Pascal André

Gilles Ardourel

Christian Attiogbé

Adaptation for Hierarchical Components and Services

Keywords: Adaptation, Components, Services, Behavioural Interface Description, Hierarchisation

Introduction

Coordination is the process of building programs by gluing together active software parts [START_REF] Gelernter | Coordination Languages and their Significance[END_REF][START_REF] Papadopoulos | Coordination Models and Languages[END_REF]. Usually the glue adheres on access points and when it does not, one uses adaptation techniques to make it adhere. Software adaptation [START_REF] Yellin | Protocol Specifications and Component Adaptors[END_REF][START_REF] Heineman | An Evaluation of Component Adaptation Techniques[END_REF][START_REF] Brogi | On the Specification of Software Adaptation[END_REF] includes the detection of interaction mismatches and their correction when it is possible. The correction can be either a dynamic adaptation at running time or the insertion of static adaptors (or transformers).

Adaptation and coordination may be considered from various perspectives. From the component perspective (the Component Based Software Engineering approach) [START_REF] Szyperski | Component Software: Beyond Object-Oriented Programming[END_REF][START_REF] Medvidovic | A Classification and Comparison Framework for Software Architecture Description Languages[END_REF][START_REF] Bergner | A Formal Model for Componentware[END_REF][START_REF] Heineman | Component-Based Software Engineering, 8th International Symposium, CBSE'2005[END_REF] the access points are interfaces, ports, services or operations. From the service perspective (the Service Oriented approach) [START_REF] Papazoglou | Service-Oriented Computing: Concepts, Characteristics and Directions[END_REF][START_REF] Papazoglou | Introduction to Service-Oriented Computing[END_REF][START_REF] Beyer | Web Service Interfaces[END_REF] the access points are interfaces, services or operations.

In a wide acceptance, a software architect would integrate software components from any provider and therefore with a non-restricted range of models. It means that the components can be components à la CBSE or services, assuming that there are many different component models and many service models. In such a context, the software architect needs a language that helps her/him either to define clearly what she/he needs or to find components on the shelf and appropriate adaptation mechanisms. Usually, such a language applies at an interface level and should be • abstract, expressive and formal to hide model specific features and implementation considerations; to provide enough information for both the component designer and the component client (the architect); to ensure consistency and to support the verification of properties such as service or component composability;

• flexible to allow partial use of components, partial descriptions of services, optional use of subservices,

• scalable to allow the combination of small elements (services, components, adaptations) into higher level components.

However, a component model may provide interfaces which are not restricted only to simple synchronous call/response operations; interacting services may be provided through the component interface, this leading to hierarchically structured interfaces. Furthermore, support for adaptation facilities increase the component model reusability.

In this article, we address these needs with a Hierarchical Behavioural IDL that is used for our Kmelia component model [START_REF] Attiogbé | Checking Component Composability[END_REF]. For (re)usability purpose we investigate adaptation issues for such a model and propose some adaptation techniques.

The article is organised as follows: Section 2 motivates and presents the hierarchical behavioural interface description language of our component model. In Section 3 we consider adaptation problems that are either introduced by the hierarchisation level or solved using specific features of our model. We conclude with the perspectives of this work in Section 4.

Hierarchical Behavioural IDL using Kmelia

This section introduces an extension to Behavioural Interface Definition Languages (BIDL) in order to handle complex service interactions and service composition, called a Hierarchical BIDL. The section motivates the use of hierarchisation for component documentation, service composition and service adaptation. The model is illustrated using the Kmelia language.

Structuring Component Interfaces

Formal and abstract descriptions are valuable to design and reason on CBSE system, especially at the interface level [START_REF] Poizat | Formal Methods for Component Description, Coordination and Adaptation[END_REF]. We assume any component model with provided and required services in which the interface specifies the component interactions with its environment [START_REF] Allen | A Formal Basis for Architectural Connection[END_REF][START_REF] Medvidovic | A Classification and Comparison Framework for Software Architecture Description Languages[END_REF].

An Interface Definition Language (IDL) is commonly used for component interoperability. The IDL describes the signatures of provided services. However more details are required (1) on the required services to get modular components, (2) on possible contract definitions, (3) on the ordering of service invocations. The use of Behavioural IDL (BIDL) meets the requirement (3).

In the BIDL approaches [START_REF] Yellin | Protocol Specifications and Component Adaptors[END_REF][START_REF] Canal | On the Dynamic Adaptation of Component Behavior[END_REF][START_REF] Canal | Adding Roles to CORBA Objects[END_REF][START_REF] Bracciali | A Formal Approach to Component Adaptation[END_REF][START_REF] Pavel | A Java Implementation of a Component Model with Explicit Symbolic Protocols[END_REF], the interface specifies the ordering of service invocations and the dynamic behaviour using protocols. A protocol specifies the valid interactions between components. For example a protocol can be a state transition system [START_REF] Pavel | A Java Implementation of a Component Model with Explicit Symbolic Protocols[END_REF], a regular expression [START_REF] Plasil | Behavior Protocols for Software Components[END_REF], or a non-regular process type [START_REF] Südholt | A Model of Components with Non-regular Protocols[END_REF]. A protocol may be associated to a component, to an interface or to a connector 2 . In the first case the protocol merely controls the component lifecycle (like a process if there is only one protocol). In the second case the protocol controls the component interactions in some identified relations: an interface can hold on peerto-peer channels (one per connected component) or on view (like database views). In the last case the protocol controls the communications on a structural access point: it manages the communication aspects of the components or it can be an explicit adaptor. The semantics and usage are slightly different from one approach to another, especially if we have in mind the adaptation and coordination issues.

A common characterisation of the existing BIDL approaches is to consider services as atomic operations and service calls as message sends on an implicit or explicit channel. Such services are defined by a signature (name and parameters) and -if the component model supports assertions-a contract (pre/post conditions). But a service may be more complex than a simple message call: it can handle complex functionalities, it can require multiple interactions and it can also call other services.

Hierarchical BIDL (HBIDL) is a solution to introduce complex services. A HBIDL is characterised by the fact that services are first class entities: (1) services may be defined by a dynamic behaviour (a protocol) in addition to their signature and contract and (2) services may be composed of other services. Each service has an enhanced service interface which includes a service dependency composed of the provided services and the required services which are used in its context. Therefore, a HBIDL should support component protocols, component composition, service protocols and service composition.

The advantages of using a HBIDL are manyfold. It supports the definition and documentation of complex interacting services. The client-side documentation of a component has detailed information on the service usage. Indeed, the client gradually discovers the documentation of the components and services. First, the component interface shows the services that are accessible at a component level; then the specific interface of each provided service; therefore the client only gets step by step what she/he needs.

Furthermore, assembling components in HBIDL focuses on services, considering them as functional connecting points rather than structural connecting points (sometimes called gates or ports). This is a convenient view when one try to fulfil a complex required service.

HBIDL can smoothly support the notion of compatibility level (see below) for component connection because it induces a layered presentation of the interface: IDL only, IDL with protocols, IDL with hierarchy and protocols. Therefore compatiblity checking is preserved by HBIDL. Last, HBIDL due to its emphasis on services, can be a gateway to service oriented models in order to compose components and services (in the sense of the Service-Oriented Approach).

Defining compatibility levels helps when handling heterogeneous models. For example, Becker and al. consider four compatibility levels: syntax, behaviour, synchronisation, and quality of service [START_REF] Becker | Classifying Software Component Interoperability Errors to Support Component Adaption[END_REF]. The compatibility of services described with an HBIDL can be defined at five levels: signature matching, enhanced service interface conformity (including subservices), contract fulfilment, behavioural compatibility (the interactions -waiting for data, synchronisation-between the caller and called services are correct) and quality of service (non-functional requirements). For example, if a component A with an IDL interface only (e.g. a component à la CORBA Component Model) is composed with a component B with an HBIDL interface (e.g. a Kmelia component) then their compatibility can be checked only at the signature level.

The use of the previous compatibility levels impacts on the adaptation techniques. One can either restrict the adaptation at one or more compatiblity levels or extend the adaptation to cover the missing compatibility levels in the considered components.

Hierarchies of Components and Services in Kmelia

The Kmelia model [START_REF] Attiogbé | Checking Component Composability[END_REF] is a simple, formal and abstract component model based on services. It uses the HBIDL features exposed in the previous section. The simplicity relies on the few number of concepts that are used to describe the components and their assembies. The notion of service is central to Kmelia and a component interface describes mainly services. This means that the components are connected via their services (functional connections). The interaction model is therefore simple: required services are directly linked to provided services. A component specification language named Kmelia and a prototype toolbox (COSTO: Component Study Toolbox) support the Kmelia model and property verification. The remainder of the section is an overview of the Kmelia model illustrated on a bank Automatic Teller Machine (ATM) example and its withdraw service.

A Kmelia component is defined through an abstract state model (made up with variables, an invariant, and an initialisation), an interface (made up with provided and required services) and a constraint definition (logic expressions). Figure 1 shows a specification of an ATM core component in Kmelia.

Basically, a Kmelia service encodes a functionality; it is defined with an interface and a behaviour. The service interface includes the service signature, the local declarations, the assertions (pre/post conditions) and the service dependency (related to service composition). The service dependency includes the references to i) provided subservices: they are the services which are provided in the context of another service and to ii) required services. The latter are required from the component itself, from the calling component or from any components. Figure 2 shows a specification of the withdrawal service of the core component for the ATM system in Kmelia.

The subprovides, calrequires, extrequires clauses in the interface of the withdrawal service make explicit the hierarchy and the dependencies between services: the withdrawal service offers an ident subservice and requires three other services, two of them being required from the component which is calling withdrawal.

Component assemblies establish the communication channel used by the communication actions. Assembling Kmelia components consists in linking their pairwise services: required services may be linked to provided services. An implicit channel is associated to this link that supports the communication actions or messages between the services. The semantics of the links is not straightforward because it must conform to the service interface hierarchy. Indeed the services that appear in the subprovides and the calrequires clauses of the service interface dependency must (i) share a common link (they are sublinks) and ( 2) their links must conform to the hierarchy levels. This constraint is recursive on service inclusion. A component composition is the encapsulation of an assembly within a component with a projection of services by promotion links. Promotion links relate the composite services to the inner component services. The main provided service behaviour of the ui component drives the user commands. For example, the user can ask for money (required service ask for money) which is linked to the service withdrawal provided by the ATM core ac component. According to Figure 3, the withdrawal service may call internal services (debit,...), external services (ask authorization), external services required from the caller (ask code, ask amount) and it provides the ident service in the context of ask code. Note that the amount and code links are sublinks: they share the ask for money-withdrawal link and its implicit communication channel.

