Vik Pant
email: vik.pant@mail.utoronto.ca

Eric Yu
email: eric.yu@utoronto.ca

Coopetition with Frenemies: Towards Modeling of Simultaneous Cooperation and Competition Among Enterprises

Keywords: Enterprise Modeling, Coopetition, Strategy, Design, Review, Characteristics

Enterprise modeling frameworks are concerned with the representation of social phenomena and researchers have proposed a number of notations and techniques for depicting social behaviors. However, coopetition, which is a specific type of social interaction, has not been explored in the enterprise modeling literature. Coopetition, which refers to simultaneous cooperation and competition, has been studied extensively in the social sciences where conceptual theorizing and empirical fieldwork have established it as a prominent field of research. It is regularly observed in dealings between many kinds of enterprises, such as businesses and governments, where it has been analyzed at both inter-as well as intra-organizational levels. Coopetition is especially relevant for enterprise modeling because goal alignment/convergence can yield cooperation among actors while goal conflict/divergence can lead to competition among actors. In this paper we (a) present an overview of academic research into coopetition, (b) discuss the requirements for representing coopetition, and (c) propose future work that will be relevant for the modeling and analysis of cooperation, competition, and coopetition between enterprises.

Introduction

A number of researchers have proposed modeling notations and techniques for expressing and evaluating organizational strategy [START_REF] Giannoulis | Modeling business strategy: A meta-model of strategy maps and balanced scorecards[END_REF][2] and a variety of modeling approaches have been developed to describe different aspects of enterprises (e.g., goal, actor, value, process, etc.) [START_REF] Johannesson | The role of business models in enterprise modelling[END_REF]. Additionally, requirements engineering (RE) researchers have applied many goal-and actor-oriented approaches to model and analyze business strategy [START_REF] López | Applying business strategy models in organizations[END_REF] [START_REF] Paja | Can Goal Reasoning Techniques be used for Strategic Decision-Making?[END_REF]. However, none of these approaches have focused directly on this phenomenon of simultaneous cooperation and competition. This is a gap in the RE literature because strategic coopetition impacts many entities (such as actors, goals, tasks, resources, boundaries, value, etc.) that are relevant for these approaches.

Coopetition, which refers to simultaneous cooperation and competition, has become "increasingly popular in recent years" [START_REF] Gnyawali | Co-opetition and technological innovation in small and medium-sized enterprises: A multilevel conceptual model[END_REF] and is "an integral part of many companies' daily agenda" [START_REF] Bengtsson | Coopetition-Quo vadis? Past accomplishments and future challenges[END_REF]. While some research papers in the RE literature have discussed competition and cooperation between enterprises [START_REF] Giannoulis | Modeling competition-driven business strategy for business IT alignment[END_REF][9]there are many characteristics of these strategic behaviors that are unexplored in the Enterprise Modeling (EM) literature. It can be argued that these gaps "make it difficult for requirements engineers to validate low-level requirements against the more abstract high-level requirements representing the business strategy" [START_REF] Bleistein | Modeling business strategy in ebusiness systems requirements engineering[END_REF]. Therefore, the ability to articulate cooperation, competition, and coopetition represents advancement in the state-of-theart in EM.

In the introductory section of this paper, we discussed the relevance of coopetition for EM. In the next section, we describe the development of coopetition research within the field of Strategic Management. In the third section, we discuss key characteristics of coopetition that are relevant for EM. In the final section, we summarize our current research into coopetition modeling and propose next steps for future research.

Enterprise Cooperation, Competition, and Coopetition

Strategic Management (SM), which is a branch of Organizational Theory (OT), is an academic discipline that is concerned with the structure, behavior, and performance of organizations [START_REF] Scott | Organizations and organizing: Rational, natural and open systems perspectives[END_REF]. It emerged in the 1950s as an explanation of the strategic dynamics between firms in competitive industries [START_REF] Linstead | Towards Euranglo research? A critical comparison of thirty years of Anglo-Saxon and French organizational analysis[END_REF]. It was closely related to Bain's SCP (structure, conduct, performance) paradigm according to which the performance of a firm was determined by its conduct, which, in turn, was impacted by various industry factors [START_REF] Bain | Barriers to New Competition: Their Character and Consequences in Manufacturing Industries[END_REF]. Starting in the late 1970s, Porter popularized this view through his advancement of economic theories of "competitive advantage" [START_REF] Porter | How Competitive Forces Shape Strategy[END_REF] [START_REF] Porter | Towards a dynamic theory of strategy[END_REF]. A number of economists, including Porter, helped to establish this competitive view of strategy as the dominant paradigm during the first three decades of SM research.

This "militaristic" view in SM was challenged throughout the 1980s and 1990s by researchers who argued in favor of "cooperative advantage" and "collaborative advantage" [16][17]. This stream of research posited that firms could improve their performance and increase their profits by partnering with other firms. Dyer and Singh promoted the notion of "relational rents" as profits that were generated through relationship-specific idiosyncratic assets and resources [START_REF] Dyer | The relational view: Cooperative strategy and sources of interorganizational competitive advantage[END_REF]. Many rationales and justifications were offered for inter-firm relationships such as strategic alliances. These included the ability for partner firms to acquire knowledge [START_REF] Jiang | An empirical investigation of knowledge management and innovative performance: The case of alliances[END_REF], share risks [START_REF] Das | Risk types and inter-firm alliance structures[END_REF], access markets [START_REF] Gebrekidan | Interorganizational cooperation: a new view of strategic alliances: The case of Swedish firms in the international market[END_REF], spread costs [START_REF] Todeva | Strategic alliances and models of collaboration[END_REF], pool resources [START_REF] Koza | Managing partnerships and strategic alliances: raising the odds of success[END_REF], and achieve strategic objectives [START_REF] Inkpen | Why do some strategic alliances persist beyond their useful life?[END_REF].

By the mid-1990s, the field of SM was divided into two camps that offered incompatible and divergent explanations of inter-firm behaviors. The competitive camp argued that cooperation among rivals led to collusion/cartelization while the coopera-tive/collaborative camp asserted that competition between allies led to mutually destructive outcomes. An esemplastic theory was needed to resolve this creative tension.

Coopetition theory was proposed as a syncretistic means for reconciling the competitive and cooperative perspectives [START_REF] Padula | Untangling the rise of coopetition: the intrusion of competition in a cooperative game structure[END_REF]. It was introduced in 1995 by two economists who adopted a game-theoretic lens for interpreting inter-firm behaviors [START_REF] Brandenburger | Co-opetition[END_REF]. In the two decades since its introduction, coopetition theory has become a prominent field of scholarly inquiry. A number of literature reviews have noted the increase in research interest in this field [START_REF] Walley | Coopetition: an introduction to the subject and an agenda for research[END_REF][28] [START_REF] Bouncken | Coopetition: a systematic review, synthesis, and future research directions[END_REF] and eminent scholarly publications have devoted special issues to this topic [30][31]. Empirical fieldwork has also been used to explore "coopetition along the antecedents-process-outcomes trail" [17][28]. Additionally, coopetition research has progressed beyond SM into other disciplines including political science [START_REF] Fleisher | Managing business political activities in the USA: Bridging between theory and practice-another look[END_REF], diplomacy [START_REF] Alber | Does Europe have something to offer the world[END_REF], and civics [START_REF] Racine | Dissolving dualities: The case for commonsense replication[END_REF].

Emerging Requirements for Modeling Enterprise Coopetition

OT researchers have identified various characteristics that define coopetitive relationships [6][35]. These include, but are not limited to, complementarity [START_REF] Tee | Industry architecture as a determinant of successful platform strategies: A case study of the i-mode mobile Internet service[END_REF], interdependence [START_REF] Luo | Toward coopetition within a multinational enterprise: a perspective from foreign subsidiaries[END_REF], trustworthiness [START_REF] Bouncken | Coopetition: performance implications and management antecedents[END_REF], and reciprocity [START_REF] Rossi | An experimental investigation of fairness and reciprocity as determinants of intraorganizational coopetition[END_REF]. It should be noted that cooperation and competition are germane to coopetition because coopetition represents the coaction of these phenomena. Therefore, a RE framework for coopetition ought to support the depiction of cooperation and competition separately as well as simultaneously (i.e., coopetition). This section discusses the key characteristics of coopetition between enterprises that are essential for modeling it.

Key features of coopetitive relationships

Table 1 presents a partial list of requirements that are relevant for modeling coopetition phenomenon. Table 2 presents a preliminary assessment of various techniques in terms of requirements for representing coopetition. We acknowledge that each of these entries merit debate and critique and are offering them to stimulate discussion and more in-depth analysis. Please note that this assessment does not consider the syntax and semantics of extensions, derivatives, or combinations of the reviewed techniques. The column titled 'Key' from Table 1 should be used to interpret the coded column headings in Table 2.

Prominent goal-and/or actor-modeling approaches such as NFR framework, KAOS, and i* are able to support the representation of some, but not all, of these requirements. Similarly, practitioner tools such as Business Model Canvas and Value Network Analysis are also deficient with respect to some of these requirements. Nonetheless, these approaches can be extended and combined in creative ways to overcome their respective limitations for modeling coopetition. This is appropriate because according to [START_REF] Giannoulis | A comparative analysis of enterprise modeling approaches for modeling business strategy[END_REF], "depending on the needs, several languages can also be used together in a complementary way".

Tab. 1. Partial list of requirements for modeling enterprise coopetition. 1.

