Jean-Christian Ralaivao

Jérôme Darmont

Knowledge and Metadata Integration for Warehousing Complex Data

Keywords: XML data warehousing, complex data, metadata, knowledge, metadata and knowledge integration

With the ever-growing availability of so-called complex data, especially on the Web, decision-support systems such as data warehouses must store and process data that are not only numerical or symbolic. Warehousing and analyzing such data requires the joint exploitation of metadata and domain-related knowledge, which must thereby be integrated. In this paper, we survey the types of knowledge and metadata that are needed for managing complex data, discuss the issue of knowledge and metadata integration, and propose a CWM-compliant integration solution that we incorporate into an XML complex data warehousing framework we previously designed.

Introduction

Decision-support technologies, and more particularly data warehousing [Inm02, [START_REF] Kimball | The Data Warehouse Toolkit: The Complete Guide to Dimensional Modeling[END_REF][START_REF] Jarke | Fundamentals of Data Warehouses[END_REF], are nowadays technologically mature. Data warehouses are aimed at monitoring and analyzing activities that are materialized by numerical measures (facts), while symbolic data describe these facts and constitute analysis axes (dimensions). However, in real life, many decision-support fields (customer relationship management, marketing, competition monitoring, medicine...) need to exploit data that are not only numerical or symbolic. For example, computer-aided diagnosis systems might require the analysis of various and heterogeneous data, such as patient records, medical images, biological analysis results, and previous diagnoses stored as texts [START_REF] Saad | Information-based Medicine: A New Era in Patient Care[END_REF]. We term such data complex data [START_REF] Darmont | An Architecture Framework for Complex Data Warehouses[END_REF]. Their availability is now very common, especially since the broad development of the Web, and more recently the Web 2.0 (blogs, wikis, multimedia data sharing sites...).

Complex data might be structured or not, and are often located in several, heterogeneous data sources. Specific approaches are needed to collect, integrate, manage and analyze them. A data warehousing solution is interesting in this context, though adaptations are obviously necessary to take into account data complexity (measures might not be numerical, for instance). Data volumetry and dating are also other arguments in favor of the warehousing approach.

In this context, metadata and domain-related knowledge are essential in the processing of complex data and play an important role when integrating, managing, and analyzing them. In this paper, we address the issue of jointly managing knowledge and metadata, in order to warehouse complex data and handle them, at three different levels: at the supplier level (data providers), to identify all input data sources and the role of source type drivers; at the user level (consumers), to identify all data sources for analysis and their source type drivers; at the manager level (administrators), to achieve good performance.

Since data warehouses traditionally handle knowledge under the form of metadata, we discuss the alternatives for integrating domain-related knowledge and metadata. Our position is that knowledge should be integrated as metadata in a complex data warehouse. On this basis, we also present an XML-based architecture framework for complex data warehouses that expands the one we proposed in [START_REF] Darmont | An Architecture Framework for Complex Data Warehouses[END_REF].

The remainder of this paper is organized as follows. In Section 2, we survey the various kinds of knowledge and metadata that are required for managing complex data. In Section 3, we discuss the issue of knowledge and metadata integration, justify our choice, and present our revised architecture framework for complex data warehouses. In Section 4, we summarize the state of the art regarding knowledge and metadata integration. We finally conclude this paper and provide future research directions in Section 5.

Knowledge and Metadata Needs

Knowledge Types

Two types of knowledge must be taken in consideration: tacit and explicit knowledge [START_REF] Nemati | Knowledge Warehouse: An Architectural Integration of Knowledge Management, Decision Support, Artifical Intelligence and Data Warehousing[END_REF]. Tacit knowledge includes beliefs, perspectives and mental models. Explicit knowledge is knowledge that can be expressed formally using a language, symbols, rules, objects or equations, and thus can be communicated to others. In data warehousing environments, we are particularly interested in explicit knowledge.

Then, different kinds of questions must be considered regarding the types of knowledge that are needed to manage complex data warehouses. These questions determine the description context (what), the organizational context (who, where and when), the processing context (how) and the motivation and business rules (why).

Responses to the "what"-type question describe business concepts. These elements guide the link between metadata and knowledge; while knowledge representation uses metadata contents and structure. The "how" and "why" questions relate to each process' motivation and the way it operates, in comparison to an existing organization. Eventually, answering to the "who", "where" and "when" questions helps in connecting the first two categories of questions to a particular organization. Furthermore, one type of knowledge that is often forgotten is universal or background knowledge. For example, the number of days in a month, the work scheduler with wrought days, public holidays, constitute some background knowledge that is essential for decision or analytical queries.

We must also consider statistical knowledge, which may include descriptive statistics about the data warehouse contents, or hypotheses about attributes' characteristics, such as probabilistic laws or sampling methods. Statistical knowledge may be provided by data analysis or data mining, and results should be reinjected into the system.

Technical knowledge is also very important at different phases of the data warehouse lifecycle. At a high level of abstraction, it is closely related to metadata. Technical knowledge includes knowledge about data sources and targets, standard and specific data types, database management systems (DBMSs), software and hardware platforms, technologies, etc. Indexing techniques available in each DBMS belong to this type of knowledge too.

Closely related is knowledge about organizational and geographical deployment, which includes information about users, their needs, their attributions and their constraints in regard to their needs (e.g., in terms of response time, volume of processed data, result format, etc.).

The last kind of knowledge we must consider relates to data warehouse administration. It provides information about how the data warehouse is used (access statistics) and how the interface between the data warehouse and the operational systems articulates, i.e., what the transactional applications and their characteristics (frequencies, response times, users...) are; and what the major Extracting, Transforming and Loading (ETL) problems (planification to satisfy user requirements with respect to work schedule, identification of peak periods...) are. The refreshment policies of the data warehouse contents are also important here, since they dictate the rotation period of summary data, the purge period and dormant data determination.

Metadata Types

We identified five transversal and complementary classifications for metadata in the literature. In the first classification [START_REF] Huynh | Metadata for Object-Relational Data Warehouse[END_REF], metadata are classified based on the data warehouse architecture layers, as follows:

• metadata associated with data loading and transformation, which describe the source data and any changes operated on data;

• metadata associated with data management, which define the data stored in the data warehouse;

• metadata used by the query manager to generate an appropriate query.

The second classification [START_REF] Huynh | Metadata for Object-Relational Data Warehouse[END_REF] divides metadata into:

• technical metadata that support the technical staff and contain the terms and definition of metadata as they appear in operational databases;

• business metadata that support business end-users who do not have any technical background;

• information navigator metadata, which are tools that help users navigate through both the business metadata and the warehoused data.

In the third classification [START_REF] Huynh | Metadata for Object-Relational Data Warehouse[END_REF], metadata may be:

• static metadata that are used to document or browse the system;

• dynamic metadata that can be generated and maintained at run time. A new kind of metadata is made of metadata that handle the mapping between systems.

In the fourth classification [START_REF] Kim | On Metadata Management Technology: Status and Issues[END_REF], metadata may be:

• system catalog metadata or data descriptors;

• relationship metadata that store information about the relationships between data entities (primary key/foreign key relationships, generalization/specialization relationship, aggregation relationship, inheritance relationships and any other special semantic relationship implying update or delete dependency);

• content metadata formed by descriptions of the contents of stored data at an arbitrary granularity. Content metadata may be as simple as one keyword, or as complex as a business rules, formulae or links to whole documents;

• data lineage metadata, which are lifecycle data about stored data (information about the creation of data, subsequent updates, transformation, versioning, summarization, migration, and replication, transformation rules, and descriptions of migration and replication);

• technical metadata that store technical information about stored data: format, compression or encoding algorithm used, encryption and decryption algorithms, encryption and decryption keys, software used to create or update the data, Application Programming Interfaces (APIs) available to access the data, etc.;

• data usage metadata or business data that are descriptions of how and for what purposes the data are to be used by users and applications;

• system metadata that are descriptions about the overall system environment, including hardware, operating system and application software;

• process metadata that describe the processes in which the applications operate, and any relevant output of each step of these processes.

Eventually, the fifth classification we identified [START_REF] Shankaranarayanan | Managing Metadata in Decision Environments[END_REF] is based upon functionality categories: infrastructure, data model, process, quality, interface and administration.

• Infrastructure metadata contain information on system components.

• Data model metadata (also called data dictionary) include definitions of data entities and the relationships among them.

• Process metadata capture information on data generation and transfer from sources to targets.

• Quality metadata contains information on the actual data stored and helps in assessing data quality (e.g., factual measurements).

• Interface metadata (also called reporting metadata) support data delivery to endusers.

• Finally, administration metadata include data that are necessary for administering the data warehouse and its associate applications (security, authentification, usage tracking...).

To conclude this section, we cite an important standardization initiative: the Common Warehouse Metamodel (CWM [START_REF]Common Warehouse Metamodel (CWM) Specification, version 1[END_REF]). CWM has been established by the Object Management Group (OMG) within its framework of Meta-Object Facilities (MOF). CWM purposes a metamodel that can be instantiated to obtain an operational data warehouse. Each of the metadata types we enumerated in the above classifications should be mapped into one or several CWM components.

Knowledge and Metadata Integration for Complex Data Warehousing

Integrating Knowledge and Metadata

Current data warehouse architectures are based on metadata. However, they are sometimes themselves a materialization of domain-related knowledge that facilitates the management of data warehouses and helps in achieving good performance. It is difficult for classical architectures to manage complex data without domain-related knowledge nor background knowledge. For example, a data warehouse administrator needs some background, domain-related knowledge in addition to metadata to select clustering or indexing techniques.

There are three possibilities to jointly manage knowledge and metadata: coding and representing knowledge as metadata; modelling metadata to match knowledge representation; managing metadata and knowledge separately. The advantages and drawbacks of each possibility are discussed below.

Coding and representing knowledge as metadata present an important advantage: we can keep on using and maintain current architectures and techniques. However, it is necessary to find a solution for knowledge representation, a kind of mapping between classical knowledge representation and metadata implementation.