The component and service usages are flexible:

• An assembly may be valid for one service only, provided that its dependency chain is fulfilled. For example, all the required services that are only needed by the unused transfer provided service have not to be fulfilled for the ATM SYSTEM assembly to be correct.

• A service can provide optional subservices. For example, the ask code service can be linked to a service that does not need identification (ident service). Similarly the ask for money service can be linked to a withdraw service that does not need code (code service).

• Provided subservices may be included as services with explicit service call or only as behaviours without a service call (see next section).

Hierarchy of Behaviours in Kmelia

The hierarchy of service interfaces is naturally reflected in the service behaviour: this permits a precise description of the use of a subservice in the context of the interaction with a service. In Kmelia, a service behaviour is an extended labelled transition system (eLTS) [START_REF] Attiogbé | Checking Component Composability[END_REF] where the states define the service evolution steps and the transitions are labelled with possibly guarded combination of actions: [guard] action*. The actions are either elementary actions or communication actions. An elementary action, an assignment for example, does not involve other services; it does not use a communication channel.

The communication actions use either the standard communication primitives ! and ? for sending/receiving simple messages or their extended forms !! and ?? to deal with service calls and service responses. They are prefixed with a communication channel which can either denote the required service or the caller. A communication channel to be used in a behaviour has to be established by a link like the ask for money-withdrawal link in Figure 3.

The services run concurrently; the communications are synchronous. For example Figure 4 is a visual representation of the withdrawal service eLTS; this figure is produced by the COSTO toolbox. In Kmelia, service behaviours may contain execution points (states or transitions) where a subservice (declared in the service's interface) can be called. These states or transitions are annotated with Kmelia's vertical structuring operators. For instance, the label of the node e1 in Figure 4 expresses that an optional service ident may be called by widthdrawal's caller when the running reaches node e1. This label features the <<>> operator that denotes an optional service call. Kmelia main vertical operators are:

• optional behaviour insertion: <||>,

• mandatory service call: [[]],

• mandatory behaviour insertion: [||].

These structuring mechanisms provide a means to reduce the LTS size, to share common services or subservices and to master the complexity of service specification.

All these structuring operators are defined in such a way that formally the unfolding of an eLTS results in a LTS (in a recursive way). The formal semantics of the structuring mechanisms can be found in [START_REF] André | Defining Component Protocols with Service Composition[END_REF].

Adaptation Problems and Solutions

The following categories of adaptation problems are especially relevant in HBIDL:

• Classic adaptation problems that can be seen through the lens of the new language and benefit from its expressiveness.

• Granularity mismatch in HBIDL: adapting services which hierarchy is organised differently. Having more expression power allows to describe precise constraints relevant for a specific context but that must be adapted when a service or a component is used in a different environment.

• Granularity mismatch between a HBIDL and a BIDL: having a more expressive language does not mean every model uses the expressiveness to the full extent. For a new language to be effective, differences of levels of detail must be dealt with, as well as interoperability with models expressed in languages which intersect with the new one. Problems from this category can be treated like granularity mismatches in HBIDL by considering BIDL models as flat HBIDL models.

In the following we describe the process that is used to detect adaptation problems in a HBIDL architecture and we provide solutions in the Kmelia model.

Adaptation Process with Kmelia and COSTO

The COSTO prototype features several verification algorithms that check compatibility of components and services at different levels: signature, interface, dependencies, behavioural compatibility. Behavioural compatibility is checked by exporting our Kmelia models to Mec [START_REF] Griffault | Contribution à l'étude des systèmes communicants et des algorithmes d'exclusion mutuelle[END_REF] or Lotos [START_REF] Lotos | A Formal Description Technique Based on The Temporal Ordering of Observational Behaviour[END_REF] and reusing their respective model checking tools. We assume that the matching between names (of different components, services or messages) has already been established, either manually or automatically (e.g. by ontology-based approaches).

For each mentioned adaptation problem we use the following pattern.

• First we indicate the earliest compatibility level at which the problem occurs.

• Next we specify how we identify which kind of adaptation problem it belongs to.

• Then we explain how to generate systematically an adaptor and verify that it ensures compatibility. Depending on the constraints of the running environment, the adaptor can take several forms: a component inserted between two mismatching components, a proxy service delegating to one of the services, or an alternative interpretation of a behaviour. We will focus here on the first one.

• Last, we precise if the adaptation problem could have been avoided at minimal cost using the Kmelia structuring operators.

We believe that designers of components and services should anticipate different uses, provided that their specification language helps them to do so at a minimal cost in design time and verification time. We name implicit adaptation this inherent ability of a service or a component to be compatible with many others by construction. At a message or service signature level, implicit adaptation focuses on optional arguments, default values, compatible subtypes for arguments and result. At a hierarchical service interface level, it includes optional subservices, implicit linking to services or subservices. At a service assertion level, it means that the compatibility between provided and required pre/post conditions is ensured via propagations from the previous levels. At a service behaviour level, all the above adaptations apply together with possible alternate behaviours (w.r.t. observational equivalence: the behaviour of the service is not changed from the point of view of client services) using the behaviour insertion operators introduced in Section 2.3.

Adaptation in HBIDL: Parameters vs messages

This problem is an example of a standard BIDL adaptation problem taken in a HBIDL context. In the Parameters vs messages problem, there are different treatments for data exchanges between related components: according to a service, one component may use parameters where the other uses messages to send the data value for the service. It is a variant of the Multiple action correspondence [START_REF] Bracciali | A Formal Approach to Component Adaptation[END_REF]. Based on different interpretations of an imprecise textual specification such as "The client must communicate an account number and an amount to the service deposit", one service could use parameters while another could use message sends. This is illustrated in Figure 5. Given that the correct data is "communicated", the communication has to be adapted when a client of the service deposit uses a different interpretation. In Figure 5 the behaviour service from USER INTERFACE calls the deposit service from ATM CORE to credit the account number 12 by 100. The signature of deposit is deposit(int account, double amount) but the call from behaviour does not contain parameters and it is followed by two messages containing the parameters.

The parameter vs messages problem is detected at level 1: signature mismatch between the deposit provided service of ATM CORE and the deposit required service of USER INTERFACE. The adaptability is checked in COSTO using a simple graph traversal algorithm which looks for an unavoidable sequence of message sends in the caller's behaviour that matches the parameters and that takes place between the service call and any other communication with the service. If such sequence is found, the problem is diagnosed as a Parameters vs messages and can be solved. Figure 6 shows an adaptor component between the deposit provided service of ATM CORE and the deposit required service of USER INTERFACE. This adaptor illustrates another Kmelia operator: channel<|>channel . This operator redirects communications from a channel to another one, thus simplifying the writing of some adaptors that require pre-processing before reverting to normal communication, like an incorrect order of messages. Furthermore, unidirectional versions of this operator exist (channel<|channel and channel|>channel). An adaptor can be automatically generated by matching with a sequence of receptions the sequence of calls found in the diagnosis phase, adding a call to the service with its parameters, then adding the redirection operator.

The parameter vs messages problem can be further complicated by the use of parameters with types of different granularity in the client and in the provider, for instance the deposit service could have had a structured type in its signature while the caller would have used primitive types in its call. The complexity of the detection and the generation is related to the complexity of the data structures used in the parameters (data might have to be constructed or decomposed) and the similarity metrics used for identifying the parameters. The diagnosis algorithm of COSTO for the parameter vs messages problem is parametrised with an identification method which have to be changed to incorporate the variants of the problem.

Adapting Hierarchical Mismatch

When a component expects to call a service which is not hierarchical and is connected to one where part of the functionality is described as a subservice, a Hierarchical Mismatch occurs.

Being designed with different granularity levels in mind, the services withdrawal and behaviour from Figure 7 are not compatible: in behaviour, identification is a simple communication made in the context of the withdrawal service but the identification is considered to be managed by the ident service in withdrawal's component, probably because it is meant to be used in the context of several other services of the component. This mismatch can be detected by a behavioural compatibility analysis using COSTO tools. For instance, the results of the analysis with MEC gives the following information :

transition_system Verif_ATM_CORE_withdrawal < width = 2; list = (ATM_CORE_withdrawal, USER_INTERFACE_behaviour )> ... deadlock = { e(i.e11) } unavoidable = { e(init.init), e(init.e10), e(i.e11) } Fig. 8. Extract of a result from the compatibility analysis using MEC It detects a deadlock at the state i of withdrawal and at the state e11 of behaviour. This incompatibility can be diagnosed as a Hierarchical Mismatch problem because one of the states (i of withdrawal) where the deadlock occurs offers a subservice which starts with the identification message that matches the one following e11 of behaviour. This diagnostic is confirmed by taking the following steps3 :

• A call to the ident subservice just before the identification message is added to a copy of the LTS of behaviour

• The compatibility check is run again. It should give another deadlock corresponding to the lack of waiting for the result of ident in behaviour (withdrawal??ident).

• The wait for the result of identis added in the copy of the LTS before the newlyfound deadlock.

• If the compatibility check passes, the problem is correctly diagnosed and can be solved. Figure 9 shows an adaptor that solves the problem. The service behaviour from ui is now linked with the withdrawal service of the adaptor, which depends on a required service arwithdrawal that is linked to the withdrawal service of ac. Calls should be read from right to left, following the required-provided links: when it is called, the withdrawal service of the adaptor calls withdrawal from ac; then it calls the subservice ident in withdrawal's context (hence the channel arwithdrawal); then it waits for the identification message; then it transmits the identification message to its initial caller (ui's behaviour).

The adaptor is created by generating a LTS that starts the called service (withdrawal from ac), relay all communication from the caller that happens before the deadlock (in our example we start directly with the deadlock), starts the subservice and relay communication again.

• First, the LTS obtained from the diagnosis phase is reused (it has been restricted to communications on the withdrawal channel and reduced).

• The withdrawal channel is renamed with the name of the required service for the adaptor (in our case arwithdrawal).

• Transitions that call and wait for the subservice are inserted at the points discovered in the diagnosis (initial and second deadlocks).

• Every other communication on the channel is forwarded:

• A transition is added after every message that is sent by the initially called service (withdrawal) for sending the information to the adaptor's caller (for instance, CALLER!identifier(i) is inserted after arwithdrawal?identifier(i)).

• A transition is added before every message that is sent to the initially called service (withdrawal) for receiving the information from the adaptor's caller (for instance, CALLER?amount is inserted before arwithdrawal!amount).

The behavioural compatibility between ui's behaviour, the adaptor's withdrawal and the withdrawal and ident services of ac can be checked using COSTO.

This Hierarchical Mismatch can be avoided using implicit adaptation when the creation of the service ident is coming from a refactoring of the service withdrawal.

