory factor analysis where two factors, which explain about60% of the total variance, are extracted. The first latent factor might be called ”firstdimension of burnout state”, as the five variables with greater weight are ”emotionalexhaustion”, ”anxiety”, ”physical exhaustion”, ”irritability” and ”feeling that the jobrequires a lot of energy which ultimately affect negatively private life”. The hierarchicalordination obtained is considered very useful by the doctors, during the clinical trialprocess of burnout state.

Keywords: Multivariate statistics, Psychological stress, Spearman’s rho.

References

[1] C. Maslach and M. P. Leiter, Early predictors of job burnout and engagement. Journalof Applied Psychology 93: 498–512 (2008).

[2] C. Maslach and M.P. Leiter, The truth about burnout. San Francisco: Jossey Bass,(1997).

[3] T. S. Kristensen, M. Borritz, E. Villadsen and K. B. Christensen, The CopenhagenBurnout Inventory: A new tool for the assessment of burnout. Work and Stress 19:192–207 (2005).

3

Modeling electricity prices

M. Filomena Teodoro1,2, Mariana A. P. Andrade3, Eliana Costa e

Silva4 and Ana Borges4

1CINAV, Escola Naval - Marinha, 2810-001 ALMADA, [email protected]

2CEMAT, Center for Computational and Stochastic Mathematics, Instituto SuperiorTecnico, Universidade de Lisboa, 1048-001 LISBOA, Portugal

3UNIDE-IUL/ISCTE-Instituto Universitario de Lisboa, 1649-026 LISBOA, Portugal4CIICESI/ESTG - P.Porto, Margaride 4610-156 FELGUEIRAS, Portugal

Abstract

The electricity Operator EDP proposed a challenge about modeling electricity pricesat the 119th European Study Group with Industry. The presented work is a conse-quence of such problem. The diagnostics and data preparation process are described,a GLM predictive model is proposed [2]. Explanatory variables such as the season ofyear, working day/holiday, month, etc, are considered. To asses the in-sample fit of themodel it is used the square root error and mean absolute percentage error. The fore-cast performance of the model is quite reasonable. When compared with multivariateapproach using the VAR approach [1] for the same period , the RMSE values are inaccordance.

Keywords: Generalized Linear Models, times series, electricity prices forecasting.

References

[1] Silva, E. C. et al., Time Series Data Mining for Energy Prices: An application to realdata. Accepted to be published in Lecture Notes in Computer Science, Springer.

[2] Teodoro, M. F. et al., Electricity Prices Forecasting Using GLM. (Submitted)

4

Animal movement: symbolic dynamics and topological

classification

Carlos Ramos1,2

1Universidade de Evora, Departamento de Matematica, [email protected] de Investigacao em Matematica e Aplicacoes (CIMA)

Abstract

The study of animal movement has attracted much attention since Mandelbrotobserved that it shows scale invariance and fractal properties. The properties, of sta-tistical nature, manifest as a power law-like tail in the distribution of movement lengths.Most of the approaches in the literature follows these aspects, and have been appliedto several different animal movements, from bird flight, insect movement and humanmovement. We present a discrete dynamical system, deterministic, which serves as amodel to produce and classify a variety of types of movements, either two dimensionalor three dimensional. The dynamical system is determined by the iteration of a cubicinterval map, dependent on two real parameters. The complexity description and thecharacterization of the movements are based on the topological classification of thediscrete dynamical system, therefore is dependent on two parameters. Techniques fromsymbolic dynamics and topological Markov chains are used.

Keywords: Animal movement, discrete dynamical system, symbolic dynamics, statisticalproperties, topological classification.

References

[1] Mandelbrot, B. (1977) The Fractal Geometry of Nature (Freeman, New York).

[2] Viswanathan, G.M. et al. (1996) Levy Flight search patterns of wandering albatrosses.Nature 381, 413 – 415.

[3] Edwards, A.M. et al. (2007) Revisiting Levy Flight search patterns of wandering alba-trosses, bumblebees and deer. Nature 449, 1044 – 1048.

[4] Mashanova A, Oliver TH, Jansen VAA (2010) Evidence for intermittency and a truncatedpower law from highly resolved aphid movement data. J R Soc Interface 7, 199 – 208.

[5] Brockmann D, Hufnagel L, Geisel T (2006) The scaling laws of human travel. Nature439, 462 – 465.

