Designing Conventional, Spatial, and Temporal Data ...

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Universit´ e Libre de Bruxelles Facult´ e des Sciences Appliqu´ ees Service Ing´ enierie Informatique et de la D´ ecision (CoDE) Designing Conventional, Spatial, and Temporal Data Warehouses: Concepts and Methodological Framework Elzbieta Malinowski Work directed by: Professor Esteban Zim´anyi Th` ese pr´ esent´ ee en vue de l’obtention du grade acad´ emique de Docteur en Sciences Appliqu´ ees Ann´ ee acad´ emique 2006-2007

Transcript of Designing Conventional, Spatial, and Temporal Data ...

Universite Libre de Bruxelles

Faculte des Sciences Appliquees

Service Ingenierie Informatique

et de la Decision (CoDE)

Designing Conventional, Spatial,

and Temporal Data Warehouses:

Concepts and Methodological Framework

Elzbieta Malinowski

Work directed by: Professor Esteban Zimanyi

These presentee en vue de l’obtentiondu grade academique de

Docteur en Sciences Appliquees

Annee academique 2006-2007

To Yamil,my one and only love and husband,who throughout this time has been

a patient friend, an untiring supporter,and a wise adviser

Abstract

Decision support systems are interactive, computer-based information systems thatprovide data and analysis tools in order to better assist managers on different levelsof organization in the process of decision making. Data warehouses (DWs) have beendeveloped and deployed as an integral part of decision support systems.

A data warehouse is a database that allows to store high volume of historical datarequired for analytical purposes. This data is extracted from operational databases,transformed into a coherent whole, and loaded into a DW during the extraction-transformation-loading (ETL) process.

DW data can be dynamically manipulated using on-line analytical processing (OLAP)systems. DW and OLAP systems rely on a multidimensional model that includes mea-sures, dimensions, and hierarchies. Measures are usually numeric additive values thatare used for quantitative evaluation of different aspects about organization. Dimen-sions provide different analysis perspectives while hierarchies allow to analyze measureson different levels of detail.

Nevertheless, currently, designers as well as users find difficult to specify multidi-mensional elements required for analysis. One reason for that is the lack of conceptualmodels for DW and OLAP system design, which would allow to express data require-ments on an abstract level without considering implementation details. Another prob-lem is that many kinds of complex hierarchies arising in real-world situations are notaddressed by current DW and OLAP systems.

In order to help designers to build conceptual models for decision-support systemsand to help users in better understanding the data to be analyzed, in this thesis wepropose the MultiDimER model – a conceptual model used for representing multidi-mensional data for DW and OLAP applications. Our model is mainly based on theexisting ER constructs, for example, entity types, attributes, relationship types withtheir usual semantics, allowing to represent the common concepts of dimensions, hier-archies, and measures. It also includes a conceptual classification of different kinds ofhierarchies existing in real-world situations and proposes graphical notations for them.

On the other hand, currently users of DW and OLAP systems demand also theinclusion of spatial data, visualization of which allows to reveal patterns that are diffi-cult to discover otherwise. The advantage of using spatial data in the analysis processis widely recognized since it allows to reveal patterns that are difficult to discoverotherwise.

However, although DWs typically include a spatial or a location dimension, thisdimension is usually represented in an alphanumeric format. Furthermore, there isstill a lack of a systematic study that analyze the inclusion as well as the managementof hierarchies and measures that are represented using spatial data.

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ii ABSTRACT

With the aim of satisfying the growing requirements of decision-making users, weextend the MultiDimER model by allowing to include spatial data in the differentelements composing the multidimensional model. The novelty of our contribution laysin the fact that a multidimensional model is seldom used for representing spatial data.To succeed with our proposal, we applied the research achievements in the field ofspatial databases to the specific features of a multidimensional model. The spatialextension of a multidimensional model raises several issues, to which we refer in thisthesis, such as the influence of different topological relationships between spatial objectsforming a hierarchy on the procedures required for measure aggregations, aggregationsof spatial measures, the inclusion of spatial measures without the presence of spatialdimensions, among others.

Moreover, one of the important characteristics of multidimensional models is thepresence of a time dimension for keeping track of changes in measures. However, thisdimension cannot be used to model changes in other dimensions. Therefore, usualmultidimensional models are not symmetric in the way of representing changes formeasures and dimensions. Further, there is still a lack of analysis indicating which con-cepts already developed for providing temporal support in conventional databases canbe applied and be useful for different elements composing a multidimensional model.

