Panos Panagiotopoulos
email: p.panagiotopoulos@qmul.ac.uk

Dennis De Widt
email: d.dewidt@exeter.ac.uk

Keywords: Social media, digital networks, networks of practice, budget cuts, local government finance

Digital networking has been shaping interactions between governments and their respective publics over the last years. At the same time, networking spaces have become hosts to informal communities of public sector professionals engaging in discussions that remain largely unexplored. This papers looks at the dynamics of interaction between public sector professionals in digital networking spaces using a dataset of tweets that contain the hashtag #localgov. This hashtag is used by a variety of accounts mainly within the UK local government. An analysis of 235,681 tweets posted during 2013-2015 shows how #localgov facilitates interactions and the sharing of expertise within the context of intense financial cuts imposed by the UK government. We discuss how networking spaces like #localgov support open discourses as part a network of practice outside organisational barriers.

Introduction

The study of networks and networking relationships has been popular in public administration research e.g. [START_REF] O'toole | Networks and Networking: The Public Administrative Agendas[END_REF][2] [START_REF] Provan | Core Concepts and Key Ideas for Understanding Public Sector Organizational Networks: Using Research to Inform Scholarship and Practice[END_REF]. Public sector networks generally include policy, collaborative and governance networks which vary in their aims but all entail interactions within or across government agencies and other actors like interest groups, businesses, professional associations and non-profits. More recently, there is increased interest in networks that emerge in more informal settings and enable individuals to share expertise according to their interests [START_REF] Isett | Networks in Public Administration Scholarship: Understanding Where We Are and Where We Need to Go[END_REF] [5] [START_REF] Siciliano | Advice Networks in Public Organizations: The Role of Structure, Internal Competition, and Individual Attributes[END_REF].

Many of these networks are emerging in social networking spaces where public sector professionals share insight about their work, connect to colleagues and even collectively discuss policy issues. Such communities include permanent (e.g. blogs, LinkedIn groups) or more ad hoc spaces (e.g. Twitter) that facilitate personal networking outside organisational boundaries [START_REF] Mergel | The use of social media to dissolve knowledge silos in government[END_REF]. It is often the case that informal networks on social media reflect trends and processes of institutional change in government agencies [START_REF] Mergel | A Three-Stage Adoption Process for Social Media Use in Government[END_REF]. So far, research on social media in the public sector has focused on adoption practices within government agencies or explored the impact on citizen-government relationships e.g. [START_REF] Mergel | A Three-Stage Adoption Process for Social Media Use in Government[END_REF] [START_REF] Mergel | Social media adoption and resulting tactics in the U.S. federal government[END_REF] [10] [START_REF] Criado | Government innovation through social media[END_REF]. Beyond communications with the public, there still more to learn about social media within the public sector. As part of this, it is important to explore the new dynamics of interaction between public sector professionals in digital networking spaces.

This paper presents an analysis of the #localgov Twitter hashtag that is mainly used within the UK local government. A dataset captured within a period of almost two years (June 2013 to May 2015) includes 235,681 tweets posted by 37,592 users. This retrospective mapping of online interactions takes place within a period of extended change caused by the UK government's financial decisions that led to significant reductions in local government budgets. Specifically, the dataset tracks reactions to budget reductions from the Spending Review announcement in June 2013 by the Chancellor of the Exchequer (Finance Minister) to the Queen's speech that identified key priorities for the newly elected government in May 2015.

The analysis shows a wide variety of exchanges amongst local government actors about the impact of the cuts and appropriate responses by local government (e.g. joining-up services). Conversations were found to be mainly driven by the need to localise the centrally imposed agenda of budget reductions. This suggests that informal networks like #localgov can facilitate the sharing of expertise even if there is no evidence that they directly drive institutional change. We briefly discuss the implications of these findings including the methodological ones.

Digital networks of practice in public administration

Networks in public administration mostly involve formal organisational structures classified as policy, collaboration or governance networks [START_REF] O'toole | Networks and Networking: The Public Administrative Agendas[END_REF][START_REF] Isett | Networks in Public Administration Scholarship: Understanding Where We Are and Where We Need to Go[END_REF][START_REF] Kapucu | The State of Network Research in Public Administration[END_REF]. Studies of digitally-enabled networks have also remained within the context of interorganisational collaborations. Janowski et al. [START_REF] Janowski | Government Information Networks -Mapping Electronic Governance cases through Public Administration concepts[END_REF] introduce Government Information Networks where actors use ICTs to connect to others and build, manage or sustain relationships. Dawes, Cresswell, & Pardo [START_REF] Dawes | From "Need to Know" to "Need to Share": Tangled Problems, Information Boundaries, and the Building of Public Sector Knowledge Networks[END_REF] describe Public Sector Knowledge Networks as sociotechnical systems that facilitate interorganisational knowledge learning in tackling complex public management problems. Both these concepts refer to organisational networks where interpersonal relationships are embedded within clearly defined professional tasks (e.g. emergency management or service delivery).

In this paper, we turn our attention to digital networks that enable individual connections on the basis of their professional identity. An established concept to describe informal interpersonal networks can be found in "networks of practice", which are spaces of collective learning that involve interactions between participants within professional practice [START_REF] Brown | Knowledge and Organization: A Social-Practice Perspective[END_REF]. Networks of practice are driven by individuals based on a loose professional identity to facilitate knowledge exchange across organisations without relying on existing relationships. Within public administration, such structures have emerged in contexts like forensic scientists in government crime laboratories [START_REF] Binz-Scharf | Searching for Answers: Networks of Practice Among Public Administrators[END_REF] and advice networks between school teachers [START_REF] Siciliano | Advice Networks in Public Organizations: The Role of Structure, Internal Competition, and Individual Attributes[END_REF]. Both Binz-Scharf et al. [START_REF] Binz-Scharf | Searching for Answers: Networks of Practice Among Public Administrators[END_REF] and Siciliano [START_REF] Siciliano | Advice Networks in Public Organizations: The Role of Structure, Internal Competition, and Individual Attributes[END_REF] conclude that informal networks deserve attention because they can have largely positive effects in public organisations -not only they facilitate knowledge sharing amongst highly-skilled professionals but also allow crossing organisational barriers in ways that have otherwise not been possible.

When considering digital networking relationships, a highly relevant stream of work can be found in digital or electronic networks of practice [START_REF] Wasko | Collective Action and Knowledge Contribution in Electronic Networks of Practice[END_REF][START_REF] Wasko | The provision of online public goods: Examining social structure in an electronic network of practice[END_REF][START_REF] Wasko | Why should I share? Examining social capital and knowledge contribution in electronic networks of practice[END_REF][START_REF] Vaast | Trans-Situated Learning: Supporting a Network of Practice with an Information Infrastructure[END_REF]. Digital networks of practice are generally open, self-organised and without formal controls [START_REF] Wasko | Collective Action and Knowledge Contribution in Electronic Networks of Practice[END_REF][START_REF] Wasko | The provision of online public goods: Examining social structure in an electronic network of practice[END_REF]. They allow individuals interact with others to exchange advice and ideas with others based on common interests related to their practice. Public or semi-public spaces like forums, knowledge portals, intranets and social networking groups are common spaces where such networks emerge. Participants tend to contribute when they think that it enhances their professional reputation, when they have something important to share and when they feel a structural part of the network -expectations of reciprocity from other participants may not even be necessary [START_REF] Wasko | Why should I share? Examining social capital and knowledge contribution in electronic networks of practice[END_REF]. As a result, digital networks of practice have been found to facilitate connections between regional networks in traditionally fragmented areas of professional practice like agriculture [START_REF] Oreszczyn | The role of networks of practice and webs of influencers on farmers' engagement with and learning about agricultural innovations[END_REF].