[6] Turchin P (1996) Fractal analyses of animal movement: A critique. Ecology 77, 2086 –2090.

[7] Sergei Petrovskiia, Alla Mashanovab, and Vincent A. A. Jansen (2011), PNAS,vol. 108,no. 21, 8704 – 8707.

5

An Introduction to Item Response Theory

Sandra Nunes1, Teresa Oliveira2 and Amılcar Oliveira2

1College of Business Administration (ESCE) of Polytechnic Institute of Setubal (IPS),Campus do IPS – Estefanilha, Setubal, Portugal, [email protected]

2Universidade Aberta, Palacio Ceia, Rua da Escola Politecnica, Lisboa, and Center ofStatistics and Applications, University of Lisbon, Portugal

Abstract

The Item Response Theory (IRT) has become one of the most popular scoring frame-works for measurement data, frequently used in computerized adaptive testing, cogni-tively diagnostic assessment and test equating. According to Andrade et al. (2000),IRT can be defined as a set of mathematical models (Item Response Models – IRM) con-structed to represent the probability of an individual giving the right answer to an itemof a particular test. The number of Item Responsible Models available to measurementanalysis has increased considerably in the last fifteen years due to increasing computerpower and due to a demand for accuracy and more meaningful inferences groundedin complex data. The developments in modeling with Item Response Theory were re-lated with developments in estimation theory, most remarkably Bayesian estimationwith Markov chain Monte Carlo algorithms (Patz and Junker, 1999). The popularityof Item Response Theory has also implied numerous overviews in books and journals,and many connections between IRT and other statistical estimation procedures, suchas factor analysis and structural equation modeling, have been made repeatedly (Vander Lindem and Hambleton, 1997). The Item Response Theory covers a variety ofmeasurement models, ranging from basic one-dimensional models for dichotomouslyand polytomously scored items and their multidimensional analogues to models thatincorporate information about cognitive sub-processes which influence the overall itemresponse process. The aim of this work is to introduce the main concepts associatedwith one-dimensional models of Item Response Theory, to specify the logistic modelswith one, two and three parameters, to discuss some properties of these models and topresent the main estimation procedures.

Keywords:

References

[1] Andrade, D.F., Tavares, H.R. and Valle, R.C.(2000) Teoria da resposta ao Item: Con-ceitos e Aplicacoes. SINAPE. Associacao Brasileira de Estatıstica.

[2] Baker, F.B. (2001) The Basics of Item Response Theory (2nd edition). ERIC Clearing-house on Assessment and Evaluation, USA.

[3] Birnbaum, A.(1968) Some Latent Trait Models and Their Use in Inferring an Exami-nee’s Ability. In F.M. Lord and M.R. Novick. Statistical Theories of Mental Test Scores.Reading, MA: Addison-Wesley.

6

[4] Hambleton, R.K., Swaminathan, H. and Rogers, H.J.(1991) Fundamentals of Item Re-sponse Theory. Sage Publications Inc.

[5] Patz, R.J. and Jumker, B.W.(1999) A straightforward approach to Markov chain MonteCarlo methods for item response models. Journal of Educational and Behavioral Statis-tics, 24, pp. 146-178.

[6] Rasch, G. (1960)Probabilistic Models for Some Intelligence and Attainment Tests.Copenhagen: Danish Institute for Educational Research.

[7] Reise, SP and Revicki, D.A.(2015) Handbook of Item Response Theory Modeling. Ap-plications to Typical Performance Assessment. Taylor and Francis.

[8] Samejima, F. A.(1969) Estimation of latent ability using a response pattern of gradedscores. Psychometric Monograph, 17.

[9] Van der Linden, W.J. and Hambleton, R.K.(1997) Handbook of Modern Item ResponseTheory. New-York: Springer-Verlag.

[10] Zimowski, M. F., Muraki, E., Mislevy, R. J. and Bock, R.D.(1996) BILOG-MG:Multiple-Group IRT Analysis and Test Maintenance for Binary Items. Chicago: Sci-entific Software, Inc..

7

Numerical range of a linear pencil

Ana Nata1,2 and Natalia Bebiano3,2

1Polytechnic Institute of Tomar, Portugal, [email protected] - Centro de Matematica da Universidade de Coimbra

3Department of Mathematics, University of Coimbra, Portugal, [email protected]

Abstract

The study of linear pencils has a rich and long history that goes back to Weier-strass and Kronecker in the nineteenth century, usually in the context of their spectralanalysis. A complex number λ is said to be an eigenvalue of the pencil if there existsa nonzero x ∈ ❈n such that Ax = λBx. The problem of finding the eigenvalues of apencil is called the generalized eigenvalue problem.