Strategic Competition between Enterprises

A number of theories have been proposed to explain the nature and characteristics of strategic competition between enterprises. These include Industrial Organization, Chamberlinian, and Schumpeterian explanations that refer to different core concepts and units of analysis [START_REF] Barney | Types of competition and the theory of strategy: Toward an integrative framework[END_REF]. For example, [START_REF] Henderson | The anatomy of competition[END_REF] claims that "there is no reason to think of business competitive systems as different in any fundamental way from other biological competition". This view posits that much like biological competition (between organisms) economic competition (between enterprises) occurs due to resource conflicts [START_REF] Henderson | Understanding the forces of strategic and natural competition[END_REF]. Indeed, this view is in line with a functional definition of economics as the "study of the allocation of 'scarce' resources among competing ends" [START_REF] Chiswick | The economics of language for immigrants: An introduction and overview[END_REF]. This means that actors (enterprises), goals (ends), and resources (means) are pertinent for the modeling of strategic competition between enterprises.

Figure 1 presents an i* SR (Strategic Rationale) diagram of competition between enterprises caused by typical resource conflicts. Two firms, A and B, are in the same industry such that their products/services are substitutes which serve similar customer needs. These firms require similar resources (capital and employees) and consume similar raw materials (ingredients and supplies). They interact in two arenas which are factor and output markets wherein a factor market is comprised of investors, suppliers, and job agencies while an output market is comprised of customers, and an intellectual property office (i.e., patent issuer). We have chosen i* SR modeling because it supports the depiction of resource dependencies across actors as well as means-ends decomposition and softgoal contributions within actors.

Each firm depends on these stakeholders for different reasons. An investor offers funds to firms (shown) in return for principal + interest and/or profits (not shown). A supplier sells raw materials to firms (shown) in return for principal + interest and/or profits (not shown). A job agency helps a firm to recruit employees (shown) in return for a charge (not shown). The Intellectual Property Office issues patents (not shown) after a firm attempt to register its design (shown). A customer offers its business to firms via orders (shown) and in return pays the firm for its products (not shown). We have excluded certain details from the Figure 1 in order to simplify the diagram.

There are two main types of interactions that can take place between two enterprises such as firms A and B. These are depicted in Figure 2 which is an i* SR diagram of abstract resource conflicts between enterprises (i.e., it represents a strategic pattern).

In the first type of interaction, an enterprise (e.g., Firm A) depends on a resource (i.e., Resource X) while another enterprise (e.g., Firm B) depends on a different resource (i.e, Resource Z). In this case, there is no conflict between these enterprises as they depend on, and are interested in, different resources. In the second type of interaction, two enterprises (e.g., Firm A and Firm B) depend on the same resource (i.e., Resource Y). In this case, there is a conflict between these enterprises as they depend on, and are interested in, the same resource. This scenario is likely to lead to strategic competition if only one of these firms is able to satisfy its resource dependency (means) that is necessary for achieving its goal (ends).

The ability to represent the heterogeneous facets of resources are also relevant for the modeling of strategic competition between enterprises. This is because [START_REF] Barney | Firm resources and sustained competitive advantage[END_REF] argues that a resource that is valuable, rare, inimitable, and non-substitutable serves as a source of competitive advantage for its owner/controller. A resource is considered to be valuable if rivals cannot: obtain/access it, mimic/copy it, or generate comparable value from alternative/replacement resources [START_REF] Barney | Is the resource-based "view" a useful perspective for strategic management research? Yes[END_REF]. In i*, an actor (i.e., depender) depends upon another actor (i.e., dependee) for a dependum (i.e., dependum). A depender benefits through its collaboration with a dependee because it is able to seize opportunities to satisfy objectives that it cannot fulfill alone. However, a dependency also makes a depender vulnerable with respect to its dependee. This is because actors in i* are autonomous actors that make self-interested decisions and as such, a dependee is under no obligation to fulfil a dependum except for legal requirements and social norms.

In i* the main conceptual entities are, Goal: Refers to an end, objective, aim, or target that reflects a state of affairs to be achieved. Task: Refers to an alternative mean for satisfying some goal. Resource: Refers to a physical or informational entity that is required to achieve some goal or perform some task. Softgoal: Refers to a goal without well-defined criteria for satisfaction and which requires further refinement and elaboration for assessing achievement.

In i* the main links are, Means-Ends: Refers to the links between a goal and the alternative tasks for achieving it. The completion of any task leads to the satisfaction of its associated goal. Decomposition: Refers to the links between an element and its sub-elements. The achievement of all sub-elements is necessary for the satisfaction of their associated element. Contribution: Refers to the impact of one element on another. The impact upon an element can be positive or negative.

Overview adapted from source: [START_REF] Yu | Towards modelling and reasoning support for early-phase requirements engineering[END_REF].

3.3

Tensions in Paradoxical Relationships

Competition and cooperation are diametric social behaviors that are undergirded by opposite logics and assumptions [START_REF] Bengtsson | Coopetition" in business Networks-to cooperate and compete simultaneously[END_REF]. Their co-occurrence in any relationship represents a paradox that creates tensions between the coopeting actors [START_REF] Raza-Ullah | The coopetition paradox and tension in coopetition at multiple levels[END_REF]. Different degrees of cooperation and competition can co-exist [START_REF] Bengtsson | Coopetition" in business Networks-to cooperate and compete simultaneously[END_REF] within vertical (i.e., buyersupplier) as well as horizontal (i.e., firm-to-firm) relationships [START_REF] Dowling | Multifaceted relationships under coopetition[END_REF]. Moreover, coopetition can occur within a dyad (i.e., between two actors) or in a network. Dyadic coopetition necessitates direct coopetition between two actors but network coopetition enables direct as well as indirect coopetition (i.e., via an intermediary). Dyadic coopetition can be regarded as procedural coopetition [START_REF] Rusko | Perspectives on value creation and coopetition[END_REF] where activity is an appropriate unit of analysis while network coopetition can be regarded as contextual coopetition [START_REF] Rusko | Mapping the perspectives of coopetition and technology-based strategic networks: A case of smartphones[END_REF] where actor is a suitable unit of analysis. Coopetition is also a multilevel phenomenon wherein an actor may exhibit different behaviors at different levels (i.e., within a dyad or network) [START_REF] Chiambaretto | Toward a Typology of Coopetition: A Multilevel Approach[END_REF].

Complementarity, Interdependence, Trustworthiness, and Reciprocity

Complementarity: According to [START_REF] Tee | Industry architecture as a determinant of successful platform strategies: A case study of the i-mode mobile Internet service[END_REF],"complementarity refers to the combined returns from the combination of two or more assets, with some combinations resulting in higher value creation than other combinations." It is informally referred to as synergy wherein: 'the whole is greater than the sum of its parts'. Complementarity motivates cooperation within competitive relationships and competition within cooperative relationships. Researchers have identified various ways through which firms can develop complementarities with their partners. These include overlap avoidance, knowledge protection, and development of common objectives. [START_REF] Gnyawali | Co-opetition between giants: Collaboration with competitors for technological innovation[END_REF] note that multifaceted dealings between Sony and Samsung illustrate a coopetitive relationship that is based on complementary R&D and manufacturing skills.

Interdependence: According to [START_REF] Luo | Toward coopetition within a multinational enterprise: a perspective from foreign subsidiaries[END_REF], "strategic interdependence is concerned with the extent to which work processes that have strategic implications are interrelated." Firms are typically incentivized to become mutually reliant when they have "partially congruent interest structures" [START_REF] Castaldo | Trust and coopetition: the strategic role of trust in interfirm coopetitive dynamics[END_REF]. Interdependence fosters coopetition because it ensures that "each competitor will have a specific individual interest in carrying out an agreement" [START_REF] Garraffo | Competitor analysis and interfirm coopetition[END_REF]. Researchers have identified various ways through which firms can become more interdependent with each other. These include investing in relationship-specific assets, interconnecting resources, and knowledge sharing. [START_REF] Bengtsson | Coopetition" in business Networks-to cooperate and compete simultaneously[END_REF] observed such coopetitive interactions between a number of European firms in the rack and pinion as well as lining industries.

Trustworthiness: According to [START_REF] Hutchinson | Inter-relationships among focal dimensions in relationship quality: a quantitative and exploratory approach[END_REF], "trust refers to the expectation that another business can be relied on to fulfill its obligations." It "is expected to reduce the level of potential and actual opportunism" [START_REF] Judge | Strategic alliance outcomes: a transaction-cost economics perspective[END_REF] through "(a) impartiality in negotiations, (b) trustworthiness, and (c) keeping of promises" [START_REF] Bouncken | Coopetition: performance implications and management antecedents[END_REF]. Moreover, "while trust is an attribute of a relationship between exchange partners, trustworthiness is an attribute of individual exchange partners" [START_REF] Barney | Trustworthiness as a Source of Competitive Advantage[END_REF]. Trustworthiness is an important consideration in coopetition because trust and contracts serve as governance mechanisms in cooperative relationships. Researchers have identified various techniques through which firms can grow their trustworthiness. These include increasing communication, avoiding coercion, and increasing linkages. [START_REF] Fernandez | Sources and management of tension in co-opetition case evidence from telecommunications satellites manufacturing in Europe[END_REF] identified trust as a "key factor for success of co-opetitive strategies" through an empirical study of the telecommunications satellite industry in Europe.

