domain: shs info

text:
David Morquin

Roxana Ologeanu Taddei

Professional facing coercive work formalization: vicious circle of the Electronic Medical Record (EMR) implementation and appropriation

Keywords: professional autonomy, electronic medical record, professional bureaucracies, hospital information system, appropriation

This paper shows that, according to many studies, the implementation of the Electronic Medical Record (EMR) does not cause efficient uses as expected in hospitals. Authors suggest explanatory factors, including both generic factors related to the implementation of ERP and specific factors related to health sector, in particular to professional bureaucracies (professional autonomy, divergence of goals, lack of coordination). The paper highlights the risk of a vicious circle of clinical process computerization, similar to bureaucratic vicious circle described by Crozier (Crozier 1965). Specifically, the convergence of two information systems, the clinical one and the administrative one inside the EMR, is a source of conflict between two logics, one focused on the professional to manage the care of a given patient, and the other focused on the resources management for all patients. The dominance of the administrative logic, consisting in monitoring and promoting coercive formalization, is likely to reduce the professional adjustment and autonomy, to cause their resistance and, consequently, the absence of effective uses, which lead back a strengthening of the control logic. The author shows interest to consider this conflict to reverse the situation by enabling approach, using professional autonomy as lever.

Introduction

Information technologies are more and more used in healthcare to follow up hospital activities, physical flows (as patients and drugs) and information flows related to patient care process [START_REF] Flower | Digital technology essential and subversive[END_REF]. Among these technologies, Electronic Medical Records (EMR) allow monitoring patient data (such as vital signs, laboratory data, radiology, patient care notes) provided by various sources and incorporating these data into a template that facilitate medical reasoning and reporting (consultation, hospitalization and medical consultation summaries) and order entry for treatments, examinations and appointments. EMR provide also administrative data for billing and management of all available resources such as beds, human resources, pharmaceutics or technical products, technical and operating room. On the medical or administrative side, EMR integrate additional functionalities as alerts, decision support, balanced scorecard and best practices guidelines.

EMR directly support both clinicians' current practices inside a hospital, and thus need to fit real-time medical work processes [START_REF] Aarts | Understanding implementation: the case of a computerized physician order entry system in a large Dutch university medical center[END_REF]), and functional activities as accountability.

Our theoretical paper highlights that coercive EMR implementation, as experienced in France, can be a threat for professional autonomy and physicians' medical dominance and, thus, negatively impact EMR effective use. We argue that management of the EMR has to avoid vicious circle of coercive implementation, driving to physicians' resistance, causing back more coercive implementation. We suggest management has to deal with a subtle mix of coercive and enabling logic to realize and assess fundamental objectives like quality of care and efficient clinical practices.

In France, EMR for hospitals are designed on the model of Enterprise Resource Planning (ERP), related to a unique data base of patients' identifiers. As for ERP, EMR is expected to decrease risk of errors related to double entries and redundancy among different specific software (designed for each specialty or each organizational function).

The stated objectives of integrated software are various [START_REF] Poba-Nzaou | Motivations underlying the adoption of ERP systems in healthcare organizations: Insights from online stories[END_REF] as follows: providing reliable data, accuracy of patients' identification, preventing duplicate data entry and related errors, improving traceability of acts and drugs, optimizing care management by facilitating availability of patient records for caregivers. Nevertheless, the complexity of the implementation of EMR is obvious in literature and resistance of clinical staff, particularly of physicians, is considered as a major barrier to EMR implementation.

Several authors consider hospital does not adequately drive organizational changes to facilitate physicians technology acceptance and to get all benefits related to EMR [START_REF] Bates | A proposal for electronic medical records in US primary care[END_REF].

Our hypothesis is integration of clinical information system for clinical staff covering administrative functions (billing, patients and resources schedules) blurs the medical and the administrative boundaries, driving to a conflict between professional and bureaucratic logics [START_REF] Mintzberg | The structuring of organization: A synthesis of the research[END_REF], between control and autonomy.

Our paper is organized as follows: in section 2 we highlight the difference between effective use and implementation. In section 3 we describe the hospital as professional bureaucracy, whose characteristics affect EMR implementation and prevent effective use or meaningful use" [START_REF] Blumenthal | Launching HIteCH[END_REF]. Section 4 is focused on the conflict between enabling and coercive logics, viewed as the conflict between professional and administrative logics, which are highlighted in the EMR design and implementation. We emphasize the risk of vicious circle of coercive implementation, increasing professionals' resistance and decreasing effective uses.

Relevance of an EMR: its use and data quality

Many positive goals explain why the Organization for Economic Co-operation and Development (OECD) consider IT as one of the most important pathway to improve healthcare : decrease medication errors rate, financial gains, better quality of care, improved performance and greater safety. However, EMR implementation is still considered as high-risk failure [START_REF] Littlejohns | Evaluating computerised health information systems: hard lessons still to be learnt[END_REF]. Furthermore, implementation of EMR has led sometimes to unintended consequences [START_REF] Park | The effects of EMR deployment on doctors' work practices: a qualitative study in the emergency department of a teaching hospital[END_REF], as increased time dedicated to the prescription and prescription errors (Koppel, Metlay et al. 2005) [START_REF] Han | Unexpected increased mortality after implementation of a commercially sold computerized physician order entry system[END_REF], Koppel, Metlay et al. 2005[START_REF] Minvielle | Gérer la singularité à grande échelle-Comment maîtriser les trajectoires des patients à l'hôpital[END_REF][START_REF] Koppel | Identifying and quantifying medication errors: evaluation of rapidly discontinued medication orders submitted to a computerized physician order entry system[END_REF]) and dangerous workarounds [START_REF] Saleem | Paper persistence, workarounds, and communication breakdowns in computerized consultation management[END_REF] [START_REF] Saleem | Paper persistence, workarounds, and communication breakdowns in computerized consultation management[END_REF][START_REF] Park | The effects of EMR deployment on doctors' work practices: a qualitative study in the emergency department of a teaching hospital[END_REF]. Total EMR implementation failures have been described [START_REF] Littlejohns | Evaluating computerised health information systems: hard lessons still to be learnt[END_REF]. Data from several studies have suggested that the mere adoption of EMR does not necessarily improve the quality of care and this does not change over time despite a number of years of use [START_REF] Zhou | The relationship between electronic health record use and quality of care over time[END_REF]). However, since recently, US developed an injunction of EMR adoption for US hospitals focused on "meaningful use" [START_REF] Blumenthal | Launching HIteCH[END_REF],with an incentive on well-defined criteria to improve safety, quality and efficiency of care [START_REF] Blumenthal | Launching HIteCH[END_REF]. Demonstrating that the use of these criteria leads to the expected benefits remains to be determined for some authors [START_REF] Classen | Finding the meaning in meaningful use[END_REF] and seems certain to others [START_REF] Xiao | Meaningful Use" of ambulatory EMR: Does it improve the quality and efficiency of health care?[END_REF]. A recent review from 179 studies published between 2004 and 2007, mostly in North America, on the costs and benefits of information technology and health communication, shows that less than 10 % of the studies detail the factors success, financial background of the project and sustainability of the system evaluated [START_REF] Goldzweig | Costs and benefits of health information technology: new trends from the literature[END_REF]. Moreover, the failure of health information technology, data loss, misuses and bypass the elements That helped to turn a failure into success are probably underreported in the literature [START_REF] Kaplan | Health IT success and failure: recommendations from literature and an AMIA workshop[END_REF]. As in other sectors, IT failures are neglected, resulting in a repetition of mistakes. Without ignoring the importance of these technical problems, there is an emerging consensus that the most important problems has sociological, cultural and financial explanations, and thus are more managerial than technical [START_REF] Kaplan | Health IT success and failure: recommendations from literature and an AMIA workshop[END_REF].

Understanding the complexity of computerization requires to distinguish between having a technology, the fact that this technology is used and the fact that this technology is used effectively according to different goals of the organization [START_REF] Markus | Technochange management: using IT to drive organizational change[END_REF], namely that this use enables users to be more efficient in patients management care. [START_REF] Cooper | Information technology implementation research: a technological diffusion approach[END_REF]) identified six stages of the implementation process on an information technology (initiation, adoption, adaptation, acceptance, routinization and infusion), but these steps were very little developed in the literature thereafter, and attention has been focused mainly on the adoption decision and the implementation project. However , adoption is not appropriation, because adoption does not reflect the full interaction between a technology and an actor, especially for complex technologies such as clinical information systems that require the active participation of the user [START_REF] Ologeanu-Taddei | La capacité d'appropriation, une capacité organisationnelle immatérielle négligée dans l'adoption des systèmes d'information et de gestion[END_REF]. We propose a simple definition of appropriation of the EMR by choosing the users point of view : the fact that this technology is used effectively by professionals, i.e they consider that the EMR is useful to do their work, that EMR enables them to improve quality of care and that they want to use it.

The integration of technology in an organization requires specific knowledge of its users and an the use assessment. As Berg assumes, "whether an information system is successful or not is decided on the workplace" [START_REF] Berg | Implementing information systems in health care organizations: myths and challenges[END_REF]. The choice of technology and its availability are not sufficient for the right or meaningful use [START_REF] Orlikowski | Using technology and constituting structures: A practice lens for studying technology in organizations[END_REF]. The importance of the points of view of the different actors in an organization is considered capital to move from the implementation of technology to the appropriation [START_REF] Mantzana | Identifying healthcare actors involved in the adoption of information systems[END_REF][START_REF] Ologeanu-Taddei | La capacité d'appropriation, une capacité organisationnelle immatérielle négligée dans l'adoption des systèmes d'information et de gestion[END_REF]. When users are convinced of the value of innovation, they are ready to generate themselves changes in their practices, often for technologies they already use in non-professional uses.