Consider a linear matrix pencil A−λB, where A or B is Hermitian and λ ∈ ❈. Weinvestigate some spectral inclusion regions for A−λB based on the numerical range ofcertain matrices.

By definition, the numerical range of the linear pencil A−λB is denoted and definedas

W (A,B) = {λ ∈ ❈ : x∗(A− λB)x = 0, x ∈ ❈n, ‖x‖ = 1},

where ‖x‖ =√

〈x, x〉 =√x∗x is the usual Euclidean norm in ❈n.

Keywords: numerical range, linear matrix pencil, eigenvalues, matrix compression.

References

[1] CHIEN, Mao-Ting, NAKAZATO, H. (2002) The numerical range of linear pencils of2-by-2 matrices. Linear Algebra and its Applications, 341, 69–100.

[2] PSARRAKOS, P. J. (2000). Numerical range of linear pencils. Linear Algebra Appl. 317,127–1241.

[3] UHLIG, F. (2013) Faster and more accurate computation of the field of values boundaryfor n by n matrices. Linear and Multilinear Algebra, 62, 554–567.

8

Topics on Problem-Based Learning in e-Learning

Teresa A. Oliveira1 and Amılcar Oliveira2 and Sandra Nunes3

1Universidade Aberta and Center of Statistics and Applications of University of Lisbon,Portugal, [email protected]

2Universidade Aberta and Center of Statistics and Applications of University of Lisbon,Portugal, [email protected]

3College of Business Administration (ESCE) of Polytechnic Institute of Setubal (IPS),Campus do IPS – Estefanilha, Setubal, Portugal, [email protected]

Abstract

Problem Based Learning (PBL) is a very promising teaching methodology allowingto improve the student’s autonomy and skills. If applied in master and post-graduatecourses of Statistics and Mathematics online, this methodology allow the students toface problems with high complexity and let them discover their own knowledge gaps.Thus it allows to foster a researcher attitude in the students and provides much morethan theoretical knowledge transmission and practical interactions between students atthe platform. In PBL the student has to face real complex problems and to look forthe best way to solve it, looking by himself for the proper tools and methods, underthe professor’s supervision. The rule of using PBL in e-Learning courses provides toall very nice experiences and many times the professor is positively surprised by thestudents, thanks to the new and original ways they find to reach the best solutions.Before designing an official proposal for applying this technique in our institutions,we decided to conduct a survey to provide us with the necessary information aboutit, including the respective advantages and disadvantages. For that, this methodologywas applied in the curricular unit of “Computational Statistics” which is a commonone of both courses - the Master on Statistics, Mathematics and Computation andthe Master on Biostatistics and Biometry of UAb (Universidade Aberta). The aim ofimplementing PBL to our classes is to increase the statistical and computational skillsof the near future professionals of these areas in Portugal. As further developments itis our aim to design a project in order to compare results of using PBL in e-Learning,b-Learning and face-to-face classes, in different courses and in different institutions.

References

[1] BOUD, D. & FELETTI, G. (1997) The challenge of problem-based learning (2nd ed.).London: Kogan Page.

[2] DE SIMONE, C. (2014) Problem-Based Learning in Teacher Education: Trajectoriesof Change. International Journal of Humanities and Social Science, Vol. 4, No. 12, pp.17–29.

[3] DERRY, S. J., HMELO-SILVER, C. E., NAGARAJAN, A., CHERNOBILSKY, E., &BEITZEL, B. (2006) Cognitive transfer revisited: Can we exploit new media to solveold problems on a large scale? Journal of Educational Computing Research, 35, pp.145–162.

9

[4] DUCH, B. J., GROH, S. E. & ALLEN, D. E. (2001). Why problem-based learning? Acase study of institutional change in undergraduate education. In B. Duch, S. Groh &D. Allen (Eds.). The power of problem-based learning. Sterling, VA: Stylus, pp. 3–11.

[5] ERICKSON, D. K. (1999) A problem-based approach to mathematics instruction. Math-ematics Teacher, 92 (6), pp. 516–521.

[6] GIJBELS, D., DOCHY, F., VAN DEN BOSSCHE, P. & SEGERS, M. (2005) Effectsof problem-based learning: A meta-analysis from the angle of assessment. Review ofEducational Research, 75, pp. 27-–61.