Reciprocity: According to [START_REF] Ashraf | Decomposing trust and trustworthiness[END_REF],"reciprocity is defined as rewarding kindness with kindness and punishing unkindness with unkindness." [START_REF] Sobel | Interdependent preferences and reciprocity[END_REF] note that a social actor should "expect this behavior from others" because "reciprocity is a rather stable behavioral response by a nonnegligible fraction of the people" [START_REF] Fehr | Fairness and retaliation: The economics of reciprocity[END_REF]. [START_REF] Lee | Faving Reciprocity in Content Sharing Communities A comparative analysis of Flickr and Twitter[END_REF] point out "reciprocity has been studied in depth in economics and game theory as a means to enforce cooperative behavior". This is why it is commonly used in game theory to explain social behavior in sequential move games such as ultimatum game and giftexchange game [START_REF] Falk | A theory of reciprocity[END_REF]. In fact, such behavior is not limited to games and has been observed in the industry by [START_REF] Krämer | A Small Step from Price Competition to Price War: Understanding Causes, Effects and Possible Countermeasures[END_REF].

Example: Inter-partner learning & knowledge-sharing among enterprises

An important justification for strategic alliances is the transfer and exchange of organizational knowledge between partners [19][22]. However, knowledge sharing can also expose partners to risks and vulnerabilities. This is because partners can engage in 'learning races' [68][69] where each firm tries to 'learn faster' than its partners [70][71]. This might be motivated by opportunism such as a firm's desire for 'knowledge expropriation' [START_REF] Heiman | Empirical evidence regarding the tension between knowledge sharing and knowledge expropriation in collaborations[END_REF][73] [START_REF] Trkman | Knowledge risks in organizational net-works: An exploratory framework[END_REF]. Such strategic interactions between enterprises can be described using models that depict factors such as complementarity, interdependence, trustworthiness, and reciprocity.

Figure 3 shows the strategic dynamics between two enterprises (i.e., Firm A and Firm B) that possess complementary knowledge. This means that each possesses a stock of information that is of use to the other and hence these firms are interdependent on each other. Information stock is a resource that allows each firm to make decisions regarding a number of business activities. These decisions include, but are not limited to, those about entering new markets, designing new products, developing new business processes, building new organizational structures, and creating new business relationships.

In such inter-partner learning arrangements, each firm must disclose its information stock to its partner in order to access the information stock of its partner in return. Each firm identifies learning opportunities from its partner by evaluating the usefulness of the information stock of its partner for its own business requirements. After identifying learning opportunities, a firm tries to access information from the information stock of its partner so as to add it to its own information stock. However, in order to access information from its partner a firm also has to disclose information from its own information stock. This is necessary because for information exchange to be mutually beneficial both firms must act on reciprocal learning opportunities.

A firm can exchange information with its partner through two main methods which are accessing and disclosing information. Accessing and disclosing information are two components of the same process because accessing information depends on the ability of a firm to get information from a dependee (i.e., someone that is depended upon) as well as the ability of the dependee to give information to the depender (i.e., someone that depends). Likewise, disclosing information depends on the ability of a firm to give information to a depender as well as the ability of the depender to get information from the dependee.

Learning ability is a socio-technical resource that enables activities related to the acquisition, assimilation, absorption, and application of organizational knowledge. This resource allows a firm to learn from its partners and also makes it possible for a firm to learn faster than its partner (i.e., allows it to get more information than it gives). The ability to learn faster than a partner is advantageous for a firm because it allows that firm to achieve a higher return from the sharing of its knowledge. Indeed, [START_REF] Jashapara | Cognition, culture and competition: an empirical test of the learning organization[END_REF] argues that superior organizational learning leads to improved organizational performance and that "the only source of sustainable competitive advantage for a company may lie in its ability to learn faster than its competitors" [START_REF] Jashapara | The competitive learning organization: a quest for the Holy Grail[END_REF].

A superior learning ability also functions as de facto insurance policy because it precludes a firm from being shut out from the information stock of its partner before it has had a chance to access all the information that it is seeking from that partner. Conversely, a firm that can learn faster than its partner can access all of the relevant information from the information stock of its partner first and then terminate the knowledge sharing arrangement before that partner has had an opportunity to learn all of the relevant information from its information stock. This is why firms evaluate the trustworthiness of partners in order to minimize the risk of exploitation through opportunism (e.g., knowledge expropriation) in knowledge-sharing scenarios.

There are three main types of interactions that can take place between two enterprises (such as firms A and B) in inter-partner learning arrangements. The top diagram in figure 3 depicts a situation in which both firms perceive the knowledge exchange to be equitable as well as fair and therefore they will continue to cooperate by sharing knowledge. This might happen if both partners have foregone opportunism in their dealings and have built up a reservoir of goodwill and understanding. In contrast, the bottom diagram in figure 3 depicts a situation in which any/all firm(s) perceive the knowledge exchange to be harmful as well as malicious and therefore they will conflict and compete with each other. For example, this might happen if any firm detects its partner(s) of engaging in opportunistic behavior because such behavior will create distrust/mistrust in the partnership. The middle diagram in figure 3 depicts a situation in which one firm is cooperating fully (i.e., Firm B) while the other firm (i.e., Firm A) is cooperating partially. This is because while Firm A is sharing its information with Firm B it is also attempting to learn faster than Firm B (i.e., it is competing). In such a situation the stability of the partnership depends on whether or not Firm B detects the opportunistic behavior of Firm A. If Firm B does not detect the opportunistic behavior of Firm A then Firm B will continue to grant unrestricted access to its information stock to Firm A while Firm A will only grant partial access to its information stock to Firm B. However, if Firm B detects the opportunistic behaviour of Firm A, as shown in the bottom diagram in figure 3, then the knowledge sharing will break down on account of Firm B feeling exploited by Firm A. This example shows simultaneous competition and cooperation between the actors because competitive behaviour is present within a cooperative relationship.

Conclusions and Future Work

This paper provided an overview of the phenomenon of coopetition as well as some of its key facets and characteristics that are relevant for EM. In addition to being an eminent research area, coopetition is also widely observed in practice. [START_REF] Baglieri | Asymmetric R&D alliances and coopetitive games[END_REF] claim that "coopetition is common in several industries" and [START_REF] Harbison | Smart Alliances: A Practical Guide To Repeatable Success[END_REF] note that roughly 50% of strategic alliances are between competitors. Nonetheless, in spite of its prominence, coopetition has not been explored in the EM literature. We intend to address this shortcoming by developing a modeling framework that is suitable for representing cooperation, competition, and coopetition.

The next logical step in our research is to identify and catalog the requirements for modeling these phenomena. Table 1 presents a partial list of these requirements however it needs further elaboration and refinement. After identifying the requirements for modeling coopetition, our next step will be to assess the adequacy of extant modeling languages for satisfying those requirements. Table 2 presents preliminary findings however they merit improvement through more rigorous and detailed assay. Moreover, any revisions to Table 1 will necessarily require Tables 2 to be revised as well. We are also interested in exploring alternate approaches for representing the information that is depicted in Figure 3.

After evaluating individual modeling languages for satisfying the requirements from our catalog, our next step will be to address their shortcomings. We will do this by developing a conceptual modeling framework that extends and combines extant notations and techniques. To verify this framework, our goal will be to share it with management practitioners and industry specialists. Additionally, our intention is to validate this framework in the field by collaborating with industry partners. This framework will allow the modeling of opportunities and alternatives for strategic coopetition in a structured and systematic manner. As a result, it is our expectation that, this framework will advance the state-of-the-art for the practice of EM.

Fig. 1 .

 1 Fig. 1. i* SR diagram of competition from typical resource conflicts among enterprises.

Fig. 2 .

 2 Fig. 2. i* SR diagram of competition depicting abstract resource conflict among enterprises.

State 3 :

 3 Knowledge exchange breakdown when one-sided opportunism detected Scenario 1: Knowledge sharing based on bilateral goodwill Scenario 2: Knowledge expropriation with undetected one-sided opportunism

Fig. 3 .

 3 Fig. 3. i* Strategic Rationale diagrams of inter-partner learning and knowledge sharing between enterprises.

Value Network Analysis     Game Tree      Payoff Table     Change Matrix     Tab. 2. Preliminary

  assessment of modeling support for requirements from Table

	Technique	A1	A2	A3	C1	C2	C3	I1	I2	I3	T1	T2	T3	R1	R2	R3
	NFR work	Frame-	   
	i* Rationale Strategic	        
	KAOS		      
	e3Value		      
	Business Model Canvas	   


Fredrik Linander
email: fredrik.linander@oru.se

Kai Wistrand
email: kai.wistrand@oru.se

Fredrik Karlsson
email: fredrik.karlsson@oru.se

Measuring and Visualising Projects' Collective Method Rationale

Keywords: Method rationale, Collective method rationale, Modelling rationale

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Introduction

Organisations choose to apply engineering methods for many reasons. These methods provide guidance through complex scenarios and tasks. Methods can be regarded as theories about actions to perform in order to reach given goals. This implies that they have an inherent conception of a desired target state. Subsequently, there are relations between this target state and the proposed actions [START_REF] Ågerfalk | Modelling the rationale of methods[END_REF]. Ultimately, methods can be viewed as reason based statements regarding target states, and as such they represent rationality [START_REF] Hirschheim | Exploring the intellectual structures of information systems development: a social action theoretic analysis[END_REF]. The concept of method rationale has been suggested as a way of describing the underlying arguments for a method's appearance [e.g. [START_REF] Rossi | Method Rationale in Method Engineering[END_REF][START_REF] Ågerfalk | Systems Development Method Rationale: A Conceptual Framework for Analysis[END_REF].

The concept intends to capture the relations between a method, or parts thereof, and the goal that this method (part) aims to fulfil. A potential method user has goals and chooses between method parts that can help reach his/hers own goals. A wise choice of method parts would of course be parts that have goals overlapping those of the method user, i.e. to achieve rationality resonance [START_REF] Stolterman | The Paradox of Information Systems Methods --Public and Private Rationality[END_REF].