Modelling metadata to match knowledge representation hedges on the domain of knowledge warehouses [START_REF] Nemati | Knowledge Warehouse: An Architectural Integration of Knowledge Management, Decision Support, Artifical Intelligence and Data Warehousing[END_REF], which supposes important adaptations and new considerations about current architectures. Some metadata cannot be converted into knowledge and there is a risk to loose some information. Moreover, finding a knowledge representation that can accept actual metadata is not obvious.

As for the third possibility, i.e., managing metadata and knowledge separately, a great change of architecture would be essential, because a structure that allows to coordinate and to compile metadata and knowledge contents must be devised. Instead of reducing complexity, this solution would increase it with the consideration of a new element: managing the connection between knowledge and metadata.

In conclusion, in order to build upon the assets of current data warehouse architectures, in particular in terms of performance, we select the first solution and explore it in this paper.

Revised Architecture Framework for Complex Data Warehousing

Global Architecture

In [START_REF] Darmont | An Architecture Framework for Complex Data Warehouses[END_REF], we have already proposed an architecture framework for complex data warehouses. The main components of this architecture (Figure 1) are: the data warehouse kernel, which may be either materialized as an XML warehouse, or virtual (where cubes are computed at run time); operational databases; source type drivers that notably include mapping specifications between the sources and XML; and finally a metadata and knowledge base layer that includes three submodules related to three management processes.

These three processes for managing a data warehouse are:

1. the ETL and integration process that feeds the warehouse with source data from the operational databases (OD) by using drivers that are specific to each source type (ST );

2. the administration and monitoring process (M D & KB) that manages metadata and knowledge (the administrator interacts with the data warehouse through this process);

3. the analysis and usage process that runs user queries, produces reports, builds data cubes, supports On-Line Analytical Processing (OLAP), etc. (result data RD).

Each of these processes exploits and updates the metadata and the knowledge base through four types of flows:

1. the external flow, which includes the ETL and integration flow and the exploitation (analysis and usage) flow (the warehouse may thus be considered as a black box);

2. the internal flow, between the warehouse kernel and the metadata and knowledge base layer, and between the metadata and knowledge base layer and the source type drivers; 4. the reference flow, which illustrates the fact that the external flow always refers to the metadata and knowledge base layer for integration, ETL, and analysis and usage in general.

XML Warehouse

The symmetric aspect between "sources" and "usages" around the data warehouse core allows us to eventually re-inject results as data sources. For instance, a data mining analysis may discover dependencies between variables and highlight causal relationships among them. We do use such techniques to determine the relevance of complex data with respect to given analysis goals. Then, knowledge obtained by mining can be integrated into the metadata repository and later re-used in the definition of complex data cubes.

Core Interface

In this section, we expand the architecture framework presented in Section 3.2.1 by integrating knowledge and metadata. Around the data warehouse core, with respect to the external components (operational data sources, result data stream and administration and monitoring), we define three metadata and knowledge base (M D & KB) repositories corresponding to the three sides of the core (Figure 2). They constitute an interface functionality. The first M D & KB repository (labeled (1) in Figure 2) lies at the data integration and ETL process level, and includes:

Core Data Warehouse

• an ontology for modelling domain-related knowledge;

• information about data sources and source types;

• mappings for the extraction and transformation processes (the E and T in ETL);

• information about the loading (the L in ETL: frequency, mode...) and cleansing (purge) processes;

• a referential or metadata repository about data, materialized views, index, clusters, aliases, etc.

The M D & KB repository that is labeled (3) in Figure 2 lies at the administration and monitoring level, and references :

• an ontology for modelling domain-related knowledge;

• deployment, hardware and software constraints;

• an interface between the integration and ETL level and the usage level;

• information on users and data providers;

• data warehouse usage information (statistics, response time, availability, feedback, dormant data...);

• a referential or metadata repository about data, materialized views, index, clusters, aliases, etc.

Eventually, the M D & KB that is labeled (2) in Figure 2 lies at the usage level and completes our interface with:

• an ontology for modelling domain-related knowledge;

• information about aggregate operators (hierarchical lattice construction [START_REF] Pei | A General Model for Online Analytical Processing of Complex Data[END_REF] if necessary) and data lineage that would allow users to go up to the sources if necessary;

• query optimizer data (query reformulation and rewriting);

• a referential or metadata repository about data, materialized views, index, clusters, aliases, etc.

Note that some of the elements we have just enumerated (e.g., ontology and referential repository) are present in more than one interface. Hence, they must be factorized at a higher level (labeled (4) in Figure 2). Moreover, this level must include metaknowledge, i.e., knowledge for acquiring, expressing, using, storing, retrieving knowledge, and even creating new knowledge. The major part of this level resides within the CWM repository.

XML as a Pivot Language

The architecture we propose necessitates a universal formalism so that all its components (core, metadata, knowledge, drivers, interface, data and knowledge interchange...) can interoperate. With its vocation for semi-structured data exchange, the eXtensible Markup Language (XML) already offers a great flexibility to represent complex data, and great possibilities for structuring, modelling, and storing them [DBB + 03]. XML indeed allows to store together data and their description, either implicitely or through a schema definition. This type of representation is particularly useful in a data warehousing environment where such metadata are casual. Furthermore, many XML and MOF-related facilities, such as the XML Metadata Interchange (XMI [START_REF]MOF 2.0/XMI Mapping Specification[END_REF]) or the Common Warehouse Metadata Interchange (CWMI), can help in managing metadata in an XML data warehouse and specify source-type drivers, while ensuring CWM compliance.

CWM compliance is ensured by the CWM repository that is integrated into the data warehouse kernel. All M D & KB modules use this repository to communicate with the data warehouse. CWM, through its five metamodels (object, foundation, resource, analysis and management), provides UML components (classes, associations and packages) for modelling all the data warehouse's elements [START_REF]Common Warehouse Metamodel (CWM) Specification, version 1[END_REF].

State of the Art

Though the litterature about metadata and knowledge is abundant, the issue of integrating metadata and knowledge is scarcely addressed. In this section, we provide a quick overview of the studies that are nonetheless related to this problem. Metadata are always present in data warehouse architectures [START_REF] Inmon | Building the Data Warehouse[END_REF]. In our particular context, some interesting efforts aim at decentralizing the management of metadata into functional components of data warehouses [HMT00, Kim05, SE06]. They do not address the issue of domainrelated knowledge, though.

Knowledge is indeed rarely exploited as such in data warehouse environments. However, issues related to knowledge management in the context of heterogeneous data warehouse environments have been addressed, by augmenting a federated warehouse with a knowledge repository [START_REF] Kerschberg | Knowledge Management in Heterogeneous Data Warehouse Environments[END_REF]. Discussions about using knowledge as a basic element for managing metadata are also regularly discussed in [START_REF] Stephens | Knowledge: The Essence of Metadata[END_REF]. However, this issue is mostly addressed by the knowledge management community, which works on knowledge warehouses [NSIH02, WAK05], and whose focus is obviously knowledge.

Finally, a study from the field of Geographical Information Systems (GISs, which are premium providers of complex data) is of particular interest to us. An extension of current metadata schemes has indeed been proposed to include context-based and tacit information about semantic attributes [START_REF] Schuurman | Ontology-Based Metadata[END_REF]. These ontology-based extended metadata improve data selection and interoperability decisions. Though we are more particularly interested in explicit knowledge in our context, we can exploit this solution in our framework.

Conclusion

In this paper, we have underlined the growing need for warehousing so-called complex data, a task that requires the management of knowledge and metadata related to these data.

We enumerated the various kinds of knowledge and metadata that must be taken into account. On this basis, we proposed to integrate knowledge as metadata in the warehouse. Finally, we expanded an XML-based, CWM-compliant architecture framework for complex data warehouses we had previously proposed in the light of the new insights discussed in this paper.

One immediate perspective of our work is to validate our present proposal by experimentation, and to evaluate the impact of metadata and knowledge integration in complex data warehouses in terms of performance. Performing performance evaluations and comparisons, basically with and without integrating knowledge and metadata, shall show the actual relevance of our solution.

A related, important follow-up of our work is to assess the consequences of metadata and knowledge integration on traditional performance optimization techniques such as view materialization, indexing, partitioning, query optimization, etc. These techniques will presumably need to be adapted to take into account domain-related knowledge and achieve the best performance.

Eventually, our position in this paper is to manage metadata and knowledge integration by representing knowledge as metadata. Though we discussed arguments in favor of this particular approach in Section 3.1, it would be interesting to explore and assess the efficacy of the other possible solutions, namely representing metadata as knowledge or managing knowledge and metadata separately.

Figure 1 :

 1 Figure 1: Complex Data Warehouse Architecture Framework

Figure 2 :

 2 Figure 2: Interface around the core

Table 1 :

 1 Table 1 illustrates the correspondences between the M D & KB modules in our architecture and the CWM metamodels. M D & KB and CWM correspondencesare intricate to express in a relational system, e.g., moving window aggregations or rollup operations on ragged hierarchies [BCC + 05]. Hence, our XML-based framework provides an architecture that is both extensible and "stable", and that can be compliant with future external elements (data sources, analytical techniques and usages...).

	Eventually, the advances in XML warehousing [Pok02, HBH03, RRT05, BMCA06] ren-
	der this solution plausible in the near future, especially since XML-related metadata in-
	terchange facilities integrate very well in data warehouses [AvM02]. Storage possibilities
	are also numerous, either into relational, XML-compatible DBMSs such as Oracle, SQL
	Server or DB2; or into XML-native DBLSs such as Lore, eXist or X-Hive. Furthermore,
	XML query languages such as XQuery allow the formulation of analytical queries that


Hadj Mahboubi

Kamel Aouiche

Jérôme Darmont

A Join Index for XML Data Warehouses

Keywords: XML data warehouses, performance, XML join index, XQuery

XML data warehouses form an interesting basis for decision-support applications that exploit complex data. However, native-XML database management systems (DBMSs) currently bear limited performances and it is necessary to research for ways to optimize them. In this paper, we propose a new join index that is specifically adapted to the multidimensional architecture of XML warehouses. It eliminates join operations while preserving the information contained in the original warehouse. A theoretical study and experimental results demonstrate the efficiency of our join index. They also show that native XML DBMSs can compete with XML-compatible, relational DBMSs when warehousing and analyzing XML data.