In order to handle in a similar manner temporal changes to all elements of a mul-tidimensional model, we introduce a temporal extension for the MultiDimER model.This extension is based on the research in the area of temporal databases, which havebeen successfully used for modeling time-varying information for several decades. Wepropose the inclusion of different temporal types, such as valid and transaction time,which are obtained from source systems, in addition to the DW loading time generatedin DWs. We use this temporal support for a conceptual representation of time-varyingdimensions, hierarchies, and measures. We also refer to specific constraints that shouldbe imposed on time-varying hierarchies and to the problem of handling multiple timegranularities between source systems and DWs.

Furthermore, the design of DWs is not an easy task. It requires to consider all phasesfrom the requirements specification to the final implementation including the ETLprocess. It should also take into account that the inclusion of different data items in aDW depends on both, users’ needs and data availability in source systems. However,currently, designers must rely on their experience due to the lack of a methodologicalframework that considers above-mentioned aspects.

In order to assist developers during the DW design process, we propose a method-ology for the design of conventional, spatial, and temporal DWs. We refer to differentphases, such as requirements specification, conceptual, logical, and physical model-ing. We include three different methods for requirements specification depending onwhether users, operational data sources, or both are the driving force in the process ofrequirement gathering. We show how each method leads to the creation of a conceptualmultidimensional model. We also present logical and physical design phases that referto DW structures and the ETL process.

To ensure the correctness of the proposed conceptual models, i.e., with conven-tional data, with the spatial data, and with time-varying data, we formally definethem providing their syntax and semantics. With the aim of assessing the usability ofour conceptual model including representation of different kinds of hierarchies as well

ABSTRACT iii

as spatial and temporal support, we present real-world examples. Pursuing the goalthat the proposed conceptual solutions can be implemented, we include their logicalrepresentations using relational and object-relational databases. Further, to show theapplicability of the proposed methodology and different approaches used for require-ments specification, we include several real-world examples related to universities.

Contents

Acknowledgements xi

1 Introduction 11.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.1.1 Conventional data warehouses . . . . . . . . . . . . . . . . . . . 21.1.2 Spatial databases and spatial data warehouses . . . . . . . . . . 41.1.3 Temporal databases and temporal data warehouses . . . . . . . 51.1.4 Conceptual modeling . . . . . . . . . . . . . . . . . . . . . . . . 61.1.5 Methodology for database and data warehouse design . . . . . . 6

1.2 Motivation and objectives of the thesis . . . . . . . . . . . . . . . . . . 71.2.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.2.2 Objectives of the thesis . . . . . . . . . . . . . . . . . . . . . . . 10

1.3 Scope and contributions of the thesis . . . . . . . . . . . . . . . . . . . 111.3.1 Conventional data warehouses . . . . . . . . . . . . . . . . . . . 111.3.2 Spatial data warehouses . . . . . . . . . . . . . . . . . . . . . . 131.3.3 Temporal data warehouses . . . . . . . . . . . . . . . . . . . . . 14

1.4 Thesis organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2 Conventional data warehouses 172.1 Data warehouse structures and data manipulation . . . . . . . . . . . . 18

2.1.1 Star, snowflake, and starflake schemas . . . . . . . . . . . . . . 182.1.2 Aspects of data manipulation in DWs . . . . . . . . . . . . . . . 18

2.2 The MultiDimER model . . . . . . . . . . . . . . . . . . . . . . . . . . 202.2.1 Model definition . . . . . . . . . . . . . . . . . . . . . . . . . . . 212.2.2 Model particularities . . . . . . . . . . . . . . . . . . . . . . . . 222.2.3 Metamodel of the MultiDimER model . . . . . . . . . . . . . . 23

2.3 Mapping from conceptual to relational models . . . . . . . . . . . . . . 232.3.1 Rationale for choosing relational model . . . . . . . . . . . . . . 242.3.2 Mapping rules . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.4 Data warehouse hierarchies . . . . . . . . . . . . . . . . . . . . . . . . . 262.4.1 Simple hierarchies . . . . . . . . . . . . . . . . . . . . . . . . . . 272.4.2 Non-strict hierarchies . . . . . . . . . . . . . . . . . . . . . . . . 392.4.3 Multiple alternative hierarchies . . . . . . . . . . . . . . . . . . 442.4.4 Parallel hierarchies . . . . . . . . . . . . . . . . . . . . . . . . . 462.4.5 Hierarchy categorization . . . . . . . . . . . . . . . . . . . . . . 48