These features suggest that digital networks of practice can facilitate the formation of relationships between individuals within but also across the strict boundaries of professional practice within the public sector (e.g. forensic scientists, school teachers). As such, these spaces can arguably facilitate the transfer of knowledge through network relationships across institutions [START_REF] Lowndes | Something Old, Something New, Something Borrowed[END_REF][START_REF] Crouch | Breaking the Path of Institutional Development? Alternatives to the New Determinism[END_REF]. For example, Mergel and Bretschneider [START_REF] Mergel | A Three-Stage Adoption Process for Social Media Use in Government[END_REF] discuss how the adoption of social media applications is often the result of informal exchanges across agencies where challenges are discussed collectively (e.g. good practice, challenges, resource implications). In this respect, digital networks can drive forthcoming trends in the public sector due to knowledge sharing across institutional barriers. As a result, it is important to look further into the dynamics of interaction between public sector professionals in these spaces.

Study methodology

User-generated content from social media applications can be an important source of data e.g. [START_REF] Halfpenny | Innovations in digital research methods[END_REF]. Twitter hashtags usually form on a dynamic basis around events like national elections, emergencies or popular television shows [START_REF] Bruns | How Long is a Tweet? Mapping Dynamic Converstation Networks on Twitter using Gawk and Gephi[END_REF]. Hashtags were initially self-assigned by Twitter users but soon became a key element of Twitter's unique proposition as an immediate information sharing platform. In professional networking, hashtags can facilitate rapid information sharing and links to resources than the exchange of in-depth opinions within long conversations. This feature makes Twitter hashtags different than social networking groups were membership is stable and clearly defined.

The Twitter hashtag #localgov provides an interesting context to study the role of informal networks particularly during the period 2013-2015. #Localgov is the most popular Twitter space used by professionals involved in different aspects of local government in the UK (e.g. policy actors, officers, elected representatives, service providers, consultants and journalists). The use of #localgov is not exclusive to the UK local government but an estimated 70-80% of the tweets that use the hashtag are related to this context. This was also confirmed by our data analysis.

Twitter posts tagged with #localgov were collected from June 2013 to May 2015 using Chorus Analytics, which is a set of applications designed to facilitate social science research [START_REF]Chorus: Chorus Analytics data harvesting and visual analytics suite[END_REF]. Chorus captures data from Twitter's application programming interface that is publicly available to developers. Keyword-based searches can retrieve tweets posted up to a week before each search. To update the database of tweets from #localgov, searches took place automatically and on a daily basis during the period of study within 2013-2015.

Following a data cleaning and validation step, the final dataset contained a total of 235,681 tweets posted by 37,592 unique accounts. This dataset includes all original tweets and retweets that were posted in this period and contained '#localgov' within their text. The analysis was carried out in several steps. For the analysis reported in the paper we focus on the following:

• Overview of #localgov activity: mapping the volume of tweets over time in relation to their structure (e.g. mentions, retweets, hashtags) and content (main topics of discussion). The latter involved keyword frequency queries using the qualitative analysis software NVivo 11. To facilitate the analysis, the dataset was divided into four roughly equal parts based on a 6-month interval within the near two years of data collection. • Social networking analysis to extract and visualise networking relationships between user accounts within the dataset in the form of mentions or retweets. The open source tool Gephi was used to visualise networking relationships.

Findings

About 2.2 million people are employed by local government authorities in the UK [26]. The institutional structure of local government is diverse with different administrative authorities having responsibilities related to transportation, planning, social care, housing and waste management -the main entities are known as councils.

Councils are strongly reliant upon central government funding at the levels of 70% on average [START_REF] Pratchett | Local Government: Selectivity and Diversity[END_REF]. As a result, budget decisions at the UK central government level have a strong impact on the financial position of local authorities. Because of this reliance, it is not surprisingly that relationships between central and local government actors have been traditionally tense.

The 2008 financial crisis and its consequences on the wider economy have put significant pressure on UK public finances. In the period 2010-2015, local government expenditure experienced unprecedented budget cuts under the Conservative-Liberal Democrat coalition government. Real local government expenditure was reduced by an estimated 40% in real terms over this period [START_REF] Hastings | Coping with the Cuts? The Management of the Worst Financial Settlement in Living Memory[END_REF]. Related to the timeframe of the tweets collected, the central level budget events during the parliamentary year 2013-14 resulted in significant reactions from local government, particularly in June 2013 when further cuts were proposed in an official Spending Review announcement by the Chancellor of the Exchequer (Finance Minister). This was the starting point of our data collection. The end point is May 2015 after the national elections with the Queen's speech that set areas of priority for the newly elected government. This is the context within which our Twitter data can reveal how #localgov acts as an information sharing and discussion space.

Overview of #localgov

Table 1 shows the overview of of tweets tagged with #localgov. The 235,681 tweets correspond to approximately 331 tweets per day -a daily posting frequency that kept increasing during the period of capturing. The volume of tweets tagged with #localgov peaks during weekdays at the levels of 400-500 tweets while weekends generate fewer tweets at the levels of 100. Daily peaks of activity were related to a combination of events like the joint local government and European elections on 22/5/2014 (986 tweets), other elections, political events, adverse weather conditions and financial announcements. For example, the Spending Review announcement on 26/6/2013 with 1,178 tweets sparked a plethora of predictions, previews of key points commentaries, official responses and other reactions. As shown in table 1, an increasing proportion of tweets over time, around 65-75%, contain links to resources in the form of commentaries, news websites, blogs or other sources. The accompanying tweets can be simply informational, ironical, critical or political. There is also a steady increase in the proportion of retweets during the time of study from about 41% to almost 50%, which to some extent accounts for the increased number of users contributing to the hashtag. The proportion of direct mentions to other users fluctuated around 7% and slightly decreased mainly in the last period -this is not unexpected in the months before the UK elections of May 2015.

We can also observe a steady increase in the number of accounts contributing in each period up to a total of 37,592 unique contributors. This might reflect three different trends: (1) increasing interest in the hashtag itself (network effects), ( 2) the growing base of Twitter users in the UK and (3) increasing use of Twitter for professional networking amongst different groups related to local government.

In terms of content, taking into account only original tweets (no retweets), contributions to #localgov focused heavily on topical and temporal keywords. Keywords like "council", "local", "new", "government", "public", "services", "social", "city" and "today" were mentioned at least 2,000 or more times. This was followed by similar themes containing "people", "committee", "meeting", "report", "digital" and "future" that received over 1,000 mentions. These more general themes were followed by terms more specific to local government finances including "cuts", "care", "communities", "funding", "sector", "elections", "finance", "tax", "leaders", "budgets", "labour" and "housing" all of which were mentioned at least 500 times.

Taking retweets into account, as expected, themes that are more nationally relevant receive more attention via reposting. For example, "cut" and "cuts" receive over 10,000 mentions combined. The overall conclusion from the keyword analysis is that, except general keywords that every council or local government officer could use, the dominant theme of discussion was centred around financial cuts and their impact. Although this conclusion can be expected, it is interesting to see how discussions took place as a conversational network of mentions between users.

Networks within #localgov

Networking relationships of accounts that contribute to #localgov can be visualised as a map of interactions in the form of mentions or retweets. Extracting this information from the 235,681 tweets led to a network that has 15,014 nodes (different accounts) and 38,509 edges (mentions or retweets). This network is very diverse in its composition and contains hundreds of different communities or clusters. Such diversity is expected in a hashtag as broad as #localgov over two years. It is interesting to observe how interactions between accounts that contribute to #localgov represent certain groups within this open network and how they reflect specific conversations during the period of study. Given the complexity of such a task, we show here one example of networking analysis.

Figure 1 represents a network of accounts that received and made at least 10 mentions or retweets. This most interactive core of the network contains 176 nodes (1.17% of the total) and 2,886 edges (7.49% of the total). The different colours are indicative of the main clusters that exist within this network. The yellow, slightly disconnected cluster represents accounts outside the UK like @icma, the @theCPBB and @careersingov. The blue cluster represents main media accounts that receive high number of references in informational tweets like popular UK media accounts (e.g. @Guardian_Local and @GdnLocalLeaders). The green and red clusters represent frequent interactions between a large group of influencers in the local government community including think tanks, the Local Government Association, magazine editors and other leaders that receive a lot attention.

Furthermore, it is important to note that central government and other political actors have an "implied" but not active presence in these networks; for example, the account of Eric Pickles (former secretary for the Department of Communities and Local Government) received over 200 mentions but made fewer than 5.