Previous research showed technologies exist only in use, as technology-in-practice [START_REF] Orlikowski | Using technology and constituting structures: A practice lens for studying technology in organizations[END_REF]. Furthermore, information technologies required proactive use and accurate data [START_REF] Markus | If we build it, they will come: Designing information systems that people want to use[END_REF], which are necessary conditions for effective or meaningful use. This means that information recorded in an EMR is relevant for a care giver in management care process only if it is available and accurate (for example, real time information related to prescribed and administrated drugs). The assessment of the information relevance may be different for different caregivers and for administrative employees. Medical information in the electronic records must be reliable, exhaustive and unique; thus, missing data cannot be accepted for critical steps as anesthesiology process. Both care managers and accountability departments need data on prescription and administration drugs but not at the same time limit. Care staff need real-time data because of the sequential interdependence [START_REF] Thompson | Organizations in action: Social science bases of administrative theory[END_REF] of care management process. Besides, accurate and real-time data are not compatible with workarounds and insufficient adoption as stated by previous literature.

Yet to date, research have not demonstrated rigorously the ability of EMR to drive down costs of clinical or administrative processes, at most a slight improvement in the quality [START_REF] Himmelstein | Hospital computing and the costs and quality of care: a national study[END_REF]). In the next section, we will propose to summarize the different factors negatively impacting the appropriation of the EMR, especially those specific to hospitals setting as professional bureaucracies.

Characteristics of professional organization impacting EMR implementation and appropriation

Research on EMR pointed out same problems already highlighted for ERP (Entreprise Resource Planning) implementation [START_REF] Paré | Implementing clinical information systems: a multiple-case study within a US hospital[END_REF][START_REF] Nohr | Development, implementation and diffusion of EHR systems in Denmark[END_REF][START_REF] Strong | Understanding organization-enterprise system fit: a path to theorizing the information technology artifact[END_REF][START_REF] Park | The effects of EMR deployment on doctors' work practices: a qualitative study in the emergency department of a teaching hospital[END_REF]. We propose first to classify these elements from the grid of Pettigrew [START_REF] Pettigrew | Context and action in the transformation of the firm[END_REF] to differentiate the elements related to the context from those related to software used and finally to the implementation process [START_REF] Pettigrew | Context and action in the transformation of the firm[END_REF]. In terms of content, that is to say, the software itself, the most commonly reported factors include the poor ergonomics and ease of use, but also the perceived non-adaptation to daily work, the lack of flexibility of the system, the lack of compatibility with the work processes, especially because of time constraints or role conflicts, and finally the lack of interoperability (Ash, [START_REF] Aarts | Understanding implementation: the case of a computerized physician order entry system in a large Dutch university medical center[END_REF], Thompson, Duling et al. 2005, Ash, Sittig et al. 2007, Ludwick and Doucette 2009, Gagnon, Desmartis et al. 2012, Bossen, Jensen et al. 2013, Cresswell, Bates et al. 2013). The implementation process includes inadequate training, insufficient support for change, lack of user involvement, lack of recognition by the top management of the key actors, the workload during the implementation phase and of the consultation of the actors, lack of time dedicated to users training, insufficient strategic alignment between the administration and the main medical leaders, the lack of effective internal communication strategy and the lack of collectively anticipation of technological risks (business interruption, software failure) (Gagnon, Desmartis et al. 2012, Cresswell and Sheikh 2013, Cresswell, Bates et al. 2013). Moreover, the importance of the "champions" and "boundary spanners" as proactive key users, able to ensure training and mediation between peers and decision-making is often highlighted as a key success factor of implementation (Greenhalgh, Robert et al. 2004, Cresswell andSheikh 2013). Most of these factors are not specific of the health sector, thus we propose to separate in Table 1 the common factors from those related to professionals and to develop in next sections why these elements are crucial for appropriation.

Table 1. Main factors impacting negatively EMR implementation and meaningful use

Professional autonomy

Mantzana et al. insist on the high importance of "the actors' views since their actions can have a great impact on Hospital Information Systems adoption" [START_REF] Mantzana | Identifying healthcare actors involved in the adoption of information systems[END_REF]. Moreover, physicians are professionals having control over the conditions, processes, procedures, or content of their work according to their own collective and, ultimately, for the adoption as ease of use or the perceived usefulness (Hu and Chau 1999).

Degrees of professional physicians' autonomy can vary. For example in France, even if the non-university hospital physicians are autonomous in managing the care of patients, there is nevertheless a hierarchical relationship informal with professor or formal with the head of a medical department [START_REF] Baszanger | Socialisation professionnelle et contrôle social: Le cas des étudiants en médecine futurs généralistes[END_REF]. Accumulated missions of teaching, research, and organization of clinical activity, generates an even greater autonomy, particularly because of multiple affiliation (hospital, university, research laboratory).

Many reservations about the effectiveness of professional bureaucracies related to professional autonomy were made by [START_REF] Mintzberg | The structuring of organization: A synthesis of the research[END_REF][START_REF] Mintzberg | The structuring of organization: A synthesis of the research[END_REF]): apart from self-regulation by peers, there is no control over the work and no how to correct deficiencies accepted by professionals [START_REF] Mintzberg | The structuring of organization: A synthesis of the research[END_REF]. The autonomy of professionals in itself tends to encourage people to misunderstand the goals of the organization for which they work. For many of them the organization is accessory, as just a convenient place to practice. Professionals consider themselves being loyal to the profession but do not necessarily feel part of their institution and are not necessarily involved in organizing. Conversely, autonomy preserves a capacity adjustment and management of essential unpredictable due to the nature of medical practice.

Walter and Lopez showed that for physician users, a sophisticated system would not be adopted if the system does not follow the workflow, or if it can be perceived by the physician user as threatening to his or her professional autonomy. Their results were similar for Clinical Decision System support and EMR. Culture of healthcare givers as end-users may be described by four values, meaning quality of care, efficiency of clinical practices, physicians' medical dominance, professional status and autonomy. These values explain the level of difficulty of a clinical information system implementation [START_REF] Rivard | An organizational culture-based theory of clinical information systems implementation in hospitals[END_REF]. Physicians differ from other types of IT users investigated in the literature [START_REF] Paul | A field study of the effect of interpersonal trust on virtual collaborative relationship performance[END_REF]

Mutual adjustment and difficulties to standardize patients care flows and management

Patients care management consists on very heterogeneous care workflows in a complex continuum. Some workflows may be standardized (i.g, cataract surgery), while others on the contrary justify a very high level of customization (overall treatment of an elderly with multiple comorbidities) [START_REF] Lamothe | La reconfiguration des hôpitaux: un défi d'ordre professionnel[END_REF]. Usually, the patient care management is not based on a single process, but on a combination of sub processes [START_REF] Pascal | La gestion par processus à l'hôpital entre procédure et création de valeur[END_REF] whose referent physician is similar to a bandmaster. His or her expertise allows mutual adjustment among different players (others physicians or radiologists or biologists) based on limited resources (availability of technical equipment, or of beds), emergency degree (prioritization of resources by each unit manager) and especially unpredictable events. If each sub process can be modeled (i.g. performing a lumbar puncture), the whole journey of a patient can be extremely complex to be modeled depending on the occurrence of adverse effects and multiple pathologies, or human factors (as refusal or misunderstanding of care by the patient, information and communication to family). Patients care modeling required for EMR design is possible for a small number of patients and thus often constitutes the exception and not the norm. A physician can manage simple situations that matches to care process formalized in the EMR, whereas singular and complex clinical situation cannot be modeled [START_REF] Minvielle | Gérer la singularité à grande échelle-Comment maîtriser les trajectoires des patients à l'hôpital[END_REF]. Lamothe highlights the ineffectiveness of control measures aiming to strongly standardize practices, since they are based on mutual adjustment and the development of an ideology shared by professionals [START_REF] Lamothe | La reconfiguration des hôpitaux: un défi d'ordre professionnel[END_REF].

Challenge of intra and inter-professionals coordination

The complexity of the organizational functioning of the hospital comes under three main features: the diversity of activities, configuration of power relations and the dynamics of evolution marked by profound changes [START_REF] Nobre | Le cas d'un balanced scorecard en contexte hospitalier[END_REF]. The high diversity of an hospital activities comes from the multiplicity of partitioned services (clinical, medicaltechnical, logistical and administrative tasks) and of the related skills and occupations , which limits the coordination of actors and projects.

For Mintzberg (Mintzberg 1979, Glouberman and[START_REF] Glouberman | Managing the care of health and the cure of disease-Part II: Integration[END_REF]) professionals tend to overlook the essential problems of coordination, control and organizational innovation ; the standardization of qualifications is not sufficient to solve coordination problems between professionals and logistic support functions or especially between the professionals themselves.