[7] HMELO-SILVER, C. E. (2004) Problem-based learning: What and how do studentslearn? Educational Psychology Review, 16(3), pp. 235–266.

[8] MCPHEE, A. (2002) Problem-based learning in initial teacher education: Taking theagenda forward. Journal of Educational Enquiry, 3, pp. 60–78.

[9] REGEHR, G. & NORMAN, G. R. (1996) Issues in cognitive psychology: implicationsfor professional education. Academic Medicine, 71(9), pp. 988–1001.

[10] ROH, K. H. (2003) Problem-Based Learning in Mathematics. ERIC Clearinghouse forScience Mathematics and Environmental Education, n. pag. ERIC Digest. Web. Sept.2012.

[11] SAVERY, J.R. (2006) Overview of Problem-Based Learning: Definitions and Distinc-tions. Interdisciplinary Journal of Problem-Based Learning, 181, pp. 9–20.

[12] SCHMIDT, H. G. (1993) Foundations of problem-based learning: some explanatorynotes. Medical Education, 27, pp. 422–432.

[13] SCHOENFELD, A. H. Mathematical problem solving. New York: Academic Press.

[14] WOODS, D. R. (1995) Problem-based learning: helping your students gain the mostfrom PBL. Hamilton CA.

10

A modified Levenberg-Marquardt method to estimate

the radius of convergence of a power series

Santiago Vila1

1Universidad de Extremadura, Departamento de Matematicas, [email protected]

Abstract

We present a method to estimate the radius of convergence of a power series∞∑

n=0

anxn when its terms behave asymptotically like

an ≈ ek1n+k2 sin(k3n+ k4)

.

Keywords: Power series, Levenberg-Marquardt, Least-squares fit.

References

[1] Okrasinski, W. and Vila, S. (1993) Power series solutions to some nonlinear diffusionproblems. Zeitschrift fur angewandte Mathematik und Physik, 44, 988–997.

[2] Vila, S. (2016). Acerca de soluciones exactas y aproximadas de un problema de difusionno lineal relacionado con la produccion de semiconductores. Ph. D. Thesis.

11

A new one-dimensional model for blood flow based on

Cosserat theory

Fernando Carapau1,2 and Paulo Correia3,4



Abstract

In this talk, we study the unsteady motion of a generalized viscoelastic fluid ofthird-grade where specific normal stress coefficient depends on the shear rate by usinga power-law model. For this issue, we use the Cosserat theory approach which reducesthe exact three-dimensional equations to a system depending only on time and on a sin-gle spatial variable. This one-dimensional system is obtained by integrating the linearmomentum equation over the cross-section of the tube, taking a velocity field approx-imation provided by the Cosserat theory. The velocity field approximation satisfiesexactly both the incompressibility condition and the kinematic boundary condition.From this reduced system, we obtain unsteady equations for the wall shear stress andmean pressure gradient depending on the volume flow rate, Womersley number, vis-coelastic coefficients and flow index over a finite section of the tube geometry withconstant circular cross-section. The attention is focused on some numerical simulationsof the proposed model.

Keywords: One-dimensional model, blood flow model, shear-thinning, volume flow rate,Cosserat theory.

References

[1] Truesdell, C. and Noll, W. (1992) The non-linear field theories of mechanics, 2nd edition, Springer, New-York.

[2] Fosdick, R.L. and Rajagopal, K.R. (1980) Thermodynamics and stability of fluids ofthird grade, Proc. R. Soc. Lond. A., 339, 351–377.

[3] Caulk, D.A. and Nagdi, P.M. (1987) Axisymmetric motion of a viscous fluid inside aslender surface of revolution, Journal of Applied Mechanics, 54 (1), 190–196.

12

Quasiconvexity and Rank-One Convexity of

Polynomials

Luıs Bandeira1,2 and Pablo Pedregal3,4


3Departamento de Matematicas, Universidad de Castilla La Mancha,[email protected]

4INEI, Universidad de Castilla La Mancha, Campus de Ciudad Real

Abstract

We report our work about non-negativeness of polynomials and the main neces-sary and sufficient conditions for weak lower semicontinuity of integral functionals invector calculus of variations. David Hilbert’s theorem about sum of squares and non-negativeness of polynomials plays a special role, providing new tools to investigaterank-one convexity of functions defined on 2×2-matrices. For these results, we exploresome consequences and examples. We also explore the relationship between quasicon-vexity and non-negativeness of certain polynomials in the case where the integrand ofan integral functional is a fourth-degree homogeneous polynomial.

