Kostyukova, O. I., Tchemisova, T. V., Yermalinskaya, S. A.
Belarusian State University
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Tchemisova, T. V., Yermalinskaya, S. A.
Belarusian National Academy of Sciences
Kharlamova, Vera I., Kharlamov, Alexander A., Malonek, Helmuth R.
Yanus
The article describes the historical place of the first Portuguese Journal “Jornal de sciencias mathematicas e astronómicas” (Teixeira´s Journal) during the development of the European mathematical community at the end of the 19th century.
Castro, L. P., Fujiwara, H., Rodrigues, M. M., Saitoh, S., Tuan, V. K.
Springer
We give a short survey of a general discretization method based on the theory of reproducing kernels. We believe our method will become the next generation method for solving analytical problems by computers. For example, for solving linear PDEs with general boundary or initial value conditions, independently of the domains. Furthermore, we give an ultimate sampling formula and a realization of reproducing kernel Hilbert spaces.
Rodrigues, M. M., Saitoh, S.
In this paper, by using the theory of reproducing kernels, we investigate integral transforms with kernels related to the solutions of the initial Whittaker heat problem.
Avelli, Diego Oscar Napp, Malonek, Paula Rocha
In this chapter, we study control by interconnection of a given linear differential system (the plant behavior) with a suitable controller. The problem formulations and their solutions are completely representation free, and specified only in terms of the system dynamics. A controller is a system that constrains the plant behavior through a certain set of variables. In this context, there are two main situations to be considered: either all the system variables are available for control, i.e., are control variables (full control) or only some of the variables are control variables (partial control). For systems evolving over a time domain (1D) the problems of implementability by partial (regular) interconnection are well understood. In this chapter, we study why similar results are not valid in themultidimensional (nD) case. Finally, we study two important classes of controllers, namely, canonical controllers and regular controllers.
Cerejeiras, Paula, Vieira, Nelson Felipe Loureiro
Birkhäuser
In this paper we generalize radial and standard Clifford-Hermite polynomials to the new framework of fractional Clifford analysis with respect to the Riemann-Liouville derivative in a symbolic way. As main consequence of this approach, one does not require an a priori integration theory. Basic properties such as orthogonality relations, differential equations, and recursion formulas, are proven.
Ferreira, Milton dos Santos, Vieira, Nelson Felipe Loureiro
In this paper, by using the method of separation of variables, we obtain eigenfunctions and fundamental solutions for the three parameter fractional Laplace operator defined via fractional Caputo derivatives. The solutions are expressed using the Mittag-Leffler function and we show some graphical representations for some parameters. A family of fundamental solutions of the corresponding fractional Dirac operator is also obtained. Particular cases are considered in both cases.
Costa, Diana, Martins, Manuel A.
Springer International Publishing
Hybrid logic is a valuable tool for specifying relational structures, at the same time that allows defining accessibility relations between states, it provides a way to nominate and make mention to what happens at each specific state. However, due to the many sources nowadays available, we may need to deal with contradictory information. This is the reason why we came with the idea of Quasi-hybrid logic, which is a paraconsistent version of hybrid logic capable of dealing with inconsistencies in the information, written as hybrid formulas. In [5] we have already developed a semantics for this paraconsistent logic. In this paper we go a step forward, namely we study its proof-theoretical aspects. We present a complete tableau system for Quasi-hybrid logic, by combining both tableaux for Quasi-classical and Hybrid logics.
Barbosa, Luís S., Martins, Manuel A., Madeira, Alexandre, Neves, Renato
Hybridisation is a systematic process along which the characteristic features of hybrid logic, both at the syntactic and the semantic levels, are developed on top of an arbitrary logic framed as an institution. It also captures the construction of first-order encodings of such hybridised institutions into theories in first-order logic. The method was originally developed to build suitable logics for the specification of reconfigurable software systems on top of whatever logic is used to describe local requirements of each system’s configuration. Hybridisation has, however, a broader scope, providing a fresh example of yet another development in combining and reusing logics driven by a problem from Computer Science. This paper offers an overview of this method, proposes some new extensions, namely the introduction of full quantification leading to the specification of dynamic modalities, and exemplifies its potential through a didactical application. It is discussed how hybridisation can be successfully used in a formal specification course in which students progress from equational to hybrid specifications in a uniform setting, integrating paradigms, combining data and behaviour, and dealing appropriately with systems evolution and reconfiguration.
Costa, Maria da Conceição, Scotto, Manuel Gonzaléz, Pereira, Isabel
The Asymmetric Power ARCH representation for the volatility was introduced by Ding et al. [3] in order to account for asymmetric responses in the volatility in the analysis of continuous-valued nancial time series like, for instance, the log-return series of foreign exchange rates, stock indices or share prices. As reported by Br ann as and Quoreshi [1], asymmetric responses in volatility are also observed in time series of counts such as the number of intra-day transactions in stocks. In this work, an asymmetric power autoregressive conditional Poisson model is introduced for the analysis of time series of counts exhibiting asymmetric overdispersion. Basic probabilistic and statistical properties are summarized and parameter estimation is discussed. A simulation study is presented to illustrate the proposed model. Finally, an empirical application to a set of data concerning the daily number of stock transactions is also presented to attest for its practical applicability in data analysis.
Costa, Mariana, Requejo, Cristina, Rodrigues, Filipe
The effective supplier evaluation and purchasing processes are of vital importance to business organizations, making the suppliers selection problem a fundamental key issue to their success. We consider a complex supplier selection problem with multiple products where minimum package quantities, minimum order values related to delivery costs, and discounted pricing schemes are taken into account. Our main contribution is to present a mixed integer linear programming (MILP) model for this supplier selection problem. The model is used to solve several examples including three real case studies from an electronic equipment assembly company.
Agra, Agostinho, Cerveira, Adelaide, Requejo, Cristina
This paper considers a multi-item inventory distribution problem motivated by a practical case occurring in the logistic operations of an hospital. There, a single warehouse supplies several nursing wards. The goal is to define a weekly distribution plan of medical products that minimizes the visits to wards, while respecting inventory capacities and safety stock levels. A mathematical formulation is introduced and several improvements such as tightening constraints, valid inequalities and an extended reformulation are discussed. In order to deal with real size instances, an hybrid heuristic based on mathematical models is introduced and the improvements are discussed. A branch-and-cut algorithm using all the discussed improvements is proposed. Finally, a computational experimentation is reported to show the relevance of the model improvements and the quality of the heuristic scheme.