Introduction

Decision-support applications nowadays exploit heterogeneous data from various sources. Furthermore, the development of the Web 2.0 and the proliferation of multimedia documents contributed to the analysis of data are not only numerical or symbolic. These so-called complex data may indeed fall in several of the following categories [START_REF] Darmont | An Architecture Framework for Complex Data Warehouses[END_REF]: data represented in various formats (databases, texts, images, sounds, videos...); diversely structured data (relational databases, XML document repositories...); data originating from several different sources (distributed databases, the Web...); data described through several channels or points of view (radiographies and audio diagnosis of a physician, data expressed in different scales or languages...); data that change in terms of definition or value (temporal databases, periodical surveys...). For example, analyzing medical data may lead to exploit jointly information under various forms: patient records (classical database), medical history (text), radiographies, echographs (multimedia documents), physician diagnoses (texts or audio recordings), etc.

In this context, XML proves a very interesting tool in the process of integrating and warehousing complex data for analysis [START_REF] Darmont | Web multiform data structuring for warehousing[END_REF]. However, decision-support queries are generally complex because they involve several join and aggregation operations. In addition, many native XML database management systems (DBMSs) present relatively poor performances when data volume is very large and queries are complex. Thus, it is crucial to design XML data warehouses that guarantee the best performance when accessing data. Indexing is one of the most frequently used techniques to achieve this goal.

Several solutions have been proposed for XML data indexing in the literature. However, the existing techniques support single labeled path expressions within one XML document. A path expression helps explore an XML document and extract a specific node (element) or subtree (sub-document). It cannot perform a join operation over several XML documents. In the context of XML data warehouses, decision-support queries are complex and involve several path expressions. Data are also generally distributed into several XML documents due to their large volume. Hence, XML queries should use specific indices to navigate these documents.

In this paper, we propose a new join index structure that is specifically adapted to multidimensional XML data warehouses. This structure is able to maintain a star schema of several XML documents and to preserve the information contained in these documents. It is actually a join index that ensures a faster execution of XQuery decision-support queries by eliminating join costs.

We theoretically and experimentally demonstrate that the use of our index significantly reduces the execution time of XQuery decision-support queries expressed on a data warehouse. In addition, our experiments show that, in our context, XML native DBMSs are competitive with relational, XML-compatible DBMSs.

The remainder of this paper is organized as follows. We first present the state of the art on XML indexing in Section 2. Then, we outline the context of this study in Section 3. We detail our join index structure in Section 4. In order to validate our proposal, we present a theoretical study in Section 5 and some experimental results in Section 6. Finally, we conclude the paper and discuss research perspectives in Section 7.

Related work

In this section, we assume that an XML document is defined as a labeled graph whose nodes represent document elements or attributes, and edges represent the element-subelement (or parent-child) relationship. Edges are labeled with element or attribute names.

Several studies address the issue of XML data indexing [START_REF] Goldman | DataGuides: Enabling Query Formulation and Optimization in Semistructured Databases[END_REF][START_REF] Milo | Index Structures for Path Expressions[END_REF][START_REF] Cooper | A Fast Index for Semistructured Data[END_REF][START_REF] Chung | APEX: an adaptive path index for XML data[END_REF]. They are more particularly devoted to optimize XML path expressions. Generally, they propose the creation of a schema or model (data structure) for XML data indexing. In practice, the index is a new XML document that is accessed instead of the original document.

The data guide is a summary structure for semi-structured and XML data [START_REF] Goldman | DataGuides: Enabling Query Formulation and Optimization in Semistructured Databases[END_REF]. This index' structure describes by one single label all the nodes whose labels (names) are identical. The definition of the data guide is based on targeted path sets, i.e., the nodes that are reached by traversing this path.

The 1-index clusters nodes that share the same path in the XML data graph [START_REF] Milo | Index Structures for Path Expressions[END_REF]. This process is performed through a bi-simulation relationship. A 1-index is normally smaller than the initial data graph and thereby facilitates query evaluation. To operate a selection of labels or a path expression, a hash table or a B-tree structure is used to index graph labels.

The data guide and the 1-index code all the paths from the root node. The size of such summary structures or indices may be large, even larger than the original XML document when XML data are represented as graphs (cyclic XML document). This problem causes degradation in query performance. The A(k)-index, a variant of the 1-index, was proposed to overcome these shortcomings [START_REF] Kaushik | Exploiting Local Similarity for Indexing Paths in Graph-Structured Data[END_REF]. It is based on the notion of kdissimilarity and builds an approximate index to reduce the size of the index graph. An A(k)index can retrieve, without referring to the data graph, path expressions of length of at most k, where k controls the resolution of the index and influences its size in a proportional manner. For large values of k, index size may become very large and this approach suffers from the same issues than the 1-index. For small values of k, the size of the index is substantially smaller, but it cannot handle long path expressions.

To accommodate path expressions of various lengths, without unnecessarily increasing the size of the whole index, the D(k)-index assigns different values of k to different index nodes [START_REF] Qun | D(k)-Index: An Adaptive Structural Summary for Graph-Structured Data[END_REF]. These values conform to a given set of frequently-used path expressions (FUPs). Large values of k are assigned to parts of the index corresponding to parts of the data graph targeted by long path expressions; while small values of k are assigned to parts of the index corresponding to data targeted by short path expressions. To facilitate the evaluation of path expressions with branching, a variant called the UD(k,l)-index also imposes downward similarity [START_REF] Wu | UD(k, l)-Index: An Efficient Approximate Index for XML Data[END_REF].

The AD(k)-index builds a coarser index than the A(k)-index, but suffers from a problem of over-refinement (He & Yang 2003). The M(k)-index, an improvement of the D(k)-index, solves the problem of large scan space in the index, without affecting path coverage. The drawback of its design, though, lies in the requirement to adapt to a given list of FUPs.

The U(*)-index (universal, generic index; [START_REF] Boulos | A New Design for a Native XML Storage and Indexing Manager[END_REF]) also exploits the notion of bisimilarity (like the 1-index). However, to overcome the problem of large search space for XPath evaluations, the index structure uses a special node labeling scheme that enables pruning the search space. Furthermore, the U(*)-index does not need to be adapted to any particular list of FUP; it has a uniform resolution, and hence is more generic.

APEX is an adaptive index that searches for a trade-off between size and effectiveness (Chang et al. 2002). Instead of indexing all the paths from the root, APEX only indexes the FUPs and preserves the source data structure in a tree. However, since FUPs are stored in the index, path query processing is quite efficient. APEX is also workload-aware, i.e., it can be dynamically updated according to changes in the query workload. A data mining method is used to extract FUPs from the workload for incremental update [START_REF] Agrawal | Mining Sequential Patterns[END_REF].

Unfortunately, all these indexing techniques are ill-suited to decision-support queries. Data structures such as the data guide, the 1-index and its variants, and APEX are indeed applicable only on XML data that are targeted by simple path expressions. However, in the context of XML data warehouses, queries are complex and include several path expressions that compute join operations. Moreover, these indices operate on one XML document only, whereas in XML warehouses, data are managed in several XML documents and decisionsupport queries are performed over these documents.

Finally, other techniques such as the extended inverted list [START_REF] Zhang | On Supporting Containment Queries in Relational Database Management Systems[END_REF] and Fabric [START_REF] Cooper | A Fast Index for Semistructured Data[END_REF]) are aimed at processing containment queries over XML data stored in relational databases. The extended inverted list includes a text index (T-index;[START_REF] Milo | Index Structures for Path Expressions[END_REF] that is similar to the traditional indices in information retrieval systems, and an element index (E-index) that maps elements into inverted lists. Fabric indexes several XML documents by encoding paths, from the root to the leaf nodes. These operations are performed by indicators that code path labels. These codes are then inserted in a Patricia trie [START_REF] Cooper | A Fast Index for Semistructured Data[END_REF], which processes them like simple characters. However, Fabric is not adapted to XML data warehouses either, because it does not take into account the relationships that exist between XML documents in a warehouse (facts and dimensions). This index is thus not beneficial to decision-support queries.

For more details about XML indexing, the interested reader may refer to a recent, complete survey [START_REF] Gou | Efficiently Querying Large XML Data Repositories: A Survey[END_REF].

Study context

XML data warehouse specification

Several studies address the issue of designing and building XML data warehouses. They propose to use XML documents to manage or represent facts and dimensions. The main objective of these approaches is to enable a native storage of the warehouse and its easy interrogation with XML query languages.

For instance, Pokornỷ (2003) models a star schema in XML by defining dimension hierarchies as sets of logically connected collections of XML data, and facts as XML data elements. [START_REF] Park | XML-OLAP: A Multidimensional Analysis Framework for XML Warehouses[END_REF] propose an XML multidimensional model in which each fact is described by a single XML document and dimension data are grouped into a repository of XML documents. [START_REF] Rusu | A Methodology for Building XML Data Warehouse[END_REF] build facts and dimensions from XML documents generated through XQueries. Eventually, [START_REF] Hümmer | XCube: XML for data warehouses[END_REF] propose a family of templates, called XCube, to describe a multidimensional structure (dimension and fact data) for integrating several data warehouses into a virtual or federated data warehouse. All these approaches assume that the warehouse is composed of XML documents that represent both facts and dimensions. They are used when dimensions are dynamic and allow the support of end-user analytical tools.

All these studies more or less converge toward a unified XML warehouse model. They mostly differ in the way dimensions are handled and the number of XML documents that are used to store facts and dimensions. To illustrate the application of our indexing strategy, we selected in this paper the XCube specification to model a reference XML data warehouse. Since other models from the literature are quite similar, this is not a binding choice.