Keywords: Quasiconvexity, Rank-one Convexity, Polynomials.

References

[1] Hilbert, D. (1888) Uber die Darstellung Definiter Formen als Summe von Formenquadraten, Mathematische Annalen, 32, 342–350.

[2] Laserre, J. B. (2010) Moments, Positive Polynomials and Their Applications, ImperialCollege Press, London.

[3] Morrey, C. B. (1952) Quasiconvexity and the lower semicontinuity of multiple integrals,Pacific J. Math., 2, 25–53.

13

On the enumeration of the set of elementary numerical

semigroups with fixed multiplicity, Frobenius number or

genus

Manuel B. Branco1,2 and J.C. Rosales3


3Universidad de Granada, Departamento de Algebra, [email protected]

Abstract

Let N denote the set of nonnegative integers. A numerical semigroup is a subsetS of N that is closed under addition, 0 ∈ S and N\S has finitely many elements. Thecardinality of the set N\S is called the genus of S and it is denoted by g(S). Forany numerical semigroup S, the smallest positive integer belonging to S (respectively,the greatest does not belong to S ) is called the multiplicity (respectively Frobeniusnumber) of S and it is denoted by m(S) (respectively F) (see [6]). We say that anumerical semigroup S is elementary if F(S) < 2m(S). Given a positive integer g,we denote by S(g) the set of all numerical semigroups with genus g. The problemof determining the cardinal of S(g) has been widely treated in the literature (see forexample [1], [2], [3], [4], [5] and [7]). Some of these works are motivated by Amoros’sconjecture [3] which says the sequence of cardinals of S(g) for g = 1, 2, · · · has aFibonacci behavior. It is still not known in general if for a fixed positive integer g thereare more numerical semigroups with genus g+1 than numerical semigroups with genusg. In this talk we give algorithms that allows to compute the set of every elementarynumerical semigroups with a given genus g, Frobenius number F and multiplicity m.As a consequence we obtain formulas for the cardinal of these sets. In particular weshow that sequence of cardinals of the set of elementary numerical semigroups of genusg = 0, 1, . . . is a Fibonacci sequence.

Keywords: Numerical semigroup, Frobenius number, Genus, Fibonacci sequence.

References

[1] V. Blanco, P. A. Garcıa-Sanchez and Justo Puerto, Counting numerical semigroups withshort generating functions, Int. J. of Algebra and Comput. 21(7), 1217-1235, (2011).

[2] M. Bras-Amoros, Bouds on the number of numerical semigroups of a given genus, J.Pure Appl. Algebra, 213(6), 997-1001 (2008).

[3] M. Bras-Amoros, Fibonacci-like behavior of the number of numerical semigroups of agiven genus, Semigroup Forum 76, 379-384 (2008).

[4] S. Elizalde, Improved bounds on the number of numerical semigroups of a given genus,J. Pure Appl. Algebra, 214(10), 1862-1873 (2010).

14

[5] N. Kaplan, Couting numerical semigroups by genus and some cases a question of Wilf,J. Pure Appl. Algebra, 216(5), 1016-1032 (2012).

[6] J. C. Rosales, P. A. Garcıa-Sanchez, “Numerical semigroups”, Developments in Mathe-matics, vol.20, Springer, New York, (2009).

[7] Y. Zhao, Constructing numerical semigroups of a given genus, Semigroup Forum 80(2),242-254 (2009).

15

Mathematics for European Research and Education:

Some Challenging Trends?

Joao Miranda1,3, Cristina Dias2,4

1Instituto Politecnico de Portalegre, Departamento de Tecnologia eDesign,[email protected]

2 Instituto Politecnico de Portalegre, Departamento de Tecnologia e Design,[email protected] Superior Tecnico, Centro de Recursos Naturais e Ambiente (CERENA)

4Centro de Matematica e Aplicacoes, Universidade Nova de Lisboa (CMA)

Abstract

Mathematics and associated research areas provide very important tools for mod-eling, understanding, and overcoming the most disparate challenges in the Europeanscientific landscape. In addition, research and education are jointly addressed in manyframeworks, being key items to promote innovation and competitiveness. Nowadays,due to the new ICT phenomena (Analytics, Big Data, Cloud, Mobile, Social Business,etc.), practitioners and researchers are re-visiting the Mathematics-based tools, namely,Data Analysis, High Performance Computing, Modeling-Simulation-Optimization, andBiomathematics are being reported as relevant for the near future. By other side,also the strategic factors concerning Higher Education are being addressed, namely,several topics such as the enrolment of students, failure rates and success promotion,teaching/learning practices, programs restructuration, and the transition into the labormarket are being studied and analyzed. In a way to better understand these emergingtrends on research and education, several studies and projects at European level arepresented, so as some mathematics-based developments are discussed.