In such a situation the designer should be conscious that while identifying, naming and factorising some part of behaviour are good from the readability point of view, that breaks compatibility with client services that predate the change. The <||> operator is a vertical composition operator that could have been used instead of the <<>> operator in the example. This operator allows to branch to the subservice either by calling it or without the call in order to be compatible with both new clients and older clients4 . . This mandatory service or behaviour call operator is used for describing protocols that control the correct ordering of service calls. We added the login and logout services to the ATM CORE component in order to describe a very simple protocol. The users of the component call the protocol withdrawprotocol then they have to call the other services in its context (i.e under its control) or have interactions that match those of the services under the control of the component.

The <||> and [||] operators are useful for implicit adaptation, but they cannot always replace their less flexible counterparts: for instance, if the mandatory service call operator [[]] had been used in the protocol of Figure 10, then the services withdrawal and account query could not have begun with the same communication action without being ambiguous at the state e0.

Conclusion

In this article we have presented the Hierarchical Behavioural Interfaces Description Language (HBIDL) that is used in the Kmelia abstract Component Model. The interface hierarchisation appeared through the interfaces of components which are complemented with the interfaces of services. The Kmelia component model is based on services and it provides several structuring mechanisms: horizontal structuring mechanisms especially

Fig. 3 .

 3 Fig. 3. Assembly for an ATM System

Figure 3

 3 Figure3is a graphical view of a Kmelia model for the bank ATM. The as component is a composition of an ATM CORE (ac) with an ATM user interface (ui). The main provided service behaviour of the ui component drives the user commands. For example, the user can ask for money (required service ask for money) which is linked to the service withdrawal provided by the ATM core ac component. According to Figure3, the withdrawal service may call internal services (debit,...), external services (ask authorization), external services required from the caller (ask code, ask amount) and it provides the ident service in the context of ask code. Note that the amount and code links are sublinks: they share the ask for money-withdrawal link and its implicit communication channel.The component and service usages are flexible:

Fig. 4 .

 4 Fig. 4. The withdrawal service eLTS

Fig. 5 .

 5 Fig. 5. Differences in communication of parameters

Fig. 6 .

 6 Fig. 6. Adapting differences in communication of parameters

Fig. 7 .

 7 Fig. 7. Differences in communication granularity

Fig. 9 .

 9 Fig. 9. Adapting differences in communication granularity

Fig. 10 .

 10 Fig. 10. Implicit Adaptation in a ProtocolFigure 10 illustrates its use with another Kmelia operator: [||]. This mandatory service or behaviour call operator is used for describing protocols that control the correct ordering of service calls. We added the login and logout services to the ATM CORE component in order to describe a very simple protocol. The users of the component call the protocol withdrawprotocol then they have to call the other services in its context (i.e under its control) or have interactions that match those of the services under the control of the component.The <||> and [||] operators are useful for implicit adaptation, but they cannot always replace their less flexible counterparts: for instance, if the mandatory service call operator [[]] had been used in the protocol of Figure10, then the services withdrawal and account query could not have begun with the same communication action without being ambiguous at the state e0.

  The service withdrawal is available if there is enough money in the cash dispenser. This services requires a bank credit card, a code, an amount to withdraw. An authorization is required from the bank consortium.

	COMPONENT ATM_CORE
	/* The ATM_CORE component is the central component for a bank cashier station.
	...
	*/
	INTERFACE
	provides : {withdrawal, account_query, deposit, transfer}
	requires : {ask_authorization, ask_account_balance}
	TYPES
	CashCard : struct {code:Integer, id:Integer, limit:Integer} // record type
	CONSTANTS
	// constants definitions
	...
	VARIABLES
	// variables definitions
	name : String,
	swallowed_cards : Set,
	available_notes : Integer
	...
	PROPERTIES
	// predicates
	cash_disp: available_notes >= 0
	...
	INITIALIZATION
	// variables assignments
	...
	SERVICES
	provided withdrawal (card : CashCard)
	// see the service withdrawal in Figure 2
	required ask_authorization (id : Integer, code : Integer) : Boolean
	...
	end
		Fig. 1. Overview of the Kmelia component syntax
	Provided withdrawal (card : CashCard)
	/* This service provides an identification subservice if needed.
	*/
	Interface
	subprovides : {ident}
	calrequires : {ask_code, ask_amount} //required from the caller
	extrequires : {ask_authorization}
	Pre
	available_notes >= available_cash
	Variables
	nbt : Integer,	// nbt : number of authorized trials of code entering
	c : Integer,	// c : input code given by the user
	...
	Behaviour
	init i
	final f
	... // see the service behaviour in Figure 4
	Post
	available_notes <= pre(available_notes)
	// (success && (available_notes = pre(available_notes) -a)) ||
	// ((not success) && available_notes = pre(available_notes))
	end
		Fig. 2. Overview of the Kmelia service syntax

Emails:pascal.andre@univ-nantes.fr, gilles.ardourel@univ-nantes.fr ,christian.attiogbe@univ-nantes.fr

• optional service call: <<>> ,

We use several optimisations reducing the LTS size that are outside the scope of this paper.

It is not as powerful as using adaptors because it does not work for several classes of services (for instance, services with parameters).

based on the linking of services and their related subservices; vertical structuring operators to enable the description of large services with encapsulated or shared (sub)services. An example of an ATM was used to illustrate the structuring of component and service specifications with hierarchical interfaces. We have considered adaptation problems encountered in BIDL and also related to our HBIDL: hierarchy mismatch and parameter vs message mismatch. We motivated and showed what solutions are used for these problems in our Kmelia model. The vertical structuring mechanisms help to tackle the adaptation problems. Compared to BIDL related works, we have emphasised the impact of the hierarchical BIDL on the adaptation problems and we have shown that the use of structuring mechanisms may simplify design and verification of both services and adaptors.

Overall, we are concerned with the verification of components with respect to their dynamic and functional properties and their preservation after adaptation.

We plan the integration of adaptation techniques into the COSTO prototype which already handles verification of components, services and compatibility of the assemblies. The investigated process is the following: after a failed compatibility verification, a module will attempt to diagnose the incompatibility as an adaptation problem and to generate an adaptor and launch the verification again. This integration of adaptation with verification techniques is an open field: the detection of mismatches must be connected with the proposition of adaptations and the decision process. A research direction could be the specification of adaptation problems and their solutions in a language that uses HBIDL and coordination patterns.


Albane Gareton
email: albanegareton@yahoo.com

Arnault Tauziède-Espariat

Volodia Dangouloff-Ros

Alexandre Roux

Raphaël Saffroy

David Castel

Thomas Kergrohen

Fréderic Fina

Dominique Figarella-Branger

Mélanie Pagès

Franck Bourdeaut

François Doz

Stéphanie Puget

Christelle Dufour

Emmanuèle Lechapt

Fabrice Chrétien

Jacques Grill

Pascale Varlet

The histomolecular criteria established for adult anaplastic pilocytic astrocytoma are not applicable to the pediatric population

Keywords: Pilocytic astrocytoma with anaplastic features, Pediatric, DNA methylation profiling, MC-AAP, FGFR1, MAPK pathway

Pilocytic astrocytoma (PA) is the most common pediatric glioma, arising from a single driver MAPK pathway alteration. Classified as a grade I tumor according to the 2016 WHO classification, prognosis is excellent with a 10-year survival rate > 95% after surgery. However, rare cases present with anaplastic features, including an unexpected high mitotic/proliferative index, thus posing a diagnostic and therapeutic challenge. Based on small histomolecular series and case reports, such tumors arising at the time of diagnosis or recurrence have been designated by many names including pilocytic astrocytoma with anaplastic features (PAAF). Recent DNA methylation-profiling studies performed mainly on adult cases have revealed that PAAF exhibit a specific methylation signature, thus constituting a distinct methylation class from typical PA [methylation class anaplastic astrocytoma with piloid features-(MC-AAP)]. However, the diagnostic and prognostic significance of MC-AAP remains to be determined in children. We performed an integrative work on the largest pediatric cohort of PAAF, defined according to strict criteria: morphology compatible with the diagnosis of PA, with or without necrosis, ≥ 4 mitoses for 2.3 mm 2 , and MAPK pathway alteration. We subjected 31 tumors to clinical, imaging, morphological and molecular analyses, including DNA methylation profiling. We identified only one tumor belonging to the MC-AAP (3%), the others exhibiting a methylation profile typical for PA (77%), IDH-wild-type glioblastoma (7%), and diffuse leptomeningeal glioneuronal tumor (3%), while three cases (10%) did not match to a known DNA methylation class. No significant outcome differences were observed between PAAF with necrosis versus no necrosis (p = 0.07), or with 4-6 mitoses versus 7 or more mitoses (p = 0.857). Our findings argue that the diagnostic histomolecular criteria established for anaplasia in adult PA are not of diagnostic or prognostic value in a pediatric setting. Further extensive and comprehensive integrative studies are necessary to accurately define this exceptional entity in children.

Introduction

Pilocytic astrocytoma (PA) is the most common pediatric brain tumor (17.6% of childhood primary brain tumors), with peak incidence between 5 and 15 years [START_REF] Louis | The 2016 World Health Organization classification of tumors of the central nervous system: a summary[END_REF]. These slow growing tumors are designated as grade I by the World Health Organization (WHO) classification of tumors of the central nervous system (CNS) and have a generally favorable outcome, with a 10-year survival rate of 95% [START_REF] Louis | The 2016 World Health Organization classification of tumors of the central nervous system: a summary[END_REF]. Patient age and extent of resection represent key prognostic factors [START_REF] Stokland | A multivariate analysis of factors determining tumor progression in childhood low-grade glioma: a populationbased cohort study (CCLG CNS9702)[END_REF]. Molecular alterations of the mitogen-activated protein kinase (MAPK) pathway are characteristics of PA, the most frequent being a fusion of the BRAF gene with KIAA1549 in 66% of cases, resulting from a tandem duplication at chromosome 7p34 [START_REF] Jones | Tandem duplication producing a novel oncogenic BRAF fusion gene defines the majority of pilocytic astrocytomas[END_REF]. Other alterations of MAPK have been observed, such as mutations of BRAF, FGFR1, KRAS, PTPN11, and NF1 genes, and fusions of NTRK2 and FGFR1 [START_REF] Jones | Recurrent somatic alterations of FGFR1 and NTRK2 in pilocytic astrocytoma[END_REF][START_REF] Louis | The 2016 World Health Organization classification of tumors of the central nervous system: a summary[END_REF]. Aside from this single 1 3 genetic alteration which drives oncogenesis, most PAs have a relatively stable karyotype, or focal gains of chromosomes 5 or 7 [START_REF] Lambert | Differential expression and methylation of brain developmental genes define location-specific subsets of pilocytic astrocytoma[END_REF].