The advantage of XCube is its simple structure for representing facts and dimensions in a star schema. One XML document is used to represent dimensions and another one to represent facts. Hence, our reference data warehouse is composed of the following XML documents: Schema.xml specifies the data warehouse metadata; Dimensions.xml defines all the dimensions, characterized by their attributes and their values; and Facts.xml specifies the facts, i.e., dimension identifiers and measure descriptions and values.

The Facts.xml document stores facts. Its tree structure is described in Figure 1(a). The document root node, CubeFact, has one child, cube, which is itself composed of cell nodes defining facts: fact nodes (measures) and dimension references. A fact node has two attributes, @id and @value, which define the measure name and value, respectively. The dimension node has two attributes, @id and @value, which define the dimensions name and its identifier's value, respectively.

The Dimension.xml document stores dimensions. Its tree structure is described in Figure 1(b). The document root node, dimensionData, has one child, classification, which is itself composed of Level nodes. A Level node is composed of node nodes defining dimension instances. A node is composed of attribute nodes that define the attributes of a dimension and their values (@name and @value).

XML data warehouse interrogation

We selected the XQuery language [START_REF] Boag | XQuery 1.0: An XML Query Language[END_REF]) to formulate decision-support queries because, unlike simpler languages such as XPath, it allows complex queries, including join queries over multiple XML documents, to be expressed with the FLWOR syntax.

However, the XQuery language does not support the type of queries that are common in business analysis [START_REF] Beyer | Extending XQuery for Analytics[END_REF]. XQuery does indeed not include an explicit grouping construct comparable to the group by clause in SQL. Hence, several papers propose to extend XQuery to formulate decision-oriented queries [START_REF] Borkar | Extending XQuery for Grouping, Duplicate Elimination, and Outer Join[END_REF][START_REF] Beyer | Extending XQuery for Analytics[END_REF]. In our implementation, we acknowledge this effort by adding to FLWOR expressions explicit group by clauses. More precisely, we added two functions: group by (attribute list) and aggregation (aggregation operations, measure list), to the XQuery syntax. Figure 2 provides an example of decision-support query with a multiple group by clause that exploits these functions.

Join index structure

Building the indices cited in Section 2 on an XML warehouse causes a loss of information in decision-support query resolution. Indeed, clustering (1-index) or merging (data guide) identical labels causes the disappearance of the relationship between fact measures and dimensions. We illustrate this problem in the following example.

The Facts.xml document is composed of Cell elements. Each cell is identified by its dimension identifiers and one or more measures. Figure 3 shows the structure of the Facts.xml document and its corresponding 1-index (we selected the 1-index as an example). The 1-index represents cells linearly, i.e., all labels for the same source are represented by one label only. Hence, recovering a cell characterized by its measures and their dimension identifiers is impossible. An index should be able to preserve the relationships between dimensions and fact measures. Thus, our index' structure is similar to that of the Facts.xml document, except for the attribute element.

XML indices usually summarize or reorganize the structure of the indexed XML documents into new XML documents that are then accessed instead of the original data. Our index structure is similar. It is stored in an XML document named Index.xml, whose structure is showed in Figure 4. Classically, graph labels starting with @ represent attributes. The others for $a in//dimensionData/classification/Level[@node='customers']/node, $x in //CubeFacts/cube/Cell let $q := $b/attribute[@name='cust name']/@value let $z := $b/attribute[@name='cust zip code']/@value where $a/attribute/@name='cust city' and $a/attribute/@value='Lyon' and $x/dimension /@id=$a/@id and $x/dimension/@id='customers' group by(cust name,@cust zip code) return name='cust name ', aggregation(sum, quantity) represent elements. Each Cell element is composed of dimensions and one or more facts. A Fact element has two attributes, @id and @value, which respectively represent measure names and values. Each dimension element is composed of two attributes: @id, which stores the dimension name, and @node, which stores the value of the dimension identifier. Moreover, the dimension element has children attribute elements. These elements are used to store the names and values of the attributes from each dimension. They are obtained from the Dimensions.xml document. An attribute element is composed of two attributes, @name and @value, which respectively store the name and value of each attribute.

Data migration from Dimensions.xml and Facts.xml to the index structure helps store facts, dimensions and their attributes in the same cell. This feature wholly eliminates join operations since all the information that is necessary for a join operation is stored in the same cell.

Theoretical study

Queries defined over an XML warehouse modeled according to the XCube specification perform several join operations between facts stored in Facts.xml and dimensions from Dimensions.xml. Thus, they must satisfy the following constraints. document(Facts.xml)/CubeFact/cube/Cell/dimension[@id = document(Dimensions.xml)/classification/Level/@id] and document(Facts.xml)/CubeFact/cube/Cell/dimension/[@value = document(Dimension.xml)/classification/Level/node/@id]

The first equality checks whether the dimension composing a cell (fact) is indeed the dimension expressed in the query. The second equality checks whether the node of a dimension (equivalent to a primary key) corresponds (can be joined) to the node, from the same dimension, defined in a cell (equivalent to a foreign key in the fact table ).

Query execution without using our index may proceed as follows. For each dimension defined by @node='name of dimension', the identifiers @id verifying the Where clause are searched for. The Dimensions.xml document is traversed in depth first, down to the Level node.

Children nodes of the Level node are then traversed in breadth first until @node is equal to the dimension name.

This traversal cost is equal to the number of Level nodes in the Dimensions.xml document, denoted |dimension|. If several dimensions are defined in the query, all Level nodes are traversed for each dimension. Each node's child is traversed in depth first, until a list of @id attributes verifying the conditions @name='name of the attribute' and @value='value of the attribute' is found. The cost of this traversal is equal to the number of attribute children. Thus, dimension cost traversal is equal to

i i d a *
, where i a is the number of attributes in each dimension and i d the number of node elements, i.e., the number of children in each dimension.

To carry out a join between dimensions of the Dimensions.xml document and facts from the Facts.xml document, the @id values found when processing dimensions are searched for in the facts. The Facts.xml document is then traversed in depth first, down to the Cell level. Cells are then traversed in breadth first until dimensions whose child @id equals to @node in Dimensions.xml and @node equals to @id in Dimensions.xml are found. The traversal cost of the Facts.xml document is cell , where cell is the number of cells. Finally, query execution cost without our index is:

( ) ( ) ( ) ( ) i i noindex a d cell E * dimension * dimension * + = .
Query execution when using our index may proceed as follows. For each dimension defined by @node='name of dimension', the identifiers @id verifying the Where clause are searched for. The Index.xml document is traversed in depth first, down to the Cell level. The cost of this traversal is equal to the number of cells in the Index.xml document. Cell dimension children nodes are then traversed until the node whose @id value is equal to the dimension name in the query is reached. The cost of this traversal is equal to the number of dimension nodes in the Index.xml document, i.e., the number of dimensions in the warehouse schema. This cost is denoted dimension . The children of each found node are traversed in depth first, down to the attribute node verifying the conditions @name='name of the attribute' and @value='value of the attribute'. The cost of this traversal is equal to the number of attribute children, denoted i a . Finally, query processing cost over our index structure is:

( ) i index a cell E + = dimension * .
Figure 6 shows the cost variation between E noindex and E index with respect to the number of cells (facts) from Facts.xml. These facts are described by five dimensions that are stored in the Dimensions.xml document. Table 1 displays the characteristics of these dimensions. We use a logarithmic scale on the Y axis to better visualize cost differences. Using our index induces a performance gain factor of 14,000 on an average.

Figure 6: Theoretical results

Facts

Experiments

In order to validate our proposal experimentally, we generated an XML data warehouse modeled according to the XCube specification. Actual data have been transferred from an existing, sample relational data warehouse derived from an Oracle example1 .

This classical test data warehouse (Table 1), modeled as a star schema, is composed of sale facts characterized by the amount (of purchased products) and quantity (of purchased products) measures. The facts are stored in the Facts.xml document. They are described by five dimensions: channels, promotions, customers, products and times that are stored in the Dimensions.xml document. Our experiments measure the execution time of the typical decision-support query from Figure 2 over our test data warehouse, with and without exploiting our join index. We also varied warehouse size. Note that, in SQL Server 2005, XML data are stored in a table field. SQL-XQuery queries must be processed for each record. This process does not allow joining XML data from different records. Hence, we only performed our experiment with our join index on SQL Server, and not with the original, multi-document warehouse. We ran our tests on a Pentium 2 GHz PC with 1 GB of main memory and an IDE hard drive. Also note that we do not consider index construction time here, since an XML index is actually a new warehouse structure that is built once and queried thereafter.

Figure 8 represents our test query execution time on the three DBMSs, with and without using our index. The X axis represents warehouse size and the Y axis the corresponding execution time. The Y axis is in logarithm scale to highlight the differences in execution costs.

Our experimental results show that using our index structure significantly improves response time. On an average, the gain factor is indeed 25,669 for eXist and 8,411 for X-Hive. Furthermore, the plots we obtain are very similar in trend to those from Figure 6, which tends to validate our theoretical study.

Select XML-DOC.Query('for $a in //dimensionData/classification/Level[@node='customers']/node, where $a/attribute/@name="cust city" and $a/attribute/@value="Lyon" return name="cust name"') From DIMENSION Though this is not plotted on Figure 8, we also pushed our "with/without index" tests further on the totality of the cells from the Facts.xml document. We achieved execution times of less than two seconds with our join index. Without index, X-Hive responded in about four minutes and eXist proved unable to answer in a reasonable time.

Finally, our experiments show that, properly indexed, native XML DBMSs can compete with, and even best relational DBMSs in terms of performance when XML documents are bulky. eXist running on our join index indeed outperforms SQL-Server by a 31.5 factor, on an average. This is because relational DBMS engines combine XQuery to SQL and must convert the result from relations to XML. XML native DBMSs, on the other hand, preserve the hierarchical structure of XML data, which allows path scans to be efficiently processed by XQuery engines. Our experiments also show that eXist's query engine performs better than Xhive when using simple path expressions. We think this is because eXist implements a specific numbering scheme that helps easily evaluate parent/child node relationships [START_REF] Meier | eXist: An Open Source Native XML Database[END_REF].