We consider a single item Production-Inventory-Routing problem with a single producer/supplier and multiple retailers. Inventory management constraints are considered both at the producer and at the retailers, following a vendor managed inventory approach, where the supplier monitors the inventory at retailers and decides on the replenishment policy for each retailer. We assume a constant production capacity. Based on the mathematical formulation we discuss a classical Lagrangian relaxation which allows to decompose the problem into four subproblems, and a new Lagrangian decomposition which decomposes the problem into just a production-inventory subproblem and a routing subproblem. The new decomposition is enhanced with valid inequalities. A computational study is reported to compare the bounds from the two approaches.
Castro, Luís Pinheiro de, Speck, Frank-Olme
Convolution type operators with symmetry appear naturally in boundary value problems for elliptic PDEs in symmetric or symmetrizable domains. They are defined as truncations of translation invariant operators in a scale of Sobolev-like spaces that are convolutionally similar to subspaces of even or odd functionals. The present class, as a basic example, is closely related to the Helmholtz equation in a quadrant, where a possible solution is "symmetrically" extended to a half-plane. Explicit factorization methods allow the representation of resolvent operators in closed analytic form for a large class of boundary conditions including the two-impedance and the oblique derivative problems. Moreover they allow fine results on the regularity and asymptotic behavior of the solutions.
Attila, Öykü Naz, Agra, Agostinho, Akartunalı, Kerem, Arulselvan, Ashwin
In this paper, we propose a decomposition procedure for constructing robust optimal production plans for reverse inventory systems. Our method is motivated by the need of overcoming the excessive computational time requirements, as well as the inaccuracies caused by imprecise representations of problem parameters. The method is based on a min-max formulation that avoids the excessive conservatism of the dualization technique employed by Wei et al. (2011). We perform a computational study using our decomposition framework on several classes of computer generated test instances and we report our experience. Bienstock and Özbay (2008) computed optimal base stock levels for the traditional lot sizing problem when the production cost is linear and we extend this work here by considering return inventories and setup costs for production. We use the approach of Bertsimas and Sim (2004) to model the uncertainties in the input.
Napp, Diego, Pinto, Raquel, Rosenthal, Joachim, Santana, Filipa
In this paper, we deal with the so-called multi-shot network coding, meaning that the network is used several times (shots) to propagate the information. The framework we present is slightly more general than the one which can be found in the literature. We study and introduce the notion of column rank distance of rank metric convolutional codes for any given rate and finite field. Within this new framework we generalize previous results on column distances of Hamming and rank metric convolutional codes [3, 8]. This contribution can be considered as a continuation follow-up of the work presented in [10].
Requejo, Cristina, Santos, Eulália
The Weight-constrained Minimum Spanning Tree problem (WMST) is a combinatorial optimization problem aiming to find a spanning tree of minimum cost with total edge weight not exceeding a given specified limit. This problem has important applications in the telecommunications network design and communication networks. In order to obtain optimal or near optimal solutions to the WMST problem we use heuristic methods based on formulations for finding feasible solutions. The feasibility pump heuristic starts with the LP solution, iteratively fixes the values of some variables and solves the corresponding LP problem until a feasible solution is achieved. In the local branching heuristic a feasible solution is improved by using a local search scheme in which the solution space is reduced to the neighborhood of a feasible solution that is explored for a better feasible solution. Extensive computational results show that these heuristics are quite effective in finding feasible solutions and present small gap values. Each heuristic can be used independently, however the best results were obtained when they are used together and the feasible solution obtained by the feasibility pump heuristic is improved by the local branching heuristic.
Freitas, Adelaide, Escudeiro, Sara, Afreixo, Vera
Evaluation of the coverage probability and, more recently, of the intervalar location of con dence intervals, is a useful procedure if exact and asymptotic methods for constructing con dence intervals are used for some populacional parameter. In this paper, a simple graphical procedure is presented to execute this kind of evaluation in con dence methods for linear combinations of k independent binomial proportions. Our proposal is based on the representation of the mesial and distal non-coverage probabilities on a plane. We carry out a simulation study to show how this graphical representation can be interpreted and used as a basis for the evaluation of intervalar location of con dence interval methods.
Jesus, Luís, Tavares, Ana Inês, Hall, Andreia
InTech
Several methods have been proposed for the perceptual evaluation of voice quality, but the GRBAS and Consensus Auditory-Perceptual Evaluation of Voice (CAPE-V) scales are the most widely used and recommended as part of standardised voice evaluation protocols. In this study, cross-cultural adaptation and translation of the GRBAS (the first translation from the original Japanese version) and CAPE-V scales to European Portuguese were carried out following international guidelines. Results from a study of the intra- and inter-rater reliability of the perceptual evaluation of voices with the GRBAS and CAPE-V scales, before and after a training programme, designed according to the most recent American Speech-Language-Hearing Association and Japan Society of Logopedics and Phoniatrics guidelines, are also reported.
Sebastião, Raquel, Silva, Margarida Martins da, Gama, João, Mendonça, Teresa
IEEE
In the clinical practice the concerns about the administration of hypnotics and analgesics for minimally invasive diagnostics and therapeutic procedures have enormously increased in the past years. The automatic detection of changes in the signals used to evaluate the depth of anesthesia is hence of foremost importance in order to decide how to adapt the doses of hypnotics and analgesics that should be administered to patients. The aim of this work is to online detect drifts in the referred depth of anesthesia signals of patients undergoing general anesthesia. The performance of the proposed method is illustrated using BIS records previously collected from patients subject to abdominal surgery. The results show that the drifts detected by the proposed method are in accordance with the actions of the clinicians in terms of times where a change in the hypnotic or analgesic rates had occurred. This detection was performed under the presence of noise and sensor faults. The presented algorithm was also online validated. The results encourage the inclusion of the proposed algorithm in a decision support system based on depth of anesthesia signals.