The division of medical knowledge and skills make it even more complex phenomenon. If each specialist control a source of uncertainty related to his or her specialty, interdependencies create a new source of uncertainty and exacerbate competition and informal professional rivalry. The different groups in an organization seeking to differentiate themselves by their cultural objects and values, which in the hospital reinforces the rivalry and competition between groups [START_REF] Davies | Organisational culture and quality of health care[END_REF] and the "tribal" organization [START_REF] Kaplan | Health IT success and failure: recommendations from literature and an AMIA workshop[END_REF].

Over time, not only physicians but many health care givers organized themselves as professional occupation (physiotherapists, occupational therapists, psychologists, radiographers, radiologists, social workers, dietitians, health managers ...) and has complicated the patients care workflow under the medical domination. All implicit rules to enable coordination of all these different professionals under medical control leads to the formation of an inter-hierarchy. This informal and flexible structure allows flexibility and adaptability, as a fundamental and protective interlayer between the care units and administrative decision process [START_REF] Lamothe | La reconfiguration des hôpitaux: un défi d'ordre professionnel[END_REF]. The confrontational balancing between groups helps to stabilize the system by defining the prerogatives of each. For example, the medical group fighting to preserve the unpredictable characteristics of the activity which he or she is responsible : it opposes the rationalization of its own domain, while fighting for the rationalization of other domains [START_REF] Lamothe | La reconfiguration des hôpitaux: un défi d'ordre professionnel[END_REF]. Users of an EMR in a hospital are not a homogeneous group of people and interests and one of the main factors of appropriation concerns the perceived adaptation of care processes. Figure 1 provides a schematic representation of the different homogeneous interest group of EMR users . This allows to distinguish between professional specialties that are not in directly at bedsides (eg, microbiologists, pathologists ) or very occasionally as support (eg radiologists , anesthesiologists ) of those who manages all the patient's care process in everyday life (eg internists, geriatricians, pediatricians) or are highly specialized on smaller areas (eg ophthalmologists, cardiologists) .

The various specialties may have very different setting goals: for example, laboratory certification procedures require that the biologist masters how are viewed the results of laboratory blood tests by clinicians, while the latter prefer to compare datas in tables or graphics. Physicians specialized in medical informatics are interested in processing information from the medical record to enable repayment of the activity by medical assurance or epidemiological monitoring. Pediatricians do not have the same expectations on the management of data associated with the weight and size of the patient as a plastic surgeon.

Additional examinations providers may request the seizure or postponement of a number of clinical information on the request for review, so that prescribers may consider that this information is already available in another part of the EMR .

Inside the same specialty, academic logic may object to the clinic, for example for structuring data in clinical research folder referred to bringing no benefit to the realization of care. Ash et al. showed the crucial nature of the customization including adapting the EMR for drug prescription: more technology is flexible more it is possible to create "customizations" and thus to led to acceptation by different medical specialties (Ash Gorman et al. 2003).

In contrast, the Information Systems Department could not to set EMR for different teams or individuals, for reasons of resources or maintenance (Guillemette and Paré 2011). The management of the institution may require prioritizing the elements that increase the completeness of information useful for hospital's manager or facilitating the reporting form of various indicators requested by different national or regional stakeholders.

Prioritization settings, such as input interfaces and visualization of information, specific developments or the integration of new features, version update or interfaces with other nonintegrated software are therefore an extremely strong challenge because it can substantially change the EMR workflow for users and therefore their perceptions and uses.

In a complex situation characterized by professional autonomy, diversity of professions, difficulty of consultation and coordination, complex hierarchies and power conflicts, the decision-making for EMR setting and customization is a key issue.

EMR on the razor's edge of enabling and coercive logic

The workflow formalization induced by technology can be coercive or enabling

On the one side, workflow formalization can trigger decreasing commitment and job satisfaction, deskilling, alienation and brakes to innovation. On the other side, workflow formalization can increase autonomy, reduce role conflicts and stress at work [START_REF] Adler | Two types of bureaucracy: Enabling and coercive[END_REF] and facilitate innovation when it allows learning from experience and it facilitates coordination for the implementation of important projects [START_REF] Craig | Achieving innovation through bureaucracy: lessons from the Japanese brewing industry[END_REF]. Technology design and implementation cannot be neutral, because it is based on algorithms design, codes and thus a representation of workflows. Various authors distinguish between coercive and enabling technologies: the one is designed to enhance deskilling and is focused on the technology features while the other is based on the users' skills and capabilities (Zuboff 1988, Adler and[START_REF] Adler | Two types of bureaucracy: Enabling and coercive[END_REF].

Coercitive EMR Enabling EMR

No involvement of the professionals in the design of the EMR Involvement of the professionals in the design :

-Test of successive new functionalities with caregivers; -The EMR design allows improvement suggestions by members at every level.

Repa ir

Technology is designed to reduce the possibility of shirking.

-Design should need no revisions after implementation -When unexpected breakdowns happen, production employees need to call a specialized technician.

-Difficult to correct -No help facilities, the user is forced to interrupt the flow of clinical activities to consult a manual or a supervisor -Low consideration for the suggestions of physicians who notice opportunities for improvement.

-The goal of design is to ensure that operator can intervene effectively to rectify problems.

Focus on the ease with which caregivers can repair the process themselves -Errors (prescription, posology, schedule) are easy to correct -"help" facilities -Enabling users to regain control if break down happens or if users make mistakes -If the system can be improved, designers enable users to formulate and evaluate suggestions for improvement.

-Hotline is optimized to fit with 24h 7d medical work -Technology information is presented only in the event of machine malfunction; it is presented in a language familiar to the technical staff but not the caregiver -Care givers are expected to follow explicit instructions (What they have to do).

-Users information overload (alarm system failure)

EMR is glass-box design -Caregivers are provided with all the information necessary for the task.

-Users' manual helps users to do their work more effective (how they have to do)

-EMR is presented in a way that is intelligible to the operator, and the operator can use the information to rectify errors.

-EMR do not overload the user with unnecessary system information.

-EMR design takes into account that users will be confronted with unforeseen contingencies and will therefore need to interact creatively with the technology -Users are aware of the different settings possibilities -The deskilling logic results in technologies that are designed to minimize reliance on caregivers' skill and discretion.

The machine takes the controlling decisions after the operator has entered the required data. (automating logic)

-The coercive procedure manual defines in detail the specific sequence of steps to be followed in the care process.

Flexibility:

-Technologies are programmed to give advice and make suggestions, and users take the controlling decisions after the system displays the requisite data.

Users can choose to retain control or can hand off control to the machine.

-Several information input modes are possible.

-The organization allows continuous setting of input interfaces.

-The system allows the construction of new channels of information (screening clinical situations, specific alerts and follow up, collaborative work).

-The organization can adapt to unpredictable situations (new user, reassignment, etc.).

-An enabling procedure manual assumes that deviations are not only risks but also learning opportunities.

This distinction may be related to the technology design or to the implementation (Ologeanu-Taddei, [START_REF] Ologeanu-Taddei | La capacité d'appropriation, une capacité organisationnelle immatérielle négligée dans l'adoption des systèmes d'information et de gestion[END_REF]. When technologies are designed for automating decisions, whose aims are fool-proofing and deskilling rationale, they are coercive (Perrow 1983, Adler and[START_REF] Adler | Two types of bureaucracy: Enabling and coercive[END_REF].The rationale is that "user is a problem to be eliminated" and a source of error [START_REF] Adler | Two types of bureaucracy: Enabling and coercive[END_REF]. When managers fear the opportunism of employees and they do not trust employees, they adopt a deskilling approach [START_REF] Adler | Two types of bureaucracy: Enabling and coercive[END_REF]. On the opposite, technologies are enabling when they are designed to enhance users' capabilities and skills. In other words, technology is thus designed for empowerment and not for enslavement [START_REF] Davison | Empowerment or enslavement? A case of processbased organisational change in Hong Kong[END_REF], according to the rationale that user is "a source of skill and intelligence to be supported" [START_REF] Adler | Two types of bureaucracy: Enabling and coercive[END_REF]. We summarize in the table 2 using the grid from Adler and Borys [START_REF] Adler | Two types of bureaucracy: Enabling and coercive[END_REF] the opposition between coercive and enabling formalization of information technology applied to Electronic Medical Record (EMR).

We argue in the next section that coercive design and implementation is driven according to administrative logic, related to unclearness between administrative and medical boundaries inside the EMR.

Design of EMR: medical or administrative logic?

Computerization of medical records has constrained physicians to replace their own clinical information system.

To elaborate diagnosis, a physician draws his or her information system through his or her representation of patients and their diseases. For this, he or she assesses medical observation, meaning patient symptoms, clinical signs and laboratory tests, prioritizes and selects relevant information for medical decision-making and asks for advice to peers if necessary. Even if this information is partly medical routine, the way they are is represented and put together is often specific to each specialty and even every physician. Organizing these elements is the core of medical reasoning. Related to type of design and implementation, enabling EMR may assist physicians to elaborate a convenient representation of a medical situation, while coercive EMR misfits medical and care management workflows, according to the standardization of medical and care management process as drawn by administrative logic.

When a therapeutic is decided, information system must provide all the information related to medication, isolation precautions or further investigations to all the caregivers. A physician may adapt medical decision only if he or she can follow back relevant information and monitor the effects of his or her decisions, taking into account evolution of patient's disease (current administration of the treatment, test results, vital signs).