As methods usually are put to use in groups, this raises the question about how to study the phenomenon of method rationale on an aggregated project team level. Most of the studies on method rationale have focused how the concept can be used as a facilitator for planning a project based on individual rationality resonance [e.g. [START_REF] Karlsson | Towards structured flexibility in information systems development: devising a method for method configuration[END_REF][START_REF] Rossi | Managing Evolutionary Method Engineering by Method Rationale[END_REF][START_REF] Ralyté | Towards a Generic Model for Situational Method Engineering[END_REF]]. An exception is Wistrand [START_REF] Wistrand | Method Rationale Revealed -Communication of Knowledge in Systems Development Methods[END_REF] and Karlsson [START_REF] Karlsson | Longitudinal use of method rationale in method configuration: an exploratory study[END_REF], they have aggregated individual rationality resonance into a collective concept. Still, both of them build on the individual preferences towards the selection of certain method parts. Moreover, there are few studies that have focused on method rationale in retrospection, i.e. studying what kind of method rationale a project has emphasized when it was carried out.

Therefore in this paper we pose the following research question: how can we measure and visualise method rationale on a project level? For this purpose we introduce the concept of "collective method rationale", complemented with newly developed metrics operationalizing this concept, and a computerized tool where the metrics are implemented as part of a process modelling approach.

Existing Research on Method Rationale

Several scholars [e.g. 11, 12, 13] have concluded that methods are based on the rationale of the method engineer, which has provided guidance through the method design. Hence, each engineering method is founded in a goal and value system [START_REF] Ågerfalk | Modelling the rationale of methods[END_REF]. Fitzgerald et al. [START_REF] Fitzgerald | Information Systems Development -Methods in Action[END_REF] have suggested that methods are adapted when applied, which is in line with Argyris' and Schön's [START_REF] Argyris | Organizational learning II. Theory, method, and practice[END_REF] theory on organizational learning. Argyris and Schön [START_REF] Argyris | Organizational learning II. Theory, method, and practice[END_REF] have highlighted that organisations' explicit action strategies, such as prescribed engineering methods, are enacted and realised through the actions taken by the individual practitioners. In other words, it has been shown that action strategies are adapted to the current situation based on the situational and local character of knowing, where the project member's rationale come into play. Argyris and Schön [START_REF] Argyris | Organizational learning II. Theory, method, and practice[END_REF] have distinguished between "espoused theory" -an ideal established by the organisation "to explain or justify a given pattern of activity" -and "theory-in-use", representing "the performance of that pattern of activity".

In the quest for situational methods, both Ågerfalk [START_REF] Ågerfalk | Towards Better Understanding of Agile Values in Global Software Development[END_REF] and Wistrand [START_REF] Wistrand | Method Rationale Revealed -Communication of Knowledge in Systems Development Methods[END_REF] have stressed the importance that the rationale of project members and the prescribed method need to match. Both scholars draw on the concept of rationality resonance [START_REF] Stolterman | The Paradox of Information Systems Methods --Public and Private Rationality[END_REF]; rationality resonance occurs when the (private) rationale of the project member and the (public) rationale of the method match and the method is perceived as support.

Most of the above-mentioned research takes an individual approach to 'theory-inuse', i.e. situational methods, and method rationale. They either focus on rationality resonance between the individual project member and the chosen method [e.g. [START_REF] Stolterman | The Paradox of Information Systems Methods --Public and Private Rationality[END_REF][START_REF] Ågerfalk | Towards Better Understanding of Agile Values in Global Software Development[END_REF], or how the private rationale of a project member can be used to transform a prescribed method into a situational one [e.g. [START_REF] Karlsson | Towards structured flexibility in information systems development: devising a method for method configuration[END_REF][START_REF] Karlsson | Method Configuration: Adapting to Situational Characteristics while Creating Reusable Assets[END_REF]. Few studies have focused on the rationale that exists on a project level. Wistrand [START_REF] Wistrand | Method Rationale Revealed -Communication of Knowledge in Systems Development Methods[END_REF] is a notable exception; he introduced the concept of collective rationality resonance in a group. However, he did not discuss how to collect data to fill and visualise this concept. Karlsson [START_REF] Karlsson | Longitudinal use of method rationale in method configuration: an exploratory study[END_REF] proposed a data collection and analysis technique for collective rationality resonance based on selfreports coming from project members. But, this approach still departures in an individual approach towards method rationale whilst focusing on resonance.

Conceptual Framework

Given the aim of this paper and the state-of-the-art in existing research there is a need for additional conceptual work in order to measure the collective method rationale of a project. Fig. 1 presents the main concepts of the existing research together with our additional concepts for addressing rationale as a project group phenomenon. The figure is illustrated using a UML Class diagram. The conceptual framework builds on the method component concept, which is in line with Wistrand [START_REF] Wistrand | Method Rationale Revealed -Communication of Knowledge in Systems Development Methods[END_REF] and Karlsson [START_REF] Karlsson | Longitudinal use of method rationale in method configuration: an exploratory study[END_REF]. Method components as espoused theories offer possible achievable goals that are anchored in values. Project members have selected method components as a means to receive guidance concerning project tasks. The goals of the selected method components constitute the collective method rationale, either as a plan (espoused theory) or as executed (theory-in-use).

In order to measure collective method rationale we need to discuss the internal structure of the method component concept. A method component is a self-contained part of an engineering method, and consists of five types of method elements that all are related to goals: artefact, actions, actor role, concept, and notation [START_REF] Karlsson | Combining method engineering with activity theory: theoretical grounding of the method component concept[END_REF]. Action expresses the activities that need to be done to transform input artefacts into defined output artefact. Actor role expresses who should carry out or participate in a specific action. Concepts guide the actor towards certain aspects of the engineering task. Finally, the method element notation expresses how the results should be represented when documented.

When examining the method elements, actions are of particular interest. Project members propel projects forward through actions that consume time. Time is often considered one of the most important volume metrics of a project, and shows the emphasis put on specific parts of a project. Time is also part of official project artefacts such as project plans and time report sheets. Hence, we have added time as a characteristic to the action method element. Considering that an engineering method contains a number of selected method components we can define the relative collective method rationale towards a specific goal, X, as follows.

!"#$ !"#$% !"# !"#!!" !"#$"%&%' ! !"#$%& !" !"#!!" !"#$"%&%'( !"#$%!&'$ !"#$%&& !"#$ ! !!! !"#$ !"#$% !"# !"#!!" !"#$"%&%' ! !"#$%& !" !"#!!" !"#$"%&%'( !" !!! !"#$"!!%$"! !"#!!" !!! (1)
and

1 = 𝑅𝑒𝑙𝑎𝑡𝑖𝑣𝑒 𝑐𝑜𝑙𝑙𝑒𝑐𝑡𝑖𝑣𝑒 𝑚𝑒𝑡ℎ𝑜𝑑 𝑟𝑎𝑡𝑖𝑜𝑛𝑎𝑙𝑒 𝑓𝑜𝑟 𝑜𝑣𝑒𝑟𝑎𝑙𝑙 𝑔𝑜𝑎𝑙 𝑚 !"#$%& !" !"#$%&& !"#$% !!! (2)
This definition of measuring relative collective method rationale introduces a restriction on the method component's conceptual model. In the original concept [START_REF] Karlsson | Combining method engineering with activity theory: theoretical grounding of the method component concept[END_REF], actions can be performed with multiple goals in mind. However, in these metrics a method component only have one overall goal.

Research Method

The research approach applied in this study is characterised as action research [START_REF] Baskerville | Diversity in information systems action research methods[END_REF], carried out as a collaboration project between academia and industry. The parties involved are companies from defence and motorsport industry. The approach follows the traditional "canonical" action research process-model with iterations through the five stages of diagnosing, action planning, action taking, evaluating and specifying learning [START_REF] Susman | An Assessment of the Scientific Merits of Action Research[END_REF]. The paper covers the second of four planned iterations to develop a method and a computerized tool for benchmarking project and organisations with regard to the rationale behind chosen engineering methods. The first iteration has been reported on in Karlsson et al. [START_REF] Karlsson | A conceptual framework for time distortion analysis in method components[END_REF]. Below we discuss each of the five stages of the second iteration.

Diagnosing

During the diagnosing stage, we analysed a subset of the overall industry and research problem. In addition, the identified state-of-the-art research was analysed together with our industrial partners during a series of workshops. Based on the results we formulated an aim for the second iteration: to develop a concept, a metric and a computerized tool to capture and visualize the collective method rationale employed in a product development project.

Action planning

During the action planning stage, we focused on conceptual work and elicitation of the requirements for the second version of the computerized tool. We introduced the concept of collective method rationale into the existing conceptual framework of method rationale. In addition, we operationalized this concept as a metric to be implemented in the computerized tool. The operationalization resulted in a number of requirements (user stories) concerning modifications and extensions of the tool. In parallel with implementing the computerized tool we searched for a suitable goal nomenclature to use during process modelling. Given the industry problem of comparing projects and organisations with regard to the rationale behind chosen engineering methods, we needed a nomenclature that could be used across projects as well as organisations. We chose to use the goal structure in the Capability Maturity Model Integration for Development (CMMI-Dev) v1.2 [START_REF]CMMI for Development[END_REF]. It contains an established set of generic goals for product and service development. These goals are structured in a hierarchical fashion; goals that can be found across projects and organisations.