Keywords: Relative Relevances, Eigenvalues, Stability.

References

[1] Bilingsley, P. (1968), Convergence of Probability Measure, John Wiley & Sons.

[2] Lavit, C. (1988), Analyse Conjointe de Tableaux Quantitatifs, Paris: Masson.

[3] Lehmann, E. L. (1986), Testing statistical hypotheses, New York: Wiley

[4] Oliveira, M. M., Mexia J. T. (2007), Modelling series of studies with a common structureComp. Stat. Data Anal. 51, 5876–5885.

[5] Mexia, J. T. (1995), Best linear unbiased estimates, duality of F tests and Scheffe’smultiple comparison method in the presence of controlled heterocedasticity Comp. Stat.Data Anal., 10, 271—281.

16

Obtaining COBS from the extension of a balanced

mixed model

Carla Santos1, Celia Nunes2 , Cristina Dias3 and Joao Tiago Mexia4

1Polytechnic Institute of Beja nad CMA - Center of Mathematics and its Applications,New University of Lisbon, Portugal

2 Department of Mathematics and Center of Mathematics and Applications, University ofBeira Interior, Portugal

3 College of Technology and Management, Polytechnical Institute of Portalegre and CMA -Center of Mathematics and its Applications, New University of Lisbon, Portugal

4 Department of Mathematics, Faculty of Science and Technology and CMA- Center ofMathematics and its Applications, New University of Lisbon, Portugal

Abstract

A model with orthogonal block structure, OBS, is a linear mixed model whosevariance-covariance matrix is a linear combinations of known pairwise orthogonal or-thogonal projection matrices, that add up to the identity matrix. When the variance-covariance matrix commutes with the orthogonal projection matrix on the space spannedby the mean vector, the OBS is called COBS (model with commutative orthogonalblock structure). This commutativity condition of COBS is a necessary and sufficientcondition for the least square estimators, LSE, to be best linear unbiased estimators,BLUE, whatever the variance components.Using the algebraic structure of the models, based on commutative Jordan algebras,and B-–matrices, we study the possibility of obtaining COBS from the extension ofbalanced mixed models.

Keywords

B-matrices, Jordan Algebra, Mixed models, Commutative orthogonal block structure.

References

[1] Carvalho, F. and Covas, R. (2015) B-matrices and its applications to linear models, AIPConference Proceedings 1648, 110010 ; doi: 10.1063/1.4912417

[2] Ferreira, S.S., Ferreira, D., Nunes, C. and Mexia, J.T. (2013). Estimation of variancecomponents in linear mixed models with commutative orthogonal block structure. Re-vista Colombiana de Estadistica, 36(2), 261– 271

[3] Nunes C., Santos C., Mexia, J. T. (2008) Relevant statistics for models with commutativeorthogonal block structure and unbiased estimator for variance components,Journal ofInterdisciplinary Mathematics 11, Vol. 4: 553–564.

17

Study of the Relative Relevances associated to a

strongly first eingenvalue

Cristina Dias1,6,Carla Santos2,6, Joao Miranda3,5, and Joao T.

Mexia4,6

1Instituto Politecnico de Portalegre, Departamento de Tecnologia e Design,[email protected] Instituto Politecnico de Beja, Departamento de Matematica e Ciencias Fısicas,

[email protected] Instituto Politecnico de Portalegre, Departamento de Tecnologia e Design,

[email protected] Nova de Lisboa, Departamento de Matematica, [email protected]

5Instituto Superior Tecnico, Centro de Recursos Naturais e Ambiente (CERENA)6Centro de Matematica e Aplicacoes, Universidade Nova de Lisboa (CMA)

Abstract

The models we consider are based on the spectral decomposition of the mean matri-ces for matrices with degree k ≥ 1. In a previous work we studied the relative relevanceof the spectral component associated to the first eigenvalue in situations where thiseigenvalue is strongly dominant. A stability analysis of our results when the secondeigenvalue increases relatively to the first is carried out. These models can be applied tocross products matrices and Hilbert-Schmidt scalar products matrices. The latter havean important role in the first stage (inter-structure) of STATIS methodology, while theformer matrices (in particular the and cross products, which have the same non-nulleigenvalues) have an important role in inference.