The Electronic Medical Records which allows to acquire and store useful medical information for a given patient, to store, organize, process and communicate it, can be considered at the individual level (physicians who uses the patient's folder to manage a clinical situation), at the collective level because many people (different specialists, paramedics, secretariat) use the same system, and at the organizational level, since all the datas from different patient are made available for the different medical departments, and finally at the inter-organizational level, since the communication of medical information between institutions are necessary to the continuity of care. The EMR can be the backbone of the collaborative care and can increase or conversely decrease for the physician his capability to master and manage medical decisions

Risk of vicious circle

Existent literature shows EMR adoption and effective use require preventing physicians' autonomy, which is a concern for EMR design for each specialty. A clinical information system, involving all the medical and care occupations, requires intra and inter-professional coordination. Furthermore, administrative and top management need accountability of available resources (as beds, human resources, pharmaceutics or technical products, technical and operating room) and measure of quality and efficiency indicators, which may be rejected by physicians. For these reasons, implementation management tends to be coercive. Doing this, it misfits medical and care workflows and can cause physicians resistance and negative unintended consequences as exposed by literature. Administrative managers then react by strengthening formalization and process standardization and, thus, increase the gap between the required enabling design and implementation and the effective clinical information systems. This is a vicious circle, similar to bureaucratic circle described by Crozier 30 that may be broken by change management of practices focused on coordination.

More precisely, Crozier showed the characteristics of bureaucratic organization (development of impersonal rules, centralization of decisions, isolating each hierarchical category and development of parallel power relationships) tend to the development of new pressures that reinforce the climate of depersonalization and centralization and lead to a vicious circle. We functional setting and support functions are based on a techno-economic logic or industrial rationalization, to the detriment of the consequences for the caregivers. This may be explained by the difficulty of consultation of professionals and their tendency to neglect the essential problems of coordination, control and organizational innovation [START_REF] Mintzberg | The structuring of organization: A synthesis of the research[END_REF].

Conclusion

We have shown in this paper that the implementation of EMR is based on the principle of integrated software as in other economic sectors. EMR makes coexist features corresponding to different logics: one bureaucratic or managerial control, and another professional (clinical).

Thus, the EMR crystallizes the very functioning of professional bureaucracies, characterized by the opposition between these two logics. But the inherent formalization caused by computerization (in terms of design or functional setting post-implementation) requires defining the processes and procedures to be formalized, with clear objectives. Another characteristic of bureaucracies, namely the chaos associated with the divergence of goals defined by Hodson & Martin [START_REF] Hodson | Rules don't apply: Kafka's insights on bureaucracy[END_REF], reinforces this phenomenon, with the risk of a lack of adoption of EMR by professionals and therefore not appropriation. Yet only appropriation by professionals, and thus the development of what we call "effective use" is likely to cause an improvement in both the hospital organization and working conditions for each professional involved in the realization of care.

The main contribution of this paper is theoretical. It links the literature on the factors of failure (and success) of EMR and the literature on professional bureaucracies, in order to highlight the most important aspects to promote appropriation, which goes beyond the implementation of the technology. The design and effective implementation of technology focused on professional autonomy constitutes the most crucial point for appropriation and EMR benefits. Furthermore, we based our argumentation on the approach of Adler & Borys, in favor of enabling formalization process [START_REF] Adler | Two types of bureaucracy: Enabling and coercive[END_REF]. We argued that only this approach would get out of a vicious circle that currently strengthen the bureaucratic logic to force appropriation, resulting in return professional resistance, and therefore not associated to EMR efficient uses.

Thus, our theoretical contribution is completed by managerial recommendations, since we propose another approach to define, implement and enable the development of EMR.

In future research, we want to provide empirical examples to support our assumptions, through case studies in French hospitals.

  individual judgment in the application of their profession's body of knowledge and expertise"(Walter and Lopez 2008). They control, monitor and define the norms of the their activity.According to Adler & Kwon professional autonomy allows professionals to have a considerable influence on the diffusion of innovation ; thus, the independence from commercial pressures allows physicians to adopt a technology based on specific values and not economic considerations : the physicians' adoption decisions of innovation reflect their individual preferences rather than the preferences of others[START_REF] Adler | The Mutation of Professionalism as a Contested Diffusion Process: Clinical Guidelines as Carriers of Institutional Change in Medicine[END_REF]). They take the example of a director of a hospital, who has sufficient authority to require the replacement of obsolete equipment , but cannot require doctors to adopt Computer Physicians Order Entry, although their interest has been demonstrated[START_REF] Adler | The Mutation of Professionalism as a Contested Diffusion Process: Clinical Guidelines as Carriers of Institutional Change in Medicine[END_REF]. According to Walter & Lopez, there is a strong correlation for physicians between the perception of the usefulness of clinical decision support systems and EMR and the perceived threat of such technologies on their professional autonomy(Walter and Lopez 2008). For the medical profession, sophisticated information technology cannot be adopted if it does not fit the physician's workflow or can be perceived as a threat to its ability of mutual adjustment. The results of the telemedicine experience observations made by the team of Hu et al. reinforce this finding, showing that the autonomy of practice and ongoing adaptation of work are the specific characteristics of the medical community and the perception of the reliability of the system is a fundamental element

  (which refers to the intelligibility for the users of the system) : asymmetry of information Global transparency: EMR is designed to provide caregivers with extensive information on global care coordination of the patient.-Physicians have full access on quality data of patients care management in their department -Caregivers' understanding of the entire care process is considered as a valuable resource in their efforts to optimize the performance of their work and to identify local and system wide opportunities for improvement.

Common with others IT implementation Specific to professional bureaucracies

	C C P	• Failure perceived utility • Lack of design, poor ergonomics • Lack of user involvement in the implementation	• Influence of EMR on care relationship • Lack of physician involvement in IT project
	o o r	strategy	Gagnon, Desmartis et al. 2012 Bossen, Jensen et al. 2013 Gagnon, Desmartis et al. 2012 Cresswell, Bates et al. 2013 Gagnon, Desmartis et al. 2012	Ludwick, Doucette 2009 Cresswell, Bates et al. Gagnon, Desmartis et al.
	n n o		Cresswell, Bates et al. 2013 Boonstra, Versluis et al. 2014 Boonstra, Versluis et al. 2014	• Privacy	Boonstra, Versluis et al.
	t t c	Boonstra, Versluis et al. 2014 • Insufficient training and support • Lack of data fiability	Boonstra, Versluis et al. 2014 Ash, Gorman et al.
			Boonstra, Versluis et al. 2014 Ash, Sittig et al. 2007	Houser and Johnson 2008
	e e e	• Ambiguity of objectives • Insufficient ease of use	Bossen, Jensen et al 2013	Poon et al.
	x n s		Cresswell, Bates et al. 2013 Gagnon, Desmartis et al. 2012 Ludwick, Doucette 2009	Ash, Gorman et al. • Highly intensive customization
	t t s	• Lack of « champions » • Lack of interoperability Boonstra, Versluis et al. 2014 Cresswell, Bates et al. 2013 Rivard, Lapointe et al 2011	• Professional autonomy Walter Ash, Sittig et al. Ash, Gorman et al. 2003
		Gagnon, Desmartis et al. 2012 Gagnon, Desmartis et al. 2012 • Inadequate change management	Gagnon, Desmartis et al.
			Cresswell, Bates et al. 2013 Cresswell, Bates et al. 2013 Gagnon, Desmartis et al. 2012	Boonstra, Versluis et al.
		Boonstra, Versluis et al. 2014 • Non-adaptation to daily work Ludwick, Doucette 2009
			Rivard, Lapointe et al 2011 Gagnon, Desmartis et al. 2012 Cresswell, Bates et al. 2013
			Ash, Gorman et al. 2003 Boonstra, Versluis et al. 2014
				Ash, Sittig et al.2007 Rivard, Lapointe et al 2011
		Cresswell, Bates et al. 2013 • Top management involvment lack
		• Lack of customization Gagnon, Desmartis et al. 2012
			Gagnon, Desmartis et al. 2012 Ludwick, Doucette 2009
				Cresswell, Bates et al. 2013 Rivard, Lapointe et al 2011

• Lack of previous experience

Gagnon,

Desmartis et al. 2012 Ludwick, Doucette 2009 Cresswell, Bates et al. 2013

• Multiplicity of objectives and divergence of goals Cresswell, Bates et al. Poba-Nzaou, Uwizyeyemengu et al. • Extreme variability of process Gagnon, Desmartis et al. Rivard, Lapointe et al • Limits of process standardization Ash, Sittig et al. Ludwick, Doucette Rivard, Lapointe et al • Conflicts between professional culture and organizational culture Gagnon, Desmartis et al. Ash, Gorman et al.

• Conflicts in professional bureaucraties

Boonstra, Versluis et al.

Table 2 .

 2 Opposition of Coercive and Enabling formalization of information technology applied to Electronic MedicalRecord (EMR), adapted from[START_REF] Adler | Two types of bureaucracy: Enabling and coercive[END_REF]

		Coercitive EMR	Enabling EMR
	Arch	Design of the EMR focus on the technical features	Design focus on usability
	itect		EMR browsing is obvious for users and fit the care
	ure		process practice
	of
	EM	Deskilling logic: technology design is left to the technical	Skilling logic: facilitate responses to real work
	R	experts.	contingencies. Physician, paramedics, secretaries can
			modify specific settings and adapt the EMR to work
			process.