Histopathologically, tumors with conventional PA morphology with signs of histopathological malignancy (mitoses, necrosis, and increased cellularity) have been designated in the literature with variable terminology, such as atypical PA, malignant PA, PA with anaplasia, PA with anaplastic features (PAAF), or anaplastic pilocytic astrocytoma (ANA PA) [START_REF] Louis | The 2016 World Health Organization classification of tumors of the central nervous system: a summary[END_REF][START_REF] Rodriguez | PI3K/AKT pathway alterations are associated with clinically aggressive and histologically anaplastic subsets of pilocytic astrocytoma[END_REF][START_REF] Rodriguez | Anaplasia in pilocytic astrocytoma predicts aggressive behavior[END_REF]. The 2016 WHO classification uses the term PA with anaplasia, but for this study we have chosen to use PAAF to discriminate the histomolecularly defined subgroup from epigenetically defined MC-AAP. These tumors may arise either de novo or in the context of malignant transformation. The WHO classification specifies brisk mitotic activity (≥ 4 mitoses per 10 high power fields (HPF)) with or without necrosis, as criteria to look for in PAAF [START_REF] Louis | The 2016 World Health Organization classification of tumors of the central nervous system: a summary[END_REF][START_REF] Rodriguez | Anaplasia in pilocytic astrocytoma predicts aggressive behavior[END_REF]. WHO grade is still to be determined. Nonetheless, this diagnosis remains difficult, as these morphological features are still compatible with the diagnoses of classical PA, grade I, with degenerative, necrotic or hemorrhagic modifications, or even glioblastoma, grade IV.

Recently, large-scale epigenetic analyses mapping methylated CpG sites on tumoral genomes have allowed for the characterization of genetically defined tumoral subtypes in the CNS [START_REF] Capper | DNA methylation-based classification of central nervous system tumours[END_REF]. Developments in DNA methylation profiling as a classifying tool have described MC-AAP as a new, distinct genetic subclass from conventional PA [DNA methylation classes: PA posterior fossa (PF), PA midline (MID), PA supratentorial (SUP)] [START_REF] Capper | DNA methylation-based classification of central nervous system tumours[END_REF][START_REF] Reinhardt | Anaplastic astrocytoma with piloid features, a novel molecular class of IDH wildtype glioma with recurrent MAPK pathway, CDKN2A/B and ATRX alterations[END_REF]. It is important to note that this new DNA methylation class was described mostly in adults. Indeed, only six pediatric patients were included in this large patient cohort [START_REF] Reinhardt | Anaplastic astrocytoma with piloid features, a novel molecular class of IDH wildtype glioma with recurrent MAPK pathway, CDKN2A/B and ATRX alterations[END_REF]. In contrast to classical PA, supplementary alterations of CDKN2A/B and loss of ATRX protein expression were found in the MC AAP in addition to the classical single MAPK alteration.

The newfound interest in this histomolecular entity raises the question of its relevance in a pediatric setting. Indeed, of the all PAAF cases described in the literature, only 22 cases were pediatric, with or without MAPK alteration [17,[START_REF] Mistry | BRAF mutation and CDKN2A deletion define a clinically distinct subgroup of childhood secondary high-grade glioma[END_REF][START_REF] Olar | ATRX protein loss and deregulation of PI3K/ AKT pathway is frequent in pilocytic astrocytoma with anaplastic features[END_REF][START_REF] Peters | Transformation of juvenile pilocytic astrocytoma to anaplastic pilocytic astrocytoma in patients with neurofibromatosis type I[END_REF][START_REF] Rodriguez | PI3K/AKT pathway alterations are associated with clinically aggressive and histologically anaplastic subsets of pilocytic astrocytoma[END_REF][START_REF] Rodriguez | Alternative lengthening of telomeres, ATRX loss and H3-K27M mutations in histologically defined pilocytic astrocytoma with anaplasia[END_REF] including 6 with DNA methylation profiling [START_REF] Reinhardt | Anaplastic astrocytoma with piloid features, a novel molecular class of IDH wildtype glioma with recurrent MAPK pathway, CDKN2A/B and ATRX alterations[END_REF]. Our study consists of a retrospective analysis of 31 pediatric (< 18 years) PAAF cases defined according to strict histomolecular criteria. We integrated clinical, radiological, histopathological, immunohistochemical, molecular, DNA methylation profiling, and copy number profile (CNP) data to better characterize these tumors in children.

Materials and methods

Cohort selection

This study was approved by the GHU Paris-Neurosciences Sainte-Anne's local ethics committee (INDS: MR 1409210519). We selected 31 pediatric cases that received the institutional diagnosis of PAAF at the Necker-Enfants Malades Hospital and the GHU Paris-Neurosciences Sainte-Anne between 2008 and 2019, out of 511 classical pediatric PA diagnosed during this time period. Selected tumors satisfied these three inclusion criteria: (i) classical morphology of PA, (ii) MAPK alteration, and (iii) at least 4 mitoses per 10 HPF (2.3 mm 2 ), with or without necrosis [START_REF] Louis | The 2016 World Health Organization classification of tumors of the central nervous system: a summary[END_REF]. Since no specific reference area has been published, we selected 2.3 mm 2 , as used for pleomorphic xanthoastrocytoma and choroid plexus tumors [START_REF] Louis | The 2016 World Health Organization classification of tumors of the central nervous system: a summary[END_REF]. These criteria were present either de novo, or in the context of malignant transformation of PA at recurrence. These data are summarized in Fig. 1.

Clinical and radiological data

Clinical data were collected from Gustave Roussy Institute, Curie Institute, and Necker-Enfants Malades Hospital. Complete clinical history was retrieved when possible: gender, age at diagnosis, family history, known tumor predisposition syndrome, symptoms at diagnosis, extent of resection, neoadjuvant or adjuvant treatments (chemotherapy, radiation), progression-free survival (PFS) defined as the date of the first radiologically confirmed relapse, long-term follow-up, and overall survival (OS). Extent of resection was noted as gross total resection (GTR), subtotal resection (STR), defined as the resection of more than 90% of the tumor volume, or partial resection (PR) (less than 90% of tumor volume). All cases were subject to local radiological review by an experienced pediatric neuroradiologist (VDR). Because of the long inclusion time period, imaging protocol varied among patients. Computed tomography (CT) scan, when available, was used to assess tumor density, calcifications, and bleeding. MRI protocol always included T1-weighted, T2-weighted, and post-contrast T1-weighted images, and inconsistently FLAIR, diffusion-weighted images, and pre-contrast Arterial Spin Labeling (ASL) perfusion-weighted images. To assess characteristic imaging features of PAAF, this cohort was compared to a previously published posterior fossa classical PA cohort and to an unpublished cohort of optic pathway gliomas [START_REF] Dangouloff-Ros | Arterial spin labeling to predict brain tumor grading in children: correlations between histopathologic vascular density and perfusion MR imaging[END_REF].

3

Histopathological examination

Formalin-fixed paraffin-embedded (FFPE) tissue samples for each patient were retrieved from the GHU Paris-Neurosciences Sainte-Anne archives. Haematoxylin-Phloxine-Saffron (HPS)-stained slides for all cases underwent central review by two experienced neuropathologists (PV, ATE) to confirm morphological diagnoses as well as mitotic count for 2.3 mm 2 . Necrosis, microvascular proliferation, Rosenthal fibers, eosinophilic granular bodies, calcifications, and lymphocyte infiltration were noted as present or absent. Tumoral architecture was labeled biphasic, oligodendroglial-like, or piloid. The infiltration pattern was assessed and tumors were described as solid, infiltrative, or both.

Immunohistochemistry

Fluorescent in situ hybridization (FISH) and molecular analyses

In order of frequency: FISH analyses for BRAF gene rearrangements using the ZytoLight SPEC BRAF dual color break apart probe (Zytovision, Bremerhaven, Germany) were carried out in all cases. Fluorescent signals were counted in 100 tumoral nuclei with the DM600 Leica fluorescent microscope (Leica Biosystems, Richmond, IL). If negative, rearrangements of NTRK2 were searched for using the ZytoLight SPEC NTRK2 dual color break apart probe (Zytovision, Bremerhaven, Germany). When negative, a brain tumor-specific sequencing panel was developed using Massarray iPlex technology and Massarray online design tools (Agena Biosciences) to detect mutations in FGFR1, and BRAF genes, as previously described [START_REF] Pagès | Co-occurrence of histone H3 K27M and BRAF V600E mutations in paediatric midline grade I ganglioglioma[END_REF]. Next-generation sequencing (NGS) was also performed in rare cases according to the Illumina NextSeq 500 protocol (Illumina, San Digeo, CA, USA), which allowed us to detect mutations of KRAS, NRAS and HRAS. When necessary, droplet digital polymerase chain reaction (ddPCR) was performed to confirm KIAA1549:BRAF fusion or to search for FGFR1 duplications, as previously described [START_REF] Appay | Duplications of KIAA1549 and BRAF screening by droplet digital PCR from formalin-fixed paraffin-embedded DNA is an accurate alternative for KIAA1549-BRAF fusion detection in pilocytic astrocytomas[END_REF].

FISH for PTEN was performed on all samples using the Vysis PTEN/CEP10 FISH probe kit (Abbott Molecular Inc., Des Plaines, IL, USA). FISH for 1p19q, using the Vysis 1p36/1q25 and 19q13/19p13 FISH probe kit (Abbott Molecular Inc., Des Plaines, IL, USA) was performed in all spinal cases. FISH for CDKN2A was performed using the Vysis CDKN2A/CEP 9 FISH probe kit (Abbott Molecular Inc., Des Plaines, IL, USA) after DNA methylation profiling, to confirm alterations observed on the CNP. Fluorescent signals were counted in 100 tumoral nuclei with the DM600 Leica fluorescent microscope (Leica Biosystems, Richmond, IL, USA).

RNA sequencing and analysis

RNAseq was performed on two cases on the Integragen platform (Evry, France). Libraries were prepared with TruSeq Stranded mRNA kit according to the supplier recommendations. Briefly, the key stages of this protocol were, successively, the purification of PolyA containing mRNA molecules using poly-T oligo attached magnetic beads from 1 µg total RNA, a fragmentation using divalent cations under elevated temperature to obtain approximately 300 bp fragments, double-stranded cDNA synthesis and finally Illumina adapters ligation and cDNA library amplification by PCR for sequencing. Sequencing was then carried out on paired-end 75 bb using Illumina NextSeq500.

The software used for RNA alignment was TopHat2.1.0, including Bowtie2. A quantitative expression profile is generated using Cufflinks 2.2.0 [START_REF] Trapnell | Transcript assembly and quantification by RNA-Seq reveals unannotated transcripts and isoform switching during cell differentiation[END_REF].