Keywords: Relative Relevances, Eigenvalues, Stability.

References

[1] Bilingsley, P. (1968), Convergence of Probability Measure, John Wiley & Sons.

[2] Lavit, C. (1988), Analyse Conjointe de Tableaux Quantitatifs, Paris: Masson.

[3] Lehmann, E. L. (1986), Testing statistical hypotheses, New York: Wiley

[4] Oliveira, M. M., Mexia J. T. (2007), Modelling series of studies with a common structureComp. Stat. Data Anal. 51, 5876–5885.

[5] Mexia, J. T. (1995), Best linear unbiased estimates, duality of F tests and Scheffe’smultiple comparison method in the presence of controlled heterocedasticity Comp. Stat.Data Anal., 10, 271—281.

18

Occurrences of failures in ANOVA

Celia Nunes1,2, Gilberto Capistrano2, Anacleto Mario2, Dario

Ferreira2,3, Sandra S. Ferreira2,4 and Joao T. Mexia5

1Department of Mathematics, University of Beira Interior, Covilha, Portugal, [email protected] of Mathematics and Application (CMA-UBI), University of Beira Interior,

Covilha, Portugal3Department of Mathematics, University of Beira Interior, Covilha, Portugal, [email protected]

4Department of Mathematics, University of Beira Interior, Covilha, Portugal,[email protected]

5 Center of Mathematics and its Applications (CMA), Faculty of Science and Technology,New University of Lisbon, Portugal

Abstract

In this work we aim to extend the ANOVA to the case where the sample sizesmay not be previously known. In these situations, assuming there are m differenttreatments, it is more appropriate to consider the sample sizes as realizations, n1, ..., nm,of independent random variables, N1, ..., Nm.

We apply this to fixed effects models when failures may occur, which may happen,for instance, when working with patients we may have incomplete or absent reports. Sowe assume that the sample sizes, N1, ..., Nm, are independent and Binomial distributed.

The approach is illustrated through an application on cancer registries. We alsoshow its relevance in avoiding false rejections.

Keywords: ANOVA, Random sample sizes, Binomial distribution, Cancer registries.

References

[1] Khuri, A.I., Mathew, T. and Sinha, B.K. (1998). Statistical Tests for Mixed LinearModels. Wiley series in Probability and Statistics. John Wiley & Sons, New York.

[2] Mexia, J.T., Nunes, C., Ferreira, D., Ferreira, S.S. and Moreira, E. (2011). Orthogonalfixed effects ANOVA with random sample sizes. Proceedings of the 5th InternationalConference on Applied Mathematics, Simulation, Modelling (ASM’11), 84-90.

[3] Nunes, C., Ferreira, D., Ferreira, S.S. and Mexia, J.T. (2010). F Tests with RandomSample Sizes. Proceedings of the 8th International Conference on Numerical Analysisand Applied Mathematics, AIP Conf. Proc. Vol. 1281(II), 1241-1244.

[4] Nunes, C., Ferreira, D., Ferreira, S.S. and Mexia, J.T. (2012). F -tests with a rarepathology. Journal of Applied Statistics. 39(3), 551-561.

[5] Nunes, C., Ferreira, D., Ferreira, S.S. and Mexia, J.T. (2014). Fixed effects ANOVA:an extension to samples with random size. J. Stat. Comput. Simul. 84(11), 2316-2328.

19

[6] Nunes, C., Capristano, G., Ferreira, D., Ferreira, S.S. and Mexia, J.T. (2015). One-wayFixed Effects ANOVA with Missing Observations. Proceedings of the 12th InternationalConference on Numerical Analysis and Applied Mathematics. AIP Conf. Proc. 1648,110008.

[7] Searl, S.R., Casella, G. and McCulloch, C.E. (1992). Variance Components. Wiley seriesin Probability and statistics. John Wiley & Sons, New York.

20

Documents

Book of Abstractsiiiwcdanm2016.yolasite.com/resources/BOOK of ABSTRACTS.pdf · Distance sampling using the minimum description length principle Fernando Ceia 1,2 and Russell Alpizar-Jara