Table 2 .

 2 Opposition of Coercive and Enabling formalization of information technology applied to Electronic MedicalRecord (EMR), adapted from[START_REF] Adler | Two types of bureaucracy: Enabling and coercive[END_REF]

Table 2 .

 2 Opposition of Coercive and Enabling formalization of information technology applied to Electronic MedicalRecord (EMR), adapted from[START_REF] Adler | Two types of bureaucracy: Enabling and coercive[END_REF]

related to patient's care process. Transposition or computing model of care process is related to the formalization of medical work. If the system does not enable physician to act as a bandmaster, it may be perceived as coercive and as a threat to professional autonomy.

Electronic Medical records (EMR) embedded in the Hospital Information System (HIS)

Frontiers between the different subsystems of the information system used in hospitals are unclear. The term "electronic medical record " (EMR) is generally used to designate the information system used by all the actors in care delivering. EMR cover all major functions of medical practice by capturing, storing and indexing of medical and paramedical notes and reports (consultation, hospitalization, consultation meeting with other medical specialists), but also the complete process of the drug delivering and administration, planning exams and appointments.

From the perspective of the staff providing a management function within the hospital (administrative staff, medical department manager, nurses managers), EMR enables the centralization and processing of data for monitoring and tracking of resources such as beds, drug stocks, consumables, technical platforms, operating theaters or human resources. It also helps to assess "cost based" reimbursement based on a specific system of classification, namely

Diagnosis-Related Group (DRG) [START_REF] Lenay | Du système d'information médicalisée à la tarification à l'activité Trajectoire d'un instrument de gestion du système hospitalier[END_REF]. The hospital information system (HIS) support the monitoring of physical flows or data associated with the production of care, such as medication management (orders, stock and delivery in care units), but also all the consumables necessary to technical support, to the management of the hostelry, of the staff and of the billing process. Enhanced by the implementation of the pricing activity (T2A) in 2005, the DRG constitutes the core of the hospital remuneration system and becomes the main tool for hospital management [START_REF] Lenay | Du système d'information médicalisée à la tarification à l'activité Trajectoire d'un instrument de gestion du système hospitalier[END_REF]. This system is based primarily on the information processing for each patient, from the EMR; thus, it is dependent on the quality and availability of this information.

The EMR is thus a clinical information system (CIS) as a part of the information flow related to patients care but also to the management of the hospital. Computerization has accelerated the convergence of management of patients care tools with administrative tools for managing the hospital. We propose in Figure 2 a schematic representation of the subsystems of the hospital information system and the connection between the administrative logic (hospital management) and the medical logic (patients care management).

suggest that the lack of effective uses of EMR is likely to result in a strengthening of the control logic, justified by arguments of economic performance, which is likely to enhance the resistance in return for users and to maintain a situation of 'inefficient uses. More so, when the finding of the mismatch between promises of technology and actual use is effective, it can be tempting for the decision maker to believe, as a form of magical thinking, that the implementation of a new technology suffice to overcome this phenomenon without trying to understand the cause. We propose a schematic description of the different stages of this phenomena concerning the EMR adoption, implementation and appropriation in figure 3.

Gadrey (Gadrey 1994) shows that there is a confusion between industrial rationalization and professional rationalization of work especially in hospitals. For this author, industrial rationalization, using massively new information technologies, aims to design and organize the production of professional services as "quasi-products", to standardize as much as possible professional work, by searching to measure productivity (Gadrey 1994). This is opposed to the professional rationalization which consist in making more accurate and systematic typifying cases. Professional formalization consists in dividing care process in routines to improve the efficacy defined as both time saving and quality of care of professional work procedures (Gadrey 1994). This distinction helps to qualify the contrast between bureaucratic logic and professional autonomy: autonomy is not opposed to formalization, but the professional vision of formalization differs from the bureaucratic vision. Design and implementation of EMR,


Abdel-Ouahab Boudraa
email: abdel.boudraa@ecole-navale.fr

Delphine Dare-Emzivat

A Joint Spectral Similarity Measure for Graphs Classification

In spite of the simple linear relationship between the adjacency A and the Laplacian L matrices, L=D-A where D is the degrees matrix, these matrices seem to reveal informations about the graph in different ways, where it appears that some details are detected only by one of them, as in the case of cospectral graphs. Based on this observation, a new graphs similarity measure, referred to as joint spectral similarity (JSS) incorporating both spectral information from A and L is introduced. A weighting parameter to control the relative influence of each matrix is used. Furthermore, to highlight the overlapping and the unequal contributions of these matrices for graph representation, they are compared in terms of the so called Von Neumann entropy (VN), connectivity and complexity measures. The graph is viewed as a quantum system and thus, the calculated VN entropy of its perturbed density matrix emphasizes the overlapping in terms of information quantity of A and L matrices. The impact of matrix representation is strongly illustrated by classification findings on real and conceptual graphs based on JSS measure. The obtained results show the effectiveness of the JSS measure in terms of graph classification accuracies and also highlight varying information overlapping rates of A and L, and point out their different ways in recovering structural information of the graph.

Introduction

Graph spectral analysis is one of the hot topics in data processing community, motivated by the prominent need to develop new mathematical tools to process networked and structured data. These data are generated from various sources, as sensor, social, biological or transportation networks, where the information resides in complex and irregular structures. For this purpose, eigen-spectrum of matrices associated with graphs are often closely studied. Recent works of the literature have emphasized the importance of matrix representations for graph characterization, pointing out the advantages and the drawbacks of some spectra associated to graphs [START_REF] Van Dam | Which graphs are determined by their spectrum?[END_REF], [START_REF] Jovanović | Spectral distances of graphs based on their different matrix representations[END_REF], including, those of adjacency (A), Laplacian (L), signless Laplacian | L | and distance (D G ) matrices. The spectrum of L matrix is indeed widely studied in spectral graph theory [START_REF] Chung | Spectral graph theory[END_REF], in reason of the symmetry and positive semi-definiteness of the matrix, which is useful for determining cuts and inherent graph components. Otherwise, the spectrum of A matrix is mainly used for the study of regularity [START_REF] Koolen | The distance-regular graphs such that all of its second largest local eigenvalues are at most one[END_REF], isomorphisms [START_REF] Conte | Thirty years of graph matching in pattern recognition[END_REF] and bipartition [START_REF] Kunegis | Exploiting the structure of bipartite graphs for algebraic and spectral graph theory applications[END_REF] of graphs. The question of choosing either A or L matrix for graph representation is still a subject of debate. For instance, in graph signal processing theory, Shuman et al. [START_REF] Shuman | The emerging field of signal processing on graphs: Extending highdimensional data analysis to networks and other irregular domains[END_REF] define the graph Fourier basis as the eigenbasis of L matrix, while Sandryhaila and Moura [START_REF] Sandryhaila | Discrete signal processing on graphs: Frequency analysis[END_REF] prefer the eigenbasis of A obtained via a Jordan decomposition. This difference can be justified in part by the nature itself of the decomposition basis, and also by the fact that not all graphs are determined by their spectra and there is a family of graphs that shares the same spectrum in respect to some matrix representation, commonly called cospectral graphs [START_REF] Godsil | Constructing cospectral graphs[END_REF]. The distinction between these cospectral graphs or between very similar graphs via their spectra is a tough task as stated in [START_REF] Van Dam | Which graphs are determined by their spectrum?[END_REF]. A big part of graph comparison algorithms aims to sort them using some structural similarity criteria without implicitly resorting to spectral analysis. This is the case of the aligned subtree kernel [START_REF] Bai | An aligned subtree kernel for weighted graphs[END_REF] that incorporates explicit subtree correspondences between the compared graphs, as well as other substructure based kernels [START_REF] Kriege | On valid optimal assignment kernels and applications to graph classification[END_REF] [START_REF] Bai | Jensen-shannon graph kernel using information functionals[END_REF] [13] [START_REF] Bai | Fast depth-based subgraph kernels for unattributed graphs[END_REF], which decompose the graphs into smaller sub-graphs and try to find the optimal bijection between them.

In spite that, spectral similarity measures remain attractive and hold many strengths [START_REF] Jovanović | Spectral distances of graphs based on their different matrix representations[END_REF]. We propose in this work to tackle the problem of graph classification using a spectral measurement of similarity called Joint Spectral Similarity (JSS) which compares two graphs using jointly the spectra of A and L. Such measure is interesting to distinguish graphs that have close spectral properties or even for sorting cospectral graphs which is a hard task when using only the spectrum of A or L at once. To understand the contribution of each matrix in graph information recovering, we investigate the framework of structural complexity measurements of graphs, more specifically, energetic and entropic measurements [START_REF] Anand | Shannon and Von Neumann entropy of random networks with heterogeneous expected degree[END_REF]. Inspired from information theory and statistical mechanics, these measures capture similarities and differences between networks and quantify the organization level of the underlying graph structure. Among them, we focus on Laplacian graph energy and VN entropy that can be used as a measure of regularity in graphs [START_REF] Neumann | Mathematical foundations of quantum mechanics[END_REF], [START_REF] Han | Graph characterizations from von neumann entropy[END_REF].

In this paper, we show the effectiveness of the JSS similarity measure for graphs classification. We highlight the graph's representation disparity between A and L matrices illustrated via entropy, connectivity and complexity measures. Combined in a heat kernel, the JSS measure shows promising results in real world graph data, built from chemical components and in real time series. These results are compared to the state-of-art graph kernels in terms of classification accuracy and computing CPU time.