Conclusion

In this paper, we presented a new join index that is specifically adapted to XML data warehouses. This data structure allows optimizing the access time to several XML documents by eliminating join costs, while preserving the information contained in the initial warehouse. Though we used an XCube-based reference data warehouse for illustration and validation purposes, our index structure can be built on any other XML warehouse model we are aware of.

To validate our proposal, we performed both a complexity study and experiments. We implemented our reference warehouse with two native XML DBMSs and one relational, XML-compatible DBMS. Our tests showed that using our index structure significantly improves the response time of a typical decision-support query expressed in XQuery. Furthermore, they also demonstrate that native XML DBMSs can compete with and even best relational DBMSs. This work also opens three broad axes of research perspectives. First, our indexing strategy could be better integrated into a host native XML DBMS. This would certainly help develop an incremental strategy for the maintenance of the join index data structure. Moreover, the mechanism for rewriting queries would also be more efficient if it was part of the system.

It is also crucial to carry on adapting or developing highly efficient optimization techniques in native XML DBMSs. XML views are getting more and more efficient, but there is still room for improvement, e.g., when generating and refreshing materialized views [START_REF] Mahboubi | Materialized View Selection by Query Clustering in XML Data Warehouses[END_REF]. Partitioning an XML warehouse could also be envisaged.

Eventually, decision-support queries bear specific needs in terms of operators. For instance, we had to extend XQuery to allow multiple group by clauses to implement our decisionoriented workload. Similar extensions do exist already [START_REF] Beyer | Extending XQuery for Analytics[END_REF], but it could be interesting to further extend XQuery to support OLAP operators such as cube, rollup or drilldown.

Figure 1 :

 1 Figure 1: Dimension and fact document's structure

Figure 2 :

 2 Figure 2: Sample decision-support XQuery

Figure 3 :

 3 Figure 3: Facts.xml structure (a) and corresponding 1-index (b)

Figure 4 :

 4 Figure 4: XML join index structure

Figure 5 :

 5 Figure 5: Query executions over our join index

Figure 7 :

 7 Figure 7: SQL-XQuery sample query

Figure 8 :

 8 Figure 8: Experimental results

Table 1 :

 1 Test data warehouse characteristics

	Number of cells

http://downloadwest.oracle.com/docs/cd/B10501 01/server.920/a96520/toc.htm

We implemented this data warehouse within two native XML DBMSs: eXist (Meier 2002) and X-Hive (Waldt 2005). Both these DBMSs allow the native storage of large documents and support the XQuery language. They also provide APIs (Application Programming Interfaces) for storing, querying, retrieving, transforming and publishing XML data.

We also implemented our XML data warehouse in a relational, XML-compatible DBMS: SQL Server (Rys 2004). SQL Server 2005 handles XML data through an XML type field. It integrates XQuery queries with the help of a function called query that is embedded into SQL Select clauses (Figure 7).


Assistant Professor, Yihan Wang
email: yihan.wang@hec.ca

Associate Professor, Ekaterina Turkina
email: ekaterina.turkina@hec.ca

Economic Complexity and Industrial Upgrading in the Product Space Network -Opportunities for the City of Laval, Canada

This paper studies a city-region's multi-level competitiveness based on the configurations of local product space network and agglomeration of Revealed Competitive Advantage (RCA) sectors. We undertake a mandate studying the economic complexity of the City of Laval and explore the opportunities of industrial upgrading in its product space network. Addressing the importance of subnational analysis of economic complexity, we find the divergence of a city-region's RCA sectors at regional, national and global levels. We also imply the contribution of the structural holes of a cityregion's product space network across RCA sectors as potential fields to attract FDI inflow and enhance economic growth. Then, we discover the correlated spatial agglomeration of RCA and structural hole sectors within a city-region's hierarchical ecosystem. Finally, we conclude the practical implications for policy makers and discusses future research directions.

Introduction

In the digital revolution, innovation and openness have become the main driving forces of economic growth. Accelerated by technological advantaces, the industrial upgrading reshape the global competition, that countries with high technological capability and global connectivity takes the lead. To capture the opportunities in the industrial upgrading, national and regional policy makers make effort to attract technology-intensive FDI and enhance local firms' capability of absorbing new knowledge inflows accordingly [START_REF] Lall | The Technological structure and performance of developing country manufactured exports, 1985-98[END_REF]. Synthesizing the arguments on the role of technological innovation and connectivity in globalization, [START_REF] Hidalgo | The building blocks of economic complexity[END_REF] developed the paradigm of economic complexity and product space network, arguing that the non-tradable capabilities in producing knowledge complex products sustain a country's global competitiveness. In other words, if a country has the competitive advantage specializing in a large variety of technology-intensive industries, its economy has higher growth potential than countries that are only good at a limited number of resourceor labor-intensive industries [START_REF] Mudambi | Location, control and innovation in knowledge-intensive industries[END_REF]. However, this original paradigm of economic complexity and product space network does not take the subnational divergence of regional economic development fully into account. [START_REF] Balland | The technological resilience of US cities[END_REF] argued that there is an increasing divergence in urban development responding to technological advances and global connectivity. When conducting economic complexity analysis, the subnational divergence in competitiveness, as well as the composition of the city-region product space network into consideration for policymaking [START_REF] Balland | Smart specialization policy in the European Union: relatedness, knowledge complexity and regional diversification[END_REF][START_REF] Wang | Economic complexity, product space network and Quebec's global competitiveness[END_REF].

This study aims to provide an outlook economic complexity as indicators for global competitiveness of a city-region and to highlight the opportunities in industrial upgrading embedded in the product space network. We elaborate on the contribution of knowledge complexity of competitive manufacturing sectors, the growth potential over the "structural hole" in the product space network, as well as spatial agglomeration of these sectors, as three key elements to understand the opportunities a city-region achieve competitiveness in industrial upgrading. To demonstrate these points, we undertake a mandate of the Economic Development Service (Service du Dé veloppement Économique, SDÉ) of the City of Laval, the third largest municipality in Quebec Province of Canada to understand the city's most competitive manufacturing sectors at regional, provincial and global levels. Thereafter, the municipal economic policy makers can better carry out its investment promotion mission to attract potential international partners and enhance the city-region's position in the global competition.

Literature Review

There is a general tendency of innovation-led industrial upgrading towards knowledge-based open economy that reshapes the global competition. Individual economic actors benefit from their connectivity in the hierarchy of network structure, where they can enhance their market performance, innovation capability and social influence [START_REF] Borgatti | The network paradigm in organizational research: A review and typology[END_REF]. In turn, their knowledge creation in the innovation activities embedded in production networks contribute to the regional economic development and global competitiveness [START_REF] Coe | Globalizing'regional development: a global production networks perspective[END_REF][START_REF] Cooke | Regional development in the knowledge-based economy: The construction of advantage[END_REF][START_REF] Yeung | Regional development and the competitive dynamics of global production networks: an East Asian perspective[END_REF]. [START_REF] Malecki | Technology and economic development: The dynamics of local, regional and national competitiveness[END_REF] urged that the global competitiveness of a country must integrate the economic dynamics and technological capacity at national, regional and local spatial scales. To enhance to the global competitiveness of local firms, national and regional policy makers seek to restructure the local economic development models and industrial policy to generate national competitive advantages. To reach such goals, they are advised to prioritize developing technological sophisticated manufacturing sectors embedded in the networks coordinated by the global value chains [START_REF] Cano-Kollmann | Knowledge connectivity: An agenda for innovation research in international business[END_REF][START_REF] Gereffi | International trade and industrial upgrading in the apparel commodity chain[END_REF][START_REF] Gereffi | The Governance of Global Value Chains[END_REF]. Hence, the regional specialization and policy perspectives should be taken into consideration to understand industrial upgrading.

The concepts of product space network [START_REF] Hidalgo | The Product Space Conditions the Development of Nations[END_REF] and economic complexity [START_REF] Hidalgo | The building blocks of economic complexity[END_REF] provide a pragmatic analytical framework to tackle the opportunities in industrial upgrading for national states. In general, a country, which takes the lead in producing a broad variety of high technology-intensive manufacturing goods for international trade, is characterized by a high degree of economic complexity. Thereafter, this country has high economic growth potential and takes more favorable position in the global competition [START_REF] Hidalgo | The building blocks of economic complexity[END_REF]. In the Atlas of Economic Complexity [START_REF] Hausmann | The atlas of economic complexity: Mapping paths to prosperity[END_REF] Based on the estimation of the propensity of co-production or co-export of two products, [START_REF] Hidalgo | The Product Space Conditions the Development of Nations[END_REF] constructed the framework of product space network of a country. Finally, by weighting the eigenvector value of diversity and ubiquity in recursion expression, [START_REF] Hidalgo | The building blocks of economic complexity[END_REF] calculated the Product Complexity Index (PCI) of each product category. High PCI value indicates the high knowledge complexity product, while high ECI represent a country's overall competitiveness in the global competition in production and trade.