Single nucleotide variants (SNV) and small insertions and deletions (Indels) were detected with Samtools/BcfTools (Broad Institute). Functional consequences of variants on genes, transcripts, and protein sequence, as well as regulatory regions, were predicted by Variant Effect Predictor (VEP release 83) (stop, splicing, missense, synonymous), as well as by location of the variants (e.g., upstream of a transcript, in coding sequence, in non-coding RNA, in regulatory regions). Regarding missense changes, two bioinformatics predictions for pathogenicity were available SIFT (sift5.2.2), PolyPhen (2.2.2). Other information like quality score, homozygote/heterozygote status, count of variant allele reads, and the presence of the variant in the COSMIC database (version 71) was reported.

DNA methylation profiling and t-SNE analysis

DNA extraction from FFPE was performed using the QIAamp DNA FFPE Tissue Kit and the Qiacube (QIAGEN, Hilden, Germany) according to the manufacturer's instructions. 250-500 ng of DNA was extracted from each tissue sample. Kits used for bisulfite conversion and reparation were the Zymo EZ DNA methylation kit and ZR-96 DNA Clean and Concentrator-5 (Zymo Research, Irvine, CA, USA) and bisulfite DNA was processed using the Illumina Infinium HD FFPE DNA Restore kit and Infinium FFPE QC kit (Illumina, San Diego, CA, USA).

The DNA was then processed using the Illumina Infinium HumanMethylation EPIC Bead-Chip array (Illumina, San Diego, CA, USA) according to the manufacturer's instructions. The iScan control software was used to generate raw data files from the BeadChip in IDAT format and analyzed using GenomeStudio version 2.0 (Illumina, San Diego, CA, USA). The following filtering criteria were applied: removal of probes targeting the X and Y chromosomes, removal of probes containing single-nucleotide polymorphisms (dbSNP132 Common) within five base pairs of and including the targeted CpG site, and removal of probes not mapping uniquely to the human reference genome (hg19), allowing for one mismatch [START_REF] Capper | DNA methylation-based classification of central nervous system tumours[END_REF]. The raw IDAT files were uploaded to https ://www.molec ularn europ athol ogy.org for supervised analysis using the Random Forest methylation class prediction algorithm, as previously described [START_REF] Capper | DNA methylation-based classification of central nervous system tumours[END_REF]. Copy number profiles were calculated as previously described [START_REF] Capper | DNA methylation-based classification of central nervous system tumours[END_REF].

Raw signal intensities were obtained from iDat files using the minfi Bioconductor package v1.28.4. Background correction and dye-bias correction were performed on each sample. After a correction for the type of material tissue (FFPE or frozen) was performed with the removeBatchEffect function (limma package v3.38.3). Filtering criteria of probes were removal of probes targeting X or Y chromosomes, removal of probes containing single nucleotide polymorphisms, and probes not included in the EPIC array. We selected the most variable probes for t-SNE (t-Distributed Stochastic Neighbor Embedding) (SD > 0.30) with parameter theta = 0, pca = TRUE, max_iter = 2500, perplexity = 30, based on the method by Capper et al. [START_REF] Capper | DNA methylation-based classification of central nervous system tumours[END_REF]. t-SNE was performed using the Rtsne package, version 0.15. The following glioma reference classes were included: MC-AAP (here annotated as ANA_PA; 21 cases); diffuse leptomeningeal glioneuronal tumor (DLGNT; 8 cases); GBM, G34 mutant (GBM_G34; 41 cases); GBM, mesenchymal subtype (GBM_MES; 56 cases); GBM of the midline (GBM_MID; 24 cases); GBM, MYCN mutant (GBM_MYCN; 16 cases); GBM, RTK I subtype (GBM_RTK_I; 64 cases); GBM, RTK II subtype (GBM_RTK_II; 143 cases); GBM, RTK III subtype (GBM_RTK_III; 13 cases); ganglioglioma (LGG_ GG; 21 cases); PA or ganglioglioma of the supratentorial 1 3 hemispheres (LGG_PA_GG_ST; 24 cases); PA of the midline (LGG_PA_MID; 38 cases); PA of the posterior fossa (LGG_PA_FP; 114 cases). Detailed descriptions of the reference methylation classes are available on https ://www. molec ularn europ athol ogy.org

Statistical analyses

Univariate analyses were carried out using chi-square or Fisher's exact test for comparing categorical variables, and the unpaired t test or Mann-Whitney rank-sum test for continuous variables, as appropriate. The Kaplan-Meier method, using log rank tests to assess significance for group comparisons, plotted unadjusted survival curves for PFS and OS. A Cox proportional hazards model was performed in a multivariate analysis. We created Cox proportional hazards regression models on the whole series using a backward stepwise approach, adjusting for predictors previously associated at the p < 0.2 level with recurrence in unadjusted analysis. A probability value < 0.05 was considered statistically significant. Statistical analyses were performed using the JMP software (version 14.1.0, SAS Institute Inc.).

Results

Clinical and radiological characteristics

The median and mean patient age were 7.0 and 6.8 years, respectively, with a range 3 months to 15.9 years. The male to female ratio showed a slight female predominance (M:F ratio 0.63). Of the 31 patients, 25 (81%) presented with PAAF de novo, whereas 6 cases (19%) originated from the re-resection of a previously known PA. In these 6 cases, the initial diagnosis of classical PA without anaplasia was reexamined and confirmed. Eighteen (58%) patients had gross total resection (GTR) (n = 9) or subtotal resection (STR) (n = 9). Thirteen (42%) patients had partial resection (PR). Patients were treated by observation only (n = 16), adjuvant or neo-adjuvant chemotherapy (n = 12), irradiation only (n = 1), or radiation and chemotherapy (n = 2) (Table 1).

Tumor location was subdivided into posterior fossa (n = 14, cerebellar hemispheres n = 11; cerebellar vermis n = 3), midline (n = 16, including hypothalamus/optic chiasm (n = 12), the spinal cord (n = 3) and 3rd ventricle (n = 1)), and supratentorial hemispheric (n = 1) (Table 1). Imaging studies revealed radiological features close to classical PA, except for perfusion values. Fourteen patients had available CT scans, showing a hypodense tissular component in all cases and 3/14 had calcifications. On MRI, all tumors were well delineated with clearly marked borders, with peritumoral edema on T2-weighted images in 48% (n = 15/31). Contrast enhancement was always present but with variable intensity. Apparent diffusion coefficient was high in 20/24 tested tumors and was intermediate in 3 cases.

Posterior fossa PAAF showed no specific features in comparison to classical PA: they were hemispheric cerebellar tumors with a cystic component and post-contrast enhancement, revealing a mural nodule (n = 12/14) or cyst wall enhancement (n = 2/14). Hypothalamic/Optic chiasm PAAF were always large tumors, ranging from 3 to 8 cm, and mostly hypothalamic, with intense post-contrast enhancement.

Seventeen patients had available ASL cerebral blood flow (CBF) values, ranging from 28 to 204 mL/min/100 g, with a median value of 56 mL/min/100 g (IQR [48-75], higher than classical PA (median 36 ml/min/100 g, IQR , p < 0.001) [START_REF] Dangouloff-Ros | Arterial spin labeling to predict brain tumor grading in children: correlations between histopathologic vascular density and perfusion MR imaging[END_REF]. ASL CBF was higher than in control groups (posterior fossa PA with anaplasia median 49 ml/min/100 g vs 34 ml/min/100 g for classical PA (p = 0.008); optic pathways PA with anaplasia median 66 ml/min/100 g vs 39 ml/ min/100 g for classical PA (p = 0.04)).

Eight patients (26%) presented with intracranial metastatic lesions at the time of discovery. When spinal MRI was available (n = 11), 36% (4/11) had metastatic lesions.

Histopathological and immunohistochemical characterization

All cases presented with typical PA morphology. Mitotic count ranged from 4 to 32 per 2.3 mm 2 (mean 7, median 7). The MIB-1 proliferation index ranged from 3 to 50% (mean 14%, median 11%). ATRX expression was maintained in all 31 cases. In all cases, H3K27me3 was preserved, allowing us to exclude potential tumors with combined MAPK alteration and H3K27M mutation [START_REF] Orillac | Pilocytic astrocytoma and glioneuronal tumor with histone H3 K27M mutation[END_REF]. Phospho-S6 staining was strongly positive in all cases except one with weak staining (patient 26). Immunohistochemistry for PTEN was interpretable in 29/31 cases and was variable, with conserved expression in 20 cases, partial loss in 5 cases, and complete loss of expression in 4 cases (patients 10, 26, 27, and 30). All morphological and immunohistochemical features are detailed in supplementary Table 1, online resource.

Genomic DNA methylation

850 K DNA methylation profiling was performed on all 31 PAAFs. Three cases did not correspond to a specific DNA methylation class and were subsequently designated as "no match cases" (patients 3, 10, and 12); since they yielded unreliably low classifier scores below 0.18 (supplementary Table 1, online resource). They did, however, cluster as PA in t-SNE analysis (case 10 to LGG_PA_MID, cases 3 and 12 to LGG_PA_PF). Twenty cases received a calibrated score superior to 0.90. Seven tumors yielded a classifier diagnosis below the established threshold of 0.90 (0.89-0.46); however, in all these cases the highest calibrated score was consistent with clinical, radiological, histomolecular data and t-SNE cluster. In one medullar case, the highest calibrated score obtained was 0.32 for GBM_IDH_WT_MID (patient 26).

Excluding the "no match cases", 24 (86%) cases were classified as pilocytic astrocytoma (LGG_PA_PF n = 14;

LGG_PA_MID n = 10) and from here onwards will be designated as classical PA. One case was classed as diffuse leptomeningeal glioneuronal tumor (DLGNT) (patient 30), and two as glioblastoma, IDH1/2 wild type (GBM_IDH_WT) (patients 26 and 28). Only one case received the DNA methylation-based diagnosis of MC-AAP (patient 27).

The results from DNA methylation profiling and t-SNE analysis (cluster analyses with 729 reference cases from 13 distinct MCs) were concordant in 29/31 samples (27 classical PA, one DLGNT, and one GBM_MID), as seen in Fig. 2.

Two cases exhibited discordant grouping between hierarchical clustering and t-SNE analysis. For the medullar tumor (patient 26), the highest calibrated score was 0.32 for GBM_MID but clustered in t-SNE close to LGG_PA_PF. It is, however, interesting to note that the calibrated score for LGG_PA_PF was 0.25. For patient 27, the main calibrated score was MC-AAP (0.89) but in t-SNE analyses, clustering was near LGG_PA_GG_ST. In this case, however, the calibrated score for LGG_PA_GG_ST was low, estimated as 0.013.