Graphs basics

An undirected graph is defined with a finite non-empty set V of N elements called vertices (or nodes), and with a set E of M unordered pairs of distinct elements of V representing the connexions between vertices. A labelled graph with N vertices and M edges is represented with an (N × N) A matrix (A = [a i j ]), where the element a i j is one if the vertex v i is connected to the vertex v j and zero otherwise. Due to the symmetric relationship between nodes in undirected graphs, their adjacency matrix is also symmetric with zeros as diagonal entries. An alternative representation of graphs is given by Laplacian matrix L = D -A, where D is a diagonal matrix in which, the i th entry is the degree d i of the node v i ∈ V, representing its number of neighbors. In the case of a weighted graph, the degree d i is equal to the sum of the weights w i j of edges related to v i , and the Laplacian matrix takes the form L = D -A, where A is the weighted A matrix.

Graphs representation via A and L spectra

The matrices A and L are compared in terms of entropic information, connectivity and complexity measures. A proposition is also formulated, giving corrective terms in the VN entropy expression due to changes in graph structure related to A and L.

Entropic information measure

In quantum mechanics, objects modify their states according to the presence or not of an observer. They take only one state among other possible states, called pure states. But, it happens also that the observer measures a mixture of states, then the object is said to be in a mixed state or in a superposition. Such phenomenon is usually studied using the so called density matrix ρ, which has the occurrence probability of each pure state in the mixture as diagonal elements, and the confusion degree between them in the off-diagonal elements. This matrix is symmetric and positive semi-definite of trace one. To measure the uncertainty degree (mixedness) of a quantum system in a superposition state, Von Neumann introduced an entropic measure [START_REF] Neumann | Mathematical foundations of quantum mechanics[END_REF] which takes the form -T r(ρ log 2 ρ), which includes the diagonal elements of ρ and determines the amount of unknown or missing information about the real state of the system. The offdiagonal elements are interpreted as confusion or noise degree in the mixed state. The link between graphs and quantum mechanics has been established in [START_REF] Braunstein | The Laplacian of a graph as a density matrix: a basic combinatorial approach to separability of mixed states[END_REF], [START_REF] Passerini | Quantifying complexity in networks: the Von Neumann entropy[END_REF]. The beginning was from the fact that L matrix is symmetric (for undirected graph) and positive semi-definite. Hence, once normalized in appropriate way, it can be treated as a density matrix of a quantum system in a superposition state. Considering nodes as pure states in the standard basis of an Hilbert space of dimension N, the graph is seen as a superposition (mixture) of those pure states (nodes). Therefore, the VN entropy could be then calculated using L matrix scaled by the degree-sum of the graph:

ρ = L i d i . Let λ N
. . . λ 2 λ 1 = 0 and λN ... λ2 λ1 = 0 be respectively the eigenvalues of L and ρ, the VN entropy takes the form :

S (ρ) = - N i=1 λi log 2 λi = -T r(ρ log 2 ρ) (1)
with 0 log 2 (0) = 0 by convention. Otherwise, Bai et al. [START_REF] Bai | Quantum kernels for unattributed graphs using discrete-time quantum walks[END_REF] [21] used an alternative density matrix σ based on both continuous-time and discrete-time quantum walk to compare graphs. Their idea is to build a kernel which compares the density matrices associated to graphs using the Quantum Jensen-Shannon divergence as a similarity measure:

D QJS (σ 1 , σ 2 ) = S [1/2(σ 1 + σ 2 )] -1/2 S (σ 1 ) -1/2 S (σ 2 )
, where σ 1 , σ 2 are a pair of density matrices. The density matrix σ is calculated using a transition matrix for the quantum walk which includes information about the degrees and the structure of the graph. This approach does not require any calculation of eigenvalues nor those of A neither of L. Since the graph VN entropy is interpreted as a measure of the information content, we wonder about the contribution of each matrix (A and L) in the measured quantity of information. A part of the answer comes from quantum perturbation theory where the sensitivity of eigenvalues to density matrix perturbations has been studied. Some of these studies have been extended by Chen to include the case of perturbations on VN entropy [START_REF] Chen | Perturbation theory of von neumann entropy[END_REF]. This opens the way to project the study on to the general case of graphs. The goal is to determine the cost of structural modifications of the graph in terms of information quantity, and to clearly understand the relationship between A and L in a purely entropic framework. To this end, A matrix is perturbed and the VN entropy of the perturbed density matrix ρ is computed.

Proposition 1. Let G be a weighted graph whose the unper-turbed density matrix is ρ 0 . If ρ 0 undergoes a perturbation ρ * , the VN entropy of the resulting perturbed matrix, ρ = ρ 0 + ξ ρ * , expanded up to the second order is given by

S (ρ) = S (ρ 0 ) + η Diagonal (ρ * ) + η Off -Diagonal (ρ * ) (2)
where

η Diagonal (ρ * ) = -ξ n ρ * nn log 2 λn - 1 2 ξ 2 n (ρ * nn ) 2 λn + o(ξ 2 ) η Off -Diagonal (ρ * ) = -ξ 2 n m n ρ * nm 2 λn -λm log 2 λn + o(ξ 2 ) ( 3
)
with ξ is a scalar parameter supposed to be small, and λn λm ∀ n m are the eigenvalues of ρ 0 .

Proof : Since ρ is a density matrix, the perturbations are introduced in such way that T r(ρ) = 1 and ρ = ρ T . Restricting Taylor expansion to the second order [START_REF] Han | Graph characterizations from von neumann entropy[END_REF], the corrections to the eigenvalues are written as :

λ(t) n = λn + ξ λ(1) n + ξ 2 λ(2) n + o(ξ 2 ) ( 4
)
where the first and second order eigenvalue perturbations are given by λ( 1)

n = ρ * nn , λ(2) n = m n ρ * nm 2 λn -λm (5)
Therefore, the perturbed VN entropy can be written as

S (ρ) = -T r(ρ log 2 ρ) ≈ - n λ(t) n log 2 λ(t) n (6)
On the other hand, the Taylor expansion of S (ρ) around zero up to second order is written as

S (ρ) ≈ S (ρ 0 ) + ξ dS (ρ 0 ) dξ + 1 2 ξ 2 d 2 S (ρ 0 ) dξ 2 + o(ξ 2 ) (7)
Chen in [START_REF] Chen | Perturbation theory of von neumann entropy[END_REF] gives the first and second order derivatives of

S (ρ 0 ) dS (ρ 0 ) dξ = - n ρ * nn log 2 λn (8) d 2 S (ρ 0 ) dξ 2 = - n (ρ * nn ) 2 λn -2 n λ(2) n log 2 λn (9)
By substituting ( 5), ( 8) and ( 9) in equation ( 7), we get

S (ρ) ≈ S (ρ 0 ) -ξ n ρ * nn log 2 λn - 1 2 ξ 2 n (ρ * nn ) 2 λn η Diagonal + ξ 2 n m n ρ * nm 2 λn -λm log 2 λn η Off -Diagonal +o(ξ 2 ) (10)
A careful examination of equation [START_REF] Bai | An aligned subtree kernel for weighted graphs[END_REF] shows that the corrective terms η Diagonal and η Off -Diagonal , include respectively both diagonal and off-diagonal perturbation elements. Since changes in edge weights of A lead to changes in node degrees, perturbations affect at first place off-diagonal elements of A. Thus, it is expected that changes in weights introduce only off-diagonal elements in the entropy expression [START_REF] Bai | An aligned subtree kernel for weighted graphs[END_REF]. But, diagonal elements related to node degrees changes appear also. Due to the linear relationship L=D-A, these diagonal elements are introduced to L via D and thus they may explain why L matrix is more sensitive to structural changes of the graph than A.

Connectivity measure

In spectral graph theory, L matrix is often used for structural properties study of graphs. This is essentially motivated by its algebraic characteristics as the non-negativeness of its eigenvalue spectrum, or its interesting quadratic form written as y T Ly = u∼v (y(u)y(v)) 2 , with y is a function that assigns to each vertex v of the graph a real value y(v), and u∼v denotes the sum over all unordered pairs (u, v) for which u and v are adjacent. This quadratic form is useful for getting a variational characterizations of the eigenvalues in terms of Rayleigh quotient [START_REF] Chung | Spectral graph theory[END_REF]. The eigenpairs (λ k , f k ) of L can be formulated as convex optimization problems

λ k = min y⊥f 1 ,...,f k-1 y 0 y T Ly y T y = min y⊥f 1 ,...,f k-1 y 0 u∼v (y(u) -y(v)) 2 v y(v) 2 (11)
f k = arg min y⊥f 1 ,...,f k-1 y 0 y T Ly y T y = arg min y⊥f 1 ,...,f k-1 y 0 u∼v (y(u) -y(v)) 2 v y(v) 2 (12)
It can be easily deduced from equation ( 11) that 0 is an eigenvalue of L corresponding to the constant eigenvector f 1 = 1.