2.5 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

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2.6 Related work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3 Spatial data warehouses 573.1 Spatial databases: General concepts . . . . . . . . . . . . . . . . . . . . 583.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.2.1 Using the object-relational model . . . . . . . . . . . . . . . . . 613.2.2 Using spatial extensions of DBMSs . . . . . . . . . . . . . . . . 623.2.3 Preserving semantics . . . . . . . . . . . . . . . . . . . . . . . . 63

3.3 Spatially-extended MultiDimER model . . . . . . . . . . . . . . . . . . 633.4 Spatial levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.4.1 Conceptual representation . . . . . . . . . . . . . . . . . . . . . 653.4.2 Logical representation of spatial levels . . . . . . . . . . . . . . 663.4.3 Mapping of levels with spatial descriptive attributes . . . . . . . 68

3.5 Spatial hierarchies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 683.5.1 Conceptual representation . . . . . . . . . . . . . . . . . . . . . 693.5.2 Topological relationships between spatial levels . . . . . . . . . 753.5.3 Logical representation of spatial hierarchies . . . . . . . . . . . . 78

3.6 Spatial fact relationships and measures . . . . . . . . . . . . . . . . . . 833.6.1 Conceptual representation . . . . . . . . . . . . . . . . . . . . . 843.6.2 Mapping of spatial fact relationships . . . . . . . . . . . . . . . 903.6.3 Mapping of spatial measures . . . . . . . . . . . . . . . . . . . . 91

3.7 Metamodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 933.8 Related work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 953.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97

4 Temporal data warehouses 994.1 Temporal databases: General concepts . . . . . . . . . . . . . . . . . . 1004.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1024.3 Temporal types in DWs . . . . . . . . . . . . . . . . . . . . . . . . . . 1034.4 Temporal extension for the MultiDimER model . . . . . . . . . . . . . 1044.5 Mapping of temporal types . . . . . . . . . . . . . . . . . . . . . . . . . 1074.6 Temporal levels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

4.6.1 Conceptual representation . . . . . . . . . . . . . . . . . . . . . 1094.6.2 Mapping of temporal levels . . . . . . . . . . . . . . . . . . . . . 110

4.7 Temporal hierarchies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1144.7.1 Conceptual representation . . . . . . . . . . . . . . . . . . . . . 1144.7.2 Mapping of child-parent relationships . . . . . . . . . . . . . . . 119

4.8 Temporal measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1254.8.1 Temporal support for non-aggregated measures . . . . . . . . . 1264.8.2 Temporal support for aggregated measures . . . . . . . . . . . . 1304.8.3 Mapping of fact relationships with temporal measures . . . . . . 133

4.9 Metamodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1344.10 Summary of mapping rules . . . . . . . . . . . . . . . . . . . . . . . . . 1374.11 Related work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1384.12 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