These discordances can be explained by differences in methods in variable selection and reference subgroups. Our analysis used a reduced number of sample references compared to the classifier, which can lead to a different t-SNE profile.

Copy number profiles (CNP)

To further characterize this entity, we analyzed chromosomal copy number variants from the CNPs. Of the tumors which received the DNA methylation classifier-based diagnosis of PA, 14/24 had flat CNPs with the characteristic focal low level 7q gain indicating the BRAF fusion. Four out of 24 showed characteristic gains of chromosomes 5 and/or 7, as it has been previously described in PA [START_REF] Lambert | Differential expression and methylation of brain developmental genes define location-specific subsets of pilocytic astrocytoma[END_REF]. One case showed only a gain of chromosome 8. Interestingly, the 5 remaining PAs had complex chromosomal rearrangements, with focal gains of chromosomes 5, 6, 7, 8, 10, 11, 12, 18, and/or 20. One of the complex cases showed a focal deletion on chromosome 9 at the CDKN2A locus. The DLGNT and one GBM, IDH-WT, had relatively flat profiles, while the other GBM, IDH-WT had a very complex CNP with a characteristic gain of chromosome 7. The MC-AAP had a very complex CNP, with deletions of chromosomes 3p, 10q, and 13q, gains of chromosomes 6, 7, and 8q.

Orthogonal validation of DNA methylation groups

DNA methylation profiling was concordant with MRI location in 26/28 conclusive cases. 12/12 cerebellar tumors were classified as LGG_PA_PF by DNA methylation profiling. 10/15 midline PAs (including the optic chiasm and spine) were classified as LGG_PA_MID by DNA methylation profiling. Two discrepancies arose: (1) patient 23 had a tumor which arose in the third ventricle from the ventral border of the tectal plate (reevaluated by an expert neuro-radiologist), and received a score for posterior fossa PA more significant than for midline PA (PF calibrated score 0.67, midline calibrated score 0.19, with a calibrated score for PA of 0.88), (2) patient 31's tumor was predominantly medullary with a small bulbar component, but classified by the DNA methylation profiling as posterior fossa PA. The three remaining cases were also midline: either spinal (the DLGNT and one GBM, IDH-WT) or hypothalamic (GBM, IDH-WT). The MC-AAP was supratentorial.

Figure 3 comparatively illustrates the different radiological, histopathological, molecular and CNP characteristics of patients 21 (LGG_PA_PF), 27 (MC-AAP), and 28 (GBM, IDH-WT)

All tumors that underwent methylation profiling with a diagnosis of PA had a radiological and histopathological diagnosis compatible with classical PA, as illustrated in Fig. 3a-d. Patient 21's tumor received the DNA methylationbased diagnosis of classical PA. MRI showed classical cerebellar PA features with both cystic and nodular portions and strong contrast enhancement (Fig. 3a). The biphasic tumor presented with Rosenthal fibers, eosinophilic granular bodies, and few mitoses (7/10HPF) (Fig. 3b), and MIB1 labeling index was estimated at 10% (Fig. 3c). The flat CNP was characteristic of classical PA (Fig. 3d).

The tumor from patient 27 received the DNA methylation profile of MC-AAP. Patient 27 was an 8-year-old girl who presented with headaches and paresis of the left arm. MRI revealed a cystic right parietal mass with contrast enhancement along the cyst border (Fig. 3e). This biphasic tumor presented with a very elevated mitotic count (17 mitoses for 2.3 mm 2 ), necrosis, and microvascular proliferation (Fig. 3f) The MIB1 labeling index was estimated at 30% (Fig. 3g). The CNP revealed an amplification of MDM2 gene which was associated with an overexpression of the protein MDM2 by immunohistochemistry (MDM2 (n = 1) [Clone IF2, 1:100; Thermofisher, Waltham, USA)] and a subtle loss of chromosome 10q, where FISH for PTEN revealed a monosomy (Fig. 3h). It harbored FGFR1 K678E and RAD50 R365Q pathogenic variants detected by RNA sequencing.

The tumor from patient 28 received the DNA methylation-based diagnosis GBM, IDH-WT. Patient 28 was a 15-year-old girl who presented with headaches and intracranial hypertension. MRI revealed a cystic hypothalamochiasmatic lesion with contrast enhancement along the cyst border (Fig. 3i). The infiltrative, biphasic tumor had Rosenthal fibers, eosinophilic granular bodies, 32 mitoses for 2.3 mm 2 , palisading necrosis, and microvascular proliferation (Fig. 3j). The MIB1 labeling index was estimated at 40% (Fig. 3k). The CNP revealed an amplification of MDM2 and CDK4 genes, as well as a loss of CDKN2A/B, frequently described in GBM (Fig. 3l). This tumor harbored both an FGFR1 in frame insertion and a PIK3CA E454K mutation detected by RNA sequencing.

The tumor from patient 26 received the DNA methylation-based diagnosis of GBM, IDH-WT with a very low score of 0.32, but clustered to PA in t-SNE. Patient 26 was an 8-month-old girl who presented with hemiparesis. MRI revealed a spinal lesion ranging from C4-T8, with necrosis and contrast enhancement along the cyst border. This oligo-like tumor displayed anaplastic features such as a high mitotic index (16 mitoses for 2.3 mm 2 ) and microvascular proliferation, but no necrosis. The tumor harbored a double FGFR1 mutation (N546S and K656E) detected by sequencing.

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Fig. 3 The tumor from patient 30 received the DNA methylation-based diagnosis of DLGNT. Patient 30 was a 7-year-old girl who presented with headaches and neck pain. On MRI, she had a large purely intramedullary spinal lesion ranging from the medulla oblongata to T7, with strong contrast enhancement and necrotic parts. This oligo-like tumor presented with microvascular proliferation, without necrosis, and 6 mitoses for 2.3 mm 2 , and harbored an NTRK2 rearrangement by FISH [ZytoLight SPEC NTRK2 dual color break apart probe (Zytovision, Bremerhaven, Germany)]. Interestingly, 1p FISH was difficult to interpret when first performed. This tumor was classified by DNA methylation as DLGNT (calibrated score 0.99), with a subtle loss of chromosome 1 on CNP. Therefore, 1p FISH was redone on multiple tumor fragments and, after reanalysis, was interpreted as a partial deletion due to probable intra-tumoral heterogeneity (Supplementary Fig. 1, online resource). Reexamination of the initial imaging found no leptomeningeal dissemination of the tumor (no MRI follow-up available). Based on the spinal location, NTRK2 rearrangement, and heterogeneous 1p loss in tumor cells, we retained the diagnosis of DLGNT.

In all "no match cases", FISH for BRAF showed a typical rearrangement. The rearrangement pattern evoked a duplication as frequently seen in the case of a KIAA1549:BRAF fusion. A sensitive secondary technique (ddPCR) confirmed the KIAA1549:BRAF fusion in all three cases. Therefore, the diagnosis of classical PA was retained.

Outcome analysis

Outcome data were available for all patients included in the cohort, with a range 2 months-9 years and a mean follow-up period of 28.2 months (σ = 26.1 months). Eighteen (58%) patients had tumor recurrence, with a mean PFS of 16.6 months (median 11.5 months; CI 95% 6.9-29.4). Four patients died of their disease, and one during surgery, with a mean OS of 41.5 months (Fig. 4).

In a univariate analysis, using the Log-rank test, no clinical or histopathological features were significantly associated with a worse OS (p < 0.05). Multivariate analyses using the Cox proportional hazards model did not find any statistically significant predictors of OS (values p < 0.05).

Univariate PFS analyses using the log-rank test put forward the following clinical features as significantly associated with a shorter PFS: age at diagnosis ≤ 6 years (p = 0.014, CI 95% 6.9-29.4), midline location compared to posterior fossa (p = 0.0293), and partial tumor resection (p = 0.0357). Outcome analyses dependent on histopathological criteria were carried out. No significant outcome differences between cases of PA with anaplasia with necrosis versus no necrosis (p = 0.07), or with 4-6 mitoses versus 7 or more mitoses were evidenced (p = 0.857). For cases with available ASL values (n = 17), no significant association was found between ASL hyper-perfusion and PFS (p = 0.197).

Multivariate analyses performed with the Cox proportional hazards model revealed age at diagnosis ≤ 6 years (adjusted hazard ratio (HR) 7.08 [95% CI 2.03-31.05], p < 0.001) and partial surgical resection (adjusted HR 9.17, [95% CI 1.95-69], p < 0.015) as independent risk factors which significantly impacted progression free survival (Fig. 5).

An excel sheet detailing all the data from this publication can be found in supplementary Table 1, online resource. Methylation array data have been deposited in the ArrayExpress database at EMBL-EBI (www.ebi.ac.uk/ array expre ss) under accession number E-MTAB-8390.

Discussion

We described the largest series of pediatric PAAF cases selected on the basis of the 2016 update of the WHO classification. Anaplasia in PA is defined by detailed criteria: ≥ 4 mitoses for 10 HPFs, with or without necrosis [START_REF] Capper | DNA methylation-based classification of central nervous system tumours[END_REF][START_REF] Louis | The 2016 World Health Organization classification of tumors of the central nervous system: a summary[END_REF][START_REF] Reinhardt | Anaplastic astrocytoma with piloid features, a novel molecular class of IDH wildtype glioma with recurrent MAPK pathway, CDKN2A/B and ATRX alterations[END_REF]. Two recent publications reinforced the existence of this entity, also called ANA PA or MC-AAP, based on a specific DNA methylation profile [START_REF] Capper | DNA methylation-based classification of central nervous system tumours[END_REF][START_REF] Louis | The 2016 World Health Organization classification of tumors of the central nervous system: a summary[END_REF][START_REF] Reinhardt | Anaplastic astrocytoma with piloid features, a novel molecular class of IDH wildtype glioma with recurrent MAPK pathway, CDKN2A/B and ATRX alterations[END_REF]. Indeed, this profile is different from the three conventional PA groups (PA PF, PA MID, PA SUP) [START_REF] Reinhardt | Anaplastic astrocytoma with piloid features, a novel molecular class of IDH wildtype glioma with recurrent MAPK pathway, CDKN2A/B and ATRX alterations[END_REF]. This large study was based on 83 histopathologically defined PAAFs, mainly in adults (77/83) in infratentorial location (63/76) [START_REF] Reinhardt | Anaplastic astrocytoma with piloid features, a novel molecular class of IDH wildtype glioma with recurrent MAPK pathway, CDKN2A/B and ATRX alterations[END_REF]. In the later study, mitotic cutoff of 4/10HPF was not reached in 61% of cases and MAPK alteration was not described in 25% of cases. The homozygous deletion of CDKN2A/B was found in 80% of cases, and loss of nuclear ATRX expression in 44% was considered important molecular distinctions, contrary to classical PA [START_REF] Reinhardt | Anaplastic astrocytoma with piloid features, a novel molecular class of IDH wildtype glioma with recurrent MAPK pathway, CDKN2A/B and ATRX alterations[END_REF]. Our cohort of pediatric PAAF, based on strict morphological and molecular WHO criteria, did not show the typical methylation pattern observed in adults. Moreover, most of the cases exhibited the classical molecular criteria described in PA (BRAF fusion) and/or clustered with one of the three conventional PA methylation groups. t-SNE analysis reinforced that a majority of these tumors clustered with classical PA. These findings led us to consider the diagnosis of PAAF based on histological criteria in children with caution since these criteria can also be observed in bona fide PA.