The second eigenvector must be orthonormal to the constant eigenvector (

f 2 , 1 = v f 2 (v) = 0)
. Therefore, a null second eigenvalue implies that the graph is composed of two disconnected components. This leads to the fundamental result of graph algebra which states that the multiplicity of zero eigenvalue corresponds to the number of the disconnected clusters in the graph. In connected graphs, the second eigenvalue is non-zero and corresponds to the minimal cost of the connections which can be lost in case of segmentation of the graph in two connected sub-graphs. This quantity has been defined by Fiedler as the algebraic connectivity of the graph, the corresponding second eigenvector is called Fiedler vector [START_REF] Fiedler | Algebraic connectivity of graphs[END_REF].

In the following example, we consider an undirected and unweighed random graph that contains implicitly two communities. We observe that the A matrix hides almost all indications about the existence of such communities or at least they remain difficult to detect (Fig. 2(a)). Fig. 1(b) shows that the Fiedler vector of L matrix associates to the nodes values of opposite signs in order to cluster them into subgroups. Using those labels, we reordered the raws and columns of A matrix in a way that reveals more structural information about the graphs (Fig. 2(b)). This example illustrates the interest of L matrix for recovering homogeneous clusters of nodes.

Complexity measure

Based on facts observed in molecular theory, Gutman et al. [START_REF] Gutman | On the energy of regular graphs[END_REF] introduced the A based graph energy (AE) as

AE(G) = N k=1 | µ k |, LE(G) = N k=1 λ k - 2M N (13)
where µ k are the eigenvalues of A. This spectrum-based graph invariant has been largely studied in both chemical and mathematical literature. An AE-like quantity LE, defined in terms of Laplacian and preserving the main features of the original AE has been proposed in [START_REF] Gutman | Laplacian energy of a graph[END_REF] where λ k are the eigenvalues of L and 2M/N is the average vertex degree. Both LE and AE measure the graph complexity. We illustrate this fact by using Erdös-Rényi random graphs parametrized with a connectivity probability parameter p. As p increases from zero to one, the model becomes more and more likely to include graphs with more edges and less and less likely to include graphs with fewer edges. As shown in Fig. 3, the quantities LE and AE are effectively relevant for measuring the complexity of graphs. Their respective curves take a smooth upward rate when the Erdös-Rényi probability increases. The growth tendency is very different, revealing the disparity between A and L in recovering the structural changes in the graphs, thus their complexity. Moreover, according to these findings, LE estimates more accurately the connectivity of the graph, and performs better than the smallest second eigenvalue (λ 2 ) of L in Erdös-Rényi random graphs.

Graphs Cospectrality Issue

The spectrum of different matrix representations of graphs holds a variety of informations that differs from one matrix to another [START_REF] Brouwer | Spectra of graphs[END_REF]. This is seen in the existence of cospectral graphs, or graphs that share the same spectrum for a particular matrix, A, L or others. They are called non-DS graphs referring to "Non Determined by the Spectrum". Among many graph families, Schwenk stated that almost all trees are non-DS graphs in respect to A [START_REF] Schwenk | Almost all trees are cospectral[END_REF]. Furthermore, Godsil and McKay proposed a method based on edge switching to make two nonisomorphic graphs A-cospectral [START_REF] Godsil | Constructing cospectral graphs[END_REF]. Likewise, many families of L-cospectral graphs were defined in literature, such those in [START_REF] Merris | Large families of laplacian isospectral graphs[END_REF]. We show in Figure 5 an example of two graphs that share the same Laplacian spectrum despite of their structural differences. As cospectrality appears to be a challenge to distinguish graphs via their spectra, it remains nevertheless surmountable by using a variety of spectral metrics simultaneously in the graph identification process. Figure 4 shows that it is possible to recognize A-cospectral graphs via their L spectrum, and inversely in Figure 5. This justifies more our idea of combining both spectra of A and L in JSS measure for comparing graphs.

Joint spectral similarity of graphs

Let G be a set of undirected graphs, and consider two graphs G 1 (A 1 , L 1 ) and G 2 (A 2 , L 2 ) ∈ G with A 1 , A 2 their adjacency matrices and L 1 , L 2 their Laplacian matrices where (λ 1i ,λ 2i ) and (µ 1i ,µ 2i ) are the eigenspectra of their Laplacian and adjacency matrices ordered in descending order. Information about the degree distribution is encoded mainly in the eigenvalues of L as well as the number of components of the graph, while information about walks, paths and the bipartition of the graph are in the eigenvalues of A [START_REF] Van Dam | Which graphs are determined by their spectrum?[END_REF]. Also to avoid the problem of cospectrality when comparing graphs via A and L spectra, we quantify the associated spectral similarity of the graphs as the trade-off between them. The introduced JSS measure aims to exploit both A and L spectral informations to better discriminate graphs. This measure, sum of two weighted spectral components, is given by the following convex linear combination :

JSS(G 1 , G 2 ) = αJSS A (G 1 , G 2 ) + (1 -α)JSS L (G 1 , G 2 ) ( 14
)
with α ∈ [0, 1], a weighting factor and where the components are given by : [START_REF] Anand | Shannon and Von Neumann entropy of random networks with heterogeneous expected degree[END_REF] where k = min(N 1 , N 2 ) and N 1 , N 2 are the numbers of eigenvalues corresponding to each graph. k represents the important common eigenvalues between the graphs, however, this criterion is particularly suitable for graphs of similar and comparable sizes. The weighting factor α controls the significance of each distance and allows more importance to be given to the A-spectral distance or to the L-spectral distance.

JSS L (G 1 , G 2 ) = k i=1 (λ 1i -λ 2i ) 2 , JSS A (G 1 , G 2 ) = k i=1 (µ 1i -µ 2i ) 2 (

Experimental Results

We illustrate the information conveyed by A and L matrices on real graphs (molecular data) and on conceptual ones obtained by mapping time series to the graph using Visibility Graph (VG) algorithm [START_REF] Lacasa | From time series to complex networks: The visibility graph[END_REF]. There are altogether nine benchmark real data sets used in our experiment.

Graphs from molecular data

Natural graphs are derived from databases built from chemical/biological data. MUTAG [START_REF] Debnath | Structure-activity relationship of mutagenic aromatic and heteroaromatic nitro compounds. correlation with molecular orbital energies and hydrophobicity[END_REF] is a data set of 188 mutagenic aromatic and heteroaromatic nitro compounds labeled according to whether or not they have mutagenic effect on the Gram-negative bacterium Salmonella typhimurium. NCI1 and NCI109 represent two data sets of chemical compounds screened for activity against non-small cell lung cancer and ovarian cancer cell lines [START_REF] Wale | Acyclic subgraph based descriptor spaces for chemical compound retrieval and classification[END_REF]. ENZYMES is a data set of protein tertiary structures obtained from [START_REF] Borgwardt | Protein function prediction via graph kernels[END_REF] consisting of 600 enzymes from BRENDA enzyme database [START_REF] Schomburg | BRENDA, the enzyme database: updates and major new developments[END_REF] where the task is to assign each enzyme to one of the 6 top-level classes. D&D is a data set of 1178 protein structures [START_REF] Dobson | Distinguishing enzyme structures from non-enzymes without alignments[END_REF], the classification task is to distinguish protein structures between enzymes and non-enzymes.

Time series data

Four problems are considered namely [35]: Computers is a data about home electricity consumption to help reduce the UK's carbon footprint, it concerns the use of computers in the houses, the purpose is to know if it is a Desktop or a Laptop computer. The ToeSegmentation data are derived from the CMU Graphics Lab Motion Capture database, walk motions in the database are classified by their nature, whether they are normal or abnormal. SonyAIBORobotSurface1 database is donated by Carnegie Mellon University. The robot Sony1 has roll/pitch/yaw accelerometers whose task is to detect the surface being walked on whether is cement or carpet. Lightning2 is a database that was built using FORTE satellite, that detects transient electromagnetic events associated with lightning. The aim is to classify power densities into two different categories of lightning.

Building Graphs from time series

To map time series into complex networks on the graph domain, the VG algorithm is used [START_REF] Lacasa | From time series to complex networks: The visibility graph[END_REF]. This algorithm defines connections between nodes and the weights of the graph from a time series. Every node of the graph corresponds, in the same order, to a sample from the series, and two nodes are connected if visibility exists between the corresponding samples. More formally, two arbitrary samples (t a , y a ) and (t b , y b ) will have visibility, and they are represented by two connected nodes in the associated graph, if any other sample (t c , y c ) placed between them fulfills :

y c < y b + (y a -y b ) t b -t c t b -t a (16)
We consider the edge weight between two nodes as the absolute value of the angle between the straight line that connects them and the horizontal axis. Formally it is written as :

w ab = arctan y b -y a t b -t a (17)
The weights w ab are the entries of A associated to the VG graph.