Xambre, Ana Raquel, Ramos, Ana Luísa, Nicolau, João Miguel, Alvelos, Helena
Imprensa da Universidade de Coimbra
O estudo de caso “Modelação e Simulação de uma Linha de Produção de Painéis Solares” foi desenvolvido em ambiente industrial e resultou de uma colaboração entre uma PME portuguesa da área das energias renováveis e a Universidade de Aveiro (Departamento de Economia, Gestão e Engenharia Industrial). O seu principal objetivo foi o de analisar uma linha de produção de painéis solares fotovoltaicos no sentido de apoiar decisões operacionais relacionadas com um desejado aumento da capacidade produtiva da referida linha. Os decisores (elementos da equipa de gestão da PME) pretendiam dar resposta a um aumento verificado na procura de painéis solares e, como tal, desejavam averiguar se um conjunto de alterações a introduzir na respetiva linha de produção, que já discutiam há algum tempo, poderia aumentar o seu volume de produção. Para tal foi inicialmente realizada a modelação do sistema usando a linguagem gráfica SysML (Systems Modeling Language) sendo, de seguida, desenvolvido um modelo de simulação por forma a testar e analisar dinamicamente o desempenho do sistema produtivo face à introdução das alterações pretendidas. Após validação do modelo de simulação do sistema atual definiu-se o cenário alternativo a testar (correspondente às alterações a introduzir na linha) e analisaram-se os resultados associados a cada um destes cenários. Todos os modelos de simulação desenvolvidos foram acompanhados pelos respetivos modelos de animação que permitiram visualizar, de um modo apelativo, o comportamento dinâmico da linha de produção e comunicar os resultados de um modo mais eficiente. Os resultados obtidos permitiram apoiar o processo de decisão e evidenciaram, perante os decisores, as vantagens da utilização de modelos de engenharia (modelos gráficos e de simulação) para analisar situações reais complexas. A empresa identificou-se com os modelos gerados e com os resultados obtidos. Esses resultados estão a ser utilizados para fazer pequenos ajustes aos investimentos inicialmente previstos e para introduzir as modificações na linha de produção de painéis solares fotovoltaicos. Os objetivos da Universidade foram também alcançados uma vez que o projeto foi completado com sucesso e os resultados do mesmo estão a ser utilizados pela empresa para melhorar o seu desempenho.
Ferreirim, Isabel, Martins, Manuel A.
In this paper we review a hidden (sorted) generalization of k-deductive systems - hidden k-logics. They encompass deductive systems as well as hidden equational logics and inequational logics. The special case of hidden equational logics has been used to specify and to verify properties in program development of behavioral systems within the dichotomy visible vs. hidden data. We recall one of the main applications of this work - the study of behavioral equivalence. Related results are obtained through combinatorial properties of the Leibniz congruence relation. In addition we obtain a few new developments concerning hidden equational logic, namely we present a new characterization of the behavioral consequences of a theory.
Almeida, Ricardo, Malinowska, A.B., Odzijewicz, T.
In this paper, the fractional order Hegselmann–Krause type model with leadership is studied. We seek an optimal control strategy for the system to reach a consensus in such a way that the control mechanism is included in the leader dynamics. Necessary optimality conditions are obtained by the use of a fractional counterpart of Pontryagin Maximum Principle. The effectiveness of the proposed control strategy is illustrated by numerical examples.
Fernandes, Maria Elisa, Leemans, Dimitri, Weiss, Asia Ivic
Springer, Cham
The rank 3 concept of a hypermap has recently been generalized to a higher rank structure in which hypermaps can be seen as “hyperfaces” but very few examples can be found in literature. We study finite rank 4 structures obtained by hexagonal extensions of toroidal hypermaps. Many new examples are produced that are regular or chiral, even when the extensions are polytopal. We also construct a new infinite family of finite nonlinear hexagonal extensions of the tetrahedron. The authors would like to thank two anonymous referees for their numerous helpful and insightful comments. This research was supported by a Marsden grant (UOA1218) of the Royal Society of New Zealand, by NSERC and by the Portuguese Foundation for Science and Technology (FCT-Fundação para a Ciência e a Tecnologia), through CIDMA - Center for Research and Development in Mathematics and Applications, within project UID/MAT/04106/2013. published
Murillo, Kelly, Rocha, Eugénio
Education is of vital importance for the competitiveness and growth of a country, but it is affected by the amount of public and private investment, in particular, by governments and the economic leverage of citizens to pay tuitions. The financial crisis, originated in 2008, had some degree of impact in the European education system, which has not been completely understood. Spain is one of the countries that has suffered most from its impact, as reflected in the report of the Organization for Economic Cooperation and Development (OECD) of 2016, see [1]. While in most European countries public spending on education has remained stable at 11%, in Spain public spending on education has fallen from 9% to 8% from 2008 to 2013. The expenditure per student was below the OECD average in all stages, from primary to university. Nevertheless, such data are usually known for the public sector whereas the impact of the private sector is neglected. Here we want to focus on precisely the Spanish private educational sector, since a considerable percentage of students in Spain received education in private institutions, turning it a good case-study for understanding the impact of economy in education. Our work examines the financial efficiency of more than 4.000 Spanish private institutions divided into four educational levels: pre-primary, primary, secondary and higher education, in the period 2013- 2016. Their evolution is evaluated at three distinct stages: efficiency levels; efficiency patterns; and efficiency determinants. Our results clarify which are the profile of institutions that are most efficient, and which are not, giving some insight about the improvements which could be applied to raise their effectiveness. To this end, we take as a starting point the financial statements of each institution, considering variables that allow us to interpret measures of leverage, liquidity, profitability, management and evaluation of the institution. The main mathematical tool used is a nonparametric deterministic method for measuring efficiency, the Multidirectional Efficiency Analysis (MEA) of Bogetoft and Hougaard [2], in combination with other techniques. In contrast with the standard DEA, MEA also allows to investigate changes in efficiency patterns. Since the selection of relevant variables is of major importance, a combination of techniques to choose the most meaningful ones is used, namely, through Principal Component Analysis and to avoid loss of information (under-fitting) or the adding random noise (over-fitting), the RV coefficient is computed, see [3]. Comparisons between groups with different levels of efficiency are made by calculating an index that measures the effort to obtain input resources in a sequence of years. published
Bohn, Lucimere, Sá Couto, Pedro, Castro, Ana Ramoa, Ribeiro, Fernando, Oliveira, José
Sociedade Portuguesa de Estatística