Action taking

During this stage we made a first full-scale test of the modified tool and the newly developed metrics. Data from an implemented product development project at a motorsport partner were collected, modelled and analysed using the computerized tool. The project was chosen based on reasonable size and complexity, and availability of data and contact persons. The data collection took place at the premises of the motorsport partner at two separate occasions. Given the industry's overall benchmarking interest of actual practices, we chose to model the theory-in-use version of the method. This meant that we collected data about the enacted method. We used semi-structured interviews, project reports and log books to reconstruct the project. Our interview questions focused on executed method components and their parts, including goals, deliverables, start and finishing dates, main activities, consumed time and applied outsourcing strategies. The interviews were held with the project manager. In the case a method component targeted multiple overall goals, the project manager was asked to a), if possible, divide the method component into two or more components, or b) pin point the main overall goal that had consumed the most work effort during the method component's execution. Notes were taken during the interviews and the project manager reviewed the documentation in order to validate the data and to authorise that it could be used as part of the research project. These notes were used for reconstructing the method in the computerized tool. Finally, each of the 23 identified method components was traced to one of the 22 top-level goals in CMMI-Dev. This analysis was carried out together with the project manager.

Evaluation

During the evaluation stage we arranged a joint workshop to discuss the initial results. First, we presented the current version of the conceptual framework and the metrics used. Second, we presented how the chosen project had been modelled. Third, we presented the analytical results (see Fig. 2) and how to interpret the way collective method rationale is visualised. Finally, we conducted a feedback session where we discussed a) the usefulness of the analysis in relation to the industry problem, and b) problematic aspects during data collection and modelling.

Specify learning

During the specify learning stage we structured and assessed the results into lessons learned and change requests for the next iteration. Lessons learned contained advices on how to use the conceptual framework, the metrics, and the computerized tool.

Results -Empirical Example

Our chosen motorsport partner develops, designs, sells and leases cars for rally cross and extreme motorsport. The company also operates its own team internationally in several rally cross championships. The analysed motorsport project was a 13-months development project of a new car. The project was executed in a fifty-fifty work share division between our motorsport partner and a business partner. Our motorsport partner had the main responsibilities for the development and the final assembly of the cars. Marketing activities of the new car were integrated into the project and executed jointly with validation activities related to driver experiences resulting in signed car contracts prior closure of the development project.

Results from action taking -modelling and analysis

Fig. 2 illustrates the results of our analysis using the relative collective method rationale as a radar diagram. This enables us to create a visual profile of the project's employed rationale, where the relative collective method rationale of each analysed goal is plotted as a value between zero and one.

The radar diagram has seven axes, one for each goal we have identified. Approaching the goals in descending order, the figure shows that the motorsport project employed most of its collective method rationale related to the "technical solution"-goal. Technical solution according to CMMI-Dev means, "to design, develop, and implement solutions to requirements" [START_REF]CMMI for Development[END_REF]. Almost 43% of the efforts have been put into this particular goal. The "verification"-goal is the second most employed rationale in the project, accounting for approximately 17%. Verification means spending resources "to ensure that selected work products meet their specified requirements" [START_REF]CMMI for Development[END_REF]. The "validation"-goal, i.e. "to demonstrate that a product or product component fulfils its intended use when placed in its intended environment" [START_REF]CMMI for Development[END_REF], is the third most focused part of the collective method rationale. In the project it accounts for 15%. The goals "product integration" and "supplier agreement management", each account for approximately 8%. Product integration aims "to assemble the product from the product components, ensure that the product, as integrated, functions properly, and deliver the product" [START_REF]CMMI for Development[END_REF], and supplier agreement management means that the project has put effort into activities in order to "manage the acquisition of products from suppliers" [START_REF]CMMI for Development[END_REF]. Finally, the collective method rationale that has been employed the least in the project is "requirement development" and "project planning". They account for approximately 4% each. Requirement development aims "to produce and analyse customer, product, and product component requirements" [START_REF]CMMI for Development[END_REF] and project planning means "to establish and maintain plans that define project activities" [START_REF]CMMI for Development[END_REF].

Results from evaluation -workshop with practitioners and researchers

The evaluation was conducted as a half-day workshop. The practitioners concluded that the concept and its operationalization were straightforward and applicable. As an example, one practitioner said: "[T]he informative and straight forward approach gives it a high potential to become widely used in practice in our organisation". However, during the workshop challenges with low data resolution were discussed. The discussion centred on how the size of the method components could affect the collective method rationale profile. Coarse-grained method components give an imprecise profile, which might be sensitive to how the components were classified with regards to the overall goal. The project's resulting profile was perceived as easyto-grasp. The practitioners used words like "informative" and "simple to interpret". However, the participants discussed how the radar diagram would work when larger projects are modelled that include all 22 goals in CMMI-Dev. This is illustrated by one of the practitioners: "The analysed project has seven goals. A project with a lot of goals will most probably have a less interpretable profile than the analysed project".

Results from specified learning

Based on the workshop and the modelling activities two lessons learned were made. First, we must be able to handle a larger number of goals than only the seven identified in the pilot project, without cluttering the visual presentation. However, this is still only a potential problem, and modelling of additional projects will show if this must be addressed. We can conclude that we need to use the area in the radar diagram more efficiently, because some of the values get cluttered in the centre of the diagram. Second, there is a need for more fine-grained method components, in order to improve the analytical precision. This does not call for design changes of the computerized tool. Instead, we need to adapt the way data is collected and which kind of data we use.

Conclusions

The concept of method rationale has in previous research mostly focused on an individual's preferences towards engineering methods and how project members choose among different method parts based on these preferences. In order to understand how method rationale can be captured on an aggregated level, such as in project teams, we have proposed the concept of collective method rationale. In this paper we have shown how a modified version of the method rationale theory can be applied to capture collective method rationale of a project. We have presented metrics for capturing relative collective method rationale and used it to analyse a project at a motorsport company. We have shown the collective method rationale using a radar diagram in a computerised tool. Based on the feedback from practitioners this seems to be fruitful way to convey the metrics and the analysis.

Fig. 1 .

 1 Fig. 1. Modified method rationale theory

Fig. 2 .

 2 Fig. 2. The motorsport project's collective method rationality profile


Z Bern

M Czakon

D A Kosower

R Roiban

V A Smirnov

Two-Loop Iteration of Five-Point N = 4 Super-Yang-Mills Amplitudes

Keywords: numbers: 11.15.Bt, 11.25.Db, 11.25.Tq, 11.55.Bq, 12.38.Bx

. This confirmation of the iteration relation provides further evidence suggesting that N = 4 gauge theory is solvable.

In his seminal work dating to the infancy of asymptotic freedom, 't Hooft [2] gave hope of solving quantum chromodynamics (QCD) in the so-called planar limit, when the number of colors is taken to be large. While this hope for ordinary QCD has not yet been realized, the Maldacena conjecture [3] has brought it closer for four-dimensional maximally-supersymmetric Yang-Mills theory (MSYM), by proposing a duality relating it at strong coupling to type IIB string theory in fivedimensional anti-de Sitter (AdS) space at weak coupling. Heuristically, this suggests that the leading-color terms of the perturbative series should be resummable, and along with possible non-perturbative contributions should yield relatively simple results matching those of weakly-coupled gravity.

While the Maldacena conjecture does not address directly the scattering amplitudes of on-shell (massless) quanta, previous work by Anastasiou, Dixon, and two of the authors [4] shows that the basic intuition holds. That paper presented a conjecture for an all-orders iterative structure in dimensionally-regulated scattering amplitudes of MSYM. Dixon and two of the authors [5] fleshed out this structure for maximally helicity-violating (MHV) amplitudes. Witten's proposal [6] of a weakweak duality between MSYM scattering amplitudes and a twistor string theory provides further indications of new structures underlying the simplicity of both MSYM and string theory in AdS space at strong world sheet coupling.

Ref. [4] verified the iteration conjecture explicitly for the two-loop four-point function (a second verification was given in ref. [7]), and ref. [5] did so for the three-loop four-point amplitude. Furthermore, the computation of the two-loop splitting amplitude in ref. [4], its own iteration relation, and consideration of limits as momenta become collinear shows that were the conjecture to hold for the five-point two-loop amplitude, it would almost certainly hold for all MHV two-loop amplitudes. The step from four-point to five-point amplitudes is non-trivial, because at five points, functions that are not detectable in the collinear limits appear [8].

An important step in closing this gap has recently been taken by Cachazo, Spradlin and Volovich [9]. They confirmed the conjecture for the terms in the two-loop fivepoint amplitude even under parity, using an earlier guess for the integrand [10]. In this Letter, we will complete the task. We compute the integrand using the unitarity method [8,11,12], confirming the form of ref. [10] for the parity-even terms, and providing the correct form for the parity-odd ones. We then integrate numerically at random kinematic points, using the MB integration package [1], to show that the conjecture holds for both parityeven and -odd terms. We also remark that the 'additional iterative structure' of ref. [9] follows from the one of ref. [4] by setting odd parity terms to zero on both sides of the iteration formula.

The unitarity method [8,11,13] has proven powerful for computing scattering amplitudes of phenomenological and theoretical interest out of reach using conventional Feynman diagrammatic methods. Improvements [14] have followed from use of complex momenta [6].

Perturbative amplitudes in four-dimensional massless gauge theories contain infrared singularities. These are well understood [15] in MSYM and are a subset of the ones appearing in QCD. As in perturbative QCD, the Smatrix under discussion here is not the textbook one for the 'true' asymptotic states of the four-dimensional theory, but rather for states with definite parton number. As in QCD, a summation over degenerate states would be required to obtain finite results for scattering [16]. We regulate these divergences in a supersymmetry-preserving fashion using the four-dimensional helicity (FDH) [17] variant of dimensional regularization, with D = 4 -2 . (This scheme is a close relative of Siegel's dimensional reduction [18].)