Experimental configuration

As for Radial Basis Function (RBF) kernel, the spectral similarity measure is integrated in a classical exponential function, leading to the following distance between the graphs G i , G j

K i, j = exp -γ s(G i , G j ) ( 18
)
where K is the kernel matrix and s(G i ,G j ) can be JSS, JSS A or JSS L measure. The parameter γ is a smoothing factor. The kernel matrix is integrated on a support vector machine (SVM) algorithm. Next, 10-fold cross-validation approach is performed using 9 folds for training and 1 for testing. Data sets are randomly shuffled before partitioning and the whole experiment is repeated 10 times to avoid random effects of fold assignments. The kernel factor γ is set to 1. Average classification accuracies and their corresponding standard deviations are summarized in Tables 1 and3. For molecular data, the measures JSS, JSS A and JSS L are compared to some kernels of the literature in terms of prediction accuracy and computation runtime. For time series data, only prediction accuracies are reported. Otherwise, the well-known graph kernels are tested: those based on walks, sub-trees and Weisfeiler-Lehman isomorphism. Else, the measures are compared to the fast geometric random walk kernel [START_REF] Vishwanathan | Graph kernels[END_REF], counts common labelled walks and to p-random walk kernel that compares random walks up to length p in two graphs [START_REF] Kashima | Marginalized kernels between labeled graphs[END_REF]. From sub-tree kernels, we chose Ramon Gärtner kernel [START_REF] Gärtner | On graph kernels: Hardness results and efficient alternatives[END_REF] which compares all pairs of nodes from two graphs by iteratively comparing their neighbourhoods. From Weisfeiler-Lehman kernels, we picked up the Weisfeiler-Lehman edge kernel [START_REF] Shervashidze | Weisfeiler-lehman graph kernels[END_REF]: it counts matching pairs of edges with identically labeled endpoints in two graphs. For molecular data, computing set-up, accuracy and runtime values of the benchmark kernels are performed in [START_REF] Shervashidze | Weisfeiler-lehman graph kernels[END_REF]. We followed the same procedures to compute random walk and Weisfeiler-Lehman edge kernels for time series data, without Ramon Gärtner and p-random walk kernels because of runtime constraint. The time series results are also compared to Linear and RBF kernels, applied directly on the samples of time series without converting them to graphs. As reported in Table 2, runtime in minutes and seconds of our method is measured using Anaconda2 4.1.1 Python 2.7.12 Lab installed on a PC with 3 GHz Intel 8-Core processor and 16GB RAM.

Results analysis

As expected, the obtained results confirm the unequal contribution of both A and L matrices and their overlapping in terms of graphs representation. The reported results in Tables 1 and3, and in figure 6 show that the achieved classification accuracies of JSS measure are promising with respect to some state-ofthe-art methods. The JSS based kernel performs well in the majority of datasets. In molecular data, it reaches second best accuracy in all datasets (MUTAG, NCI1, NCI109, ENZYMES and D&D) compared to the benchmark kernels. But in terms of CPU time, the JSS based kernel is faster than other kernels in many cases, such as in MUTAG, ENZYMES and mostly in D&D, where JSS kernel performs almost as well as Weisfeiler-Lehman edge kernel (75.75 Vs 77.95), while execution time is 600 times faster. In Table 3, the JSS based kernel provides good results applied to time series classification problems. Especially in the Lightning2, ToeSegmentation1 and Computers databases, it performs better than other graph kernels, and even better than kernels applied directly to time series. The representation of time series as VG allowed a clear improvement of the classification accuracy, approaching 12% for ToeSegmen-tation1, 8% for Lightning2 and 6% for Computers. The reported results, on different data sets with varying complexity and heterogeneity, in terms of classification accuracy and computational cost, demonstrate the effectiveness and the interest of the proposed JSS measure. This spectral similarity generalizes the spectral distance between graphs based on purely A (JSS A ) or L (JSS L ) matrix.As reported in Tables 1 and3, and figure 6, JSS is well sensitive to these graph properties and allows to effectively handle them. Figure 6 shows that the JSSbased method highly outperforms the method purely based on JSS A or JSS L . A careful examination of figure 6 shows that for both α = 0 and α = 1, corresponding respectively to JSS L and JSS A , neither of JSS A nor JSS L is able to perform better than JSS. However, overall, JSS A achieves better results than JSS L and this can be attributed, as expected, to the less sensitivity of A to structural changes, compared to L matrix, but more efficient for graph discrimination. According to these results, the weighting parameter lies in ]0; 1[, showing that L and A are complementary and thus carry different information about the underlying graph. For all data sets, we have the parameter α 0.5, which indicates that JSS L and JSS A are unequally contributed and highlights that the A and L representation matrices recover different structures of the graph. Also, these results show that JSS effectively captures information conveyed by A and L matrices. The fact that the assigned weighting parameter α varies from one data set to another emphasizes that each graph has its own structure and also that both A and L matrices convey different information.

Conclusion

The representation of graphs using matrices plays an important role in graph spectral theory and in many other applications dealing with graphs. In this paper a new joint spectral similarity (JSS) measure for graphs classification is introduced. We have shown that both adjacency and Laplacian matrices carry different structures information of the underlying graph. The adjacency matrix characterizes the topological graph complexity in terms of connections between nodes and their intensities, and also underscores the local cohesiveness of nodes. These properties explain why the good classification accuracies achieved by JSS measure are more attributed to adjacency matrix (α > 0.5). Through VN entropy, it is easy to see that Laplacian matrix brings out changes in node degrees information. Furthermore, this matrix is well suited to recover information about clusters of the graph and thus capture its inherent structure. The obtained results highlight the fact that JSS combines both advantages of Laplacian and adjacency matrices. Also, these findings confirm that these matrices contribute unequally and emphasize the fact that they represent differently information about structures of the underlying graph. Additionally, these results show the interest of the VG approach for classification of time series. As a result of this work, we hope to have increased the awereness about the importance of the properly choice of the representation matrix for graph spectral analysis purposes. Even the JSS measure handles cospectral graphs with respect to both A and L, it can be extended to the case of graphs that are cospectral in regard to a large class of graph representation matrices. At last, the optimal value of α is in general not known and is determined only through experimentation. As future work we plan to develop a strategy to find automatically the optimal value of α .

Table 1: Classification accuracy on molecular data. Ramon and Gärtner [START_REF] Gärtner | On graph kernels: Hardness results and efficient alternatives[END_REF], p-random walk [START_REF] Kashima | Marginalized kernels between labeled graphs[END_REF], Random walk [START_REF] Vishwanathan | Graph kernels[END_REF], Weisfeiler-Lehman edge [START_REF] Shervashidze | Weisfeiler-lehman graph kernels[END_REF] [START_REF] Vishwanathan | Graph kernels[END_REF], Weisfeiler-Lehman edge [START_REF] Shervashidze | Weisfeiler-lehman graph kernels[END_REF] are some state of the art kernels.

Method/Data ToeSegmentation1 SonyAIBORobotSurface1 Computers Lightning2

Fig. 1 :

 1 Fig. 1: Laplacian's second eigenvector (Fiedler vector) of a connected random graph with 300 nodes. In the left: labels associated to nodes before sorting (a). In the right: After sorting (b).

Fig. 2 :

 2 Fig. 2: Adjacency matrix of the connected random graph with 300 nodes. In the left: the original A matrix (a). In the right: the reordered A matrix using the Fiedler labels order (From L matrix) (b).

Fig. 3 :

 3 Fig. 3: A and L based graph energy evolution in terms of the graph's structural complexity. Illustrated in Erdös-Rényi random graphs with 700 nodes.

Fig. 4 :Fig. 5 :

 45 Fig. 4: TwoA-cospectral graphs σ a (A) = σ b (A) = [-1.9, -1, -1, 0.2, 1, 2.7] σ a (L) = [0, 1, 1, 3, 3, 6] σ b (L) = [0, 0.5, 1.2,3.4, 4, 4.7]

Fig. 6 :

 6 Fig. 6: Accuracy variation of JSS based kernel as function of α.

Table 2 :

 2 are some state of the art kernels. ±0.22 67.74 ±0.14 66.21 ±0.28 32.35 ±1.15 75.71 ±0.14 JSS L 82.48 ±0.36 63.07 ±0.25 62.07 ±0.26 24.86 ±0.93 75.49 ±0.24 JSS 83.81 ±0.48 68.10 ±0.16 66.22 ±0.13 36.35 ±0.90 75.75 ±0.19 [38] 85.72 ±0.49 61.86 ±0.27 61.67 ±0.21 13.35 ±0.87 57.27 ±0.07 [37] 79.19 ±1.09 58.66 ±0.28 58.36 ±0.94 27.67 ±0.95 66.64 ±0.83 [36] 80.72 ±0.38 64.34 ±0.27 63.51 ±0.18 21.68 ±0.94 71.70 ±0.47 [39] 81.06 ±1.95 84.37 ±0.30 84.49 ±0.20 53.17 ±2.04 77.95 ±0.70 CPU runtime for kernel computation on molecular data. Ramon and Gärtner[START_REF] Gärtner | On graph kernels: Hardness results and efficient alternatives[END_REF], p-random walk[START_REF] Kashima | Marginalized kernels between labeled graphs[END_REF], Random walk[START_REF] Vishwanathan | Graph kernels[END_REF], Weisfeiler-Lehman edge[START_REF] Shervashidze | Weisfeiler-lehman graph kernels[END_REF].

	Method/Data	MUTAG	NCI1	NCI109	ENZYMES	D&D
	JSS A 83.67 Method/Data MUTAG	NCI1	NCI109 ENZYMES	D&D
	JSS A	0.32	2 29	2 27	3	3 24
	JSS L	0.88	2 28	2 30	3.50	3 34
	JSS	1.30	4 14	4 19	5.88	6 53
	[38]	40 6	81 days 81 days	38 days	103 days
	[37]	4 42	5 days	5 days	10	4 days
	[36]	12	9 days	9 days	12 19	48 days
	[39]	3	1 5	58	11	3 days

Table 3 :

 3 Classification accuracy on time series data sets. Random walk