CONTENTS vii

5 A methodology for conventional DW design 145

5.1 Conventional database design . . . . . . . . . . . . . . . . . . . . . . . 146

5.2 Current approaches for data warehouse design . . . . . . . . . . . . . . 147

5.2.1 Data warehouse lifecycle . . . . . . . . . . . . . . . . . . . . . . 147

5.2.2 Data mart and data warehouse design . . . . . . . . . . . . . . 150

5.2.3 Design phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

5.2.4 Methods for requirements specifications and DW design . . . . . 151

5.3 Phases for data warehouse design . . . . . . . . . . . . . . . . . . . . . 152

5.4 A motivating case study . . . . . . . . . . . . . . . . . . . . . . . . . . 153

5.5 Requirements specification and conceptual design . . . . . . . . . . . . 155

5.5.1 Demand-driven approach . . . . . . . . . . . . . . . . . . . . . . 156

5.5.2 Supply-driven approach . . . . . . . . . . . . . . . . . . . . . . 168

5.5.3 Demand/supply-driven approach . . . . . . . . . . . . . . . . . 176

5.6 Logical design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

5.6.1 Logical representation of DW schemas . . . . . . . . . . . . . . 179

5.6.2 Defining ETL processes . . . . . . . . . . . . . . . . . . . . . . . 183

5.7 Physical design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

5.7.1 DW schema implementation . . . . . . . . . . . . . . . . . . . . 184

5.7.2 ETL processes and staging area implementation . . . . . . . . . 189

5.8 Related work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

5.8.1 Overall process . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

5.8.2 Requirements specifications . . . . . . . . . . . . . . . . . . . . 192

5.8.3 Conceptual, logical, and physical level design . . . . . . . . . . . 195

5.9 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196

6 Spatial and temporal DW design 197

6.1 Spatial and temporal database design . . . . . . . . . . . . . . . . . . . 198

6.2 A methodology for spatial DW design . . . . . . . . . . . . . . . . . . . 198

6.2.1 Requirements specification and conceptual design . . . . . . . . 198

6.2.2 Logical and physical design . . . . . . . . . . . . . . . . . . . . 203

6.3 Methodological framework for temporal DW design . . . . . . . . . . . 203

6.3.1 Requirements specification and conceptual design . . . . . . . . 204

6.3.2 Logical and physical design . . . . . . . . . . . . . . . . . . . . 208

6.4 Related work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209

6.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 210

7 Conclusions and future work 211

7.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 211

7.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214

7.2.1 Conventional data warehouses . . . . . . . . . . . . . . . . . . . 214

7.2.2 Spatial data warehouses . . . . . . . . . . . . . . . . . . . . . . 215

7.2.3 Temporal and spatio-temporal data warehouses . . . . . . . . . 216

7.2.4 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217

viii CONTENTS

A Formalization of the MultiDimER model 219

A.1 Notations and assumptions . . . . . . . . . . . . . . . . . . . . . . . . . 219

A.2 Meta variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

A.3 Abstract syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220

A.4 Examples using the abstract syntax . . . . . . . . . . . . . . . . . . . . 222

A.4.1 Level definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . 222

A.4.2 Child-parent relationship definitions . . . . . . . . . . . . . . . . 222

A.4.3 Dimension definitions . . . . . . . . . . . . . . . . . . . . . . . . 222

A.4.4 Fact relationship definitions . . . . . . . . . . . . . . . . . . . . 223

A.4.5 Constraint definitions . . . . . . . . . . . . . . . . . . . . . . . . 223

A.5 Auxiliary functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

A.6 Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224

A.6.1 Semantics of predefined data types . . . . . . . . . . . . . . . . 224

A.6.2 Semantic domains . . . . . . . . . . . . . . . . . . . . . . . . . . 224

A.6.3 Semantic functions . . . . . . . . . . . . . . . . . . . . . . . . . 224

B Formalization of the spatial MultiDimER model 229

B.1 Meta variables for the spatial extension . . . . . . . . . . . . . . . . . . 229

B.2 Abstract syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

B.3 Examples using the abstract syntax . . . . . . . . . . . . . . . . . . . . 230

B.3.1 Level definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . 230

B.3.2 Child-parent relationship definitions . . . . . . . . . . . . . . . . 232

B.3.3 Dimension definitions . . . . . . . . . . . . . . . . . . . . . . . . 232

B.3.4 Fact relationship definitions . . . . . . . . . . . . . . . . . . . . 232

B.3.5 Constraint definitions . . . . . . . . . . . . . . . . . . . . . . . . 232

B.4 Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233

B.4.1 The space model . . . . . . . . . . . . . . . . . . . . . . . . . . 233

B.4.2 Semantic domains . . . . . . . . . . . . . . . . . . . . . . . . . . 235

B.4.3 Semantic functions . . . . . . . . . . . . . . . . . . . . . . . . . 235

C Formalization of the temporal MultiDimER model 241

C.1 Meta variables for the temporal extension . . . . . . . . . . . . . . . . 241

C.2 Abstract syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241

C.3 Examples using the abstract syntax . . . . . . . . . . . . . . . . . . . . 242

C.3.1 Level definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . 242

C.3.2 Child-parent relationship definitions . . . . . . . . . . . . . . . . 244

C.3.3 Dimension definitions . . . . . . . . . . . . . . . . . . . . . . . . 245

C.3.4 Fact relationship definitions . . . . . . . . . . . . . . . . . . . . 245

C.3.5 Constraint definitions . . . . . . . . . . . . . . . . . . . . . . . . 245

C.4 Auxiliary functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246

C.5 Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 246

C.5.1 The time model . . . . . . . . . . . . . . . . . . . . . . . . . . . 246

C.5.2 Semantic domains . . . . . . . . . . . . . . . . . . . . . . . . . . 247

C.5.3 Semantic functions . . . . . . . . . . . . . . . . . . . . . . . . . 247

CONTENTS ix

D Graphical notations 255D.1 Notations for the ER model . . . . . . . . . . . . . . . . . . . . . . . . 255D.2 Notations for relational and object-relational databases . . . . . . . . . 257D.3 Notations for conventional data warehouses . . . . . . . . . . . . . . . . 258D.4 Notations for spatial data warehouses . . . . . . . . . . . . . . . . . . . 260D.5 Notations for temporal data warehouses . . . . . . . . . . . . . . . . . 261

Bibliography 263

Acknowledgements

First of all, I would like to express my gratitude to the Universe for the opportunityand challenging events that allow me to grow both professionally and personally.