The economic complexity indices quantify the knowledge intensity of products global competitiveness of countries as reference for international comparison. Understanding the local economic complexity and configurations of the product space network has strong practical implications for economic policy making at multiple levels [START_REF] Balland | Smart specialization policy in the European Union: relatedness, knowledge complexity and regional diversification[END_REF]. Nonetheless, the general economic complexity and product space network frameworks consider the national context as homogeneous and ignores impact of subnational regional differences [START_REF] Wang | Economic complexity, product space network and Quebec's global competitiveness[END_REF]. We call for a more refined view on economic complexity at the city-region level for following reason:

First, the city-region division highlights the increasing subnational regional specialization in networks facilitated by spillover effect. A city-region consists of the urban center (core) and the adjacent suburban territories (periphery) of a municipality. It is the basic spatial unit of large-scale production, and encompasses the economic factors endowment (products, labor, capital, technology), organizational structure and institutional settings embedded in networks [START_REF] Gibbs | Fractures in Meta-Narratives of Development: An Interpretive Institutionalist Account of Land Use Development in the Boston City-Region[END_REF][START_REF] Leibovitz | Institutional barriers to associative city-region governance: The politics of institution-building and economic governance in'Canada's Technology Triangle[END_REF][START_REF] Parr | Perspectives on the city-region[END_REF]. Within the realm of a city-region, a firm with high capacity in absorbing and proceeding knowledge act as anchor firms to orchestrate knowledge flows local business relationships [START_REF] Sorenson | Complexity, networks and knowledge flow[END_REF]. Meanwhile, thanks to the brokerage of the anchor firms, other local firms specialized in the same or related industry get in contact with each other and integrate themselves into the local networks [START_REF] Arikan | Interfirm knowledge exchanges and the knowledge creation capability of clusters[END_REF][START_REF] Fabrizio | Absorptive capacity and the search for innovation[END_REF][START_REF] Sturgeon | How Do We Define Value Chains and Production Networks?*[END_REF]. In this process, co-located economic players exchange complementary knowledge and generate new ideas based on common knowledge base and mutual trust [START_REF] Bathelt | Clusters and Knowledge: Local Buzz, Global Pipelines and the Process of Knowledge Creation[END_REF][START_REF] Buckley | Knowledge Accession and Knowledge Acquisition in Strategic Alliances: The Impact of Supplementary and Complementary Dimensions[END_REF][START_REF] Jaffe | Geographic localization of knowledge spillovers as evidenced by patent citations[END_REF][START_REF] Malmberg | Towards an explanation of regional specialization and industry agglomeration[END_REF].

Entailing the spatial, social and institutional proximity of local economic players, such positive spillover contributes to the aggregated specialized knowledge stock and technological capability in the city-region (Porter, 1998;Feser and Bergman, 2000;[START_REF] Balland | The technological resilience of US cities[END_REF]. In this sense, the contributions of economic complexity to a country's global competitiveness ultimately reside in the agglomeration of knowledge-intensive industries at the level of city-region [START_REF] Balland | The geography of complex knowledge[END_REF].

Secondly, the core-periphery hierarchy affects the overall competitiveness of city-regions based on the unequal distribution of technological capacity. This system forms as the result of unequal distribution of technology-related factors, including physical plants and facilities, highly skilled human capital, infrastructural connectivity, as well as the institutional support (Porter, 1998;Humphrey and Schmitz, 2002;Lorenzen and Mudambi, 2013). [START_REF] Friedmann | Regional development policy: a case study of Venezuela[END_REF] argued that driven by technological advances, the centripetal force of "core" attracts the labor forces and other factors of productions at the "periphery" into the sphere of dominance. At a result, the city-region will reach an equilibrium of interconnection between core and periphery in the process of urbanization [START_REF] Pain | Examining 'core-periphery'relationships in a global city-region: the case of London and South East England[END_REF]. Endowed with these favorable conditions, core metropolises are more apt to concentrate strategic resources and attract knowledge intensive FDI and business ventures. In contrast, peripheral suburban or rural regions are more likely to "fall behind" facing stagnation of investment and losing human qualified workforce [START_REF] Copus | From core-periphery to polycentric development: concepts of spatial and aspatial peripherality[END_REF][START_REF] Felzensztein | Entrepreneurship at the Periphery: Exploring Framework Conditions in Core and Peripheral Locations[END_REF][START_REF] Scott | Pathways to industrialization and regional development[END_REF].

Thirdly, enhancing competitiveness of the city region requires active engagement and coordination of policy makers of multiple levels in the innovation system. An innovation system integrates the roles of firms, governments, communities and many other economic players in a comprehensive sociotechnological ecosystem [START_REF] Lundvall | National innovation system: towards a theory of innovation and interactive learning[END_REF][START_REF] Nelson | National Innovation Systems: A Comparative Analysis[END_REF]. In an open innovation system, local firms not only adopt new knowledge from in-house innovation activities, but also absorb external knowledge inflow by interacting with other regional or national economic actors beyond their organizational boundaries [START_REF] Belussi | Learning at the boundaries in an "Open Regional Innovation System": A focus on firms' innovation strategies in the Emilia Romagna life science industry[END_REF][START_REF] Chesbrough | Open innovation: The new imperative for creating and profiting from technology[END_REF]. Considering the spatial hierarchy, [START_REF] Bathelt | Innovation, Institution und Region: zur Diskussion über nationale und regionale Innovationssysteme (Innovation, Institution and Region: A Commentary on the Discussion of National and Regional Innovation Systems)[END_REF] suggest four perspectives to observe the development of such ecosystem, namely, sectorial, national, regional and metropolitan innovation systems. They argue that in addition to the self-referential system of individual economic entities, the coordination and support of national or regional institutions also play a crucial role. In other words, well-coordinated institutional support and innovation policy from regional development agencies at multiple administrative levels enhance the regional integration in the national innovation system and ultimately contributes to a country's global competitiveness [START_REF] Berger | Concepts of national competitiveness[END_REF][START_REF] Gibbs | Ecological modernisation, regional economic development and regional development agencies[END_REF].

In sum, the subnational divergence of industrial specialization, urban hierarchy and institutional setting all address the importance of understanding economic complexity and product space network from the city-region level. In the empirical analysis, we will use the example of manufacturing sectors of the City of Laval to address these concerns.

Product Space Network of the City of Laval

The City of Laval

The City of Laval (la Ville de Laval) is the third largest municipality in Quebec by population. Located on the north shore of the Saint Lawrence River, the City of Laval is integrated as a subcenter of the Montreal Metropolitan Community (MMC, also known as "Greater Montreal"), the second most populous metropolitan area in Canada after Greater Toronto Area (GTA). The City of Laval was created in 1966 by merging 14 independent municipalities on the Jesus Island (Î le Jé sus) to accommodate the development of urbanization and population spillover in suburban areas in Montreal [START_REF] Fischler | restructuring in Montreal: An historical analysis[END_REF]. The local economy of the City of Laval is well developed and highly diversified. The economic growth of the City of Laval is propelled by knowledge-intensive industries including the life sciences, ICT, agri-food, metal products, machinery and transportation vehicles sectors1 .

Thanks to its spatial proximity to Montreal, the innovation hub of the Quebec, the city of Laval benefits the positive knowledge spillover effects. Home to the Biotech City (Cité Biotech) and a large number of R&D centers (including a suburban campus of the University of Montreal) and high-tech firms. On the other hand, Laval has lower population density, net rent price, and net absorption/inventory rate than Montreal that encounters the challenges of land scarcity, rising property value, and high costs of demolition. It undertakes multiple commercial and industrial development functions, especially largescale building projects from Montreal. Meanwhile, the demand for industrial space in Laval is rising as the vacancy rate of real estate occupation sharply drops below the average of the Greater Montreal Area.

As the municipal policy maker of regional economic development, the City of Laval Economic Development Service (Service du Dé veloppement é conomique de Ville de Laval, SDÉ) offers support to the business development of local firms, attracts potential investors, and coordinates interorganizational relationships on its territory 2 . SDÉ has already identified life sciences, aeronautics and food processing industries as the city's strategic sector to sustain economic growth. According to the industrial agglomeration tendency of manufacturing subsectors, SDÉ divides the industrial development into west, central and east divisions along the Highway 440. Meanwhile, SDÉ aims to identify other crucial manufacturing sectors that support the growth of existing strategic industries as well as sustain the connectivity of local business networks by analyzing the local product space network configurations. Following this mandate, the research aims to us the analytical techniques of economic complexity and produst space network to identify the most competitive economic sector, then compare to regional (provincial), national and global benchmark. Moreover, we explore the structural holes of the RCA sectors embedded in the product space network as potential areas to attract FDI. Then we depict the geographic features of RCA sector agglomerations and structural holes in the product space network.

Data Collection and Product Space Network Construction

Following the paradigm of economic complexity and product space network (See Appendix), we collected the municipal-level data of the City of Laval and incorporate the available data in the analytical framework. We first track to the dyadic linkages between four-digit harmonized system 1992 standard (HS92) provided by the Atlas of Economic Complexity [START_REF] Simoes | The economic complexity observatory: An analytical tool for understanding the dynamics of economic development[END_REF], and build up the inter-sectorial product space network framework accordingly. Then, we also calculate the 6-year average PCI index of each HS92 product category from 2012 to 2017 as measurement for the knowledge complexity of production activities. If the average PCI is positive, we note the manufacturing sector producing this product as high-PCI sector, vice versa.

Next, we match the trade data provided by regional (Institut de la statistique du Qué bec), national After that, we integrate available corporate data to the municipal-level product space network framework. First of all, since the product space network mostly focus on good production, we only include firms specialized in agriculture (NAICS 11), mining (NAICS 21) and manufacturing sectors by referring to the first two digits of their main industrial categories. Since the NAICS code identifies the main economic activities a firm is specialized in, whereas the HS code register the main type of final product a firm prepares to export, we conducted concordance between the registration of NAICS 6-digit codes with HS 4-digit codes by keyword matching [START_REF] Pierce | A concordance between ten-digit US Harmonized System Codes and SIC/NAICS product classes and industries[END_REF].

Since a large majority of local enterprises in the City of Laval do not engage in export activities, instead of referring to trade data, we calculate the municipal level RCA index by referring to the number of employment in each economic sector over the total number of employed population. This adjustment combined with the calculation of the Location Quotient (LQ), a broadly applied method to identify industrial agglomeration by comparing the regional employment in each manufacturing sector overall national average [START_REF] Delgado | Clusters and entrepreneurship[END_REF][START_REF] Resbeut | Impact of clusters on regional economic performance: A methodological investigation and application in the case of the precision goods sector in Switzerland[END_REF][START_REF] Turkina | Global connectedness and local innovation in industrial clusters[END_REF]. Since high degree of LQ is strongly correlated with the trade volume of the final products of each economic sector [START_REF] Chiang | Location quotient and trade[END_REF][START_REF] Lesage | Forecasting Metropolitan Employment Using an Export-Base Error-Corbection Model[END_REF], we calculate the adjusted RCA of a municipality as follows: Suppose export value of industry i in municipality m is a return-to-scale constant function of employment of industry i in municipality m, that is, 2017). The layout of the product space network of the City of Laval is displayed as Figure 9. The node size represents the number of employees in each manufacturing sector, and the node colors represents the degree of complexity of RCA sectors.