Concluding remarks

The dynamics of interaction in #localgov reveal the existence of an open community that reflects many of the characteristics of professional networking (e.g. decreased activity over weekends). Conversations within #localgov are driven by both endogenous (what happens in local authorities) and exogenous sources (central government financial measures). Many of the posts are purely informational (e.g. retweeting news items), but we also find a large amount of direct interactions and exchange of opinions. Existing local government networks and organisations, civil society actors, news and media accounts act as main hubs in different topics but discussions are not highly centralised around a few key contributors. This is not unexpected given that local government is a large tier of administration that brings together sub-communities around common professional interests (e.g. care services, local development, financial planning).

This open, dynamic and highly flexible nature makes #localgov much different from networks that exist within formal organisational and institutional structures [START_REF] Janowski | Government Information Networks -Mapping Electronic Governance cases through Public Administration concepts[END_REF][START_REF] Dawes | From "Need to Know" to "Need to Share": Tangled Problems, Information Boundaries, and the Building of Public Sector Knowledge Networks[END_REF]. At the same time, the extent to which contributors experience #localgov as a network of practice certainly fluctuates. Twitter hashtags remain unexplored in this context but literature within networks of practice indicates that members have can varying levels of participation, unclear membership and strong motivations to increase their reputation [START_REF] Wasko | Collective Action and Knowledge Contribution in Electronic Networks of Practice[END_REF][START_REF] Wasko | The provision of online public goods: Examining social structure in an electronic network of practice[END_REF][START_REF] Wasko | Why should I share? Examining social capital and knowledge contribution in electronic networks of practice[END_REF][START_REF] Vaast | Trans-Situated Learning: Supporting a Network of Practice with an Information Infrastructure[END_REF]. In #localgov, levels of participation change depending on the topic, for example, in themes like budget reductions activity peaked when there was high interest to discuss the impact of the cuts. Reliance on existing relationships is minimal although it is likely that conversations tagged with #localgov are also determined by "following" relationships or result in new connections between users. While conversations and relationship formation takes place in a very open way, #localgov still exhibits some boundaries. Central policy actors are mentioned in the network but do not engage in discussions, which reflects the traditional setting of intergovernmental relationships especially in England.

The contribution of this study lies in improving our understanding of how networking relationships in the public sector are moving on digital spaces where new types of interactions are being enabled. In particular, open networks like Twitter allow both collective discourses to take place and the ad hoc formation of ties between participants. For public managers, it is important to be aware of how digital networking relationships affect knowledge sharing across public organisations and tiers of government. At the next level, they might need to consider facilitating those relationships with or without claiming institutional ownership. For example, the way the central-local government duality was reflected in our networking analysis is an interesting starting point.

Methodologically, the study applies emerging digital research methods to new phenomena that have gradually gained importance. Understanding the evolution of digital discussions is challenging due to the novelty of the phenomena and the exploratory nature of the analysis. As a result, the study has limitations inherent to most digital research methods where inferences are attempted between online and offline activity. Information flows in a popular hashtag like #localgov are driven by a large number of events that might be difficult to understand using summary measures like keyword analysis and network visualisation. The choice of #localgov, motivated by intense discourses over local government finances during the study, increases the complexity of analysis compared to more contained hashtags.

Finally, as a self-assigned hashtag, #localgov might not even include all relevant tweets and is certainly an intentional tagging method for users that want to increase the reach of their tweets. We cannot know what motivated each individual user to assign #localgov to their tweets and the extent to which they monitor other discussions within the hashtag. These issues have to be taken into account in more indepth interpretations of findings while further work is needed to map and understand digital interactions in social networking spaces.

Figure 1 .

 1 Figure 1. Network of accounts that received at least 10 mentions or retweets during the whole period.

Table 1 .

 1 Overview of #localgov activity

	Period	Total tweets	Tweets per day	Retweets	Direct Mentions	Tweets with links	Accounts
	20/06/2013 to 31/12/2013	56,762	291	23,154 (40.8%)	4,067 (7.2%)	37,567 (66.1%)	11,142
	01/01/2014 to 30/06/2014	58,085	321	24,722 (42.6%)	4,459 (7.7%)	42,062 (72.4%)	11,826
	01/07/2014 to 31/12/2014	63,335	344	29,949 (47.3%)	4,235 (6.7%)	45,150 (71.3%)	13,731
	01/01/2015 to 31/05/2015	57,499	381	28,558 (49.6%)	3,650 (6.3%)	42,617 (74.1%)	14,408
	Total	235,681	331	106,383 (45.1%)	16,411 (7%)	167,396 (71%)	37,592 (unique)

Acknowledgments. The dataset used in this study was collected and analysed with the help of Chorus software, which is an analytics suite designed to facilitate social science research using Twitter data. The authors gratefully acknowledge the Chorus team: Timothy Cribbin, Julie Barnett, Philip Brooker and Hiran Basnayake.

Digital networks in public administration:

the case of # localgov


Bojan Cestnik
email: bojan.cestnik@temida.si

Alenka Kern
email: alenka.kern@ssrs.si

Cross-Context Linking Concepts Discovery in E-Government Literature

Keywords: document clustering, linking concepts discovery, e-government, public housing, social media

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Every modern organization in both government and private sector needs to process, organize and store information that is required to conduct its business. In this task, ontologies typically play a key role in providing a common understanding by describing concepts, classes and instances of a given domain. They are frequently built manually by extracting common-sense knowledge from various sources in some sort of representation. Many computer programs that support manual ontology construction have been developed and successfully used in the past, such as Protégé [START_REF] Gennari | The Evolution of Protégé: An Environment for Knowledge-Based Systems Development[END_REF].

Since manual ontology construction can be a complex and demanding process, there is a strong need to provide at least partially automated support for the task. With the emergence of new text and literature mining technologies, large corpora of documents can be processed to semi-automatically construct structured document clusters [START_REF] Kietz | A Method for Semi-Automatic Ontology Acquisition from a Corporate Intranet[END_REF]. Resulting document clusters can be viewed as concepts (classes, topic descriptions) that can be used to describe domain properties in the form of topic ontologies. In recent years, various tools that help constructing document clusters from texts in a given problem domain were developed and successfully implemented in practice [START_REF] Kietz | A Method for Semi-Automatic Ontology Acquisition from a Corporate Intranet[END_REF]. One example of such tool that enables interactive construction of clusters of text documents in a selected domain is OntoGen [START_REF] Fortuna | System for semi-automatic ontology construction[END_REF]. It can be used to extract concepts from input documents and organize them into high-level topics. By using modern data and text processing techniques OntoGen supports individual phases of ontology construction by suggesting concepts and their names and defining relations between them [START_REF] Fortuna | OntoGen: Description[END_REF].

Literature mining is a process of applying data mining techniques to sets of documents from published literature. Essentially, literature mining is a technique used to tame the complexity of high dimensional data and extract new knowledge from the available literature. It can be used in many ways and for various purposes, also, for example, when dealing with problems spawning from economic crisis that the society is facing in our time. For instance, in [START_REF] Sørensen | Enhancing Collaborative Innovation in the Public Sector[END_REF] the authors analyze and compare innovation in public and private sectors. They identify three factors for improved interest for innovation in public sector. First, the requirements and expectations of the public sector services have grown considerably. Second, the number of complex problems that the public sector has to face in the areas like public safety, poverty reduction, and climate mitigation has also grown. And third, innovative capabilities of governments and localities play an important role in the competitive globalization game [START_REF] Sørensen | Enhancing Collaborative Innovation in the Public Sector[END_REF].

Documents that are of interest for an organization might come from various sources. They can be stored in the organization's Intranet storage, or can reside in a more or less organized form and format on the Internet. Among many publicly accessible potential sources we can identify semi-structured Semantic Web entities and Linked Data sources, as well as more organized public libraries such as Medline and PubMed [6], E-Government Reference Library [START_REF] Scholl | E-Government Reference Library (EGRL) version 11[END_REF], and Google Scholar [8]. A general text processing management and ontology learning process from text consists of several steps [e.g. 2]. First, the documents (natural language texts) and other resources (e.g. semi-structured domain dictionaries) are obtained from designated sources. Then, they are preprocessed and stored on text processing server. In the next step, domain ontology is built with ontology learning and ontology pruning algorithms. In the last step, the constructed ontology is visualized, evaluated and stored on a repository for further use and exploration.