This study evaluated the effects of a health education and counseling intervention program, in a primary healthcare setting, on daily physical activity (PA) in individuals with moderate-to-high risk of cardiovascular disease. This was a parallel-group study with a 4-month-long intervention, plus 8 months of follow-up. Participants were 164 individuals with moderate-to-high cardiovascular risk, allocated to either an intervention (IC, n=87) or a control group (CG, n=77). The intervention consisted by 3 walking and face-to-face group sessions plus text messages. The primary outcome was daily PA measured by sedentary time, light and moderate-to-vigorous PA. After the intervention (4 months) and follow-up (8 months) periods, the results show significant differences between Groups (IC, CG) for sedentary time and light PA, but not for moderate-to-vigorous PA. No significant changes were found for the variable Time (baseline, 4 months, 8 months) and for the correspondent interaction between Groups and Time, even after adjustments for age, gender, BMI, and variables that were different between groups at baseline. The health education and counseling program did not improve daily PA of participants with moderate-to-high cardiovascular risk. The European Regional Development Fund through the Operational Competitiveness Program, and the Foundation for Science and Technology (FCT) of Portugal support this study and the research unit CIAFEL within the projects FCOMP-01-0124-FEDER-020180 (References FCT: PTDC/DES/122763/2010,UID/DTP/00617/2013,UID/BIM/04501/2013,UID/MAT/04106/2013). The FCT supported the author Lucimére Bohn (SFRH/BD/78620/2011). published
El Oued, Mohammed, Napp, Diego, Pinto, Raquel, Toste, Marisa
Springer Verlag
An important class of codes widely used in applications is the class of convolutional codes . Most of the literature of convolutional codes is devoted to convolutional codes over finite fields. The extension of the concept of convolutional codes from finite fields to finite rings have attracted much attention in recent years due to fact that they are the most appropriate codes for phase modulation. However convolutional codes over finite rings are more involved and not fully understood. Many results and features that are well-known for convolutional codes over finite fields have not been fully investigated in the context of finite rings. In this paper we focus in one of these unexplored areas, namely, we investigate the dual codes of convolutional codes over finite rings. In particular we study the p-dimension of the dual code of a convolutional code over a finite ring. This contribution can be considered a generalization and an extension, to the ring case, of the work done by Forney and McEliece on the dimension of the dual code of a convolutional code over a finite field. published
Cação, Isabel, Falcão, M. I., Malonek, Helmuth
The so-called Vietoris' number sequence is a sequence of rational numbers that appeared for the rst time in a celebrated theorem by Vietoris (1958) about the positivity of certain trigonometric sums with important applications in harmonic analysis (Askey/Steinig, 1974) and in the theory of stable holomorphic functions (Ruscheweyh/ Salinas, 2004). In the context of hypercomplex function theory those numbers appear as coe cients of special homogeneous polynomials in R3 whose generalization to an arbitrary dimension n lead to a n-parameter generalized Vietoris' number sequence that characterizes hypercomplex Appell polynomials in Rn. published
Macedo, E., Freitas, A.
Clustering and Disjoint Principal Component Analysis (CDP CA) is a constrained principal component analysis recently proposed for clustering of objects and partitioning of variables, simultaneously, which we have implemented in R language. In this paper, we deal in detail with the alternating least-squares algorithm for CDPCA and highlight its algebraic features for constructing both interpretable principal components and clusters of objects. Two applications are given to illustrate the capabilities of this new methodology.
Cerejeiras, P., Kahler, U., Sommen, F., Vajiac, A.
In this paper we describe the foundation of a new kind of discrete geometry and calculus called Script Geometry. It allows to work with more general meshes than classic simplicial complexes. We provide the basic definitions as well as several examples, like the Klein bottle and the projective plane. Furthermore, we also introduce the corresponding Dirac and Laplace operators which should lay the groundwork for the development of the corresponding discrete function theory.
Cerejeiras, Paula, Qiuhui Chen, Gomes, Narciso, Hartmann, Stefan
We study the problem of compressed sensing for nonlinear Fourier atoms and Takenaka–Malmquist systems. We show that reconstruction by means of a l 1-minimization is possible with high probability.
Castro, L.P., Fujiwara, H., Rodrigues, M.M., Saitoh, S., Tuan, V.K.
We found a very general discretization method for solving wide classes of mathematical problems by applying the theory of reproducing kernels. An illustration of the generality of the method is here performed by considering several distinct classes of problems to which the method is applied. In fact, one of the advantages of the present method -- in comparison to other well-known and well established methods -- is its global nature and no need of special or very particular data conditions. Numerical experiments have been made, and consequent results are here exhibited. Due to the powerful results which arise from the application of the present method, we consider that this method has everything to become one of the next generation methods of solving general analytical problems by using computers. In particular, we would like to point out that we will be able to solve very global linear partial differential equations satisfying very general boundary conditions or initial values (and in a somehow independent way of the boundary and domain). Furthermore, we will be able to give an ultimate sampling theory and an ultimate realization of the consequent general reproducing kernel Hilbert spaces. The general theory is here presented in a constructive way, and containing some related historical and concrete examples.
Castro, L.P., Fujiwara, H., Qian, T., Saitoh, S.
We would like to propose a new method in view to catch smoothing properties and analyticity of functions by computers. Of course, in the strict sense, such goal is impossible. However, we would like to propose some practical method that may be applied for many concrete cases for some good functions (but not for bad functions, in a sense). Therefore, this may be viewed as a procedure proposal which includes numerical experiments for the just mentioned challenge and within a new method.
Castro, L.P., Rodrigues, M.M., Saitoh, S.
For some general linear integral operator equations, we investigate consequent initial value problems by using the theory of reproducing kernels. A new method is proposed which -- in particular -- generates a new field among initial value problems, linear integral operators, eigenfunctions and values, integral transforms and reproducing kernels. In particular, examples are worked out for the integral equations of Lalesco-Picard, Dixon and Tricomi types.
Castro, Luís P., Duduchava, Roland, Speck, Frank-Olme
Springer Basel
The aim of this work is to construct explicitly resolvent operators for a class of boundary value problems in diffraction theory. These are formulated as boundary value problems for the three-dimensional Helmholtz equation with Dirichlet or Neumann conditions on a plane screen of polynomial-conical form (including unbounded and multiply-connected screens), in weak formulation. The method is based upon operator theoretical techniques in Hilbert spaces, such as the construction of matrical coupling relations and certain orthogonal projections, which represent new techniques in this area of applications. Various cross connections are exposed, particularly considering classical Wiener-Hopf operators in So-bo-lev spaces as general Wiener-Hopf operators in Hilbert spaces and studying relations between the crucial operators in game. Former results are extended, particularly to multiply-connected screens.