𝑋 𝑖𝑚 = 𝑓(𝐸 𝑖𝑚 )= 𝐸 𝑖𝑚 × 𝐶,
[Figure 1 here]

Industrial Competitiveness in the Product Space Network

To identify the industrial competitiveness of the City of Laval, we calculate the RCA indices (RCA World3 ) of good producing sectors and compare their PCI indices. Among 1224 manufacturing sectors included in the original Product Space Network, enterprises in the City of Laval conduct production activities in 132 sectors. There are in total 55 RCA sectors by world standard, which count for 41.7% of all local manufacturing sectors. More than half of local manufacturing sectors are of high-PCI (N=73, p=55.3%). The percentage of RCA sectors of high PCI of the city of Laval (N=35, p=63.64%) is higher than the same ratio of Quebec (p=52.49%) and of Canada (p=50.75%) [START_REF] Wang | Economic complexity, product space network and Quebec's global competitiveness[END_REF].

The leading employment sectors are mostly concentrated in life sciences (special pharmaceuticals, medical instruments), aerospace industry (aircraft parts), food processing industries (pig meat, baked goods), which align with the strategic sectors identified by SDÉ (See Table 1). Meanwhile, specialized papermaking (newsprint), housewares (bell and other metal ornaments, furniture), and machinery and transportation vehicles (iron structures, vehicle bodies, interchangeable tool parts, lifting machinery, construction vehicles, vehicle parts) sectors also attract large amount of employment. Among these leading manufacturing sectors in terms of employment, the main global competitors are the exporters from Germany and China. On the other hand, the USA, the largest trade partner of Canada and Quebec [START_REF] Wang | Economic complexity, product space network and Quebec's global competitiveness[END_REF], serves as the largest import market for many local firms of the City of Laval.

In this sense, the City of Laval can take the advantage of geographic proximity and existing free trade agreement (FTA) in the USA over other global competitors from Asia-Pacific and Europe.

[Table 1 here]

Notwithstanding, re-ranking the manufacturing sectors by RCA indices, we find out that the most competitive manufacturing sectors of the City of Laval exceed beyond the 3 strategic industries of the City of Laval (See Table 2), including housewares (bell and other metal ornaments), specialized papermaking (newsprint, other carbon paper), textiles (gum coated textile fabric, knit clothing accessories), machinery and transportation vehicles (metalworking machines, traffic signals, vehicle bodies, other construction vehicles) and chemicals (soap, scrap plastic). Though aircraft parts sector is still an RCA sector (RCA Index= 1.827), its competitiveness is not as evident as many other sectors.

From the geographic perspectives, the distribution of competitors and partners turns out to be more versatile. On the one hand, similar to main employment sectors, exporters from Germany and China are the major global competitors of RCA sectors, while the USA is the main export market. On the other hand, the competition from other emerging economies (e.g. Thailand, Turkey, Indonesia) also challenges the global competitiveness of local firms of Laval, whereas Japan and EU countries (France and the Netherlands) emerge as potential destinations to form collaboration. Interestingly, there are also sectors the location of main competitors and partners swap the position. For example, the world's largest export of scrap plastic is the USA while the largest importer is China. Given Laval's competitiveness in the sector (RCA =5.658, PCI=-0.891), local plastic manufacturers should be aware of the high competition in the US market meanwhile consider forming supply chain partnership with customers in China.

[Table 2 [Table 3 here]

[Table 4 here]

Structural Holes in the Product Space Network

Our next step is to identify the structural holes in the product space network of the City of Laval. The structural holes represent the separation between non-redundant contacts in a social network [START_REF] Burt | Structural Holes : the Social Structure of Competition[END_REF]. In other words, adding a "common third party" bridging the structural holes between two unconnected network players facilitates the knowledge flows and new opportunity exploration, thereafter, enhances the overall network connectivity and structural cohesion [START_REF] Gargiulo | Trapped in Your Own Net? Network Cohesion, Structural Holes, and the Adaptation of Social Capital[END_REF].

In this study, we look into the ego networks of RCA sectors, that is the whole body of the alter nodes of an ego node has direct connection with, as well as the linkages between them [START_REF] Everett | Ego network betweenness[END_REF]. Hence, the adjacent non-RCA in the ego networks of RCA sectors are regarded as structural holes in the product space network. [START_REF] Hidalgo | The Product Space Conditions the Development of Nations[END_REF] argued that a direct linkage between two manufacturing sectors in the product space network represents the complementary capability a region can produce and export products of both sectors. In this sense, a structural hole between RCA sectors and non-RCA sectors indicate a potential field of growth, since local firms specialized in the structural hole sectors benefits from knowledge sharing of other firms specialized in RCA sectors based on cognitive, social and geographic proximity [START_REF] Boschma | Proximity and Innovation: A Critical Assessment[END_REF]. In addition, bridging the structural hole between RCA sectors and non-RCA sectors enhances the overall connectedness and cohesion of local product space network, which, in turn, contributes to economic complexity and growth potential of the region [START_REF] Hidalgo | The building blocks of economic complexity[END_REF].

To identify the structural holes, we segregate all RCA sectors in a separate network and reach their first-degree ego networks of direct connects (See Figure 2). From the first-degree ego network of RCA Sectors of the City of Laval, we can, first of all, observe a clear core-periphery structure. At the center of this network, there is a densely connected giant component that mixes both RCA and non-RCA sectors. At the network core, there are strong clustering tendencies in machinery, construction, food processing and textiles industrial of RCA sectors surrounded by a large number of non-RCA sectors in the structural holes. On the other hand, strategic manufacturing sectors such as life sciences and aerospace industries lack dense connections to other RCA sectors via the bridges over structural holes.

At the network peripheral, we can also observe a few isolates without connection to the giant core.

Some of these isolates even turn out to be RCA sectors with a large amount of employment such as aircraft parts, bells and other metal ornaments, other construction vehicles. Such results indicate that the intra-regional coordination of these peripheral sectors is not as sufficient as core sectors. Thereafter, filling the structural holes by either incubating scale-up of local firms or attracting FDI from countries that has global competitiveness in these complementary structural hole sectors of local RCA sectors.

[Figure 2 here] Finally, we rank the PCI of all non-RCA sectors of the City of Laval and selected those of high PCI (See Table 5). These industries are those with the closest knowledge proximity to existing RCA sectors in the City of Laval, and of high growth potential. Most of these industries are concentrated in machinery and transportation vehicles, chemicals, housewares and textile sectors, which are all among the three strategic sectors. Regard to the global competition, we discover that, the most competitive economies of these high-PCI structural hole sectors are either in China or Germany, while the USA is the world's largest importer of these products. Therefore, the City of Laval can consider strengthening attraction of FDI from China and Germany, while continue exploring and exploring the final product market in the nearby US market.

[Table 5 here]

Local Clustering in the Product Space Network

In this section, we detect the agglomeration tendency of RCA sectors and structural hole sectors in municipal districts of the city of Laval. We refer to the first 3 digits of postal code of a firm's registration location in the CRIQ and REQ datasets, then assort employment and industrial categories (HS codes and NAICS codes) by district. Then we count the number of RCA sectors (regional/national/global), high-PCI sectors, and structural hole sectors (See Table 6).

[Table 6 here Therefore, within the city-region of the City of Laval, there is a clear core-periphery distribution of manufacturing sectors. Meanwhile, East Division (Saint-Vincent-de-Paul, Duvernay) and West Division (Fabreville) also attract substantial number of manufacturing firms and absorb the population spillover from Central Division of the City of Laval, as well as from the nearby metropolis Montreal (See Figure 3). Hence, in the City of Laval, there is the anchoring effect of functions diffusion from the core to the periphery [START_REF] Friedmann | Regional development policy: a case study of Venezuela[END_REF].

[Figure 3 here] Meanwhile, we observe the high correlation of a number of RCA sectors, high-PCI sectors and structural hole sectors among municipal districts (See Figure 4). Most of these sectors are agglomerated in Sainte-Rose District, followed by Chomedey, Saint-Vincent-de-Paul, Fabreville,and Duvernay.

These districts have higher national and global competitiveness than regional competitiveness.

Considering the high local competition of many strategic manufacturing sectors in Quebec (e.g. aircraft parts, newsprint, meat processing, machinery), outgoing strategies exploring new opportunities in the national or international market can enhance the overall competitiveness of local industries. Finally, we also observe the concentration tendency of structural hole industries in Central Division (Sainte-Rose and Chomedey) of the City of Laval. Hence, this central industrial hub serves the role as the coordinators of knowledge flows between firms specialized in RCA sectors as well as the most potential area to attract FDI from countries of global competitiveness in these sectors.

[Figure 4 here]

Conclusions and Discussions

This research demonstrates the mechanisms how city-regions can capture opportunities in industrial upgrading and achieve global competitiveness. Such goal can be achieved by developing knowledgeintensive advantageous sectors and enhancing the connectivity with global leaders in closely related industries. To elaborate these points, we apply the paradigm of economic complexity and product space network to identify the high-PCI RCA sectors and the structural sectors of the City of Laval. This study integrates multiple levels of a city-region's industrial competence -sectorial diversification, knowledge intensiveness, labor force specialization, spatial agglomeration and inter-sectorial connectivity.