The main motivation for our case study was to demonstrate how the text processing can be used for public documents and government data. We wanted to present the utility and evaluation of the approach from the interested parties' (i.e. public bodies) viewpoint. In particular, our aim was to offer some interesting insights, such as how the document clustering technology can be used to identify mutual subsets of papers from one context (document source) that were more close to the subset of papers from the other context. Such a cross-context approach to linking term discovery has been introduced in medical field [e.g. 9, 10, 11] and has been used to identify hidden relations between domains of interest with a great success.

In the case study described in this paper we used E-Government Reference Library of articles [START_REF] Scholl | E-Government Reference Library (EGRL) version 11[END_REF] and PubMed [6] as a document source. In the first experiment we obtained an overview of the topics addressed in the recently published e-government papers. In particular, we were interested in the shift of focus of the papers through the years; the keywords describing document clusters gave us clues about which topics are trending in certain time periods. In the second experiment we formed a cluster of papers related to a preselected term (in our case we used two arbitrarily selected terms: "social media" and "housing") in order to explore the characteristic keywords that discriminate this cluster with respect to the rest of the documents. The underlying assumption was that while it is often easy to automatically collect data, it requires considerable effort to link and transform them into practical information that can be used in concrete situations. In the third experiment we combined the papers addressing the similar topic from two document sources, e-Government Reference Library and PubMed. Then, we identified characteristic similarities and differences between the two origins, with a particular aim to identify outlier papers that are worthy of further exploration for finding potential cross-context concept links. Here, the underlying assumption was that while the majority of papers in a given domain describe matters related to a common understanding of the domain, the exploration of outliers may lead to the detection of interesting associating concepts among the sets of papers from two disjoint document sources. In addition, focusing on a potentially interesting subset of outlier papers might considerably reduce the size of article corpora under investigation. The presented case study results suggest that the document exploration aided by OntoGen can, in comparison to the traditional manual one, be more focused, efficient and effective.

This paper is organized as follows. In the second section we describe the construction of the input sets of documents. In the third section we describe the methods used in the study and present three cases in which OntoGen was used to generate and visualize clusters of documents with similar properties. In section 4, we assess and discuss the main lessons learned from the case study. The paper is concluded in section 5.

Document sources

Documents and papers that are of interest for an organization can be obtained from many publicly accessible sources on the Internet. There are several semi-structured Semantic Web entities and Linked Data sources, as well as more organized public libraries such as Medline and PubMed [6], E-Government Reference Library [START_REF] Scholl | E-Government Reference Library (EGRL) version 11[END_REF], and Google Scholar [8]. Majority of the contemporary published papers can be, depending on the copyright issues, obtained in an electronic form from the Internet. It is particularly useful when a set of documents from a selected domain is available in some sort of standard format.

One such example is E-Government Reference Library -EGRL - [START_REF] Scholl | E-Government Reference Library (EGRL) version 11[END_REF] that in the current version 11.5 contains 9.690 references of peer-reviewed articles predominant-ly in English language. It is available in XML format for public download and use. Another example of a resource of papers on the Internet is PubMed [6], which contains papers largely from the medical field.

The first step in the process of text mining and document clustering is retrieval and preprocessing of text documents. For our study we took 7.810 documents from the EGRL library in XML format as an input for further processing. Text mining and document clustering methods were shown to produce useful results on scientific papers when used on titles and abstracts [START_REF] Cestnik | Ontological representations for supporting learning in business communities[END_REF]. Therefore, in the preprocessing phase we excluded the papers that contain only title in the XML file and included only those library papers that have also their abstracts available. There are 5.223 such papers in the library. Each relevant paper was described with the year of publication, the title and the abstract. Short statistics of the included papers according to the year of publication is shown in Table 1. The first input document collection was used in the experiments described in subsections 3.1 and 3.2.

Table 1. Number of papers from E-Government Reference Library [START_REF] Scholl | E-Government Reference Library (EGRL) version 11[END_REF] by the year of publication. In the last two columns the papers with included abstract are given. To process the papers that address a similar topic from two document sources we prepared the second input document collection from the PubMed papers responding to the search string "social media" and "government". The criteria for the search were arbitrarily selected with the aim to focus on the papers related to "government" topic and narrow the number of retrieved papers. Note that any other specific topic of interest can be used instead of "social media". The concrete search query was "government AND social AND (media OR network)". As a result, we obtained 9.690 papers, from which 5.327 papers had abstracts and were published after the year 2004. The second input document collection was used together with the first document collection in the experiment, described in subsection 3.3.

All papers

Document clustering with OntoGen

The process of forming clusters of documents from a set of documents and naming them by keywords can be considered as creating topic ontology in a domain under study. Ontologies include descriptions of objects, concepts, attributes and relations between objects. They conceptualize and integrate the domain terminologies that can be identified in text. Therefore, ontologies reflect the content and the structure of the knowledge as it can be recognized through the use of terms in the inspected collection of texts. Note that the documents that are used in the construction of topic ontologies must be carefully selected before they are processed and considered for analyses.

Ontologies for a given domain can be constructed manually using some sort of language or representation. In manual extraction, an expert seeks common sense concepts and organizes them in hierarchical form. Since manual ontology construction is a complex and demanding process, several computerized programs have been created that support semi-automatic construction of ontologies from a set of documents [e.g. 2]. Based on text mining techniques that have already been proved successful for the task, OntoGen [START_REF] Fortuna | OntoGen: Description[END_REF] is a tool that enables the interactive construction of ontologies from text in a selected domain. Note that OntoGen is one representative of the tools that help constructing ontologies from texts. With the use of machine learning techniques, OntoGen supports individual phases of ontology construction by suggesting concepts and their names, by defining relations between them and by the automatic assignment of text to the concepts. The most descriptive words of each concept are obtained by the SVM [START_REF] Ben Ayed | Keyword Spotting Using Support Vector Machines, Text, Speech and Dialogue[END_REF] from the documents grouped in each cluster.

The input for OntoGen is a collection of text documents. Documents are represented as vectors; such representation is often referred to as Bag of Words (BoW) representation [START_REF] Sebastiani | Machine learning in automated text categorization[END_REF]. In the BoW vector space model, each word from the document vocabulary stands for one dimension of the multidimensional space of text documents. This way, the BoW approach can be employed for extracting words with similar meaning. Therefore, it is commonly used in information retrieval and text mining for representing collections of words from text documents disregarding grammar and word order, which enables to determine the semantic closeness documents. BoW vector representation can also be used to calculate average similarity between the documents of a cluster. The similarity is also called cosine similarity, since the similarity between two documents is computed as cosine of the angle between the two representative vectors.

Topic focus shift through time

In the first experiment we set a goal to acquire an overview of the topics (keywords) prevailingly addressed in the recently published e-government papers. In particular, we were interested in the shift of topic focus of the papers through the years. The characteristic keywords describing document clusters, which were generated automatically with OntoGen, gave us clues about which topics are trending in certain time periods. By using OntoGen users can construct a complex ontology more efficiently and in shorter time period than manually. They can create concepts, organize them into topics and also assign documents to concepts. Simultaneously, they have full control over whole process (therefore semi-automatic) by choosing or revising the suggestions provided by the system [START_REF] Fortuna | System for semi-automatic ontology construction[END_REF].

Fig. 1. 5.223 papers from EGRL library clustered according to the year of publication. Each cluster is described with SVM [START_REF] Ben Ayed | Keyword Spotting Using Support Vector Machines, Text, Speech and Dialogue[END_REF] keywords that characterize the contained papers.

We constructed a topic ontology with OntoGen from the abstracts of 5.223 papers from EGRL [START_REF] Scholl | E-Government Reference Library (EGRL) version 11[END_REF], shown in Table 1 and Figure 1. The topics represent temporal divisions (clusters) of documents according to the year of publication and are labeled with the most descriptive words. The topic ontology from Figure 1 can be regarded as a structure of folders for the input set of papers. In such way it can enrich our prior knowledge about the domain, motivating creative thinking and additional explanations of the constructed concepts. Moreover, the descriptions of clusters (keywords) in Figure 1 can be used to analyze trends in the published topics. For example, keyword "media" (or "social media") appeared in the descriptions only after year 2011 and gained more importance after 2013. Keyword "citizens" is spotted from 2005 on, while "cities" gained importance in 2015 with the smart cities initiative. Many other interesting relations can be observed directly from Figure 1. Note that average similarity measure for each cluster is also shown in Figure 1.

Grouping papers by selected characteristic keywords

In the second experiment we generated a special cluster of papers related to a preselected term (in our case we used two arbitrarily selected terms: "social media" and "housing") in order to explore the characteristic keywords that discriminate this cluster with respect to the rest of the documents. The underlying assumption was that while it is often easy to automatically collect data, it requires considerable effort to link and transform them into practical information that can be used to help decision makers in concrete situations. As input we took the abstracts of 5.223 papers from EGRL and manually (overriding OntoGen's document similarity feature) constructed four clusters. In the first cluster we included documents containing term "social media" (503 papers); the remaining 4.720 documents were included in the second cluster. In the third cluster we included documents containing term "housing" (21 papers); the remaining 5.202 papers were included in the fourth cluster. Then, we generated SVM keyword descriptions for each cluster that distinguish it from its counterpart cluster (the first from the second, and the third from the fourth cluster). The goal was to explore the characteristic keywords that discriminate the documents in one cluster with respect to the rest of the documents. In our case, we wanted to identify common concepts (keywords) between the two clusters, since "social media" and "housing" are both topic of high interest for our organization, and pinpoint the most relevant papers describing the two topics.

The four clusters and descriptions are shown in Figure 2. The cluster for "social media" is described with the following keywords: "social, media, social media, networks, political, social networks, community, twitter, participants, citizens", while the remaining cluster is described by "service, systems, government, models, data, citizens, public, information, participants, processes". The cluster for "housing" is described with the following keywords: "housing, community, service, digital, divide, digital divide, social, citizens, website, government website", while its counterpart cluster is described by "service, government, systems, citizens, models, public, data, participants, political, social". The descriptions of two distinguished clusters share two common keywords: "social" and "citizens". The central document for "social media" cluster is the document with id 1998 [START_REF] Effing | Social media participation and local politics: a case study of the Enschede council in the Netherlands[END_REF], while the central document for "housing" cluster is the document with id 6588 [START_REF] Sipiror | Bridging the Digital Divide for e-Government inclusion: A United States Case Study[END_REF]. The two documents were used for more detailed preliminary study of the two topics and for finding new, potentially uncovered ideas for social media applications in housing.

3.3

Combining papers from two document sources

In the third experiment we combined the papers addressing the similar topic from two document sources, e-Government Reference Library and PubMed. Our aim was to identify characteristic similarities and differences between the papers from the two origins. In particular, we were interested in outlier papers that are worthy of further exploration for finding potential cross-context concept links [e.g. 11]. Here, our assumption was that while the majority of papers in a given domain describe the matters related to a common understanding of the domain, the exploration of outliers may lead to the detection of interesting associating concepts among the sets of papers from two disjoint document sources. In addition, focusing on a potentially interesting subset of outlier papers might considerably reduce the size of article corpora under investigation, which might also help decision-makers narrowing down the mere quantity of papers to read for further study. Fig. 2. Two document clusters for preselected terms "social media" (left) and "housing" (right).

The characteristic keywords that discriminate the two clusters with respect to the rest of the documents are shown in the rectangles.

For practical purposes, we have joined the first and the second input document collections to obtain 10.550 papers with abstracts. Then, we have constructed with On-toGen two clusters of documents based on their similarity. I the papers from the two sources were completely different, the two clusters would most probably contain the documents from one document source, respectively. However, the situation depicted in Figure 3 shows that this assumption is only partially correct. The two top level clusters are labeled "health, careful, patients" and "service, citizens, government".

The first cluster (lets denote in with P) contains 8.416 documents, while the second one (denoted with E) contains 5.734 documents. Second level clusters reveal that in cluster P there is a majority of papers (4.749) from PubMed and only a minority (67 papers in cluster denoted P-E) of papers from eGov field. The situation is reversed in cluster E: here, the majority is from eGov (5.156 papers) and slightly bigger minority from PubMed (578 papers in cluster denoted E-P). In cluster P-E there are 67 documents from EGRL library that are described with keywords "information, information systems, health careful, fire, developing, applications, education, government, safety, students". They are "outliers" from eGov (EGRL) library because they are more similar to PubMed documents. Clearly, they prevailingly deal with the health-related issues. On the other hand, in cluster E-P there are 578 documents from PubMed that are more similar to EGRL library documents. The can be described with the following keywords: "social, health, science, human, environmental, fund, scientific, water, research, resource".

In our preliminary study we took into account the outlier papers from both P-E and E-P clusters and formed combined blended input document collection for further analysis. Our aim was to investigate the potential of outlier clusters for uncovering linking concepts between the two fields in our further work. In order to reduce the search space, the white list of interesting potential linking concepts for further consideration (shown in Table 2) that was prepared with OntoGen and further refined and validated by the domain expert. All the listed terms appear to be interesting to the domain expert that was included in the process. The identified outlier papers for each term seem worth for further exploration. For example, the single outlier paper from EGRL that contains the term "family" states how job clarity, effective communications with management, a participatory management approach, organizational support of career development, opportunities for advancement, and family-friendly policies are all significant variables affecting the job satisfaction of IT employees [START_REF] Kim | IT Employee Job Satisfaction in the Public Sector[END_REF]. The two papers from EGRL that include term "disability" deal with health status impact to information consumers [START_REF] Goldner | How health status impacts the types of information consumers seek online[END_REF] and regional disparities in occurrences of diseases due to unsafe water resources in China [START_REF] Carlton | Regional disparities in the burden of disease attributable to unsafe water and poor sanitation in China[END_REF]. We have observed that the last paper is indexed also in the PubMed library. When considering "disadvantage" as a linking term, the outlier document indexed in EGRL that deals with poverty and health in the good society [START_REF] Cattell | Poverty, community, and health: Co-operation and the good society[END_REF] was identified. It is actually a book published by Palgrave Macmillan and is definitely worth reading and referencing in further studies. Last but not least, we found two outlier documents containing term "big data". The first document indexed in PubMed deals with big data analysis framework for healthcare and social sectors in Korea [START_REF] Song | Big data analysis framework for healthcare and social sectors in Korea[END_REF], while the second document is indexed in EGRL and deals with incentivizing health information exchange [START_REF] Jarman | Incentivizing health information exchange: collaborative governance, market failure, and the public interest[END_REF].

Conclusion

In this paper we describe three experiments in using text processing and clustering methods to model and visualize existing but often overlooked knowledge that is hidden in documents and papers. The issue addressed is the information integration in e-Government domain ontologies and their visualization through the similarity maps. The ontologies were constructed semi-automatically with the computational support of [START_REF] Fortuna | System for semi-automatic ontology construction[END_REF] using scientific papers from EGRL [START_REF] Scholl | E-Government Reference Library (EGRL) version 11[END_REF] and PubMed as input. The use of OntoGen has enabled a quick insight into a given domain by semi-automatically generating the main ontology concepts from the domain's documents.

Our observations show that ontologies help gaining understanding in a given subject area. Therefore, using tools for semi-automatic ontology construction from textual data can significantly speed up the process of becoming acquainted with the domain of interest. We can first generate top-level domain ontology concepts and thus obtain a general overview and understanding of the domain, and only then concentrate on reading an extra load of information. In such a way, semi-automatically constructed ontologies actually helped us to review and understand the variety of topics of interest prior to further investigation.

Encouraged by the growing demands for public innovation, one of the aims of this article was also to explore technological possibilities for supporting creative processes in public sector. In order to exploit existing but often overlooked knowledge that is hidden in public information we investigated the potential of text processing and document clustering. In the third experiment we focused on identifying outlier documents from two document sources (PubMed and EGRL libraries), since the exploration of outliers may lead to the detection of interesting associating concepts among the two sets of documents. We have demonstrated that focusing on a potentially interesting subset of outlier papers considerably reduces the size of document corpora under investigation. Our observations show that using tools for semi-automatic ontology construction from text can significantly speed up the process of becoming acquainted with the domain of interest, thus making the process more focused and effective.

Fig. 3 .

 3 Fig. 3. Combining papers from two sources: e-Government Reference Library and PubMed. Clusters containing outlier documents are shown in bottom-left and top-right rectangle.

Table 2 .

 2 The list of potential linking terms between outliers E-P (PubMed) and P-E (eGov library of documents). Number of outlier papers containing each term is shown.

		Number of papers
	Term	E-P (PubMed)	P-E (eGov)
	safety	14	5
	media	96	2
	privacy	12	1
	family	13	1
	education	32	7
	disability	6	2
	disadvantage	3	1
	economy	13	1
	low income	2	2
	financial incentive	3	1
	electronic health	1	3
	public fund	9	1
	big data	1	1

Acknowledgement

The presented work was partially carried out for the Housing Fund of the Republic of Slovenia, Public Fund. The authors wish to thank the Fund's management for their continuous cooperation and support.


Jérémy Charlier

Sofiane Lagraa

Radu State
email: radu.state@uni.lu

Jérôme François
email: jerome.francois@inria.fr

Profiling Smart Contracts Interactions with Tensor Decomposition and Graph Mining

Keywords: Tensor, Stochastic Process, Graph mining, Smart Contract

Smart contracts, computer protocols designed for autonomous execution on predefined conditions, arise from the evolution of the Bitcoin's crypto-currency. They provide higher transaction security and allow economy of scale through the automated process. Smart contracts provides inherent benefits for financial institutions such as investment banking, retail banking, and insurance. This technology is widely used within Ethereum, an open source block-chain platform, from which the data has been extracted to conduct the experiments. In this work, we propose an multi-dimensional approach to find and predict smart contracts interactions only based on their crypto-currency exchanges. This approach relies on tensor modeling combined with stochastic processes. It underlines actual exchanges between smart contracts and targets the predictions of future interactions among the community. The tensor analysis is also challenged with the latest graph algorithms to assess its strengths and weaknesses in comparison to a more standard approach.

Introduction

Since the appearance of Bitcoin's crypto-currency in 2009 by Nakamoto, different counterparts have tried to extend Bitcoin's design beyond the currency. The most visible is the Ethereum platform, an open source platform relying on blockchain technology and using Ether as a crypto-currency. They implemented a protocol relying on smart contracts for automatic exchanges without a central gatekeeper. Originally, smart contracts have been first mentioned by Nick Szabo in 1998. He exposed the idea as "a computerized transaction protocol that executes the terms of a contract [...] to satisfy common contractual conditions, minimize exceptions [and] the need for trusted intermediaries". Smart contracts appear as a technology for higher transparency without the requirement of trusted intermediaries for currency exchanges. A smart contract is a set of transactions. A transaction has the following fields: Hash, Block height, Sender, Receiver, Amount representing the hash of the transaction, the timestamps in terms of block height numbers, the contract issuer, the contract recipient and the scalar value to be transferred from the sender to the receiver, respectively. Due to the vast number of inter-connected contracts over time, the modeling of the interactions is non trivial and requires an efficient model to predict transactions over time. Predicting and analyzing new contracts has important practical applications in financial instruments where recommendation would be based on likely future contracts interactions.

The main contribution of the paper resides in the modeling of smart contracts interactions using a tensor approach. In addition, a novel technique consisting in the combination of stochastic processes and tensors allows to reproduce existing interactions and to predict future interactions over time. The tensor approach is then challenged with state-of-the-art graph algorithms to assess its performance.

To describe our methodology, section 1 presents the latest research concerning the smart contracts and the tensors. Section 2 introduces the concepts related to the chosen tensor decomposition and the stochastic model used for interactions simulations. In section 3, a short description of the graph theory is suggested and section 4 demonstrates the experiments performed on the tensor approach and challenged with the graph analytics.

Related Work

Since its first definition by Nick Szabo, the security and the programming patterns of the automated protocols have been highlighted. More specifically, in [START_REF] Luu | Making smart contracts smarter[END_REF], the authors investigate the security on smart contracts. They underline the possibility of manipulation of smart contracts within the Ethereum platform with the goal of gaining profit. They also provide a symbolic execution tool to find potential bugs within the running Ethereum smart contracts. In [START_REF] Bartoletti | An empirical analysis of smart contracts: platforms, applications, and design patterns[END_REF], the authors quantify smart contracts use according to their application domain as well as the common coding patterns in Ethereum. However, even with security issues raised around automated protocols, smart contracts still offer lower transactional and running costs. In [START_REF] Morabito | Smart contracts and licensing[END_REF], the authors explain how entities can make use of smart contracts to gain in competitiveness and push further innovation. In [START_REF] Idelberger | Evaluation of logic-based smart contracts for blockchain systems[END_REF], the authors propose a new way of programming smart contracts with a logic-based programming. It introduces new coding behavior with the goal of further efficiency. Last but not least, the use of smart contracts and its extension towards various domains also raise the question of their legal status. In [START_REF] Kõlvart | Smart contracts[END_REF], the authors address the new challenges and the evolution of the law following the use of the smart contracts in the Legal Tech companies.

However, analysis of the smart contracts using tensor based approach has not yet been deeply studied among the scientific community. Different decompositions have been applied on various subjects as the survey written by Kolda and Bader in [START_REF] Tamara | Tensor decompositions and applications[END_REF] exposed it. Our work concentrates on the CANDECOMP/PARAFAC (CP) decomposition which has been presented simultaneously by Harshman et al. in [START_REF] Richard A Harshman | Foundations of the parafac procedure: models and conditions for an" explanatory" multimodal factor analysis[END_REF] and [START_REF] Carroll | Analysis of individual differences in multidimensional scaling via an n-way generalization of eckart-young decomposition[END_REF]. It has been applied a lot in neuroscience due to the image processing and its uniqueness property. In [START_REF] Anders | Structure-seeking multilinear methods for the analysis of fmri data[END_REF], Andersen and Rayens used the CP decomposition for functional magnetic resonance images (fMRI) data analysis in three and four dimensions. Sen and Parhi also applied in [START_REF] Sen | Extraction of common task signals and spatial maps from group fmri using a parafac-based tensor decomposition technique[END_REF] CP decomposition for fMRI processing with a novel algorithm for the extraction of the common task signals and spatial maps from a fMRI group as rank-1 tensors. Other authors extended the use of the CP decomposition in other domains than neuroscience: Acar et al. in [START_REF] Acar | Modeling and multiway analysis of chatroom tensors[END_REF] used for data mining, Shen et al. for Inferring network topologies in [START_REF] Shen | Inferring directed network topologies via tensor factorization[END_REF] and Dinç, Ertekin and Bker applied it to the quantitative resolution of related drug substances.

In this paper, we propose a tensor-based approach based on the CP decomposition on crypto-currency domain by combining the tensor decomposition to stochastic process. This new approach allows to identify and predict smart contracts interactions.

To the best of our knowledge, this is the first work of the tensor-based approach combined with the stochastic variance gamma model for analyzing and modeling smart contracts.

Tensor Analysis

In this section, we present the tensor theoretical background and the tensor decomposition used for the experiments. Finally, we describe the stochastic process used for the predictions of the interactions.

Tensor Description

Notation Mathematical notations and formulation follow the notations proposed by Kolda and Bader in [START_REF] Tamara | Tensor decompositions and applications[END_REF]. The notations have been reused by different articles related to tensor decomposition. Scalars are identified by lowercase letters, a. Vectors and matrices are denoted by boldface lowercase letters and boldface capital letters, respectively a and A. The transpose of the matrix A ∈ R I×J is denoted by A T . Tensor Definition Let define a N -th multidimensional array denoted by X such as X ∈ R I1×I2×I3×...×I N . X is called a N -way tensor. Tensors are denoted by Euler script letters. Tensor Operations The square root of the sum of all tensor entries squared determines the tensor norm.

||X|| = I1 j1=1 I2 j2=1 ... I N j N =1 x 2 j1,j2,...,j N (1)
The vector outer product denoted by • between u∈ R I and v∈ R J results in a matrix W∈ R I×J .

u • v = u T v =    u 1 . . . u I    v 1 ... v J =    u 1 v 1 u 1 v 2 ... u 1 v J . . . . . . ... . . . u I v 1 u I v 2 ... u I v J    (2)
A N -way tensor X ∈ R I1×I2×I3×...×I N is a rank one tensor if it can be written such as

X = a (1) • a (2) • • • • • a (N ) (3)
The Khatri-Rao product between two matrices A∈ R I×K and B∈ R J×K , denoted by A B, results in a matrix C of size R IJ×K . It is the column-wise Kronecker product.

C = A B = [a 1 ⊗ b 1 a 2 ⊗ b 2 • • • a K ⊗ b K ] (4)

Tensor Decomposition

For the analysis of the interactions between smart contracts, the CP decomposition is used. It has been introduced by Harshman in [START_REF] Richard A Harshman | Foundations of the parafac procedure: models and conditions for an" explanatory" multimodal factor analysis[END_REF] and Carroll and Chang in [START_REF] Carroll | Analysis of individual differences in multidimensional scaling via an n-way generalization of eckart-young decomposition[END_REF]. It allows a tensor X ∈ R I1×I2×...×I N to be written as the sum of component of rank-one tensors.

X = R r=1 a (1) r • a (2) r • • • • • a (N ) r (5)
The minimization equation min X ||X -X|| with X the approximate tensor constructed with matrices a i randomly initialized and X the original tensor is solved with the Alternating Least Squares (ALS) method as presented by Harshman in [START_REF] Richard A Harshman | Foundations of the parafac procedure: models and conditions for an" explanatory" multimodal factor analysis[END_REF] and Carroll and Chang in [START_REF] Carroll | Analysis of individual differences in multidimensional scaling via an n-way generalization of eckart-young decomposition[END_REF]. The matrices

A = R r=1 a (1) r ∈ R I×R , B = R r=1 a (2) r ∈ R J×R and C = R r=1 a (3) r
∈ R I×R are successively updated according to the non-negative scheme presented by Lee and Seung in [START_REF] Daniel | Learning the parts of objects by non-negative matrix factorization[END_REF].

               a ir ← a ir [X (1) (C B)] ir [A(C B) T (C B)] ir b jr ← b jr [X (2) (C A)] jr [B(C A) T (C A)] jr c kr ← c kr [X (3) (C A)] kr [C(B A) T (B A)] kr (6)
The non-negative algorithm plays a key role in the convergence of the historical calibration of the parameters of the stochastic model.

Stochastic Model For Interactions Predictions

Interactions between smart contracts can be very discontinuous among time. Some interactions appear for short period of time before vanishing, other interactions are present in all time periods while some contracts never interacts. As a consequence, a deterministic model cannot be used but a stochastic model with jumps should be preferred.

The Variance-Gamma (VG) model has been introduced by Madan, Carr and Chang in [START_REF] Dilip B Madan | The variance gamma process and option pricing[END_REF]. This stochastic model is a pure jump process. One of its main application is in quantitative finance as illustrated by Hull in [START_REF] John | Options, futures, and other derivatives[END_REF]. The VG model is defined with three parameters denoted θ, σ and ν ∈ R. θ represents the drift in the Brownian motion among time. A Brownian motion, denoted by W , is a continuous time process representing the random motion of a small particle immersed in a fluid having the same density as the particle. σ is the volatility and ν is the variance rate of the gamma time change. The drift is represented by ωt, the gamma process by h and the process to be simulated by S.

     ω = 1 ν ln(1 -θν -0.5σ 2 ν) h = θg + σ √ gz with g ∼ Γ ( t ν , ν), n ∼ N (0, 1) S t = S 0 exp(rt + ωt + h) (7)
Based on the empirical observations, no VG drift free rate could have been identified. As a result, the parameter r is set to 0.

Graph Mining

In this section, we present briefly the graph analytics used as a comparison of the tensor-VG model in the experiments.

Graph Analytics

Centrality score measures the communication importance of a vertex. In this paper, degree (baseline) centrality and betweenness (flow-based) centrality have been applied. A degree centrality represents the number of vertex neighbors and gives a local view of the graph around each node. In a directed graph, each vertex has an indegree and an outdegree. Let G = (V, E) ∀T x ∈ V . In smart contracts, we can distinguish between the senders and receivers. Indegree of vertex T x , denoted by deg -(T x ), is the number of edges which are coming into the vertex T x . Outdegree of vertex T x , denoted by deg + (T x ), is the number of edges which are going out from the vertex T x . The centrality of a sender, is based on the amount of Ether, Ethereum crypto-currency. We measure this using the betweenness centrality measure [START_REF] Linton C Freeman | Centrality in social networks conceptual clarification[END_REF], which measures how much a given vertex lies in the weighted shortest paths of other vertices. Let δ sr = δ rs denote the number of shortest paths from T s ∈ V to T r ∈ V where by convention δ TsTs = 1. Let δ TsTr (T x ) denote the number of shortest paths from T s to T r that some

T x ∈ V lies on: betweenness = Ts =Tx =Tr δ TsTr (T x ) δ TsTr (8)
A bi-clique measure allows to discover common interaction between two sets of objects in a graph. Often, bipartite graphs can be used to represent relationships across pairs of heterogeneous data [START_REF] Zhang | On finding bicliques in bipartite graphs: a novel algorithm and its application to the integration of diverse biological data types[END_REF]. A bipartite graph is partitioned into two sets of vertices which are non-empty disjoint partitions. In bipartite graph, there is no edge within the same partition. In smart contracts, an interpretation of common senders to a set of receivers member's relationships is performed by an enumeration of maximum bicliques.

Maximum biclique, the largest biclique, is used as an approach to group the senders and receivers members into groups to identify most common senders of a set of receivers. In the experiments, the algorithm developed in [START_REF] Alexe | Consensus algorithms for the generation of all maximal bicliques[END_REF] has been applied.

Link Predictions

Link predictions methods are used to identify new connections in graphs. To predict newer links among two entities at a later point in time, the path based link predictions approach is applied using the SimRank algorithm presented in [START_REF] Jeh | Simrank: a measure of structural-context similarity[END_REF]. It assumes that two vertices are similar if they share the common connected vertices. Numerically, this is specified by defining a score. The set of all neighbors of vertex T x is denoted by Γ (T x ).

     score(T x , T x ) = 1 score(T x , T y ) = γ a∈Γ (Tx) b∈Γ (Ty) score(a, b) |Γ (T x )|.|Γ (T y )| with γ = [0, 1] (9)
Finally, the SimRank corresponds to the link predictions in a bi-clique.

Experiments and Discussions

This section presents the experiments and the results of the tensor and the graph based approaches on smart contract data.

Dataset Characteristics

Smart contracts data have been collected from the Ethereum platform from 7 August 2015 to 2 March 2016. In this period of time, two millions of transactions have been realized between 241,385 sender accounts and 359,798 receiver accounts. A sender account is defined as an account sending Ether, the Ethereum crypto-currency, and a receiver account as an account receiving Ether. However, 60% of the sender contracts only send one Ether payment from August to March and 70% of the receiver contracts only receive once. We concentrate on contracts having the most activities, and thus we keep only the 1% most active contracts over time. In 1% of contracts, the average of contracts by sender is 46.91 and by receiver is 26.06. In our experiments, 459 smart contracts senders are considered as well as 813 smart contracts receivers.

Tensor Decomposition And Stochastic Simulation For Interactions Predictions

Tensor Decomposition Applied to Smart Contracts A three-way topological tensor is built using the data from Ethereum. A value of zero means no Ether were exchanged between a sender account and a receiver account at a given time, and a value of one corresponds to the opposite. The first dimension of the tensor, denoted by I, characterizes the list of the sender accounts, the second dimension, J, the list of the receiver accounts and the third dimension, K, the time. Ether exchanges have been gathered in fifty-two time intervals. The size of the resulting tensor is 459×813×52.

Se1 Se2 Se3 . . . . . . . . . . . . . . . Re1 Re2 Re3 • • • • • • • • • • • • 1 0 0 0 1 1 0 1 0 Se2 Se1 Re1 Re2 Re3 • • • • • • • • • • • • . . . 1 1 0 1 1 0 0 . . . Se1 Se2 Re1 Re2 Re3 • • • • • • • • • • • • . . . . . .