Agra, Agostinho, Christiansen, Marielle, Hvattum, Lars Magnus, Rodrigues, Filipe
We consider a single product maritime inventory routing problem in which the production and consumption rates are constant over the planning horizon. The problem involves a heterogeneous fleet of ships and multiple production and consumption ports with limited storage capacity. In spite of being one of the most common ways to transport goods, maritime transportation is characterized by high levels of uncertainty. The principal source of uncertainty is the weather conditions, since they have a great influence on sailing times. The travel time between any pair of ports is assumed to be random and to follow a log-logistic distribution. To deal with random sailing times we propose a two-stage stochastic programming problem with recourse. The routing, the order in which the ports are visited, as well as the quantities to load and unload are fixed before the uncertainty is revealed, while the time of the visit to ports and the inventory levels an be adjusted to the scenario. To solve the problem, a MIP based local search heuristic is developed. This new approach is compared with a decomposition algorithm in a computational study.
Bayour, Benaoumeur, Torres, Delfim F.M.
We introduce a notion of fractional (noninteger order) derivative on an arbitrary nonempty closed subset of the real numbers (on a time scale). Main properties of the new operator are proved and several illustrative examples given. © Springer International Publishing Switzerland 2016.
Silva, Carina, Freitas, Adelaide, Roque, Sara, Sousa, Lisete
Wiley
Among various available array technologies, double-channel cDNA microarray experiments provide numerous technical protocols associated with functional genomic studies. The chapter begins by detailing the arrow plot, which is a recent graphical-based methodology to detect differentially expressed (DE) genes, and briefly mentions the significance analysis of microarrays (SAM) procedure, which is, in contrast, quite well known. Next, it introduces the correspondence analysis (CA) and explains how the resultant graphic can be interpreted. Then, CA in both class comparison and class prediction applications and over the data sets lymphoma (lym), lung (lun), and liver (liv) is executed. The CA is applied to all three databases in order to obtain graphical representations of background correction (BC) and normalization (NM) profiles in a two-dimensional reduced space. Whenever possible, more than one preprocessing strategy on microarray data could be applied and results from preprocessed data should be compared before any conclusion and subsequent analysis.
Costa, Carolina, Alvelos, Helena, Teixeira, Leonor
IGI Global
This chapter analyzes Learning Management Systems (LMSs) and their main features and compares the most popular LMSs platforms considering their utilization and the services they offer. Additionally, it presents a study carried out at the University of Aveiro (UA) that analyses the functionalities and tools of the Moodle platform and their use by students. The data was collected based on content analysis, one non-structured interview with the responsible of the Moodle from the UA and a questionnaire applied to 278 students. The results show that the most mentioned purposes of the Moodle@UA were ‘Download materials’, ‘News’ and ‘Deliver assignments’ and that the most used information materials are ‘Texts’ and ‘Slides’, showing that despite Moodle has a great potential, it is mainly used as a repository of materials. The results also highlighted the existence of two groups of students distinguished by the degree of importance given to the Moodle tools.
Fedotova, Olga, Teixeira, Leonor, Alvelos, Helena
The Edelman trust barometer measures, since 2001, public trust in businesses, governments, non government organizations and media, across 25 countries. The 2012 survey (Edelman, 2012) showed that, in more than half of the studies countries, citizens distrust their own governments. According to their opinion there are two main actions governments must implement in order to improve public trust: (i) incorporate listening and feedback mechanisms within the governments, as well as (ii) develop transparent and open practices. Since the 1960s public participation has been an effective instrument used by governments in order to obtain citizens’ support, guarantee transparency of decision making processes as well as improve public trust in government policies. The development of information and communication technologies (ICTs) has enabled new cost-effective and convenient ways of citizens’ engagement, resulting in the emergence of the electronic participation (e-participation) concept. E-participation is believed to be a key strategy so governments can improve the efficiency, acceptance, and legitimacy of political processes as well as public trust. The main objectives of this work are to present and discuss the e-participation concept, analyze different classifications of e-participation, identify the main existing e-participation frameworks and explore integration between Web 2.0 and e-participation research fields. It is believed that this can be of interest to researchers and practitioners new to the e-participation area, in order to get familiarized with the fundamentals inherent to this domain. Moreover, this work presents ground for future analysis and investigation of the e-participation field.
Cardoso, Domingos Moreira, Pinheiro, Sofia J.
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 $(omega(G)-1)$-regular induced subgraph, respectively, were $omega(G)$ 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.
Andrade, Enide, Freitas, Maria Aguieiras A. de, Robbiano, María, San Martin, B.
I. Gutman, B. Furtula, C.K.Das, E. Milovanovic, I. Milovanovic
The definition of Randic matrix comes from a molecular structure descriptor introduced by Milan Randic in 1975, known as Randic index. The plethora of chemical and pharmacological applications of the Randic index, as well as numerous mathematical investigations are well known and presented in the literature. In spite of its connection with Randic index this matrix seems to have not been much studied in mathematical chemistry however, some graph invariants related with this matrix such as Randic energy (the sum of the absolute values of the eigenvalues of the Randic matrix), the concept of Randic spread (that is, the maximum difference between two eigenvalues of the Randic matrix, disregarding the spectral radius) were recently introduced and some of their properties were established. We review some topics related with the graph invariant Randic spread, such as bounds that were obtained from matrix and/or numerical inequalities establishing relations between this spectral parameter and some structural parameters of the underlying graph. Moreover, some new bounds for the Randic spread are obtained. Comparisons with some upper bounds for the Randic spread of regular graphs are done. Finally, a possible relation between Randic spread and Randic energy is established.
Almeida, P., Napp, D., Pinto, R.
In this paper, we investigate extended row distances of Unit Memory (UM) convolutional codes. In particular, we derive upper and lower bounds for these distances and moreover present a concrete construction of a UM convolutional code that almost achieves the derived upper bounds. The generator matrix of these codes is built by means of a particular class of matrices, called superregular matrices. We actually conjecture that the construction presented is optimal with respect to the extended row distances as it achieves the maximum extended row distances possible. This in particular implies that the upper bound derived is not completely tight. The results presented in this paper further develop the line of research devoted to the distance properties of convolutional codes which has been mainly focused on the notions of free distance and column distance. Some open problems are left for further research.