When focusing on the rare pediatric cases of PAAF (summarized in Table 2), the histomolecular characteristics of our single MC-AAP (patient 27) were in fact not substantially different from the literature, although available detailed histomolecular data were less extensive than for adult MC-AAP [17,[START_REF] Olar | ATRX protein loss and deregulation of PI3K/ AKT pathway is frequent in pilocytic astrocytoma with anaplastic features[END_REF][START_REF] Reinhardt | Anaplastic astrocytoma with piloid features, a novel molecular class of IDH wildtype glioma with recurrent MAPK pathway, CDKN2A/B and ATRX alterations[END_REF][START_REF] Rodriguez | PI3K/AKT pathway alterations are associated with clinically aggressive and histologically anaplastic subsets of pilocytic astrocytoma[END_REF][START_REF] Rodriguez | Alternative lengthening of telomeres, ATRX loss and H3-K27M mutations in histologically defined pilocytic astrocytoma with anaplasia[END_REF]. Interestingly, PAAF and/or MC-AAP in children do not share the main characteristics described in their adult counterparts. In the 10 out of 22 published pediatric cases with a known MAPK alteration, very few presented with the classical KIAA1549:BRAF alteration (n = 3). One harbored a double MAPK and H3K27M mutation, whose biological significance in this setting is still uncertain, but which must clearly be distinguished from both single MAPK altered tumors and single H3K27M mutated tumors [START_REF] Louis | cIMPACT-NOW update 2: diagnostic clarifications for diffuse midline glioma, H3 K27M-mutant and diffuse astrocytoma/anaplastic astrocytoma, IDH-mutant[END_REF][START_REF] Pagès | Co-occurrence of histone H3 K27M and BRAF V600E mutations in paediatric midline grade I ganglioglioma[END_REF]. In the remaining 9 cases, only four presented with a molecular profile similar to MC-AAP as defined in adults with a homozygous CDKN2A/B deletion, and only one also harbored a loss of ATRX protein expression. These findings have also been mentioned by Mistry et al. as alterations defining a subgroup of low-grade glioma with a tendency towards progression, including a single case with PA morphology [START_REF] Mistry | BRAF mutation and CDKN2A deletion define a clinically distinct subgroup of childhood secondary high-grade glioma[END_REF]. However, in our cohort, no cases presented with a loss of ATRX and only one case showed a homozygous CDKN2A deletion, but was nonetheless classified as PA by DNA methylation profiling. Thus, the loss of ATRX and/ or CDKN2A deletion, considered as hallmarks of MC-AAP in adults, does not seem to be strong indicators of MC-AAP in children. Overall, of the 7 pediatric cases (including the one from our cohort) with a diagnosis of MC-AAP confirmed by DNA methylation profiling, none presented with the most common anomalies described by Reinhardt et al.: NF1 mutation, CDKN2A deletion, and ATRX loss. Therefore, we consider that the diagnostic criteria established for adult MC-AAP are not accurately applicable to the pediatric population. This reinforces the importance of comparing molecular anomalies of pediatric tumors between themselves and separately from adult tumors. Furthermore, it should be highlighted that the study on adult MC-AAP found somatic NF1 mutations as the most frequent MAPK alteration, associated with CDKN2A/B and ATRX loss [START_REF] Reinhardt | Anaplastic astrocytoma with piloid features, a novel molecular class of IDH wildtype glioma with recurrent MAPK pathway, CDKN2A/B and ATRX alterations[END_REF]. Interestingly, a study on gliomas arising in neurofibromatosis 1 (NF1) found the same frequent CDKN2A and ATRX genetic alterations in NF1 high-grade gliomas [START_REF] Angelo | The molecular landscape of glioma in patients with Neurofibromatosis 1[END_REF]. These cases were subjected to DNA methylation profiling and did not correspond to MC-AAP [START_REF] Angelo | The molecular landscape of glioma in patients with Neurofibromatosis 1[END_REF]. It would, therefore, be misleading to use only molecular criteria to define MC-AAP within or outside the setting of background NF1-associated tumor predisposition. The only case of clinical NF1 in our cohort (patient 31) presented with a loss of CDKN2A/B. In this circumstance, a germline NF1 mutation followed by a somatic mutation lead to the loss of heterozygosity of the NF1 gene, thus causing the development of glioma [START_REF] Angelo | The molecular landscape of glioma in patients with Neurofibromatosis 1[END_REF]. This strongly supports the cooperation between an NF1 alteration and the loss of CDKN2A/B to bypass oncogene-induced senescence [START_REF] Jacob | Genetic aberrations leading to MAPK pathway activation mediate oncogene-induced senescence in sporadic pilocytic astrocytomas[END_REF]. Few of the existing studies reported alterations of the PIK3/AKT pathway, with 3/7 tested cases presenting with a loss of PTEN, phospho-S6, and/or phospho-AKT expression (Table 2) [START_REF] Olar | ATRX protein loss and deregulation of PI3K/ AKT pathway is frequent in pilocytic astrocytoma with anaplastic features[END_REF][START_REF] Rodriguez | PI3K/AKT pathway alterations are associated with clinically aggressive and histologically anaplastic subsets of pilocytic astrocytoma[END_REF]. Within our cohort, loss of PTEN expression was described in 17% of PA, and our single MC-AAP showed monosomy at the PTEN locus by FISH analyses, but no homozygous deletion as previously described [START_REF] Olar | ATRX protein loss and deregulation of PI3K/ AKT pathway is frequent in pilocytic astrocytoma with anaplastic features[END_REF]. Immunohistochemistry for our cases revealed phospho-S6 loss in 3% of cases, conserved PTEN staining in 69% of cases, and partial or complete loss in 31% (17% and 14%, respectively). In PAAF, PTEN homozygous deletion was suggested to be associated with worse survival [START_REF] Olar | ATRX protein loss and deregulation of PI3K/ AKT pathway is frequent in pilocytic astrocytoma with anaplastic features[END_REF], but this was not confirmed by the present study.

Radiological characteristics of PAAF/MC-AAP have not yet been described. After central neuroradiological review, the tumors presented with an aspect compatible with classical PA. The single MC-AAP was slightly different, since it was the only hemispheric case, and suggested the differential MRI diagnoses of ependymoma, RELA-fusion positive or cortical PA. No ASL values were available for this case. However, it was noticed that ASL values were higher than previously described in classical PA [START_REF] Dangouloff-Ros | Arterial spin labeling to predict brain tumor grading in children: correlations between histopathologic vascular density and perfusion MR imaging[END_REF].

Considering the clinical and prognostic aspects of our cohort, pediatric PAAF are not substantially different from classical PA. A large study on pediatric PA put forward patient age and extent of resection as the key prognostic factors, both of which were also the significant variables associated with PFS in our multivariate analyses [START_REF] Stokland | A multivariate analysis of factors determining tumor progression in childhood low-grade glioma: a populationbased cohort study (CCLG CNS9702)[END_REF]. Mitotic count above 4 per 10 HPF and the presence of necrosis were not of prognostic value among the cases analyzed in this study.

One study has suggested that PAAF in children had a better prognosis than in adults, but the DNA methylation class of these tumors is not known [START_REF] Rodriguez | Anaplasia in pilocytic astrocytoma predicts aggressive behavior[END_REF] and survival data on MC-AAP confirmed by DNA methylation profiling are not described in the literature (Table 2). The outcome for the only patient with MC-AAP seemed rather unfavorable, with an OS of 3.1 years following GTR and combined radiotherapy and chemotherapy. Further studies with extensive follow-up data are needed to define the prognostic significance of MC-AAP in children.

The large proportion of PAAF reclassified by DNA methylation profiling as classical PA suggests that the diagnoses to consider when faced with histopathological PA with elevated mitotic count with or without necrosis in children are firstly classical PA, and more rarely DLGNT, GBM IDH-WT, or MC-AAP.

The differential diagnosis of DLGNT may be complicated by its wide spectrum of histopathological and radiological features [START_REF] Deng | Molecularly defined diffuse leptomeningeal glioneuronal tumor (DLGNT) comprises two subgroups with distinct clinical and genetic features[END_REF]. The molecular hallmarks of this tumoral entity are the same recurrent MAPK alterations as described in classical PA, associated with a loss of chromosome 1p [START_REF] Deng | Molecularly defined diffuse leptomeningeal glioneuronal tumor (DLGNT) comprises two subgroups with distinct clinical and genetic features[END_REF]. The distinction from classical PA may be complicated due to the variety of possible MAPK alterations, tissular heterogeneity (major piloid component, absence of neuropil islands), and sub-clonal 1p deletion. In our case, 1p deletion was heterogeneous, not observed in all the tumoral components.

In our case of MC-AAP, the main differential diagnosis radiologically was ependymoma, RELA-fusion positive, and histopathologically was hemispheric GBM. The mitotic activity of this tumor was considerably more elevated than the aforementioned 4 mitoses described in PAAF (17 mitoses for 2.3 mm 2 ), and it featured necrosis and microvascular proliferation. The CNP also revealed an amplification of MDM2 gene, confirmed by immunohistochemistry, as previously described in GBM [START_REF] Jovčevska | Sequencing the next generation of glioblastomas[END_REF]. The 2 GBMs, IDH-WT in our series had 16 and 32 mitoses for 2.3mm 2 and microvascular proliferation, with or without necrosis. The diagnosis of supratentorial pediatric GBM can in itself be complex if IDH1/2 and histone gene mutations are not found [START_REF] Korshunov | H3-/IDH-wild type pediatric glioblastoma is comprised of molecularly and prognostically distinct subtypes with associated oncogenic drivers[END_REF].

The distinction is further complicated by the fact that the MC-AAP and GBMs, IDH-WT all harbored FGFR1 alterations. Alterations of FGFR1 have been described in the form of somatic mutations, gene fusions, and intragenic tyrosine kinase domain (TKD) duplications both in pediatric lowgrade gliomas and glioblastomas [START_REF] Jones | Recurrent somatic alterations of FGFR1 and NTRK2 in pilocytic astrocytoma[END_REF][START_REF] Rand | Sequence survey of receptor tyrosine kinases reveals mutations in glioblastomas[END_REF][START_REF] Zhang | Whole-genome sequencing identifies genetic alterations in pediatric low-grade gliomas[END_REF]. The same hotspot FGFR1 mutations have been described in PA and GBM alike, and were found in our cohort in both a classical PA (N546K) (patient 25) and the spinal GBM, IDH-WT (N546S and K656E) (patient 26) [START_REF] Jones | Recurrent somatic alterations of FGFR1 and NTRK2 in pilocytic astrocytoma[END_REF][START_REF] Rand | Sequence survey of receptor tyrosine kinases reveals mutations in glioblastomas[END_REF]. Our MC-AAP harbored an FGFR1 K687E mutation. The other GBM, IDH-WT (patient 28), harbored both an FGFR1 TKD-duplication and an E454K PIK3CA mutation. Activation of the PIK3CA pathway is considered an important genetic event in the development of GBM and can be associated with MAPK pathway activation [START_REF]Comprehensive genomic characterization defines human glioblastoma genes and core pathways[END_REF].

This reinforces the notion that isolated anomalies of FGFR1 are not a diagnostic or grading argument in pediatric glioma, as they have been described in benign glioneuronal (dysembryoplastic neuroepithelial tumors, and Rosette-forming glioneuronal tumor), glial (PA) and malignant neoplasms alike (GBM, and diffuse midline glioma, H3 1 3 K27M-mutant) [START_REF] Ellison | cIMPACT-NOW update 4: diffuse gliomas characterized by MYB, MYBL1, or FGFR1 alterations or BRAFV600E mutation[END_REF][START_REF] Johnson | Comprehensive genomic profiling of 282 pediatric lowand high-grade gliomas reveals genomic drivers, tumor mutational burden, and hypermutation signatures[END_REF]. Pediatric gliomas compatible with PAAF with a very high mitotic index (in our experience, more than 10 mitoses for 10 HPFs) should benefit from DNA methylation profiling, especially in the context of nonspecific FGFR1 alterations. We suggest that in cases of pediatric tumors with piloid features and > 10 mitoses for 10 HPFs the diagnoses of GBM and MC-AAP can be considered, but should be confirmed by DNA methylation profiling.

Therefore, based on our cohort and on the few published pediatric cases, the histological and molecular criteria that define anaplasia in adult PA cannot be applied for diagnosis in children. In this setting specifically, these tumors correspond either to PA or various other diagnoses including DLGNT and GBM. As the specific molecular alterations (CDKN2A deletion and ATRX loss) described by Reinhardt et al. have not been found in this cohort, one can conclude that the MC-AAP is rare in children, justifying further cooperative studies to define this entity in the pediatric population through the integration of multiple layers of information.

  Immunohistochemical analyses were carried out with antibodies specific for ATRX (n = 31) (Clone BSB108, 1:200; Bio SB, Santa Barbara, USA), MIB-1 labeling index (n = 31) (Clone M7240, 1:200; Aligent-Dako, Les Ulis, France), monoclonal mouse anti-human PTEN (n = 31) (Clone 6H2.1, 1:100; Dako, Les Ulis, France), Phospho-S6 (n = 31) (Ser235/236, 1:400; Cell Signaling Technology Inc, Leiden, The Netherlands), H3K27me3 (n = 31) (Clone A0821D, 1:1250; Diagenode, Seraing, Belgium), and BRAFV600E (n = 18) (Clone VE1, 1:100; Spring Biosciences, Pleasanton, USA) on the Benchmark XT immunostainer.

Fig. 1

 1 Fig. 1 Clinical, Radiological, Histopathological, and Molecular Characterization of 31 pediatric PAAF

Fig. 2

 2 Fig. 2 t-SNE plot of the 31 PAAF cases. Reference classes: ANA_PA anaplastic pilocytic astrocytoma, DLGNT diffuse leptomeningeal glioneuronal tumor, GBM_G34 glioblastoma with G34 mutation, GBM_MES glioblastoma, mesenchymal subtype, GBM_MID glioblastoma of the midline, GBM_MYCN glioblastoma, MYCN mutant

Fig. 4

 4 Fig. 4 OS and PFS of 31 pediatric PAAF, in months (Kaplan Meier curves)

Fig. 5

 5 Fig. 5 PFS according to age and extent of resection

  deceased, het del heterozygous deletion, IHC immunohistochemistry, MC AAP methylation class anaplastic astrocytoma with piloid features, NA not available, NEC not elsewhere classified, NOS not otherwise specified, PA pilocytic astrocytoma 1 3

1 3 Table 1

 31 Clinical characteristics of 31 pediatric patients with PAAFA alive, CT chemotherapy, DOD dead of disease, DOS dead of surgery, F female, GTR gross total resection, M male, PR partial resection, RT radiotherapy, STR subtotal resection

	Case Age Sex Tumor location	APA on first	Resection type Adjuvant treatment Recurrence	Status at	OS (months)
				resection or other			interval	last follow-
				resection			(months)	up
	1	1.9 M Optic chiasm	De novo	STR	CT	9.6	A	27.4
	2	13.0 M Right cerebellar	De novo	GTR	None	None	A	3.7
			hemisphere
	3	4.2 F	Cerebellar hemi-	De novo	STR	None	10.8	A	38.3
			spherse
	4	0.4 M Hypothalamus	De novo	PR	CT	2.4	A	71.3
	5	3.3 M Left cerebellar	De novo	GTR	None	None	A	15.6
			hemisphere
	6	0.7 F	Hypothalamus	De novo	PR	CT	2.1	A	86.1
	7	1.0 M Right cerebellar	De novo	STR	None	3.1	A	39.4
			hemisphere
	8	10.0 F	Left cerebellar	De novo	GTR	None	None	A	4.1
			hemisphere
	9	5.5 F	Right cerebellar	De novo	GTR	None	None	A	6.8
			hemisphere
	10	0.4 M Optic chiasm	De novo	PR	CT	8.2	DOD	27.5
	11	10.1 F	Cerebellar vermis	De novo	STR	None	None	A	24.6
	12	5.3 F	Left cerebellar	De novo	GTR	None	None	A	13.3
			hemisphere
	13	0.5 F	Hypothalamus	De novo	PR	CT	3.4	DOD	46.7
	14	15.0 M Hypothalamus	De novo	PR	None	None	A	27.6
	15	7.8 F	Optic chiasm	Malignant transfor-	STR	CT + RT	29.4	A	103.8
				mation
	16	3.3 F	Cerebellar vermis	De novo	STR	None	1.0	A	6.5
	17	1.7 M Right cerebellar	De novo	STR	None	None	A	8.8
			hemisphere
	18	9.8 M Left cerebellar	Malignant transfor-	PR	CT	11.9	A	51.1
			peduncle	mation
	19	12.7 F	Right cerebellar	De novo	GTR	None	39.4	A	53.5
			hemisphere
	20	15.2 F	Right cerebellar	Malignant transfor-	GTR	None	None	A	49.7
			hemisphere	mation
	21	13.0 M Vermis and left cer-	De novo	STR	None	None	A	2.5
			ebellar hemisphere
	22	8.8 F	Hypothalamus	Malignant transfor-	PR	CT	None	A	1.4
				mation
	23	7.5 M 3rd ventricle	De novo	PR	CT	13.8	A	13.7
	24	0.6 F	Hypothalamus	De novo	PR	none	None	DOS	0.0
	25	15.4 F	Hypothalamus	Malignant transfor-	PR	RT	11.5	A	37.7
				mation
	26	0.8 F	Spinal	De novo	PR	CT	1.2	A	12.9
	27	8.0 F	Right parietal	De novo	GTR	CT + RT	13.4	DOD	37.0
	28	15.9 F	Hypothalamus	Malignant transfor-	STR	CT	6.9	DOD	8.2
				mation
	29	1.6 F	Hypothalamus	De novo	PR	CT	1.0	A	18.9
	30	7.0 F	Spinal	De novo	PR	None	None	A	1.7
	31	8.8 M Bulbo-medullary	De novo	GTR	CT	2.5	A	12.2
			junction
									1 3

Table 2 22

 2 Published pediatric cases of PAAF, with or without DNA methylation profiling Authors

	Other	alterations
	PIK3/ATK	alteration
	Loss of	ATRX
	Homozy-	gous	CDKN2A	deletion
	MAPK	alteration
	Necro-	sis
	Mitotic	count/10HPFs
	PFS	(months)
	Pro-	gres-	sion
	Death OS	(months)
	Gender	[M:	male;	F:	female]
	Location Age at	diag-	nosis	(years)
	DNA	meth-	ylation	profile
	Institu-	tional	histo-	patho-	logical	diagnosis
						Reinhardt	2018

Table 2 (

 2

		Other	alterations
		PIK3/ATK	alteration
		Loss of	ATRX
		Homozy-	gous	CDKN2A	deletion
		MAPK	alteration
		Necro-	sis
		Mitotic	count/10HPFs
		PFS	(months)
		Pro-	gres-	sion
		Death OS	(months)
		Gender	[M:	male;	F:	female]
		Location Age at	diag-	nosis	(years)
		DNA	meth-	ylation	profile
	continued)	Authors Institu-	tional	histo-	patho-	logical	diagnosis	Rodriguez Anaplas-	2011 tic pilo-	case 1 cytic	/2019 astrocy-	case 17 toma

Table 2 (

 2

		Other	alterations
		PIK3/ATK	alteration
		Loss of	ATRX
		Homozy-	gous	CDKN2A	deletion
		MAPK	alteration
		Necro-	sis
		Mitotic	count/10HPFs
		PFS	(months)
		Pro-	gres-	sion
		Death OS	(months)
		Gender	[M:	male;	F:	female]
		Location Age at	diag-	nosis	(years)			Cerebel-	lum
		DNA	meth-	ylation	profile			NA
	continued)	Authors Institu-	tional	histo-	patho-	logical	diagnosis	Rodriguez PA with	2019 anapla-	case 4 sia

Acknowledgements

We would like to thank the laboratory technicians at the GHU-Paris Neuro Sainte-Anne for their assistance, clinical research assistant Elise Akan, Karen Silva and the RENOCLIP Network (REseau National de Neuro-Oncologie CLInico-Pathologique, France), as well as the Integragen platform for their help with DNA methylation sequencing.

Funding No funding was received for this study.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflicts of interest.

Ethical approval

This study was performed in compliance with the local GHU Paris Sainte Anne's ethics board, INDS: MR 1409210519.

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