(b) (a) (c)
FIG. 1: The three-and two-particle cuts of the five-point amplitude.

We write the leading-color contributions to the L-loop SU (N c ) gauge-theory n-point amplitudes as,

A (L) n = g n-2 2e -γ g 2 N c (4π) 2- L ρ Tr(T a ρ(1) . . . T a ρ(n) ) × A (L) n (ρ(1), ρ(2), . . . , ρ(n)) , (1)
where γ is Euler's constant, the sum is over non-cyclic permutations of the external legs. We have suppressed the momenta and helicities k i and λ i , leaving only the index i as a label. This decomposition holds for all particles in the gauge super-multiplet as all are in the adjoint representation. We will find it convenient to scale out the tree amplitude, defining

M (L) n ( ) ≡ A (L) n /A (0)
n . At two loops the iteration conjecture expresses n-point amplitudes entirely in terms of one-loop amplitudes and a set of constants [13]. For MHV amplitudes up to O( 0 ),

M (2) n ( ) = 1 2 M (1) n ( ) 2 + f (2) ( ) M (1) n (2 ) + C (2) , (2)
where

f (2) ( ) = -(ζ 2 +ζ 3 +ζ 4 2 +• • •), and
C (2) = -ζ 2 2 /2.
Ref. [5] provides analogous equations for higher-loop MHV amplitudes. Subtracting out the known infrared divergences [15] provides an all-loop form for the finite remainder, expressed in terms of the one-loop finite re-mainder and two constants, one of which is an anomalous dimension. A conjecture for the required anomalous dimension was very recently presented [19], based on a proposed all-loop Bethe Ansatz [20]. It is rather interesting that this anomalous dimension corresponds to one of the terms appearing in the QCD one [21].

To check whether the iteration relation holds in the critical five-point case, we have evaluated a set of cuts sufficient to determine the five-gluon integrand completely. These include the three-particle cuts depicted in fig. 1a as well as the contributions to the two particle cuts from fig. 1b. The three-particle cuts on their own determine all integral functions, except for those which are simple products of one-loop integrals. The two-particle cuts rule out the latter (double cuts suffice).

The use of a dimensional regulator involves an analytic continuation of the loop momenta to D dimensions. At one loop, the discrepancy between treating loop momenta in four or D dimensions does not modify the amplitudes of a supersymmetric gauge theory through O( 0 ). No such proof exists for higher loops. Thus, to ensure that no contributions are dropped, we compute the unitarity cuts in D dimensions [22]. This does complicate the analysis, because standard helicity states can no longer be used as the intermediate states. We can avoid some of the additional complexity by considering instead the D = 10, N = 1 super-Yang-Mills theory. When compactified on a torus to D = 4 -2 dimensions this is equivalent to dimensionally-regulated MSYM in the FDH scheme.

After reducing all tensor integrals we obtain an expression for the amplitude in terms of the integrals shown in fig. 2. The color-ordered amplitude with fourdimensional external momenta is given by a sum over the cyclic permutations of those momenta,

M (2) 5 ( ) = 1 8 cyclic s 2 12 s 23 I (2)
(a) ( ) + s 2 12 s 15 I

(b) ( ) + s 12 s 34 s 45 I

(c) ( ) + R 2 I (2) (d) ( ) -2 s 12 I (2)
(e) ( ) +

s 12 s 34 s 45 δ -++ s 23 I (2) (b) ( ) - δ -+- s 51 I (2) (a) ( ) + δ +-+ s 23 s 51 I (2) (c) ( ) . (3)
Here,

s ij = (k i + k j ) 2 ,
ε 1234 = 4i ε µνρσ k µ 1 k ν 2 k ρ 3 k σ 4 = tr[γ 5 / k 1 / k 2 / k 3 / k 4 ] , (4)
and G 1234 = det(s ij ) , (i, j = 1, . . . , 4). (In δ, a, b, c = ±1.) The terms lacking a factor of ε 1234 are even under parity, while those with such a factor are odd. The even terms match the guess originally given in ref. [10], but the odd terms differ (the odd terms in ref. [10] do match the four-dimensional double two-particle cuts).

Because of the 1/ 2 infrared singularity in one-loop amplitudes, and because these appear squared in the iteration relation, we need expressions valid through O( 2 ). A representation of the one-loop five-point amplitude, extending ref. [8] to all orders in , may be found in ref. [23], FIG. 2: The two-loop integrals appearing in the five-point amplitude, with all external momenta flowing outwards. The normalization is as given in eq. ( 8), and the numerical labels on the internal propagators in (c) specify the arbitrary powers ai. The prefactor in (c) is understood to be inserted in the numerator with power -a9; in eq. ( 3), -a9 = 1. FIG. 3: The one-loop integrals required to all orders in for the one-loop five-point amplitude. The normalization is as given in eq. ( 7), and the numerical labels on the internal propagators in (b) specify the arbitrary powers ai.

M (1) ( ) = - 1 4 cyclic s 12 s 23 I (1) (a) ( )-2 ε 1234 I (1)6-2 (b) ( ) , (5)
in terms of the integrals of fig. 3. As indicated by the superscript, the second integral (fig. 3b) is to be evaluated in 6 -2 dimensions. In D = 6 it is completely finite, but because it appears multiplied by an infrared-singular integral in eq. ( 2) we need its value through O( ).

To obtain Laurent expansions in for our integrals we use the Mellin-Barnes (MB) technique, successfully applied in numerous calculations (see, e.g., refs. [5,[24][25][26][27] and chap. 4 of ref. [START_REF] Smirnov | Evaluating Feynman integrals[END_REF]). It relies on the identity

1 (X + Y ) λ = β+i∞ β-i∞ Y z X λ+z Γ(λ + z)Γ(-z) Γ(λ) dz 2πi , (6)
where -Re λ < β < 0. This basically replaces a sum over terms raised to some power with a product of factors.

The box function in fig. 3a was given to all orders in in terms of a hypergeometric function in ref. [START_REF] Bern | [END_REF]. Here we need its value through O( 2). Evaluating the pentagon in fig. 3b with arbitrary powers of propagators also allows a parallel evaluation of this integral to the required order.

The derivation of a fourfold MB representation for the one-loop pentagon diagram is straightforward, after Feynman parameterizing,

P (1) (a 1 , . . . , a 5 ; s 12 , . . . , s 51 ; ) = -i e γ (4π) D/2 d D (2π) D 1 [ 2 ] a1 [( + k 1 ) 2 ] a2 [( + K 15 ) 2 ] a3 [( -K 23 ) 2 ] a4 [( -k 2 ) 2 ] a5 = e γ (-1) A Γ(4 -A -2 ) 1 5 j=1 Γ(a j ) +i∞ -i∞ 4 j=1 Γ(-z j ) dz j 2πi (-s 45 ) z1 (-s 34 ) z2 (-s 23 ) z3 (-s 12 ) z4 (-s 15 ) A+ -2+z1234 Γ(a 2 + z 14 ) × Γ(A + -2 + z 1234 )Γ(2 --a 2345 -z 124 )Γ(2 --a 1245 -z 134 )Γ(a 4 + z 13 )Γ(a 5 + z 24 ) (7)
where

K ij = k i + k j , a 2345 = a 2 + a 3 + a 4 + a 5 , A = a i , z 124 = z 1 + z 2 + z 4 , etc.
We have allowed for arbitrary powers of propagators so that we can obtain all one-loop integrals. Taking a 5 → 0, with other a i = 1, gives the box integral I , corresponding to fig. 3b.

The various two-loop pentabox integrals have a sevenfold MB representation obtained by inserting a threefold MB representation for a two-mass double box into eq. ( 7),

P (2) ({a i }; {s ij }; ) = e 2γ (-
× Γ(2 -a 124z 57 )Γ(2 -a 234z 67 )Γ(a 1234 + -2 + z 567 )Γ(2 -a 5789z 134 + z 567 ) .

The limit a 6 → 0 or a 7 → 0 with a 9 = 0 and the other a i = 1 yields the double box with one massive leg (fig. 2a andb) in agreement with ref. [27,30]. Moreover, P (2) (1, . . . , 1, -1), P (2) (1, . . . , 1, 0) and P (2) (1, . . . 1, 0, 0) yield the integrals in fig. 2c, fig. 2e and fig. 2d, respectively. An essential step in the use of the MB technique is the resolution of singularities in or zeros that appear as a i → 0. There are two strategies for doing this [24,25]. Quite recently, the second strategy was formulated algorithmically [1,31] and implemented in the MB package [1]. It produces code that allows the integrals to be evaluated numerically to reasonably high accuracy.

The even terms in eq. ( 3) were recently evaluated in ref. [9] using the MB package [1] along with the guess of ref. [10]. Those authors observed that an iterative structure holds for the parity-even terms alone. We may observe that this structure is not independent of the complete iteration formula eq. ( 2): use the results for the oneloop five-point amplitude in eq. ( 5), set the odd terms to zero and use the fact that the one-loop MHV amplitudes have even parity through O( 0 ). At higher loops, we do not expect a clean separation between 'even' and 'odd' terms, as non-vanishing terms of the form ε 2 1234 will arise. These are even under parity.