Pinto, Raquel, Simões, Rita
In this paper we study the minimality of input-state-output (ISO) representations of basic two-dimensional (2D) convolutional codes. For that we consider the Fornasini-Marchesini ISO representations of such codes. We define the novel property of strongly modally reachable representations and we show that such representations are minimal representations of a basic 2D convolutional code. Moreover, we prove that the dimension of such minimal representations equals the complexity of the code.
Rodrigues, Maria Manuela Fernandes, Vieira, Nelson Felipe Loureiro
Birkhäuser Basel
In this paper, we present a fractional extension of the classical circle Zernike polynomials defined via g-Jacobi functions. Some properties of this new class of functions are studied, such as recurrence relations for consecutive and distant neighborhoods, and differential relations. A graphic representation for the proposed fractional circle Zernike polynomials will be presented in the final section of the paper.
In this paper we present integral and series representations for the fundamental solution of the time fractional diffusion equation in an arbitrary dimension. The series representation obtained depends on the parity of the dimension. As an application of our results we study the diffusion and stress in the axially symmetric case for plane deformation associated to generalized thermoelasticity theory.
Castro, L. P., Guerra, R. C., Tuan, N. M.
Birkhauser
We consider a class of integral equations characterized by kernels of cosine and sine type and study their solvability. Moreover, we analyse the integral operator T, which is generating those equations, by identifying its characteristic polynomial, characterizing its invertibility, spectrum, Parseval type identity and involution properties. Additionally, a new convolution is here introduced, associated with T, for which we deduce a corresponding factorization property.
Alonso, Hugo, Rocha, Paula
In this work, we study the connection of the stability of multidimensional positive systems with the stability of switched positive systems. In a previous work, we showed that the stability of a multidimensional positive system implies the stability of a related switched positive system. Here, we investigate the reciprocal implication.
Cerejeiras, Paula, Fonseca, Aurineide, Kähler, Uwe, Vieira, Nelson
In this paper we present the basic tools of a fractional function theory in higher dimensions by means of a fractional correspondence to the Weyl relations via Gelfond-Leontiev operators of generalized di erentiation. A Fischer decomposition is established. Furthermore, we give an algorithm for the construction of monogenic homogeneous polynomials of arbitrary degree.
Ferreira, Susana, Afreixo, Vera, Moura, Gabriela, Tavares, Ana H. M. P.
Epigenetics can be defined as changes in the genome that are inherited during cell division, but without direct modification of the DNA sequence. These genomic changes are supported by three major epigenetic mechanisms: DNA methylation, histone modification and small RNAs. Different epigenetic marks function regulate gene transcription, some of them when altered can trigger various diseases such as cancer. This work is focus on the epigenetic signals in the human genome, studding the dependency between the nucleotide word context and the occurrence of epigenomic marking. We based our study on histone epigenomes available in the NIH Roadmap Epigenomics Mapping Consortium database that contains various types of cells and various types of tissues. We compared genomic contexts of epigenetic marking among chromosomes and among epigenomes. We included a control scenario, the DNA sequence regions without epigenetic marking. We identified significant differences between context occurrence of control and epigenetic regions. The genomic words in epigenetic marking regions present significant association with chromosome and histone modification type.
Abreu, Carlos, Miranda, Francisco, Mendes, Paulo M.
Biomedical wireless sensor networks enable the development of real time patient monitoring systems, either to monitor chronically ill persons in their homes or to monitor patients in step-down hospital units. However, due to the critical nature of medical data, these networks have to meet demanding quality of service requirements, ensuring high levels of confidence to their users. These goals depend on several factors, such as the characteristics of the network deployment area or the network topology. In such context, this chapter surveys the main applications of biomedical wireless sensor networks, taking into account the key quality of service requirements of each one of them. Finally, it presents an analytic method, and its experimental validation, to help engineers managing the radio power of the network nodes in order to improve the communications and the quality of service provided by the network while minimising the energy consumption and, thus, maximising the network lifetime.
Jesus, Luís, Belo, Inês, Machado, Jéssica, Hall, Andreia
A new open access resource called Advanced Voice Function Assessment Databases (AVFAD) was developed, based on a sample of 709 individuals (346 clinically diagnosed with vocal pathology and 363 with no vocal alterations) recruited in Portugal. All clinical conditions were registered according to the Classification Manual of Voice Disorders-I. Participants were audio-recorded, producing the following vocal tasks: Sustaining vowels /a, i, u/; reading of six CAPE-V sentences; reading a phonetically balanced text; spontaneous speech. The AVFAD are comprised of 8648 uncompressed audio files and an additional database file with 19 Praat Voice Report parameter values and 16 clinical data entries per participant. An annotated segment of the vowel /a/ for each participant was analysed automatically with a Praat script. Radial graphs were generated considering that all variables had an approximately normal distribution, and using previously calculated average and standard deviation values for all parameters. The normal and pathological f0 mean, Jitter ppq5, Shimmer apq11 and Harmonics-to-Noise-Ratio characteristics were compared. An additional analysis of the relation between the acoustic parameters and gender, age group, smoking habits, body mass index and voice usage, was considered. The AVFAD will allow future cooperative work and testing of non-invasive methods for voice pathology diagnosis.
Neves, Renato, Madeira, Alexandre, Barbosa, Luís, Martins, Manuel A.
Asymmetric combination of logics is a formal process that develops the characteristic features of a specific logic on top of another one. Typical examples include the development of temporal, hybrid, and probabilistic dimensions over a given base logic. These examples are surveyed in the paper under a particular perspective—that this sort of combination of logics possesses a functorial nature. Such a view gives rise to several interesting questions. They range from the problem of combining translations (between logics), to that of ensuring property preservation along the process, and the way different asymmetric combinations can be related through appropriate natural transformations.
Gonçalves, João N. C., Rodrigues, Helena Sofia, Monteiro, M. Teresa T.