Evaluation Of Interactions Probabilities Using VG Model

The VG model is calibrated historically with the Maximum Likelihood Estimator (MLE) as presented in [START_REF] Loregian | Approximation of the variance gamma model with a finite mixture of normals[END_REF] based on the results of the tensor decomposition as described in Fig. 1. The first twenty-six time events are used for calibration and the simulations are done on the next twenty-six time events for a comparison between the true data and the simulated data.

The future probabilities of Ether exchanges at maturity T are computed with a digital function denoted by C based on the simulations of the process S.

C T = 1 N N n=1 1 S (n) T ≥K (10)
At maturity T , if the simulated series is equal or higher than K, then the value of C is equal to one, otherwise the value of C is equal to 0. In our simulation, we define K = 0.99 due to the numerical error from the tensor decomposition and the calibration of the stochastic model. The number of Monte-Carlo simulations, denoted by N , is equal to one million.

Simulation of Interaction Probabilities Using CP and VG

We define a threshold of 60% as the threshold identifying an interaction or not. At the end of the time horizon of the simulation, if an interaction probability between one sender and one receiver is below the threshold, it is more likely that no interaction happen. On the opposite, if an interaction probability is higher than the threshold, it is more likely that an interaction happen. Regarding Fig. 2a, interaction probabilities decrease over time for a given sender and a given receiver. At the end of the simulation, the interaction probability is around 55%. Given the threshold definition, it is more likely no interactions happen. The results are cross-validated with the true data that confirm no interaction happened. Similarly, for another sender and receiver extracted from the CP decomposition in Fig. 2b, the simulation indicates that the interaction probability is 0. It is also confirmed by the true data where no interaction have been realized.

Constructing a smart contract graph

We define the smart contract graph to be constructed from each transaction as a directed graph representing semantically relevant relationships between two vertex-entities which represent senders and receivers performing a transaction in a smart contract. Each vertex represents a sender s and receiver r and each edge s, r indicates that the sender s sends amount of coins to r, where s = r. The data size is reduced by the representation of intermediate vertex-entities, especially for transactions with the same senders and receivers. This is a labeled directed graph G = (V, E, β):

-V is the set of senders and receivers; -E is a set of edges in G. Assuming T s and T r , sender s ∈ V and receiver r ∈ V , there is an edge (T s , T r ) ∈ E if and only if it exists a transaction between T s and T r . β is a function that assigns for each edge (T s , T r ) the average amount of transactions l Ts,Tr .

The smart contract graph represents the behavior of transactions between each vertex-entities.

Graph Mining Results

According to Fig. 3c, the frequency of group sizes follows a highly skewed distribution. There are few and very large groups using modularity class as well as many very small bi-clique groups. 68.54% of bi-clique groups have only three members. In modularity groups, the frequency distribution for group membership is even more skewed. 10.78% of modularity groups have more than 4672 members which represents 52.95% of vertices. According to Fig. 3a, a highly skewed distribution is also observed in frequency of users' link counts. Fig. 3b highlights the most important betweenness centrality vertices. More than 51% of vertices have a degree lower than 10. The vertex degree can be higher but less important, which is equivalent to lower betweenness centrality. The betweenness centrality shows the importance of vertices or intermediate vertices during transactions. From these experiments, bi-clique groups appear more adequate to analyze smart contracts interactions by obtaining small groups leading to easier analysis.

Interactions Probabilities And Link Predictions Comparison

Four types of contracts have been tested. First, contracts having stable interactions over time or contracts having no exchange over time have been chosen. Then, two contracts, defined as type three, have been randomly selected. Type three contracts have an interaction at the initial time step and no interaction at the final time step. Finally, two contracts type four, have been selected for which an interaction have been realized at the final time step but not at the beginning of the experiment.

Based on the first seven lines of the Table 1, the calibrated VG model is able to reproduce permanent interactions over time as well as the absence of interactions. In addition, for contracts of type three, interactions probabilities at the final time step are between 55% and 61%. It means there are very high probabilities for having no interaction. For contracts of type four, interactions probabilities at final time step are between 81% and 99.6%. As a result, the interactions probabilities determined by the VG model appear strongly correlated to the actual interactions values among the data set.

The graph probabilities could reproduce satisfyingly the absence of interactions. However, two false positives have been found with the graph approach in the illustrated sample for which no interactions have been found. One of them is linked to contracts of type four for which the interactions are the most difficult to predict. The other false positive is linked to permanent interactions which is easier to model in theory. For interactions probabilities of 29%, one is a true positive and another one is a false positive. Finally, for interactions probabilities higher than 30%, only true positives have been found.

To better compare interactions probabilities between the tensor approach and the graph approach, a curve displaying the Area Under the Curve (AUC) for Receiver Operating Characteristic (ROC) curve is shown on Fig 4.

For an interaction threshold of 20%, all interactions probabilities higher than 20% are considered as true interactions. As a result, the Fig. 4 highlights slightly better results for the graph approach for lower thresholds of interaction probabilities. However, for thresholds higher than 61% the tensor approach gives significantly better results. Overall, the tensor approach combined with the VG model appears to lead to better interactions probabilities.

Conclusion And Future Work

We proposed a tensor-based approach combined with the stochastic variancegamma model for analyzing and modeling smart contracts operating over the Ethereum blockchain platform. The approach has been challenged with graph analysis to assess its weakness and its strengths. The tensor approach is less efficient for detecting communities in the data, but it is more appropriate for the modeling part since it can capture the interaction probabilities. The two techniques complement well each other since the weakness of one technique is the strength of the other. In addition, the accuracy of the stochastic predictions allows to identify which contract to select for speculative investment.

Our twofold future plans consist on proposing graph based link prediction on streaming smart contract and an automated process for a calibration of the stochastic parameters with lower dependency to the initial guess in the tensor approach.

Fig. 1 :

 1 Fig. 1: Description of the tensor dimensions and interactions between sender and receiver contracts

  between [...]7d7be3b5 and [...]db757a10 in function of Time (a) Interaction Probabilities between ...7d7be3b5 and ...db757a10.

  between [...]e7e74d09 and [...]aedb0efb in function of Time (b) Interaction Probabilities between ...e7e74d09 and ...aedb0efb.

Fig. 2 :

 2 Fig. 2: Simulation of Interactions Predictions For 26 Time Events.

  Number of vertices (log scale) Number of group memberships (log scale) Modularity class Biclique (c) Frequency distributions for group membership and group size.

Fig. 3 :

 3 Fig. 3: Main Graph Mining Results

Fig. 4 :

 4 Fig. 4: Comparison between AUC of ROC curves for graph and tensor approaches for varying thresholds of interactions probabilities

Table 1 :

 1 Comparison between graph and tensor based estimated interaction probability.

	Sender	Receiver	Value at Value at Interaction Prob. ∆T = 0 ∆T = 26 Tensor Graph
	[...]35398226 [...]d5ea2e63	1	1	1.0000 0.0000
	[...]35398226 [...]a1a8170c	1	1	1.0000 0.7020
	[...]01825cb5 [...]8c102d88	1	1	1.0000 0.8040
	[...]b3121069 [...]9f0b1b4e	1	1	1.0000 0.4865
	[...]b3121069 [...]804af9db	1	1	1.0000 0.2945
	[...]2f0acb76 [...]3df1b5a3	0	0	0.0000 0.2957
	[...]e7e74d09 [...]aedb0efb	0	0	0.0000 0.0000
	[...]7d7be3b5 [...]db757a10	1	0	0.5587 0.0000
	[...]bcda34d4 [...]c6b005d0	1	0	0.6093 0.0000
	[...]35398226 [...]fdd31c8a	0	1	0.8114 0.8079
	[...]49a601da [...]41f79adc	0	1	0.9963 0.0000

Acknowledgments

This work was partially funded by HuMa, a project funded by Bpifrance and Region Lorraine under the FUI 19 framework. It is also supported by the High Security Lab hosted at Inria Nancy Grand Est (http://www.lhs.loria.fr).