We have evaluated all the two-loop integrals in fig. 2 through O( 0 ) and the one-loop integrals in fig. 3 through O( 2 ) using the representations in eqs. (7) and (8). We have checked to a numerical accuracy of five significant digits at three independent kinematic points that the iteration formula (2) is indeed correct for the complete amplitude. This is a crucial check on the conjecture because the parity-odd terms in the five-point amplitude are precisely the ones which are not constrained by collinear factorization onto four-point amplitudes.

The calculation presented here makes a nontrivial addition to the existing body of evidence for the iteration conjecture [4,5]. The conjecture itself gives us good reasons to believe that MSYM is solvable. Within the context of the planar perturbative expansion, this would imply the resummability of the series. Parallel developments in uncovering the integrable structure of the theory (see e.g. refs. [20,32]) also lend credence to this belief.

  in fig. 3a. Setting all a i = 1 and shifting all terms except the e γ prefactor by → -1 yields the D = 6 -2 pentagon, I (1)6-2 (b)

  R = ε 1234 s 12 s 23 s 34 s 45 s 51 /G 1234 , δ abc = s 12 s 51 + a s 12 s 23 + b s 23 s 34s 51 s 45 + c s 34 s 45 ,

  + z 13 )Γ(a 5 + z 14z 5 )Γ(a 8 + z 24z 6 ) Γ(a 5z 5 )Γ(a 8z 6 )Γ(a 9z 7 ) × Γ(2 -a 5678z 124 + z 56 )Γ(a 4 + z 7 )Γ(a 2 + z 567 )Γ(a 56789 + -2 + z 1234z 567 ) Γ(4 -2a 56789 + z 567 )

		1) A j=1,2,3,4,6,7 Γ(a j )Γ(4 -a 1234 -2 )	+i∞ -i∞	7 j=1	Γ(-z j )	dz j 2πi
	×	(-s 15 ) a56789 + -2+z1234-z567 (-s 45 ) z1 (-s 12 ) 2-a1234-+z4-z567 (-s 23 ) z3 (-s 34 ) z2	Γ(a 7

We thank Lance Dixon for many helpful discussions, and participation in early stages of the collaboration. This research was supported by the US DOE under contracts DE-FG03-91ER40662, by the Direction des Sciences de la Matière of the Commissariat à l'Energie Atomique of France, and by the Russian Foundation for Basic Research through grant 05-02-17645. The work of MC was supported by the Sofja Kovalevskaja Award of the Alexander von Humboldt Foundation sponsored by the German Federal Ministry of Education and Research. DAK and VAS also acknowledge the support of the ECO-NET program of the Egide under grant 12516NC.

fr/articles/T06/032/ UCLA/06/TEP/09 Saclay-SPhT-T06/032 WUE-ITP-2006-003


Pierre-Yves Oudeyer

What do we learn about development from baby robots?

Keywords: Infant development, developmental robotics, complex systems, self-organization, pattern formation, embodiment, biped walking, curiosity, learning

Understanding infant development is one of the great scientific challenges of contemporary science. In addressing this challenge, robots have proven useful as they allow experimenters to model the developing brain and body and understand the processes by which new patterns emerge in sensorimotor, cognitive, and social domains. Robotics also complements traditional experimental methods in psychology and neuroscience, where only a few variables can be studied at the same time. Moreover, work with robots has enabled researchers to systematically explore the role of the body in shaping the development of skill. All told, this work has shed new light on development as a complex dynamical system.

INTRODUCTION

To understand the world around them, human beings fabricate and experiment. Children endlessly build, destroy, and manipulate to make sense of objects, forces, and people. To understand boats and water, for example, they throw wooden sticks into rivers. Jean Piaget, one of the pioneers of developmental psychology, extensively studied this central role of action in infant learning and discovery [START_REF] Piaget | The Origins of Intelligence in Children[END_REF] .

Scientists do the same thing: To understand ocean waves, we build giant aquariums. To understand cells, we break them down to their component parts. To understand the formation of spiral galaxies, we manipulate them in computer simulations. Constructing artifacts helps us construct knowledge.

But what if we want to understand ourselves? How can we understand the mechanisms of human learning, emotions, and curiosity? Here, the physical fabrication of artifacts can also be useful. Researchers can actually build baby robots with mechanisms that model aspects of the infant brain and body, and then alter these models systematically (see Figure 1). We can compare the behavior we observe with the mechanisms inside. Indeed, robots are now becoming an essential tool to explore the complexity of development, a tool that allows scientists to grasp the complicated dynamics of a child's mind and behavior.

EXPLORING COMPLEX SYSTEMS

Modern developmental science has now invalidated the old divide between nature and nurture. We now know that genes are not a static program that unfolds independently of the environment. We also understand that learning in the real world can only work if there are appropriate constraints during development [START_REF] Gottlieb | Experiential Canalization of Behavioral-Development -Results[END_REF][START_REF] Lickliter | Rethinking Epigenesis and Evolution in Light of Developmental Science[END_REF] . Finally, we know that many behavioral and cognitive patterns cannot be explained by reducing them to single genes, organs, or isolated features of the environment: they result from the dynamic interaction among cells, organs, learning mechanisms, and the physical and social properties of the environment at multiple spatiotemporal scales. Development is a complex dynamical system, characterized by spontaneous self-organization or "emergent patterns" 4 at multiple scales of time and space (Spencer et al., 2011).

The concepts of complex systems and self-organization revolutionized physics in the 20 th century. They characterize phenomena as diverse as the formation of ice crystals, sand dunes, water bubbles, climatic structures, and galaxies. A key to these scientific advances was the use of mathematics and computer simulations. Indeed, it is hard to imagine how we could understand the dynamics of ice crystals or the formation of clouds without mathematics and computer simulations. At the end of the 20 th century, biologists began to use these concepts, for example, to understand the formation of termite nests (Ball, 2001 5 , see Figure 2). They used computer simulations to show how local interactions among thousands of little termites, with no plan of the global structure, could self-organize sophisticated and functional large-scale architectures. Other mathematical and computational models were similarly used to study the self-organization of stripes and spots on the skin of animals, the spiral patterns of horns and mollusk shells, the dynamics of predator-prey populations, and of the dynamics of a heart beat [START_REF] Ball | The Self-Made Tapestry: Pattern Formation in Nature[END_REF] .

Child development also involves the interaction of many components, but in a way that is probably orders of magnitude more complicated than crystal formation or termite nest construction. Hence, to complement the (tremendously useful) verbal conceptual tools of psychology and biology, researchers have begun building machines that model pattern formation in development. Such efforts can play a key role in 21 st century developmental science.

Building machines that learn and develop like infants is actually not a new idea. Alan Turing, who helped invent the first computers in the 1940s, already had the intuition that machines could be useful for understanding psychological processes: "Instead of trying to produce a programme to simulate the adult mind, why not rather try to produce one which simulates the child's? If this were then subjected to an appropriate course of education one would obtain the adult brain. Presumably the child brain is something like a notebook as one buys it from the stationer's. Rather little mechanism, and lots of blank sheets." [START_REF] Turing | Computing machinery and intelligence[END_REF] For several reasons, Turing's vision was not transformed into a concrete scientific program until the very end of the 20 th century. First, the 1950s saw the rise of cognitivism and artificial intelligence, views that promoted the (unsuccessful) idea that intelligence could be seen as an abstract symbol manipulation system that could be handcrafted directly in its adult form. Second, Turing missed two important elements: a) Learning from a blank slate-a tabula rasa-could not work in real organisms facing the complex flow of information and action in the world. Rather, development needs constraints; and b) Turing missed the role of the body: behavior and cognition arise in a physical substrate, and this physical substrate strongly influences development [START_REF] Pfeifer | How the Body Shapes the Way We Think[END_REF] . The central role of the body in psychological development is the reason why robots, and not simply abstract computer simulations, will play such a key role in future progress (Cangelosi and Schlesinger, 2015).

THE ROLE OF THE BODY IN BIPEDAL WALKING

Let us look at some examples, beginning with the behavior of bipedal walking. While this is a very familiar skill, we are nevertheless far from understanding how we walk with two legs, and how infants learn to do this. What is walking? What does it mean to acquire the capability to walk on two legs? Walking requires the real-time coordination of many body parts. Our bones and muscles are like the musicians of a symphonic orchestra: each must move (and be still) at exactly the right moment. And it is the juxtaposition and integration of all these movements that builds the symphony of the whole body walking forward with elegance and robustness.

Is there a musical score that plans and coordinates walking? Is there a conductor driving the movement? In technical terms, is walking equivalent to calculating? Does the brain, every few milliseconds, observe the current state of the body and environment and compute the right muscular activations to maintain balance and move forward with minimal energy consumption?

Viewing walking as pure computation is the approach that has long been taken by specialists who study human walking. Viewed in this context, understanding the development of walking requires understanding how the child could develop the capability to achieve all these real-time computations and make predictions about the dynamics of its body. Some roboticists interested in walking bipedal robots also tried this approach. Yet, even though they sometimes produced beautiful performances [START_REF] Hirose | Honda humanoid robots development[END_REF] , this approach has so far led to robots that fell too easily and looked unnatural.

Perhaps, then, walking is much more than calculation. Twenty years ago, a roboticist named Tad McGeer conducted an experiment that changed our understanding of biped walking in humans and machines. He built a pair of mechanical legs (see Figure 3 and video https://www.youtube.com/watch?v=WOPED7I5Lac) without a motor and without a computer (thus without the possibility to make calculations), and reproduced the geometry of human legs [START_REF] Mcgeer | Passive walking with knees[END_REF] . Then, he threw the robot on a mild slope and-remarkably-the robot walked: automatically, through the physical interaction among the various mechanical parts and gravity, the two legs generated a gait that looked surprisingly similar to a human gait The robot even responded robustly to disturbances. Other laboratories replicated the experiment many times (e.g. see video https://www.youtube.com/watch?v=rhu2xNIpgDE) and showed that this bipedal walking would persist on a treadmill [START_REF] Collins | Efficient bipedal robots based on passivedynamic walkers[END_REF] . The coordination of the set of mechanical parts of this robot, interacting only locally through their physical contacts, is an example of self-organization: there is no predefined plan for coordination and no conductor synchronizing every part of the score. Walking is a dynamic emergent pattern where the physics of the body and environment plays a fundamental role in interaction with the (learning) neural system, with each component part of the system structuring and constraining the others, as conceptually investigated by the dynamic systems approach to development (Thelen and Smith, 1996; Adolph and Robinson, 2015). These very clever experiments show how robots can be used to disentangle the roles of the body and the nervous system in walking. At the same time, they articulate concretely concepts that enlighten our understanding of human development. Here, we observe the self-organization of a pattern (bipedal walking) that is neither innate (there are no genes and no program) nor learned (there is no learning taking place). Therefore, this simple robot concretely demonstrates how the divide between innateness and learning can be meaningless. Structure can appear spontaneously through complex biophysical interactions. And such structure can then be leveraged for learning and development. This robotic approach also helps reinforce and 'ground' the hypothesis that learning how to walk can be facilitated by reusing and tuning a movement structure already embedded in the dynamics of the body (Adolph and Robinson, 2015).

SELF-ORGANIZATION OF CURIOSITY-DRIVEN DEVELOPMENTAL PROCESSES

Let's now examine a second robot example that shows how local short term mechanisms (here curiosity-driven attention and exploration) can generate macro-organized developmental structure on the long term in child development (here sequences of behavioural and cognitive phases of increasing complexity). Human children learn many things, often in a progressive way with specific timing and ordering. For example, before they learn to walk on their two legs, infants typically first explore how to control their neck, then to roll on their belly, then to sit, to stand up, and walk with their hands on the walls. Why and how do they follow this particular progression? Although most infants follow a similar ordering, some children do not. Why do some children follow quite different developmental paths? How can we explain the apparent universal tendencies on one hand and the individual variability on the other? Is universality the result of a "program"? And when we observe a different developmental path, does this imply that something in the "program" is broken?

The social environment plays a big role in guiding developmental process, and has been the object of study of robot modeling work focusing on the roles of imitation [START_REF] Breazeal | Robots that imitate humans[END_REF][START_REF] Demiris | The robot in the crib: A developmental analysis of imitation skills in infants and robots[END_REF][START_REF] Nehaniv | Imitation and Social Learning in Robots, Humans and Animals: Behavioural, Social and Communicative Dimensions[END_REF] , joint attention [START_REF] Nagai | Learning for joint attention helped by functional development[END_REF] , language [START_REF] Cangelosi | Integration of Action and Language Knowledge: A Roadmap for Developmental Robotics[END_REF][START_REF] Steels | Experiments in Cultural Language Evolution[END_REF] , and interactive alignment of tutor and learner [START_REF] Vollmer | Robots Show Us How to Teach Them: Feedback from Robots Shapes Tutoring Behavior during Action Learning[END_REF] . But there is another fundamental force that drives all of us: curiosity, which pushes us to discover, to create, to invent.

Research in psychology and neuroscience has shown how our brains have an intrinsic motivation to explore novel activities or stimuli for the sake of learning and practicing [START_REF] Loewenstein | The Psychology of Curiosity -a Review and Reinterpretation[END_REF] . Yet we still understand little about curiosity-driven attentional and motivational mechanisms, and how it impacts learning and development in the long term. Neuroscientists are only beginning to identify brain circuits involved in spontaneous exploratory behaviors [START_REF] Gottlieb | Information-seeking, curiosity, and attention: computational and neural mechanisms[END_REF] .

Several research teams have proposed to advance our understanding of curiosity and its impact on development by fabricating robots that learn, discover, and generate their own goals with formal models of curiosity-driven learning [START_REF] Gottlieb | Information-seeking, curiosity, and attention: computational and neural mechanisms[END_REF][START_REF] Baldassare | Intrinsically Motivated Learning in Natural and Artificial Systems[END_REF][START_REF] Oudeyer | What is intrinsic motivation? A typology of computational approaches[END_REF] . An example comes from the Playground Experiment (see Figure 4 and video https://www.youtube.com/watch?v=uAoNzHjzzys; [START_REF] Oudeyer | What is intrinsic motivation? A typology of computational approaches[END_REF][START_REF] Oudeyer | How evolution may work through curiosity-driven developmental process[END_REF] ). Here, a robot learns by conducting experiments: it tries actions, observes effects, and detects regularities between these actions and their effects. This allows it to make predictions. The way the robot chooses actions is like a little scientist: it chooses experiments that can improve its own predictions, which can provide new information, which makes learning progress, while continuously allocating some proportion of time to exploring other activities in a search for new possibilities. The robot is also equipped with a mechanism that simultaneously categorizes its sensorimotor experiences into different categories based on how similar they are in learnability and controllability.

At any moment in its development, the robot mainly focuses on exploring activities that are sources of learning progress, those that are neither too easy nor too difficult. This models the idea that what the brain finds interesting to practice is what is just beyond the current level of knowledge or competencies [START_REF] Csikszenthmihalyi | Flow: The Psychology of Optimal Experience[END_REF][START_REF] Kidd | The Goldilocks Effect: Human Infants Allocate Attention to Visual Sequences That Are Neither Too Simple Nor Too Complex[END_REF][START_REF] Schmidhuber | Curious Model-Building Control-Systems[END_REF] , and as observed in recent experiments with infants (Kidd et al., 2012). Such a model also leads to a concrete definition of epistemic curiosity as a motivational mechanism that pushes an organism to explore activities for the primary sake of gaining information (as opposed to searching for information to achieve an external goal like finding food or shelter, see (Oudeyer and Kaplan, 2007) for a review of formal models of intrinsic motivation and curiosity-driven exploration).

In the Playground Experiment, not only is the robot able to learn skills based on its own initiative-for example, learning how to grasp an object in front of it-but the robot is also able to spontaneously evolve and self-organize its behavior, which progressively increases in complexity. Cognitive stages appear, but they are not pre-programmed. For example, after beginning through relatively random body babbling, the robot often focuses first on moving the legs around to predict how it can touch objects, then focuses on grasping an object with its mouth, and finally ends up exploring vocal interaction with another robot. Critically, the engineer preprogrammed none of these activities, nor did the engineer preprogram their timing and ordering. This self-organization results from the dynamic interaction between curiosity, learning, and the properties of the body and environment. If the same experiment is repeated several times with the same parameters, one observes that often the same course of developmental stages appear. Yet, sometimes individual robots invert stages, or even generate qualitatively different behaviors. This is due to random small contingencies, to even small variability in the physical realities, which are amplified through closed-loop exploration and learning, and leading this developmental dynamic system into different paths that mathematicians call "attractors": a collection of differentiated patterns towards which the system spontaneously evolves as soon as it finds itself in their vicinity, so-called "basins of attraction."

This robot experiment helps us to understand and formulate hypotheses about aspects of how development works. It suggests a way to model the mechanisms of curiosity-driven learning, and to assess how a form of epistemic curiosity can be modeled as a concrete mechanism within a physical agent. It also shows how, over the long term, curiosity-driven attentional processes can self-organize learning and developmental phases of increasing complexity, without a predefined maturational schedule. Finally, it offers a way to understand individual differences as emergent in development, making clear how developmental processes might vary across contexts, even with an identical underlying mechanism and an identical environment.

CONCLUSION

We are only beginning to uncover the basic mechanisms of infant development. Much of the difficulty comes from the fact that the development of infant skills results from the interactions of multiple mechanisms at multiple spatial (molecules, genes, cells, organs, bodies, social groups) and temporal scales. Like spiral galaxies with shapes that result from neither the programmatic unfolding of a plan nor from learning, infant development consists of complex patterns that form spontaneously out of a distributed network of forces. Such patterns cannot be explained within the confines of a false dichotomy like "innate vs. acquired." Rather, what is needed is a shift to a systems perspective.

As physicists realized a long time ago, systemic explanations of pattern formation in complex systems require the use of formal models based on mathematics and algorithms that allow us to fabricate and simulate aspects of reality. In the words of the physicist and Nobel laureate Richard Feynman:

"What I cannot create I cannot understand" Such an approach is now being brought to developmental science, where algorithmic and robotic models are used to explore the dynamics of pattern formation in sensorimotor, cognitive, and social development. Formulating hypotheses about development using such models, and exploring them through experiments with simulation and robots, allows us to consider the interaction among many mechanisms and parameters. This approach crucially complements traditional experimental methods in psychology and neuroscience where only a few variables can be studied at the same time.

In this context, the use of robots is of particular importance. The laws of physics generate everywhere around us spontaneous patterns in the inorganic world (ice crystals, clouds, dunes, river deltas, and so on). They also strongly impact living beings, and in particular constrain and guide infant development through changes in the body and its interaction with the physical environment. Being able to consider the body as an experimental variable, something that can be systematically changed in order to study its impact on skill formation, has been a longstanding dream for many developmental scientists. Robotics is making that dream a reality [START_REF] Kaplan | Stable kernels and fluid body envelopes[END_REF] .

ACKNOWLEDGMENTS

Preparation of this article was partially supported by ERC Starting Grant Explorers, 240007.