Nowadays, the interest in analyze and study the behavior of uncontrollable nature phenomena related to the impact of marketing campaigns is an action of prime importance to prevent chaotic dynamics. In this paper we assess the influence of Dynamical Systems theory and Mathematical Epidemiology on a real viral marketing campaign: Dove Real Beauty Sketches, based on a SIR epidemiological model. Motivated by the overwhelming success of this campaign, we study the mathematical properties and dynamics of the campaign real data - from the parameters estimation and its sensitivity to the stability of the mathematical model, simulated in Matlab. Mathematically, we show not only that the campaign was a viral epidemic, but also that it can be leveraged and optimized by epidemiological and mathematical modeling, which offer important guidelines to maximize the impact of a viral message and minimize the uncertainty related to the conception and outcome of new marketing campaigns.
Kostyukova, O. I., Tchemisova, T. V.
United Institute of Informatics Problems of the National Academy of Sciences of Belarus
We are concerned with convex problems of infinite optimization, namely a linear problem of Semidefinite Programming (SDP). For this problem, we introduce a subspace of immobile indices, prove that in the case when the Slater condition is not satisfied, this subspace is not vanishing, and suggest an algorithm that constructs a base of this subspace. We show that the subspace of immobile indices is an important characteristic of the feasible set that can be successfully used for formulation of efficient optimality conditions. These conditions do not use any constraint qualifications and therefore can be applied to wide classes of SDP problems. 1. Introduction. In the
Ozogur-Akyuz, S., Akteke-Ozturk, B., Tchemisova, T., Weber, G.-W.
Data mining is a modern area of science dealing with the learning from given data in order to make predictions and estimations. Applications of Data mining can be found in various areas of academical and non academical life. This paper introduces new contributions by continuous optimization as a key technology in data mining. The methods suggested for solution of such important problems as clustering and classification, were recently obtained by the authors in collaboration with members of EURO working group EUROPT.
Cardoso, Domingos M., Luz, C. J., Pacheco, Maria de Fátima
In this paper, relevant results about the determination of (k,t)-regular sets, using the main eigenvalues of a graph, are reviewed and some results about the determination of (0,2)-regular sets are introduced. An algorithm for that purpose is also described. As an illustration, this algorithm is applied to the determination of maximum matchings in arbitrary graphs.
Fornasini, Ettore, Pinho, Telma, Pinto, Raquel, Rocha, Paula
In this paper we consider a special class of 2D convolutional codes (composition codes) with encoders G(d1;d2) that can be decomposed as the product of two 1D encoders, i.e., G(d1;d2) = G2(d2)G1(d1). In case that G1(d1) and G2(d2) are prime we provide constructions of syndrome formers of the code, directly from G1(d1) and G2(d2). Moreover we investigate the minimality of 2D state-space realization by means of a separable Roesser model of syndrome formers of composition codes, where G2(d2) is a quasi-systematic encoder.
Climent, Joan-Josep, Napp, Diego, Pinto, Raquel, Simões, Rita
In this paper we address the problem of decoding 2D convolutional codes over the erasure channel. In particular, we present a procedure to recover bursts of erasures that are distributed in a diagonal line. To this end we introduce the notion of balls around a burst of erasures which can be considered an analogue of the notion of sliding window in the context of 1D convolutional codes. The main result reduces the decoding problem of 2D convolutional codes to a problem of decoding a set of associated 1D convolutional codes.
Mano, Vasco Moço, Martins, Enide A., Vieira, Luís Almeida
We consider association schemes with d classes and the underlying Bose- Mesner algebra, A. Then, by taking into account the relationship between the Hadamard and the Kronecker products of matrices and making use of some matrix techniques over the idempotents of the unique basis of minimal orthogonal idempotents of A , we prove some results over the Krein parameters of an association scheme.
Madeira, Alexandre, Neves, Renato, Martins, Manuel A., Barbosa, Luís S.
This paper introduces a method to build dynamic logics with a graded semantics. The construction is parametrized by a structure to support both the spaces of truth and of the domain of computations. Possible instantiations of the method range from classical (assertional) dynamic logic to less common graded logics suitable to deal with programs whose transitional semantics exhibits fuzzy or weighted behaviour. This leads to the systematic derivation of program logics tailored to specific program classes.
Neves, Renato, Martins, Manuel A., Barbosa, Luís S.
Adding to the modal description of transition structures the ability to refer to specific states, hybrid(ised) logics provide an interesting framework for the specification of reconfigurable systems. The qualifier ‘hybrid(ised)’ refers to a generic method of developing, on top of whatever specification logic is used to model software configurations, the elements of an hybrid language, including nominals and modalities. In such a context, this paper shows how a calculus for a hybrid(ised) logic can be generated from a calculus of the base logic and that, moreover, it preserves soundness and completeness. A second contribution establishes that hybridising a decidable logic also gives rise to a decidable hybrid(ised) one. These results pave the way to the development of dedicated proof tools for such logics used in the design of reconfigurable systems.
Figueiredo, Daniel
When studying a biological regulatory network, it is usual to use boolean network models. In these models, boolean variables represent the behavior of each component of the biological system. Taking in account that the size of these state transition models grows exponentially along with the number of components considered, it becomes important to have tools to minimize such models. In this paper, we relate bisimulations, which are relations used in the study of automata (general state transition models) with attractors, which are an important feature of biological boolean models. Hence, we support the idea that bisimulations can be important tools in the study some main features of boolean network models.We also discuss the differences between using this approach and other well-known methodologies to study this kind of systems and we illustrate it with some examples.
Lobato, Miriam, Carvalho, Filipe, Pereira, Ana Sofia, Agra, Agostinho
Worldwide air traffic tends to increase and for many airports it is no longer an op-tion to expand terminals and runways, so airports are trying to maximize their op-erational efficiency. Many airports already operate near their maximal capacity. Peak hours imply operational bottlenecks and cause chained delays across flights impacting passengers, airlines and airports. Therefore there is a need for the opti-mization of the ground movements at the airports. The ground movement prob-lem consists of routing the departing planes from the gate to the runway for take-off, and the arriving planes from the runway to the gate, and to schedule their movements. The main goal is to minimize the time spent by the planes during their ground movements while respecting all the rules established by the Ad-vanced Surface Movement, Guidance and Control Systems of the International Civil Aviation. Each aircraft event (arrival or departing authorization) generates a new environment and therefore a new instance of the Ground Movement Prob-lem. The optimization approach proposed is based on an Iterated Local Search and provides a fast heuristic solution for each real-time event generated instance granting all safety regulations. Preliminary computational results are reported for real data comparing the heuristic solutions with the solutions obtained using a mixed-integer programming approach.
Macedo, Eloísa
This paper presents a study of regularity of Semidefinite Programming (SDP) problems. Current methods for SDP rely on assumptions of regularity such as constraint qualifications (CQ) and well-posedness. In the absence of regularity, the characterization of optimality may fail and the convergence of algorithms is not guaranteed. Therefore, it is important to have procedures that verify the regularity of a given problem before applying any (standard) SDP solver. We suggest a simple numerical procedure to test within a desired accuracy if a given SDP problem is regular in terms of the fulfilment of the Slater CQ. Our procedure is based on the recently proposed DIIS algorithm that determines the immobile index subspace for SDP. We use this algorithm in a framework of an interactive decision support system. Numerical results using SDP problems from the literature and instances from the SDPLIB suite are presented, and a comparative analysis with other results on regularity available in the literature is made.
Rodrigues, Helena Sofia, Monteiro, M. Teresa T., Torres, Delfim F. M., Silva, Ana Clara, Sousa, Carla, Conceição, Cláudia
Dengue is a vector-borne disease and 40% of world population is at risk. Dengue transcends international borders and can be found in tropical and subtropical regions around the world, predominantly in urban and semi-urban areas. A model for dengue disease transmission, composed by mutually-exclusive compartments representing the human and vector dynamics, is presented in this study. The data is from Madeira, a Portuguese island, where an unprecedented outbreak was detected on October 2012. The aim of this work is to simulate the repercussions of the control measures in the fight of the disease.
Rodrigues, Helena Sofia, Monteiro, M. Teresa T., Torres, Delfim F. M.
Nova Science Publishers
Optimal Control (OC) is the process of determining control and state trajectories for a dynamic system, over a period of time, in order to optimize a given performance index. With the increasing of variables and complexity, OC problems can no longer be solved analytically and, consequently, numerical methods are required. For this purpose, direct and indirect methods are used. Direct methods consist in the discretization of the OC problem, reducing it to a nonlinear constrained optimization problem. Indirect methods are based on the Pontryagin Maximum Principle, which in turn reduces to a boundary value problem. In order to have a more reliable solution, one can solve the same problem through different approaches. Here, as an illustrative example, an epidemiological application related to the rubella disease is solved using several software packages, such as the routine ode45 of Matlab, OC-ODE, DOTcvp toolbox, IPOPT and Snopt, showing the state of the art of numerical software for OC.
Rodrigues, Helena Sofia, Monteiro, M. Teresa T.
MPCC can be solved with specific MPCC codes or in its nonlinear equivalent formulation (NLP) using NLP solvers. Two NLP solvers - NPSOL and the line search filter SQP - are used to solve a collection of test problems in AMPL. Both are based on SQP (Sequential Quadratic Programming) philosophy but the second one uses a line search filter scheme.
Santos, S. P. S., Martins, N., Torres, D. F. M.
We address the generalized variational problem of Herglotz from an optimal control point of view. Using the theory of optimal control, we derive a generalized Euler-Lagrange equation, a transversality condition, a DuBois-Reymond necessary optimality condition and Noether’s theorem for Herglotz’s fundamental problem, valid for piece- wise smooth functions.
Almeida, Paulo J., Pinto, Raquel, Napp, Diego
In this paper we introduce a new type of superregular matrices that give rise to novel constructions of two-dimensional (2D) convolutional codes with finite support. These codes are of rate 1=n and degree d with n d +1 and achieve the maximum possible distance among all 2D convolutional codes with finite support with the same parameters.
Miranda, Francisco
A survey about approaches developed around the controllability of control systems on time scales is presented. Certain conventional dynamic models are described in the two parallel areas: continuous and discrete times. The results obtained in these two theories produce similar conclusions, but require different techniques for solving them. Then, it is important to create a technique that unifies these different times. Created by Stefan Hilger, the language of time scales seems to be an ideal tool for this purpose. Since that creation, many classical results of controllability were extended to this new theory and applied in mixed time control systems. In this chapter is presented the evolution of these results for linear control systems.
Developments of observability of control systems on time scales are presented. Certain conventional dynamic models are described in the two parallel areas: continuous and discrete times. The results obtained in these two theories produce similar conclusions, but require diferente techniques for solving them. In 1988, Time Scales Calculus introduced by Stefan Hilger in his Ph.D. thesis, had the purpose to initiate an unification of the continuous and discrete time cases. This theory seems to be an ideal tool to create a unified technique. Since that time, many classical results of observability were extended to this new theory and applied in mixed time control systems. In this chapter is presented an overview of these results for linear control systems.
Plakhov, Alexander
This is a review of results recently obtained by the author, related to problems of the body of minimal and maximal resistance. The cases of purely translational motion, as well as (rotational & translational) motion are considered. The notions of rough body and law of scattering on a body are discussed. Connections with the Monge-Kantorovich problem of optimal mass transportation are revealed, and applications to the Magnus effect and retroreflectors are discussed.
Almeida, R., Malinowska, A. B., Torres, D. F. M.
We review some recent results of the fractional variational calculus. Necessary optimality conditions of Euler–Lagrange type for functionals with a Lagrangian containing left and right Caputo derivatives are given. Several problems are considered: with fixed or free boundary conditions, and in presence of integral constraints that also depend on Caputo derivatives.
Malonek, Helmuth R., Kharlamova, Vera I.
Universidade do Minho. Centro de Matemática
This article emphasizes some moments in the life of the German mathematician August Gutzmer (1860-1924), who started his scientific career 1887 with 3 publications in the Jornal de Sciências Matemáticas e Astronómicas (Teixeira’s Journal) created by the famous Portuguese mathematician Francisco Gomes Teixeira in 1877, and continued to publish therein until the volume of 1897. A brief analysis of the correspondence between both scientists makes clear that among all foreign authors of this journal Gutzmer played a singular role as link between Gomes Teixeira and Germany, probably also motivated by some coincidence of interests and areas of their academic work. Becoming later the successor of Georg Cantor at the Vereinigten Friedrichs-Universitat Halle-Wittenberg and a closed collaborator of Felix Klein, Gutzmer kept contact with Gomes Teixeira until the end of his life and contributed significantly to the recognition of the Portuguese mathematician in Germany.