I am also very thankful for my family’s support. This work would be impossible tofinish without the constant, daily encouragement from my husband. Thanks, Yamil, forbelieving in me more than I could believe in myself. I am also grateful to you for helpingme balance my life between different everyday activities. Thanks, Bartosz, for beingsuch a self-sufficient son during these four years. You are a strong guy who knows howto face challenges with mom constantly making you move to a different country, learnnew languages, and shape your new life. Thanks, Carito, my unbelievable daughter,for taking all the responsibilities in Costa Rica. Without your help I would not havebeen able to study in Belgium.

I would also like to express my gratitude to the Director of this thesis, EstebanZimanyi. His critical observations helped me improve the analytical skills required forthe research process as well as the writing skills required for disseminating the results.I also appreciate the freedom that Esteban gave me in choosing research directionsand methods. I believe that the ability that I acquired during my doctoral studies oflooking for new problems and finding their solutions is an important skill to achievefuture professional goals. I also had a privilege to have Esteban’s friendship for fouryears and to witness the birth of his first daughter, Elenita. I will take with me thememory of these moments of hard work and fun.

Special thanks goes to my research committee, Dr. Jef Wijsen and Dr. RoelWuyts. You cannot imagine how much your encouragement and appreciation of myacademic effort meant to me during the presentation sessions over these four years.I am also particularly grateful for the valuable comments from Professor Wijsen whomade me analyze my proposal more in-depth to improve its quality. I have also receivedimportant advice from professor Wuyts who contributed to the accuracy and readinessof this thesis. Thanks also both of you for unbelievable support in different occasionsduring the last period of writing my dissertation.

I would also like to show my appreciation to Dr. Marco Dorigo and Professor Jean-Luc Hainaut for the help in the final phase of writing my dissertation. The detailedrevision of professor Dorigo and his positive feedback motivated me to keep on workingto improve my thesis. I would like to acknowledge that, in spite of time constraintsand your busy schedule, you were able to read this thesis and give me your valuablecomments. Special thanks goes also to Professor Hainaut. I was fortunate to haveyou in my committee and to benefit from your expertise. Thank you for dedicatingyour valuable time to revise my work and to give me additional recommendations forincreasing its quality.

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xii ACKNOWLEDGEMENTS

I would also like to express my gratitude to many anonymous reviewers who eval-uated my articles, either accepting or rejecting them, for conferences, workshops, andjournals. The feedback I received from them helped to improve the quality of thisthesis and to expand my research scope. Thanks you for this enormous effort, which Iknow was time-consuming and did not have a direct appreciation gesture.

I am also thankful for the continuous administrative support from Natasha VanderHeyden. I know very few people who help the way you do without asking recognitionfor your job.

Last, but not least, I am dedicating my appreciation to two universities: the Uni-versite Libre de Bruxelles, specially to Service de Cooperation, and the Universidadde Costa Rica. Thanks to the former I received the scholarship that allowed me toaccomplish the dream of my professional life: a PhD degree. This financial and humansupport gave me the necessary comfort to focus on my research. I would like to expressmy gratitude to Mme. Dominique Mertens and Larondelle Arlette from the Service deCooperation for helping me with all administrative issues. Thanks also to Dominiquefor being such a special person and sharing her friendship with me. I strongly believethat the time and effort you invested in me and financial support you gave me willreplicate enormously when I share my knowledge with my students at the Universidadde Costa Rica.

Special thanks to the Universidad de Costa Rica that provided financial supportto my family. I believe this university is one of a kind, as it strongly supports thehuman side of scientists and encourages them to develop their professional growth bysimultaneously promoting family union. I would like to particularly express my appre-ciation to the former and current directors of the Oficina de Asuntos Internacionales(International Affairs Bureau) of the Universidad de Costa Rica, Dr. Manuel Murilloy Dra Ana Sittenfeld, respectively. Thank you for providing very efficient and rapidadministrative procedures and for offering all the necessary conditions to completemy doctoral studies. Special thanks goes also to Patricia Alfaro, Fatima Acosta, andYamileth Damazio, from the same bureau. You were very supportive and patient withall the questions I had during these four years of study.

Bibliography

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