Characterized by high degree of industrial diversification and strong competence in knowledgeintensive sectors, the economy of the City of Laval not only benefits from the spillover effect from the nearby metropolis Montreal, but also incubates a complete and independent micro-ecosystem integrating local firms, employees and governmental authorities. Overall, this study is a pioneer research on the economic complexity and product space network at the city-region level and has strong practical implication for regional industrial policy addressing the regional, national and global layers of a city-region's global competitiveness. In this research, we claim the contributions as follows:

First and foremost, we address the importance of city-region level analysis of economic complexity for the local and global competitiveness as well as the policy implications. By applying adjusted RCA analysis, we analyze the regional, national and global competitiveness of manufacturing sectors of the City of Laval. Moreover, the RCA sectors of the City turn out to be of high degree of versatility from following perspectives. From the aspect of economic complexity, high-PCI sectors count as the majority of all RCA sectors of the City of Laval. Their proportion over all RCA sectors at the municipal-level weights higher than the regional and national average. Hence, the local policy makers should also be aware of the "potential champions" of high-PCI RCA sectors in additional to the strategic sectors already identified. For low-PCI RCA sectors, though they may not directly serve as local economic growth engine, they may still play crucial roles in local employment and bridge the connectivity between high-PCI RCA sectors in the product space network.

Secondly, we introduce the concept of the structural hole in the framework of product space network and argue that first-degree non-RCA connections of the RCA sectors bridge these structural holes for intersectoral knowledge flows. Specifically, structural hole sectors with high PCI serve as the potential fields of industrial upgrading and economic growth. Therefore, the policy makers should also be aware of their growth potential and attract FDI accordingly.

Finally, we detected the tendency of spatial agglomeration of manufacturing sectors in municipal districts. We clearly illustrate the core-periphery of hierarchical urban systems of the City of Laval, which is independent from the nearby metropolis Montreal. Moreover, there is a strong correlated tendency between the number of firms specialized in RCA sectors and those specialized in high PCI sectors and structural hole sectors. In this process, whereas coordination with neighbouring city-regions is important for the urban development, the policy making of the City of Laval can take more autonomy by orchestrating the industrial structure in its own urban system.

Though we made our best efforts to accomplish the mandate, due to the constraints of the analytical framework and data availability, there are still numerous limitations of the research leaving open questions for further exploration. We suggest exploring how the configurations of the municipal product space networks contribute to the innovation capability of local manufacturing firms at the micro-level. From spatial perspective, we can compare the intra-municipal industrial transfer from the core to peripheral with the inter-municipal spillover over from the metropolis to the adjacent suburban areas. From chronological perspective, the timeline of local firm establishment as well as the growth of industrial clusters can also be a direction to understand the processes of industrial upgrading. In all, economic complexity and product space network provide practitioners and policy makers with highly applicable tools to identify their strategic goals, competitiveness, and potential for future development of city-regions.

⁄

  , the authors analyzed the global trade flows from 1995 to 2017 of more than 1200 types of commodities categorized in the harmonized system (HS) and ranked all nation states and trade commodities by calculating following indicators: Revealed Comparative Advantage (RCA), Diversity Index, Ubiquity Index, Proximity Index, and Product Complexity Index (PCI) For a given country c, if the proportion of the export value of product p over the total export value of country c is above the average proportion of total export value product p in global export values, this category of product is recognized as a country's revealed comparative advantage (RCA) sector. Hence, for country c, Xcp represents the annual dollar value of product p from country c. If RCAcp≥1, product p is an RCA sector of country c.

(

  Statistics Canada), and global (UN Comtrade Database) statistics authorities with the distribution of economic sectors embedded in the product space network. To acquire municipal data of the City of Laval, we record valid registration information of operating enterprises in 2019 located in the City of Laval from the provincial manufacturing datasets provided by Banque d'information industrielle of the Centre de recherche industrielle du Qué bec (CRIQ) and Registraire des entreprises du Qué bec (REQ). The municipal dataset includes name of the enterprise, Quebec enterprise number (le numé ro d'entreprise du Québec, NEQ), industrial sector (North American Industry Classification System (NAICS) Canada 2017), location (postal code), number of employees, year of foundation, and revenue.

]

  Aligning the strategic outlook of SDÉ, the large majority of employment in manufacturing sectors are located in the three industrial divisions -Central (Sainte-Rose, Chomedey Nord-est, Chomedey Est, Chomedey Nord-ouest), East (Saint-Vincent-de-Paul, Duvernay),and West (Fabreville). Among all municipal districts, Sainte-Rose district attract most of the employment and firms specialized in high-PCI sectors, RCA sectors and structural hole sectors. Located to the north of 440 Highway, Sainte-Rose District is located next to Chomedey District, the administrative center of the City of Laval, but exceeds the latter in all aforementioned indicators. Meanwhile, both districts are positioned in the central industrial hub of the City of Laval, counting for 71.93% of the total employment of the city.

FiguresFigure 1 :

 1 Figures

Figure 2 :Figure 3 :Figure 5 :

 235 Figure 2: First-degree Ego Network of RCA Sectors of the City of Laval

  After these concordance and adjustment processes, we calculate the RCA indices of all good producing sectors of the City of Laval by comparing municipal employment proportion by sector to world average trade value by sector (

	therefore,
	𝐿𝑄 𝑖𝑚 =	𝐸 𝑖𝑚 𝐸 𝑚 ⁄ 𝐸 𝑖𝑛 𝐸 𝑛 ⁄	=>𝐸 𝑖𝑚 𝐸 𝑚 ⁄ =𝐿𝑄 𝑖𝑚 × (𝐸 𝑖𝑛 𝐸 𝑛 ) ⁄
	𝑅𝐶𝐴 𝑖𝑚 = 𝑋 𝑖𝑚 𝑋 𝑚 ⁄ 𝑋 𝑖𝑔 𝑋 𝑔 ⁄	=	𝑓(𝐸 𝑖𝑚 ) 𝑓(𝐸 𝑚 ⁄ 𝑋 𝑖𝑔 𝑋 𝑔 ⁄	)	=	𝐸 𝑖𝑚 𝐸 𝑚 ⁄ 𝑋 𝑖𝑔 𝑋 𝑔 ⁄

E: Employment; X: Value of exports; i: category of goods; m: municipality; n: national average; g: global average; C is a constant.

  here]Replacing the denominator of RCA to 𝑋 𝑖𝑔 𝑋 𝑔 ⁄ (the world's average value of exporting goods of manufacturing sector i over total exporting goods value), to the sate ratio of export value by sector in Quebec ( 𝑋 𝑖𝑟 𝑋 𝑟 ⁄ ) and Canada ( 𝑋 𝑖𝑛 𝑋 𝑛 ⁄ ), we can also calculate the RCA indices of Laval's manufacturing sectors over regional (RCA Quebec) and national (RCA Canada) average. The regional, national and global competitiveness are not always in coherent with each other. We find out that, for some industries, the City of Laval has even higher competitiveness in the regional or national market than in the global market (e.g. bells and other metal ornaments (HS8306, PCI=-0.866): In contrast, some other manufacturing sectors are more competitive in the global market than in the domestic market (See Table3 and Table 4). For example, the City of Laval has global sectors have higher potential exploring the global market to offset the high competition in the domestic market. Therefore, we suggest diversified competitive strategies in the domestic and global markets. Local firms should consider coordinate their competitive relations with counterparts in other city-regions in Quebec and Canada.

	RCAWorld=54.137, RCACanada=123.031, RCAQuebec=331.988; special pharmaceuticals (HS3006,
	PCI=1.087): RCAWorld=22.524, RCACanada=45.639, RCAQuebec=23573.010); other metal fasteners
	(HS8308, PCI=0.392): RCAWorld=18.11, RCACanada=442.43, RCAQuebec=107.042. Moreover, there are
	industries that do not have global competitiveness but rather local competitiveness (e.g. air pumps
	(HS8414, PCI=1.543): RCAWorld=0.413, RCACanada=1.223, RCAQuebec=1.302). Hence, local firms
	specialized in these industries should prioritize exploiting existing domestic market exploring the
	global market. competitiveness in large iron containers (HS7309, PCI=0.111) sector (RCAWorld=1.364), but neither
	regional nor national competitiveness (RCACanada=0.980, RCAQuebec=0.573). Hence, firms specialized
	in these manufacturing

Table 6 : Manufacturing sectors in Municipal Districts of the City of Laval Ran k

 6

		District	Posta	Employmen	High	RCA	RCA	RCA	Structura
			l code	t	PCI	Quebe	Canada	World	l Holes
						c
	1	Sainte-Rose	H7L	8908	160	105	153	149	26
		Chomedey*		5377	88	59	81	75	18
	2	Chomedey Nord-	H7S	2875	47	24	35	36	11
		est
	3	Saint-Vincent-de-	H7C	2274	40	26	37	38	6
		Paul
	4	Chomedey Est	H7V	1361	19	16	21	16	4
	5	Fabreville	H7P	982	30	28	34	33	6
	6	Duvernay	H7E	684	14	22	22	22	6
	7	Chomedey Nord-	H7T	656	15	16	17	14	2
		ouest
	8	Vimont	H7M 583	14	14	16	16	7
	9	Chomedey Sud	H7W 485	7	3	8	9	1
	10	Pont-Viau	H7G	300	9	7	9	9	3
	11	Saint-Franç ois	H7B	158	4	4	5	6	0
	12	Laval-sur-le-Lac	H7R	154	4	9	6	9	2
	13	Sainte-Dorothé e	H7X	148	6	15	16	15	2
	14	Auteuil-Nord-est	H7J	101	3	13	8	8	8
	15	Auteuil	H7H	61	2	5	4	6	0
	16	Laval-des-Rapides H7N	60	6	10	10	9	2
	17	Auteuil-Sud	H7K	48	3	3	3	2	2
	18	Duvernay-Est	H7A	18	4	5	5	2	3
	19	Î les-Laval

Canada Economic Development for Quebec Regions (CED)-Laval: www.dec-ced.gc.ca/eng/regions/laval/index.html

The City of Laval Economic Development Service (in French): lavaleconomique.com

Unless specified, the RCA indices represent the ratio local employment rate of this manufacturing sector over the world average value of export goods of the same sector.

Tables

 Table 1: