Mouaadh Abdelkarim

Sandrine Caron

Christian Duhem

Janne Prawitt

Julie Dumont

Anthony Lucas

Emmanuel Bouchaert

Olivier Briand

John Brozek

Folkert Kuipers

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.


Thomas Clausen
email: thomas@thomasclausen.org

Ulrich Herberg
email: ulrich@herberg.name

Comparative Study of RPL-Enabled Optimized Broadcast in Wireless Sensor Networks

Keywords: RPL, Sensor Network, Broadcast

Recent trends have suggested convergence to Wireless Sensor Networks (WSNs) becoming IPv6-based. To this effect, the Internet Engineering Task Force has chartered a Working Group to develop a routing protocol specification, enabling IPv6-based multi-hop WSNs. The current effort of this working group is development of a unicast routing protocol denoted RPL. RPL constructs a "DAG-like" logical structure with a single root, at which the majority of the traffic flows terminate, and assumes restrictions on network dynamics and traffic generality, in order to satisfy strict constraints on router state and processing.

This memorandum investigates the efficient network-wide broadcast mechanisms in WSNs, using the logical structure already established by RPL. The aim hereof is to impose minimal additional state requirements on WSN routers, beyond that already maintained by RPL. This memorandum presents a selection of such broadcast mechanisms for RPL routed WSNs, and evaluates their performances. As part of this evaluation, the memorandum compares with MPR Flooding -an established efficient flooding optimization, widely used in MANETs.

Comparative Study of RPL-Enabled Optimized

Broadcast in Wireless Sensor Networks

Résumé :

Les tendances récentes suggèrent une convergence des réseaux de capteurs sans fils (WSNs ou Wireless Sensor Networks) vers IPv6. C'est pourquoi l'IETF (Internet Engineering Task Force) a mis en place un groupe de travail, chargé de spécifier un protocole de routage permettant aux réseaux de capteurs sans fil multi-sauts de fonctionner avec IPv6. Les efforts du groupe de travail se concentrent actuellement sur le développement d'un protocole de routage unicast appelé RPL. RPL construit une architecture logique de type DAG (graphe orienté acyclique) avec un noeud racine unique sur lequel se termine la majorité des flux de trafic, et suppose des restrictions sur les dynamiques du réseau et sur les types de trafic supportés afin de satisfaire les contraintes fortes des routeurs en terme d'états et de traitement.

Cet article examine la possibilité de fournir aux réseaux de capteurs sans fil des mécanismes efficaces de broadcast (diffusion), en utilisant la structure logique déjà proposée par RPL. Le but est ici de ne pas imposer d'exigences supplémentaires aux routeurs WSN fonctionnant déjà avec RPL. De tels mécanismes de broadcast pour les réseaux WSN utilisant le routage RPL, l'article en présente plusieurs et évalue leur performance. Dans le cadre de cette évaluation, ils sont comparés aux mécanismes reconnus et efficaces d'optimisation de diffusion du protocole MPR Flooding, largement utilisé dans les réseaux MANETs.

Mots-clés : RPL, Réseaux de capteurs, Diffusion

Introduction

The general context for routing in Wireless Sensor Networks (WSNs) is small, cheap devices whose primary function is data acquisition, and for which communications capabilities are a "commodity to their primary function" -a necessary, but in preference unobtrusive, functionality, specifically targeted to the precise goal which the WSN is deployed to satisfy. As an example, a WSN deployed for environmental monitoring might contain a set of temperature sensors, sending "notifications" to a central controller when the temperature exceeds certain thresholds -and occasional "keepalive" messages otherwise, to let the controller know that the sensors are still operational. Traffic from the controller to the individual sensors may be limited to "setting the thresholds" -possibly rarely, such as at system deployment.

Routing Protocol for Low power and Lossy Networks

Recent trends have suggested convergence to WSNs becoming IPv6-based. To this effect, the ROLL working group of the IETF is currently specifying an IPv6-based unicast routing protocol for WSNs, denoted RPL ("IPv6 Routing Protocol for Low power and Lossy Networks" [START_REF] Winter | RPL: IPv6 Routing Protocol for Low power and Lossy Networks[END_REF]). The basic construct in RPL is the DODAG -a destination oriented DAG, rooted in a "controller". In the converged state, each WSN router has identified a stable set of parents, on a path towards the "root" of the DODAG, as well as one among these as its preferred parent. Each router, which is part of a DODAG (i.e. has selected parents) will emit DODAG Information Object (DIO) messages, using link-local multicasting, indicating its respective Rank in the DODAG (i.e. its distance from the root according to some metric(s), in the simplest form hop-count). Upon having received a (number of such) DIO messages, a router will calculate its own rank such that it is greater than the rank of each of its parents, and will itself start emitting DIO messages. Thus, the DODAG formation starts at the root, and spreads gradually to cover the whole network. The root can trigger "global recalculation" of the DODAG by way of increasing a sequence number in the DIO messages.

RPL Operational Requirements

The minimal set of in-router state required in a WSN router running RPL is, (i) the identifier of the DODAG root, (ii) the address and rank of the preferred parent, (iii) the configuration parameters shared by the DODAG root and (iv) the maximum rank that the WSN router has itself advertised. For redundancy, a WSN router running RPL can maintain information describing additional parents, which may allow rapidly changing its preferred parent in case the former preferred parent becomes unreachable.

RPL control message generation is timer-based, with the root able to configure suitable back-off of message emission intervals using trickle timers [START_REF] Lewis | Trickle: A Self-Regulating Algorithm for Code Propagation and Maintenance in Wireless Sensor Networks[END_REF].

RPL Traffic Patterns

"Upward paths" or "multipoint-to-point paths" from the sensors towards the controller are supported by installing the "preferred parent" in each WSN router as the next hop on the path towards the DODAG root. The DODAG root may in its DIO messages have advertised a set of destination prefixes, to which it provides connectivity. These prefixes can be used to populate the routing table in the WSN routers in the network, or a default-route via the preferred parent and the DODAG root can be installed.

"Downward paths" or "point-to-single-sensor paths" are supported by having WSN routers, which wish to be reachable, issue Destination Advertisement Object (DAO) messages. These propagate via parents towards the DODAG root, and describe which prefixes can be reached via which WSN router. Each intermediate WSN router, forwarding a DAO message towards the root, adds its address to a reverse routing stack in the DAO message, thereby providing the DODAG root with the ability to do source routing for reaching destinations in the WSN.

"Sensor-to-sensor paths" are as default in [START_REF] Winter | RPL: IPv6 Routing Protocol for Low power and Lossy Networks[END_REF] supported by having the source sensor transmit via its default route to the root, which will add a source-route to the received data for reaching the destination sensor.

Problem Statement

RPL, as currently specified in [START_REF] Winter | RPL: IPv6 Routing Protocol for Low power and Lossy Networks[END_REF], supports only unicast traffic. RPL does, however, not explicitly provide support for any form of "optimized broadcasting" -delivery of the same data packet to all routers in the WSN. One important application of broadcasting in a WSN is for a controller to request that all sensors in the WSN transmit their sensor information -e.g. to verify if an alarming condition, signaled by a single sensor, is confirmed by other sensors in the WSN.

While such a "broadcast" could be accomplished by the DODAG root performing "bulk-unicast" to all sensors in the network, this is hardly efficient due to redundant transmissions of the same packets. Thus, this memorandum investigates ways of providing a reasonable optimized broadcast capability for an RPL routed network.

Memorandum Outline

The remainder of this memorandum is organized as follows: section 2 suggests a selection of different mechanisms for, by way of using the data structures and topologies already maintained by RPL, providing support for broadcast traffic in a WSN, and also briefly presents MPR Flooding. Section 3 provides a comparative performance study of the suggested broadcast mechanisms. Section 4 concludes this paper.

Data Broadcasting in RPL

This section suggests mechanisms for exploiting the DODAG, as constructed by RPL, in order to undertake better-than-classic-flooding for WSN-wide broadcasting. The fundamental hypothesis for these mechanisms is that all broadcast operations are launched from the root of the DODAG. If a sensor needs to undertake a network-wide broadcast, the assumption is that this broadcast is INRIA sent to the root using unicast, from where the DODAG root will launch the broadcast operation.

Classic Flooding (CF)

A common baseline for broadcast operations is that of classic flooding: each router relays a broadcast packet upon its first receipt by that router; subsequent receipts of the same packet are suppressed and do not cause retransmissions. This has to its merit that no control traffic is required -however also entails (i) that each data packet must be uniquely identifiable (e.g. by embedding a unique sequence number for a given source), (ii) that each router must maintain state for each already received and relayed data packet so as to enable suppression of duplicates, and (iii) each data packet is retransmitted by each router in the network -often with a large degree of redundant transmissions as consequence.

Redundant retransmissions cause increased battery drain, both when transmitting and receiving (and discarding) the redundant packets, and increase contention on the wireless media, increasing the probability of data loss due to collisions. CF is, for these reasons, not suggested as a mechanism for data broadcast in WSNs, but is described here as a baseline for data broadcasting in RPL.

MultiPoint Relay Flooding (MPRF)

A common improvement over Classic Flooding is for each router to select and designate a subset of its neighbors (MultiPoint Relays -MPRs [START_REF] Qayyum | Multipoint relaying: An efficient technique for flooding in mobile wireless networks[END_REF]) for relaying broadcast transmissions, thereby reducing the number of redundant retransmissions of each packet. This has been shown to offer dramatic reductions in the network load (fewer transmissions), as well as a dramatic reduction in data loss due to collisions [START_REF] Clausen | Investigating Broadcast Performance in Mobile Ad-hoc Networks[END_REF].

In order for MPRF to work, a router must select its MPRs such that a message relayed by these MPRs will be received by all routers two hops away. To this end, each router must maintain, at a minimum, state describing both its neighbor routers, as well as its 2-hop neighbors. MPRF -as CF -requires identification of each broadcast packet, and maintenance of state allowing elimination of duplicate packets.

MPRF is a common approach in wireless ad hoc networks, where it is used e.g. for network-wide broadcast of routing protocol control traffic by [START_REF] Clausen | Optimized Link State Routing Protocol (OLSR)[END_REF], [START_REF] Clausen | SPF Multipoint Relay (MPR) Extension for Ad Hoc Networks[END_REF] and [START_REF] Clausen | The Optimized Link State Routing Protocol version 2 (OLSRv2)[END_REF] -as well as for network-wide data broadcast [START_REF] Macker | Simplified Multicast Forwarding[END_REF]. Comparing RPL-specific broadcast mechanisms with MPRF is therefore, to a certain extend, a comparison with "state of the art" of broadcasting in wireless multi-hop networks.

Parent Flooding (PF)

Admitting the RPL "philosophy" of data transmission to sensors originating at (or relaying via) the DODAG root, RPL lends itself to a first and simple broadcast optimization: restricting a RPL router to retransmit only broadcast packets received from a "parent". Logically, the basic performance hereof should be similar to that of classic flooding: with the broadcast operation initiated from the DODAG root, each router will retransmit the packet upon receipt from a parent. PF does not require any additional control traffic over that which is caused by RPL. PF may apply identification of each broadcast packet, and maintenance of state allowing elimination of duplicate packets in order to avoid multiple retransmissions of the same packet received from different parentssimilar to MPRF and CF.

Preferred Parent Flooding (PPF)

In order to not incur any additional in-router state requirements for detecting and suppressing retransmission of duplicate packets, preferred parent flooding utilizes the existing relationship between RPL routers, in order to ensure that no router will forward a broadcast packet more than once. Each RPL router is required to select exactly one Preferred Parent. Restricting retransmissions of broadcast packets to only those received from the router's preferred parent ensures that duplicates received from other routers are ignored for retransmission.

Preferred Parent MPR Flooding (PPMPRF)

PPF is fundamentally a derivative of the MPRF optimization, attempting further to decrease the number of retransmissions necessary for a network wide broadcast. The idea is as follows: each router, selected as "Preferred Parent", must designate a subset of its "selectees" (children which have selected it as preferred parent) as "Preferred Children". These "Preferred Children" must be selected such that a message, relayed by these "Preferred Children", will reach all its "grand children" -i.e. the children of its "selectees".

Whenever a router receives a data packet that is to be broadcast throughout the network, that router will only then forward the packet if (i) at least one parent of that router has selected it as preferred child and (ii) the packet has not been previously received (as determined by a duplicated detection mechanism). It is to be noted that it is not sufficient to restrict forwarding to packets received from the preferred parent of a router, but that packets from any parent of that router have to be forwarded if the router has been selected as preferred child by at least one of its parents. The rationale is illustrated in figure 1. Assuming that the root of the network (router 0) has selected B as preferred child as indicated by the downward arrow, and B forwards a packet originating from the root. If forwarding was restricted to packets received from the preferred parent of a router, D would not forward the packet from B (since it is no preferred parent of D), and thus X would never receive the packet.

Compared to "classic" MPR selection, the "Preferred Children selection" (i) concerns only coverage of "grand children" (i.e. "downward" in the DODAG as constructed by RPL) and (ii) is restricted by the preferred parent selection from RPL.

This restriction entails less liberties with respect to selecting relays for "best 2-hop coverage". It is quite possible that the child providing the "best" coverage of a router has not selected that router as Preferred Parent, and that therefore PPMPRF will result in more relays than MPRF. In RPL, the Preferred Parent selection is intended to optimize for "best upwards paths towards the DODAG root" (possibly according to some deployment specific optimization criteria), which may not coincide with what would be optimal for "best downwards coverage". The PPMPRF mechanism also requires that each router knows (i) which children have selected it as Preferred Parent (i.e. its selectees), and (ii) which routers are Preferred Children of these selectees. This information can be made available through adding an option to DIO messages, emitted by all routers running RPL.

Optimized Preferred Parent MPR Flooding (PPMPRFopt)

This mechanism represents a small optimization over PPMPRF, in that it provides all neighboring routers with the same rank with information, encouraging coordinated Preferred Parent selection so as to try to reduce the number of routers selected as Preferred Parent. Thus, a router will select as its Preferred Parent among its parents, the one which most of its adjacent routers also have in their parent set. Given a tie, the parent which a majority of the adjacent routers have already selected as Preferred Parent will be chosen. Thus, in addition to the information indicated for PPMPRF, PPMPRF-opt requires all parents to be advertised. Figure 2(a) depicts an example of Preferred Parent selection, as may happen in basic RPL: a router selects its Preferred Parent amongst all its parents with the lowest rank in an uncoordinated way. Worst case (in terms of redundant transmissions and therefore possible collisions when broadcasting), routers D, E and F all select different Preferred Parents (C, B, and A respectively). Similarly, I, H, and G may select three different Preferred Parents. For PPMPRF, this means that all routers, other than 0, will be selected as MPRs and thus retransmit a broadcast.

Figure 2(b) depicts a coordinated Preferred Parent selection. Router D will advertise all its parents (C and B) in its control messages, as will E (parents C, B and A) and F (parents B and A). D has an equal choice between parents C and B, and F has the same choice between B and A. E will select B as Preferred Parent because this is the only parent that both of its adjacent routers can also select as Preferred Parent. Once D and F receive a control message from E, advertising that B is selected as Preferred Parent, they will also select B. Thus, only routers B, E and H will be selected as Preferred Parents and therefore retransmit a broadcast. Such coordinated Preferred Parent selection may be a double-edged sword for RPL. While it is a potential benefit for broadcast traffic from the DODAG root, unicast traffic flows towards the DODAG root via Preferred Parents. Thus, coordinated selection of Preferred Parents implies that unicast traffic is concentrated through a subset of the routers in the network, possibly increasing congestion in these routers, increasing the battery drain in these routers etc.

RPL Broadcast Performance Study

In order to explore the performance of RPL-enabled broadcast, simulations of MPRF, PPMPRF(-opt), PF and PPF have been performed using the Ns2 network simulator. The RPL protocol itself, providing the basic DODAG, used by PF and PPF, has been implemented in Java according to [START_REF] Winter | RPL: IPv6 Routing Protocol for Low power and Lossy Networks[END_REF]. For MPRF and PPMPRF, the neighborhood discovery and MPR selection part of the Java based OLSRv2 implementation [START_REF] Herberg | JOLSRv2 -An OLSRv2 implementation in Java[END_REF] has been used. The specific scenario settings are detailed in table 1; for each datapoint in the results presented in this section, ten different scenarios have been simulated, with the results presented being the average from these runs.

For the purpose of this study, only a single RPL instance with a single DODAG is considered (but for each run with different, random positions of all routers). At the beginning of the simulation, only the root (which is the WSN router with the ID of 0) starts transmitting DIOs. Upon successful convergence of the DODAG, the root starts sending broadcast data with a data rate of 1280 bytes/s (64 byte long packets, sent every 50 ms).

In the following, the broadcast mechanisms presented in section 2 are analyzed in terms of MAC layer collisions, delivery ratio, overhead, delay, and path

INRIA

Basic Results

Figure 3 depicts the number of collisions of frames on the MAC layer, for the different broadcast mechanisms. MPRF and PPMPRF-opt yield the lowest number of collisions among the analyzed protocols, with PPMPRF causing about the same number of collisions as PF+DD (PF with duplicate packet detection). This is expected, as in MPRF, relays are explicitly selected so as to avoid redundant retransmission by topologically close routers, and the coordinated preferred parent selection in PPMPRF-opt also reduces the number of relays. PPMPRF without coordination entails more relays, as more routers in the network will be selected as preferred parents, which in turn select the relays (i.e. preferred children). In PPF, topologically close routers are likely to have chosen the same Preferred Parent and so will explicitly produce redundant retransmissions. Consider the example in figure 4, wherein a broadcast transmission is made by router 0 and relayed as indicated by the solid arrows. In PPF, as indicated in figure 4(a), each router will select its Preferred Parent and retransmit the packet once upon receipt from that preferred parent. Routers A, B and C all receive the transmission directly from router 0. Routers D, E and F have all chosen one of A, B and C as Preferred Parent and will thus all retransmit when receiving the transmission from their chosen preferred parent -similar for I, H, G, even though these three do not have any routers further down the network. In contrast, in figure 4(b), MPRs have been selected. Router 0 has selected B as MPR (as B "covers" D, E, F) and router B has chosen router E as MPR (as it covers all of G, H, I). As there are no further routers "below" in the network, router E has chosen no MPRs downwards. Thus, only B and E retransmit the broadcast packet from 0 -i.e. for each "level" in this simple network, only a single transmission occurs, with no collisions at each level. Figure 5 depicts the delivery ratio of broadcast packets. The delivery ratio of the MPRF and PPMPRF mechanisms are the highest of the compared broadcast mechanisms, with PPMPRF-opt being not much below MPR. This can be interpreted as a tradeoff between redundancy and efficiency: in relatively scarce INRIA networks (such as the simulated scenario) a higher redundancy of relays, such as in PPMPRF, can lead to a higher delivery ratio, despite of the increased number of collisions. as observed in figure 3. In dense networks, however, the large number of collisions with more redundant delays can reverse that effect and reduce the delivery ratio. A detailed analysis of the MPR relaying mechanism can be found in [START_REF] Qayyum | Multipoint relaying: An efficient technique for flooding in mobile wireless networks[END_REF]. PF+DD has a higher delivery ratio than PPF, due to the redundancy of transmissions -when a router receives the same broadcast packet from several of its parents, chances are higher that at least one of the packets will reach the router, while if the one transmission from the preferred parent in PPF is lost due to a collision, the router will not forward the other incoming packets from its (non-preferred) parents. The higher delivery ratio of PF+DD is at the expense of vastly higher media load, as depicted in figure 6: the cumulative number of bytes transmitted during the simulations are significantly higher for PF+DD and for PPMPRF without the optimization. PPF incurs a lower overhead than PF+DD with MPRF still outperforming PPF by a large, and constant, margin. PPMPRF-opt has a similar overhead as MPRF. Figure 7 depicts the average end-to-end delay for data traffic from the root to every WSN router in the network, and figure 8 depicts the average path length of successfully delivered data packets. The optimized MPR-based broadcast mechanisms incur the lowest delay of the protocols, while PPF causes a slightly lower delay than does PF+DD. The, on average, longer path lengths of MPRF are due to the data delivery ratio being higher -MPRF successfully "reaches" routers farther away from the root (as depicted in figure 9). It has been shown ( [START_REF] Qayyum | Multipoint relaying: An efficient technique for flooding in mobile wireless networks[END_REF]) that MPR leads to optimal path length. That means that every mechanism indicating a shorter path in the figure entails a lower reachability of routers further away from the broadcast source. Longer paths indicate suboptimal paths. It is worth observing that MPRF achieves the optimal path length with a lower delay still. This can in part be explained by the fact that MPRF ensures that data is flooded via shortest paths, and in part by the fact that with fewer retransmissions, less media and queue contention occurs.

PPF with Jitter

In the results presented in section 3.1, data traffic has been promptly forwarded by each WSN router, without explicit delay. As has been shown in [START_REF] Clausen | The Optimized Link State Routing Protocol, Evaluation through Experiments and Simulation[END_REF][START_REF] Clausen | Jitter Considerations in Mobile Ad Hoc Networks (MANETs)[END_REF], adding a random jitter before retransmitting a broadcast packet can significantly reduce the number of collisions and, therefore, increase the delivery ratio for broadcast packets. In the following, the effect of adding jitter to PPF is investigated.

Figure 10 depicts the collision ratio of frames when using no jitter, and a random jitter uniformly distributed between 0 and 500 ms respectively. With jitter, the collision ratio is much lower than it is without. This is due to the fewer concurrent retransmissions by adjacent WSN routers. Comparing to figure 3, PPF with jitter yields a collision ratio comparable to, or lower than, MPRF without jitter. As a consequence of the lower collision ratio, the delivery ratio of PPF with jitter is higher than it is without, as depicted in figure 11. Comparing to figure 5, the delivery ratio of PPF still remains consistently below that of MPRF, even when PFF is used with jitter. The drawback of using jitter is a higher end-to-end delay of packets, as depicted in figure 12. With jitter, the delay is considerably higher than it is without. This memorandum presents a comparative study of broadcast mechanisms for RPL routed wireless sensor networks. Broadcast mechanisms, using the rooted DAG-like logical structure, maintained by the unicast routing protocol RPL, are introduced, and their performance studied. These broadcast mechanisms, denoted "Parent Flooding" (PF), "Preferred Parent Flooding" (PPF) and "Preferred Parent MPR Flooding" (PPMPRF) adhere to the "root-oriented" concept of RPL, in that all broadcast operations are to be initiated by the root of the DAG. PF, PPF and PPMPRF are studied and compared by way of network simulations -and as a point of comparison, MPR Flooding (MPRF), known from wireless ad hoc networks, is also subjected to the same network scenarios in the simulator.

Contents

Figure 1 :

 1 Figure 1: PPMPRF: Example showing the need to forward packets not only received by the preferred parent, but by any parent if the router is selected as preferred child by at least one of its parents. Upward arrows depict preferred parent selection, downward arrows preferred child selection.

Figure 2 :

 2 Figure 2: Uncoordinated PP selection (a) and coordinated PP selection (b) in the same network. Solid arrows indicate the selection of a Parent as Preferred Parent; dotted lines the connectivity of the network.

Figure 3 :

 3 Figure 3: Broadcast: total number of MAC layer collisions

Figure 4 :

 4 Figure 4: PPF (a) and MPRF (b) in the same network. Solid arrows indicate transmission of a packet; dotted lines the connectivity of the network.

Figure 5 :

 5 Figure 5: Broadcast: delivery ratio

Figure 8 :Figure 9 :

 89 Figure 6: Broadcast: total retransmission overhead

Figure 10 :

 10 Figure 10: Collision ratio of PPF with jitter

Figure 11 :

 11 Figure 11: Delivery ratio of PPF with jitter

Figure 12 :

 12 Figure 12: Average delay of PPF with jitter

4 2

 4 Protocol for Low power and Lossy Networks . . . . . . . 3 1.1.1 RPL Operational Requirements . . . . . . . . . . . . . . . 3 1.1.2 RPL Traffic Patterns . . . . . . . . . . . . . . . . . . . . . 3 1.2 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Memorandum Outline . . . . . . . . . . . . . . . . . . . . . . . . Data Broadcasting in RPL 4 2.1 Classic Flooding (CF) . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 MultiPoint Relay Flooding (MPRF) . . . . . . . . . . . . . . . . 5 2.3 Parent Flooding (PF) . . . . . . . . . . . . . . . . . . . . . . . . 5 2.4 Preferred Parent Flooding (PPF) . . . . . . . . . . . . . . . . . . 6 2.5 Preferred Parent MPR Flooding (PPMPRF) . . . . . . . . . . . 6 2.6 Optimized Preferred Parent MPR Flooding (PPMPRF-opt) . . . 7 3 RPL Broadcast Performance Study 8 3.1 Basic Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3.2 PPF with Jitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 4 Conclusion 15

Table 1 :

 1

		Ns2 parameters
	Parameter	Value
	Ns2 version	2.34
	Mobility scenarios	No mobility, random uniform distribution of
		WSN routers
	Grid size	variable
	WSN router density	50 / km 2
	Communication range	250m
	Radio propagation model Two-ray ground
	Simulation time	200 secs
	Interface type	802.11b
	Radio frequency	2.4 GHz
	length. CF and PF (without duplicate detection) are not considered since their
	performance is expectedly much worse than any of the other mechanisms.

RR n°7296


Nicolas Puech

Eric Grelet

Philippe Poulin

Christophe Blanc

Paul Van Der Schoot

Nematic droplets in aqueous dispersions of carbon nanotubes

Keywords: numbers: 61.30.Hn, 61.30.Dk, 82.70.Dd

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

Carbon nanotubes or CNTs are colloidal particles with a very large aspect ratio, typically in the range from many tens to hundreds up to even thousands. Hence, it is not surprising that, provided they are properly stabilized against aggregation, fluid dispersions containing CNTs exhibit an Onsager-type isotropic-nematic transition [1][2][3][4][5][6]. This happens at concentrations in excess of a critical value that depends on the aspect ratio of the rods.

The relevant concentration scale here is the volume or packing fraction because the driving force for the spontaneous alignment is the anisotropic volume exclusion between the particles. For the nematic to become stable the volume fraction of CNTs should be in excess of a few times the reciprocal of some average of their aspect ratios [7].

It follows that the nematic transition must occur at very low concentrations of, say, one per cent of CNTs. This, by and large, is in agreement with experimental observation, allowing for instance for the effects of polydispersity [1][2][3][4][5][6]. Often, before isotropic-nematic phase separation occurs on a macroscopic scale in dispersions of elongated colloidal particles, the nematic phase establishes itself in the form of droplets called tactoids. Tactoids have been observed in many dispersions, such as tobacco mosaic virus [8,9], boehmite rods [10], poly(butyl glutamate), self-assembled chromonics [11], fd virus [12], f-actin [13], vanadium pentoxide [14,15]. These droplets have in common their unusual elongated, spindle-like shape.

This shape can be explained by the preferential planar anchoring of the nematic director at the interface with the isotropic phase. The competition between surface tension and the elastic deformation of the bipolar director field that accommodates this preferential planar anchoring plausibly determines the optimal aspect ratio (Figure 1). If the director field of a tactoid is indeed bipolar with field lines connecting two boojum surface defects, then its shape, as described, e.g., by the aspect ratio or the tip angle, depends on its physical dimensions. This seems to be the case in all systems investigated so far. Indeed, information on the ratio of (an average of) the elastic constants and the surface tension can be obtained from the measured relation between, say, the aspect ratio and length of the droplets [13,[15][16][17][18].

In this letter, we show that aqueous dispersions of surfactant-stabilized carbon nanotubes deviate from the usual picture of a bipolar director field. The tactoids that we observe in these dispersions are also quite elongated, but display a uniform director field as it is evidenced by polarization microscopy. This ties in with our finding that the aspect ratio of the tactoids is independent of their size, at least for the one decade range of sizes present in our samples. Theoretically, the aspect ratio of tactoids is predicted to be independent of their size if dictated by the surface tension anisotropy [16]. This is plausible if the director field is uniform and as a result of that the anchoring conditions at the surface of the drops are suboptimal. From our observations we find that the anchoring strength is about four times larger than the bare surface tension. We put forward that the surface tension must be very small indeed, possibly as low as 1 nN/m. We prepared our CNT tactoid dispersions from an aqueous suspension of single-wall carbon nanotubes (furnished by Elicarb batch K3778) and dispersed by bile salts, at respective concentrations of 0.5% w/w CNTs and 0.5% w/w bile salts. To exfoliate the CNT bundles, sonication was applied to the suspension for three hours. A purification process by selective centrifugation was then performed on the CNT suspensions. After removing CNT aggregates by centrifugation at low speed (30 min, 3500 rpm), the longest carbon nanotubes exhibiting some entanglements and defects were removed by ultracentrifugation (45 min, 45000 rpm). A second ultracentrifugation (180 min, 45000 rpm) was applied to the CNT suspensions to obtain the nematic liquid crystalline phase, which appeared as a black pellet on the bottom of the centrifugation tube. Finally, CNT tactoids were obtained by diluting the nematic phase up to the coexistence region with the isotropic phase. Thin samples of only a few µm thick were prepared at the isotropic-nematic phase coexistence between cover slip and glass slide. The CNT tactoids were observed by optical microscopy at different magnifications between crossed polarizers.

Figure 2 shows an image by polarization microscopy of the kind of tactoids that we find in our carbon nanotube dispersions. The background is dark because the tactoids float in the coexisting isotropic liquid phase. The tactoids are indeed quite elongated and have the typical spindle-like shape. A perfect extinction is observed when the tactoids are aligned along the polarizer or analyzer direction, demonstrating that the director field is uniform, as shown on a typical tactoid in figure 3. A further study under confocal Raman microspectroscopy also confirms that the director filed is aligned along the tactoid long axis [19], which coincides with the main optical axis.

In figure 4 the aspect ratios of a large collection of tactoids is plotted against their length, which, within experimental error, is constant as advertised. Apparently, the mean aspect ratio of the tactoids is about four for tactoids up to 36 µm in length. This result is consistent with a uniform director field in the droplets, as the aspect ratio of the drops is then dictated by the ratio of the anchoring strength and surface tension. Applying an inverse Wulff construction [20] to the shape of a typical tactoid, we have been able to probe the anisotropy of the surface free energy, σ. Shown in figure 5 is σ(θ)/τ , where, τ is the bare surface tension and θ the angle between the surface tangent and the director field. We find that this angle dependence is consistent with the often-used Rapini-Papoular model for the surface free energy, i.e., σ = τ (1 + ω sin 2 θ) with ω the ratio of the anchoring energy and surface tension [21]. For the tactoid shown in the figure, we find ω ≈ 3.4.

From the Wulff construction, we can in fact predict the aspect ratio of a nematic drop that within a Rapini-Papoular model must be equal to 2

√ ω if ω ≥ 1 [16]. It follows from figure 4 that for our coexisting isotropic and nematic phases of CNTs in water, ω = 4 ± 1.

This is quite larger than theoretical predictions according to which 0.5 ≤ ω ≤ 1.5, at least for cylindrical particles interacting via a harshly repulsive potential [22][23][24][25].

Additional information that we can deduce from figure 4 can be obtained by realizing that according to recent calculations [16], a tactoid changes its director field from a uniform to a bipolar one if its volume V ≈ (4π/3)(L/2)(D/2) 2 is larger than (K/τ ) 3 (6.25/ω) 18/5 , with K an average of the Frank elastic constants. Remarkably, this crossover has so far only been observed in computer simulations [26]. It seems that even the largest tactoid in our samples with a length of 36 µm, has a uniform director field. This implies that a lower bound for the ratio K/τ of the nematic of CNTs is approximately 5 µm. Interestingly, this lower bound is comparable to values found for vanadium pentoxide and fd virus [15][16][17], although that tactoids in these two systems do exhibit a bipolar field if larger than a few µm. It is not quite clear why single-wall CNTs behave so differently from other types of elongated particle. Indeed, CNTs exhibit a phase behavior that is in good agreement with the behavior expected for bulk suspensions of rod-like particles [3]. But the structure of tactoids results from a delicate interplay of bulk and surface properties. Therefore the difference of CNTs from other materials may arise from features that could more specifically affect the surface properties. They could include particular forms of the interaction potential or specific features of the size distribution. CNTs are polydisperse and a small fraction of very long or very short particles could affect the surface properties with a little effect on the bulk behavior. Of course this is still speculative and further work will be needed to confirm whether or not the size distribution of the CNTs confined at the I-N interface differs from that in bulk.

Finally, the scatter in the data of figure 4 potentially provides physical information because in part it must be caused by thermal fluctuations of the aspect ratio of the tactoids.

The Wulff construction provides only the optimal aspect ratio but does not give an indication of its variance. Using a simple scaling Ansatz based on the Rapini-Papoular surface free energy [16] and making use of the equipartition of free energy, we find that the standard deviation of the aspect ratio must approximately be equal to (k B T /τ L 2 ) 1/2 ω 3/4 , so depend on the size of the tactoids. In figure 4 we have indicated around the estimated average aspect ratio the standard deviation presuming a surface tension of 0.5 nN/m. The prediction follows the magnitude and size dependence of the experimental scatter in the data reasonably well. Obviously, we should not over interpret this result because we have ignored any influence of the intrinsic error in the size measurement of the tactoids.

If we accept the very small value of the surface tension that we find at face value, then it is very much smaller than values in the range of tenths to tens of µN/m typically found for coexisting isotropic and nematic phases in dispersions of rod-like particles [27]. Values of nN/m have been found for coexisting isotropic and nematic phases but only in dispersions of colloidal platelets [28]. Clearly, the scaling theory does not give the numerical pre-factor, and this could increase the found surface tension by another factor of, say, ten. Still, this by no means takes our value within the range of the other experimentally found values.

One might of course conclude from this, that the presumption that the scatter in the data is dominated by thermal fluctuations must be wrong. Indeed, some flow can occur just after sample preparation, which can induce droplet alignment and some shape distortion. The latter is clearly seen in the largest CNT tactoids, see also figure 2. Explicit surface tension measurements, e.g., by the capillary rise method [28] on macroscopic interfaces between coexisting isotropic and nematic phases are necessary to confirm our finding, but these are outside the scope of the present paper.

In conclusion, we find nematic tactoids of aqueous dispersions of surfactant-stabilized single-wall carbon nanotubes that have a uniform director field. Our observation accounts that the aspect ratio of about four is independent of the size of these tactoids at least for lengths up to 36 µm. The crossover to a bipolar director field must occur for sizes much larger than this value, but we have not been able to confirm this.

FIG. 1 :FIG. 2 :

 12 FIG. 1: (Color online) Schematic representation of the shape and director field in a uniform (left) and a bipolar (right) tactoid.

FIG. 3 :

 3 FIG. 3: (Color online) Observation by polarization microscopy of a tactoid with the main body axis at 45 degrees relative to the polarizers (left) and along one of the polarizers (right). Indicated by the dashed line is the outline of the tactoid if oriented at 45 degrees with respect to the polarizers.

FIG. 4 :

 4 FIG. 4: Aspect ratio of the tactoids versus their length in microns. Full squares: experimental data points. Drawn line: average value deduced from the experiments. Dashed lines: predicted standard deviation presuming that the surface tension is equal to 0.5 nN/m.

FIG. 5 :

 5 FIG. 5: (Color online) Inverse Wulff construction applied to a tactoid providing the form of surface tension anisotropy. The experimental data points (indicated by the squares) are well fitted with a Rapini-Papoular anchoring expression (drawn line).

Acknowledgments

PvdS gratefully acknowledges the hospitality and a supporting grant from Université Bordeaux 1.


B Cocquelin

D Holleville

G Lucas-Leclin
email: gaelle.lucas-leclin@institutoptique.fr

I Sagnes

A Garnache

M Myara

P Georges

Tunable Single-frequency operation of a diode-pumped Vertical-External Cavity Laser at the Caesium D 2 line

Keywords: 42.55.Px Semiconductor lasers, laser diodes, 42.62.Eh Metrological applications, 42.55.Xi Diode-pumped lasers 1. Introduction

We report on a diode-pumped vertical external-cavity surface-emitting laser emitting around 852 nm for Cesium atomic clocks experiments. We have designed a 7quantum-well semiconductor structure optimized for low laser threshold. An output power of 330 mW was achieved for 1.1 W of incident pump power. Furthermore a compact setup was built for low-power single-frequency emission. We obtained an output power of 17 mW in a single longitudinal mode, exhibiting both broad (9 nm) and continuous (14 GHz) tunability around the Cesium D 2 line. The laser frequency has been stabilized on an atomic transition with residual frequency fluctuations ~ 300 kHz. Through a beatnote experiment the -3 dB laser linewidth has been measured to < 500 kHz over 10 ms.

relatively high optical gain. We have made a diode-pumped VECSEL emitting 330 mW in a transverse singlemode operation with a semiconductor active device on a GaAs substrate. Finally, in a very simple and compact cavity setup, we studied the coarse and fine tunability of the single frequency emission around the Cesium D 2 line. The frequency stabilization on an atomic line has been performed, and the laser linewidth has been characterized through a beat note with a reference laser.

Description of the semiconductor structure

The active region of the semiconductor structure has been specifically designed for laser emission around 852 nm. It is optically pumped in the quantum-well barriers, which prescribes a pump wavelength below 720 nm. Since red laser sources are neither as efficient nor as powerful in that spectral range than in the infrared, the active structure need to be carefully designed with the aim to reach a low laser threshold while keeping the highest gain achievable. We have especially optimized the number of quantum wells (QWs) and their position in the active region. The pump intensity at threshold I th is expressed as a function of the roundtrip losses L :

! I th = N QW I tr " exp L 2N QW L QW #g 0 $ % & ' ( ) (1)
where L QW and N QW are respectively the thickness and the number of QWs, Γ = 2 is the longitudinal confinement factor and I inc the incident pump intensity [START_REF] Coldren | Diode Lasers and Photonic Integrated Circuits[END_REF]. From the experimental characterization of I th as a function of intracavity losses at different device temperature T [START_REF] Cocquelin | Proc. SPIE[END_REF], a linear gain per well g 0 = 1000 cm -1 and an incident pump intensity at transparency per quantum well I tr =105 W/cm 2 have been considered at T = 10°C, and g 0 = 830 cm -1 and I tr =105 W/cm 2 at T = 40°C. According to Figure 1, seven QWs correspond to an optimum which minimizes the pump intensity at threshold for roundtrip losses (including output coupler transmission) about a few percents, even at high temperature. Further increase of the QWs number would result in a larger threshold intensity.

The semiconductor chip (so-called ½-VCSEL) has been grown by metal-organic chemical-vapor deposition on a 350-µm thick GaAs substrate. It contains a multilayer Distributed Bragg Reflector (DBR) and an active region (Figure 2). The DBR bottom mirror consists of 32.5 pairs of AlAs/Al 0.225 Ga 0.775 As quarter-wave layers resulting in a 99.95 %-reflectivity 70-nm-wide stop-band centered on 852 nm. Grown on the top of the Bragg mirror is the 29 λ/4-thick anti-resonant cavity; seven 8-nm thick GaAs QWs, embedded between Al 0.225 Ga 0.775 As barriers, are distributed among the optical standing-wave antinodes positions, with a repartition 1-1-1-1-0-1-0-1-0-0-1 (from the top surface) which has been calculated in order that the excited carrier density remains constant in all QWs and about 14% of the total photogenerated electron-hole pairs. The pump absorption in the barriers is evaluated to 90% in single-pass for wavelengths around 680 nm. Finally, two 30 nm-thick Al 0.39 Ga 0.61 As layers produces a potential barrier at the Bragg mirror/active region interface and at the top surface for carrier confinement, and the structure has been protected by a 20 nm-thick In 0.48 Ga 0.52 P capping layer against oxidation of the Al-rich barrier layers. This cap layer is requisite to improve the operating lifetime of the structure; no degradation nor failure have been observed within months of laser operation under high power pumping. In the end the wafer is antireflection coated at 852 nm with a λ/4 Si 3 N 4 layer to increase the transmission of the incident pump laser and to reduce any intracavity etalon effect at the laser wavelength.

Laser Characterization and Optimization

In order to evaluate the laser performance of our structure, the 7-QW ½-VCSEL was placed in a three-mirror cavity, and optically pumped with a laser diode module from Brightpower emitting up to 5 W at λ p = 690 nm on a 100 µm-diameter-core fibre. The laser cavity consists of a R C = 100-mm concave mirror with a high reflectivity (R>99.97 %) at λ l = 852 nm, and a plane output coupler (Figure 3). The semiconductor structure was simply fixed on a copper heatsink which temperature T sub was controlled by a Peltier cooler. We optimized the pump beam radius and the transmission of the output coupler to obtain the highest output power [START_REF] Cocquelin | Proc. SPIE[END_REF]. With a 40-µm pump spot radius on the semiconductor structure we achieved a maximum output power of 330 mW for a pump power of 1.1 W and a T=1.1%-output coupler, at a substrate temperature T sub = 0°C (Figure 4). The slope efficiency hext reached 35 %, and the overall optical-to-optical efficiency was 30% with regard to the incident pump power (35% with absorbed pump power). The laser threshold was as low as 158 mW, corresponding to a pump intensity of 3 kW/cm 2 in good agreement with the predictions from Figure 1. The laser line was 2-nm broad; the central wavelength shifted from 848 nm at the laser threshold to 855 nm at the maximum output power because of the pump-induced heating of the QWs.

The laser output power was limited by a strong thermal roll-over at 1.1-W incident pump power, induced by the high thermal resistance of the active device. Actually the 350-µm thick GaAs substrate, which has not been removed in this work, contributes to more than 75% of the total heating of the ½-VCSEL, with a thermal resistance ! R th = dT QW dP inc (T QW : QWs temperature, P inc : incident power) evaluated to ~ 145 K/W out of 190 K/W for the whole structure. Nevertheless the maximum output power, one of the highest ever reported without any thermal management in that spectral range, demonstrates the well-thought design of the active structure, as well as its growth quality.

Single-frequency operation in a compact prototype

Description

With the aim to develop a low-power single-frequency source dedicated to the detection of Caesium atoms, a compact monolithic external cavity with improved thermal and mechanical stability has been designed. We chose a single-transverse-mode laser diode as the pump source in order to limit intensity noise transfer from the pump to the laser emission [START_REF] Baili | [END_REF]. The pump was thus a commercial Mitsubishi red laser diode delivering up to 150 mW at 658 nm for an operating current of 245 mA. The pump beam was focused on a 20 µm radius spot with a pair of aspheric lenses (f' =4.5 mm / f' = 12.7 mm), at the incidence angle of 70° relatively to the structure, which circularizes the elliptic shape of the incident pump beam on the semiconductor chip. The external cavity was formed by a 12 mm-concave mirror R = 99 % at 852 nm mounted on a piezo-electric transducer (PZT) (see Figure 5). The laser cavity length was carefully adjusted in order to optimize the overlap between the cavity mode and the pump one. The active structure is directly fixed on a thermoelectric (TE) cooler with thermal heatpaste, which allows to control its temperature with a precision better than 10 -3 K. The temperature of the whole laser external cavity was separately stabilized with another TE element close to room temperature in the following. The pump system, the semiconductor chip and the external mirror have been integrated on the same mount. The overall setup fitted within a 52×52×58 mm 3 cube, and was protected by acoustic isolating covers to improve both its thermal and acoustic isolation. Then the laser remains running for weeks without needs for realignment.

Laser operation without any intracavity frequency-selective element

In this compact prototype, the laser output power is limited by the available pump power to 17 mW (Figure 6) at a substrate temperature of 10° C. The threshold was reached for an incident pump power of 52 mW, and the slope efficiency was 17% (with regard to incident pump power) without any evidence of thermal roll-over up to the maximum 150-mW pump power. The emission was linearly polarized, and the beam was diffraction-limited with a quality factor M 2 < 1.1. The emitted wavelength shifted from 850.5 nm at threshold to 852.2 nm at maximum pump power.

Without any frequency-selective intracavity element, we observed a stable single-frequency operation within a large range of operating conditions of the substrate temperature and pump current, with a side-mode suppression ratio higher than 30 dB (measurement-limited). This was checked with a high finesse (F=130) scanning Fabry Perot (Figure 6) with a free-spectral range (FSR) of 37.5 GHz larger than the FSR of the laser cavity. This is attributed to the nearly-ideal gain homogeneity of VECSELs sources which has been extensively studied in [START_REF] Garnache | [END_REF]. Actually the characteristic time needed for the laser spectrum to collapse to a single-mode is about 1 ms in our experimental conditions, faster than acoustic and thermal fluctuations in our laser set-up.

Concerning the wavelength tunability, the laser line shifts towards longer wavelengths, as the QWs gain does, either with the substrate temperature or the incident pump power. A broad tunability over 6 nm is thus obtained from 850 nm to 856 nm by changing the substrate temperature from 7°C to 20°C, with a rate of 0.24 nm/K which is typical for these AlGaAs-based materials. Furthermore the laser wavelength moves with the incident pump power at 17 pm/mW (with regard to the incident pump power).

Operation with an intracavity Fabry-Perot etalon

To force the laser wavelength independently of the operating conditions, we chose to insert a 26-µm thick uncoated silica etalon inside the cavity. The laser wavelength is then only set by the etalon orientation over 9 nm, and does not change with either the temperature (over ∆T = 30°C) or the available pump power. In the meantime the output power and the efficiency decreased respectively to 8 mW at the maximum available pump power and 12% with respect to the incident pump power; the threshold increased to 85 mW due to the extra losses introduced by the etalon. By tuning the external-cavity length with the piezoelectric transducer, we achieved a continuous tunability over 14 GHz (0.03 nm) without any mode hop. It is worth noticing that this large continuous tunability of the laser frequency, owing to our short-length cavity, is favourable in atomic physics experiments; actually it makes it possible to scan continuously the optical transitions of interest, distant from 9.192 GHz, corresponding to the hyperfine levels ( 62 S 1/2 , F = 3) and ( 62 S 1/2 , F = 4) of the 133 Cs-atom ground state. A Doppler-free saturated-absorption spectrum of the ( 62 S 1/2 , F = 4) → (6 2 P 3/2 , F') transitions obtained in a Cs gas cell is shown in Figure 7. The ~5-MHz wide hyperfine lines are clearly resolved.

Evaluation of the spectral properties

With the etalon inside the cavity, the laser frequency has been locked at the side of a Doppler-free transition of the D 2 line, through a low-frequency (f < 2 kHz) 2-integration-stage servo loop on the piezoelectric transducer. The root-mean-square (RMS) frequency error signal, which is an evaluation of the global frequency fluctuations of the OP-VECSEL relatively to the atomic reference, is assessed at 300 kHz over 10 s and above (inset in Figure 7). We have checked that the intensity noise (RIN) remains negligible and do not contribute significantly to these measurements. The power spectral density of the frequency noise, measured from the error signal with a Fast Fourier Transform analyser, reveals that the main contributions to the laser frequency noise are below 4/15/ 100 kHz, and are attributed to residual electronic and acoustic instabilities of the set-up (Figure 8). A strong correction of the frequency fluctuations is obtained below 1 kHz. In the high frequency range, the white noise floor of the frequency noise spectrum reached ~13 Hz 2 /Hz, which would correspond to a Schawlow-Townes fundamental linewidth of 40 Hz [START_REF] Petermann | Laser Diode Modulation and Noise[END_REF]; this value is within the order of magnitude of the theoretical limit for a 10 mm-long external-cavity semiconductor laser.

The laser linewidth of our source has been further validated through the beat note measurement between our OP-VECSEL and an extended-cavity diode laser (ECDL) similar to the one described in [4], which linewidth has been previously evaluated to 130 kHz at -3 dB. In order to suppress low-frequency drifts of the laser frequencies, the OP-VECSEL and the ECDL were locked to distinct sub-Doppler Cs lines. The beat note signal around F 0 = 135 MHz was detected by a fast InGaAs photodiode, then amplified and measured with a radiofrequency spectrum analyzer. The relevant time scale for the evaluation of the laser spectrum is the typical light/atoms interaction duration in atomic physics experiments, in the 10-ms range for atoms detection in Cs clocks. Thus the full width at half maximum of the beat note measured over 10 ms is 500 kHz, which is mainly attributed to the OP-VECSEL (see Figure 9). Actually assuming Gaussian shapes for both laser lines, the VECSEL linewidth is ~ 480 kHz. The FWHM of the Lorentzian fit of the spectrum wings (|ν-ν 0 | > 1 MHz) is 70 kHz -55 kHz imputed to the VECSEL line, which is still larger than our previous evaluation of the ultimate linewidth from the white-noise magnitude; this is regarded as a consequence of the low-frequency extra acoustic, thermal and electrical noise peaks observed in the error signal spectrum (Figure 7) which are unavoidable under normal laboratory environment. Indubitably the laser linewidth could still be reduced with a better control of our environmental conditions and an enlarged servo bandwidth.

Conclusion

By giving extra care to the conception and the fabrication of the semiconductor component, we have demonstrated a diode-pumped VECSEL emitting at 852 nm with a low threshold intensity (I th = 3 kW/cm²). We have obtained a 330-mW laser emission around 852 nm from a structure on a GaAs substrate, without any complex additional thermal management nor post-processing of the wafer.

From a low-power compact prototype we have obtained a pump-limited output power of 17 mW under single-frequency operation on the Caesium D 2 transition. The spectral tunability of the source around the desired optical frequency was at least 14 GHz without mode-hopping. Moreover the laser has been locked to an absolute atomic reference, and complete frequency noise measurements have been performed. The residual frequency fluctuations of the laser line as compared to the atomic transition were about 300 kHz RMS over 10 s. Last but not least an independent evaluation of the laser linewidth through a beat-note experiment has established that the FWHM laser linewidth was below 500 kHz over 10 ms. We believe that this work results in an actual characterization of the frequency noise of a single-frequency VECSEL under single-mode diode pumping.

Finally the potentialities of a diode-pumped VECSEL as an alternative in the optical source architecture of Caesium atomic clocks have been investigated. Our laser performance are already adequate for optical detection of atoms in these setups. The further increase of the output power will require a reduction of the thermal resistance of the semiconductor chip in order to withstand high-power pumping. We could utilize wellestablished solutions as long as they remain compatible with the tunability of the single-frequency emission attempted here, such as substrate removing, bonding to a high-conductivity substrate or intracavity wedged heatspreader technique [START_REF] Maclean | [END_REF].

Ackowledgements

This work has been partly supported by the Délégation Générale à l'Armement (Poseida N°0534004) and the Agence Nationale de la Recherche (ANR-07-BLAN-0320-03). B. Cocquelin acknowledges the CNRS and CNES for the funding of his PhD.

List of figure captions

Figure 1 :

 1 Figure 1: Threshold intensity vs. number of quantum wells in the structure for different intracavity losses L : 0.5%, 1% and 2% at T QW =10°C and 40°C, following Equation (1).

Figure 2 :

 2 Figure 2 : Design of the semiconductor structure.

Figure 3 :Figure 4 :

 34 Figure 3: Experimental setup for OP-VECSEL optimizationFigure 4: Laser output power and laser wavelength vs. incident pump power at the substrate temperature T sub = 0°C .

Figure 5 :

 5 Figure 5: Photograph of the low-power single-frequency prototype.

Figure 6 :

 6 Figure 6: Laser output power vs. incident pump power in single-frequency operation at 7°C; inset: transmission of the scanning 37.5 GHz-FSR Fabry-Perot demonstrating single-frequency operation.

Figure 7 :

 7 Figure 7 : Doppler-free Cs absorption spectrum in a vapor cell, from the (6 2 S 1/2 , F = 4) hyperfine ground state; inset : error signal measured at the side of the atomic line.

Figure 8 :Figure 9 :

 89 Figure 8: Spectral density of the error signal with/without optimized servo gain Figure 9: Beat note measurement between the VECSEL and a known ECLD. The resolution bandwidth is 10 kHz, the sweep time is 20 ms; the signal has been averaged 10 times.

Figure 1 Cocquelin

 1 Figure 1

Figure 2 CocquelinFigure 3

 23 Figure 2

Figure 4 Cocquelin

 4 Figure 4

  Figure 5

Figure 6 Cocquelin

 6 Figure 6

Figure 7 Cocquelin

 7 Figure 7

Figure 8 Cocquelin

 8 Figure 8

Figure 9

 9 Figure 9


Audrey Versini

Nicolas Ramoz
email: nicolas.ramoz@inserm.fr

Yann Le Strat

Susann Friedel

Stefan Ehrlich

Claudette Boni

Anke Hinney

Johannes Hebebrand

Lucia Romo

Julien-Daniel Guelfi

Philip Gorwood

Estrogen receptor 1 gene (ESR1) is associated to restrictive anorexia nervosa

Keywords: Anorexia nervosa, restrictive type, binge-eating/purging type, estrogen receptors, transmission disequilibrium test, population-based sample

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Anorexia nervosa (AN, MIM 606788) is an eating disorder characterized by weight loss (body mass index < 17.5 kg/m 2 ) or failure to make expected weight gain during period of growth, intense fear of gaining weight or becoming fat, body image disturbance and amenorrhea (American Psychiatric Association, 1994;[START_REF] Gorwood | The human genetics of anorexia nervosa[END_REF][START_REF] Ramoz | Eating disorders: an overview of treatment responses and the potential impact of vulnerability genes and endophenotypes[END_REF]. The prevalence of AN is between 0.3 to 0.6% [START_REF] Hudson | The prevalence and correlates of eating disorders in the National Comorbidity Survey Replication[END_REF][START_REF] Ramoz | Eating disorders: an overview of treatment responses and the potential impact of vulnerability genes and endophenotypes[END_REF], with one of the highest mortality rate (about 10% per decade) mainly due to cachexia and suicide [START_REF] Harris | Suicide as an outcome for medical disorders[END_REF][START_REF] Hoek | Incidence, prevalence and mortality of anorexia nervosa and other eating disorders[END_REF]. Furthermore, the heritability of AN is high (70%), thus increasing the potential interests of genetic approaches [START_REF] Gorwood | The human genetics of anorexia nervosa[END_REF][START_REF] Ramoz | Eating disorders: an overview of treatment responses and the potential impact of vulnerability genes and endophenotypes[END_REF]. Studies have found evidence of a high genetic risk for AN, especially in the restrictive AN subgroup probably because of heterogeneity reduction of the phenotype, with, therefore, an increased power to detect an association [START_REF] Grice | Evidence for a susceptibility gene for anorexia nervosa on chromosome 1[END_REF][START_REF] Gershon | Clinical findings in patients with anorexia nervosa and affective illness in their relatives[END_REF].

According to the DSM-IV, AN patients are subdivided in two categories: restrictive type (RAN), characterizing patients with restricted food intake without binge eating or purging episodes, and binge eating/purging type (BPAN), characterizing patients with binge eating/purging episodes during anorexia and bulimia phases (American Psychiatric Association, 1994). RAN and BPAN patients represent two subtypes with specific clinical features, including significant lower BMI in RAN than in BPAN, and an increased impulsivity and a higher rate of self-harm and suicide in BPAN than RAN [START_REF] Eddy | Longitudinal comparison of anorexia nervosa subtypes[END_REF][START_REF] Foulon | Switching to the bingeing/purging subtype of anorexia nervosa is frequently associated with suicidal attempts[END_REF][START_REF] Milos | Suicide attempts and suicidal ideation: links with psychiatric comorbidity in eating disorder subjects[END_REF]. Hormone concentrations may also help to distinguish these two subtypes, since leptin is decreased in RAN compared to BPAN [START_REF] Eddy | Longitudinal comparison of anorexia nervosa subtypes[END_REF]. Biological pathways of sexual hormones were poorly investigated in AN, although the involvement of the estrogenic pathway in AN is supported by several cues. First a female predominance is observed in patients with a ratio of 9 women to 1-3 men [START_REF] Hudson | The prevalence and correlates of eating disorders in the National Comorbidity Survey Replication[END_REF][START_REF] Ramoz | Eating disorders: an overview of treatment responses and the potential impact of vulnerability genes and endophenotypes[END_REF]. Second, the onset of AN around puberty is correlated to the presence of estrogenic peaks. ). Third, recent studies proposed that sex hormones have a role in the risk of eating disorders [START_REF] Culbert | Prenatal hormone exposure and risk for eating disorders: a comparison of opposite-sex and same-sex twins[END_REF][START_REF] Procopio | Intrauterine hormonal environment and risk of developing anorexia nervosa[END_REF] but this observation was not replicated by other authors [START_REF] Raevuori | Anorexia and bulimia nervosa in same-sex and opposite-sex twins: lack of association with twin type in a nationwide study of Finnish twins[END_REF][START_REF] Baker | Genetic risk factors for disordered eating in adolescent males and females[END_REF].

Fourth, the anorexic effect of high estrogen levels was found in animal models (Couse and Korak, 1999;[START_REF] Wade | Gonadal effects on food intake and adiposity: a metabolic hypothesis[END_REF]. Moreover, estradiol levels were lower in anorexia patients than in controls [START_REF] Ohwada | The relationship between serum levels of estradiol and osteoprotegerin in patients with anorexia nervosa[END_REF][START_REF] Brambilla | Persistent amenorrhoea in weight-recovered anorexics: psychological and biological aspects[END_REF]. Fifth, the ESR1 and ESR2 genes, which code for estrogen alpha and beta receptors and are expressed in nonoverlapping brain regions [START_REF] Osterlund | Estrogen receptor beta (ERbeta) messenger ribonucleic acid (mRNA) expression within the human forebrain: distinct distribution pattern to ERalpha mRNA[END_REF][START_REF] Osterlund | Estrogen receptors in the human forebrain and the relation to neuropsychiatric disorders[END_REF], colocalize with corticotrophin releasing factor and modulate its expression [START_REF] Dagnault | Involvement of the medial preoptic area in the anorectic action of estrogens[END_REF][START_REF] Bao | Colocalization of corticotropin-releasing hormone and oestrogen receptor-alpha in the paraventricular nucleus of the hypothalamus in mood disorders[END_REF]. They participate in the regulation of the hypothalamic pituitary adrenal (HPA) axis [START_REF] Licinio | The hypothalamic-pituitary-adrenal axis in anorexia nervosa[END_REF]. Thus, the disruption of the HPA axis reported in AN might be due to an alteration in the estrogen pathway in patient (Van de [START_REF] Van De Stolpe | Estrogen receptor (ER)-mediated transcriptional regulation of the human corticotropin-releasing hormone-binding protein promoter: differential effects of ERalpha and ERbeta[END_REF]. Finally, the involvement of the estrogen alpha receptor in the regulation of food intake and eating behaviour was confirmed in mouse models [START_REF] Musatov | RNAi-mediated silencing of estrogen receptor {alpha} in the ventromedial nucleus of hypothalamus abolishes female sexual behaviors[END_REF][START_REF] Musatov | Silencing of estrogen receptor alpha in the ventromedial nucleus of hypothalamus leads to metabolic syndrome[END_REF]. Two case-control studies of AN with ESR1 and ESR2 genes were previously published [START_REF] Eastwood | Variation in the ESR1 and ESR2 genes and genetic susceptibility to anorexia nervosa[END_REF][START_REF] Rosenkranz | Systematic mutation screening of the estrogen receptor beta gene in probands of different weight extremes: identification of several genetic variants[END_REF]. They reported no association of the ESR1 gene with AN, and an inconsistent association of AN with different variants within ESR2 gene. Thus, our hypothesis is to identify an association between estrogen receptor and anorexia nervosa, especially in RAN subgroup, because a diminution of estradiol level was Versini et al.

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7 more important in the restrictive compared to the binging-purging subtype [START_REF] Ohwada | The relationship between serum levels of estradiol and osteoprotegerin in patients with anorexia nervosa[END_REF]. We more precisely expect to find an association between anorexia nervosa and ESR1 gene because ovariectomized rat showed an implication of ESR1 but not of ESR2 receptor in food intake, body weight and meal size (Santonello, et al 2007). Finally, we have been also analysing the role of parental imprinting of this estrogen receptor in anorexia nervosa, because ESR1 belongs to the 6q25 region which could be subjected to parental imprinting according to database (Nikawa, et al 1996;[START_REF] Morison | A census of mammalian imprinting[END_REF].

Furthermore, the absence of ESR1 transcription could be a result of aberrant methylation of promoter CpG islands, as shown for example in breast cancers [START_REF] Wilson | Dynamic regulation of estrogen receptoralpha gene expression in the brain: a role for promoter methylation?[END_REF].

Here, we performed the first family-based association study on a large number of AN families of French origin looking for an association between ESR1 gene and AN, and we took advantage of the narrowing definition of the disorder to show that this association is driven by the restrictive subtype of AN. We attempted to replicate the family-based association in an independent sample of German families (replication of the TDT approach), as well as in an independent population-based sample recruited from the general population.

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MATERIALS AND METHODS

Subjects and Phenotype

The study was approved by each national ethics committee. All participants (and if underage, their parents) gave written informed consent.

The first family-based cohort was composed of 321 families of French origin, including 210 complete trios, of whom 102 were described previously [START_REF] Gorwood | The human genetics of anorexia nervosa[END_REF]. All participants were assessed by clinicians using the face-to-face semi-structured Diagnostic Interview for Genetic Studies (DIGS) [START_REF] Nurnberger | Diagnostic interview for genetic studies. Rationale, unique features, and training. NIMH Genetics Initiative[END_REF]. Diagnosis of AN were made according to DSM-IV criteria (American Psychiatric Association, 1994), and included AN restrictive type (RAN) with no lifetime binge-eating/purging episode (N=153 families), and AN binge-eating/purging type (BPAN) with at least one lifetime bingeing/purging episode, during anorexia or bulimia phases (N=154 families). Information for subtype was incomplete for 14 probands.

Furthermore, the Eating Disorder Inventory (EDI-2) [START_REF] Garner | Development and validation of a multidimensional eating disorder inventory for anorexia nervosa and bulimia[END_REF] and the Eating Attitude Test (EAT-26) [START_REF] Garner | The eating attitudes test: psychometric features and clinical correlates[END_REF] were used to measure the psychological and behavioural dimensions and the broad range of symptoms of AN respectively.

A second family-based cohort was composed of 41 RAN trios of German origin, the probands being assessed with the Composite International Diagnostic Interview (CIDI) [START_REF] Robins | The Composite International Diagnostic Interview. An epidemiologic Instrument suitable for use in conjunction with different diagnostic systems and in different cultures[END_REF]. The clinical features of the two family-based cohorts and subgroups are described in Table 1.

A third sample was composed of young women (mean age 20.30 ± 0.05 years) with Caucasian origin recruited for a genetic analysis of addictive behaviours, including eating disorders (SAGE study) [START_REF] Strat | First positive reactions to cannabis constitute a priority risk factor for cannabis dependence[END_REF]. Eating disorders were assessed using the SCOFF scale, a brief and reliable questionnaire developed as a screening test of eating Versini et al.

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9 disorders in the general population with a sensitivity of 84.6% and a specificity of 89.6% [START_REF] Hill | SCOFF, the development of an eating disorder screening questionnaire[END_REF]. Participants were asked the following questions: 1. Do you make yourself sick because you feel uncomfortably full? 2. Do you worry you have lost control over how much you eat? 3. Have you recently lost more than 6 kg in a 3 month period? 4. Do you believe yourself to be fat when others say you are too thin? 5. Would you say that food dominates your life?

Participants were considered as having an eating disorder if they had a SCOFF score equal or above 2 (n=126), and were considered as control if they had a SCOFF score lower than 2 (n=567).

SNPs and Genotyping

Genomic DNA from probands and parents was extracted from peripheral blood leukocytes. Thirteen SNPs encompassing ESR1 gene and four SNPs within ESR2 gene were screened using TaqMan SNP genotyping assays (Applied Biosystems, Les Ullis, France). The selection of SNPs is based on tagged SNPs that depict the haplotype blocks across the genes, according to available databases (Perlegen and Hapmap) and positive associations with diseases. 2 andSupplementary Table 2 andtheir position within genes are shown on Figure 1 and Supplementary Figure 1 for ESR1 and ESR2 genes, respectively. A total of 362 AN patients and 613 parents were genotyped. Furthermore, 30 samples were genotyped in duplicate to assess the accuracy of the allelic call. SNP rs3798577 was genotyped using SNPlex technology Applied Biosystems, Les Ullis, France) for 693 women from the population-based sample [START_REF] Tobler | The SNPlex genotyping system: a flexible and scalable platform for SNP genotyping[END_REF].

Details of SNPs are indicated in Table

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Statistical analysis

Comparisons of clinical features between cohorts and subsets were performed using Student's t-test and Chi-square test. Hardy-Weinberg equilibrium tests, linkage disequilibrium D' values and minor allele frequencies were computed using Haploview 4.1 software [START_REF] Barrett | Haploview: analysis and visualization of LD and haplotype maps[END_REF]. Transmission disequilibrium tests for SNPs and haplotypes were carried out with FBAT and PLINK programs [START_REF] Horvath | The family based association test method: strategies for studying general genotype--phenotype associations[END_REF][START_REF] Purcell | PLINK: a tool set for whole-genome association and population-based linkage analyses[END_REF]. Parental origin of the association was calculated using ASPEX 2.5 package [START_REF] Hinds | The ASPEX package: affected sib-pair exclusion mapping[END_REF]. Gene-gene interaction was computed using the gene-based test of the PLINK program. The power of sample size for association tests was calculated using the Genetic Power Calculator program (http://statgen.iop.kcl.ac.uk/gpc/) [START_REF] Purcell | Genetic Power Calculator: design of linkage and association genetic mapping studies of complex traits[END_REF].

To take account the linkage disequilibrium between each SNP, we computed correction for multiple testing for SNPs using Single Nucleotide Polymorphism Spectral Decomposition (SNPSpD) (http://gump.qimr.edu.au/general/daleN/SNPSpD/) [START_REF] Nyholt | A simple correction for multiple testing for single-nucleotide polymorphisms in linkage disequilibrium with Each Other[END_REF].

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RESULTS

Association of ESR1 gene with AN and RAN subset

We first genotyped 17 SNPs, encompassing ESR1 and ESR2 genes, in a French cohort of 321 AN families. All SNPs analyzed in this study were in Hardy-Weinberg equilibrium in the patients and parents. No discrepancy was observed in the genotyping of 30 duplicated samples. Two families were excluded due to Mendelian inheritance errors in the paternal transmissions.

Using transmission disequilibrium tests (TDTs), we found a significant overtransmission in AN with ESR1 SNPs rs726281 (p=0.024, odds ratio [OR]=1.5, 95% confidence interval [95%CI]=1-2) and rs2295193 (p=0.024, OR=1.4, 95%CI=1-1.8), (Table 2). We showed that RAN and BPAN subjects differed significantly for several clinical variables, particularly regarding the age of onset of anorexia and the minimum lifetime BMI (Table 1). Therefore, we performed TDT analyses according to the RAN and BPAN subsets. Three ESR1 SNPs were significantly over-transmitted in the RAN subset, rs726281 (p=0.005, OR=2.1, 95%CI=1.2-3.6), rs3798577 (p=0.021, OR=1.6, 95%CI=1.1-2.3) and rs2295193 (p=0.007, OR=1.7, 95%CI=1.2-2.5) (Table 3). In contrast, no SNP was associated with the BPAN subgroup (Supplementary Table 1).

No preferential transmission was found for the ESR2 SNPs in any of the AN subgroups (Supplementary Table 2). Furthermore, only one haplotype block encompasses the 112 kb of the ESR2 gene that renders unlikely the association between ESR2 gene with AN, or with the RAN or BPAN subsets (Supplementary Figure 1).

No significant epistatic association was found for combinations of ESR1 and ESR2

SNPs and the AN cohort, neither for the RAN nor for the BPAN subgroups (data not shown). ). This 8-SNPs haplotype presents an odds ratio of 3.1 (95%CI=1.8-5.1) for RAN.

Parental origin of association

In addition, we analyzed the parental origin of the association with RAN subset.

Considering the combined TDT of the 13 ESR1 SNPs, we detected a highly significant excess of paternal transmission (p=9.10 -7 ) and a significant excess of maternal transmission (p=0.0004). More precisely in RAN, a paternal over-transmission of four SNPs (rs726281 p=0.024, rs2228480 p=0.05, rs3798577 p=0.008 and rs2295193 p=0.004) and a maternal over-transmission of rs726281 only (p=0.041) were observed (Table 3). Interestingly, the rs726281 over-transmitted by both parents is located in haplotype block 1, while the three SNPs solely transmitted in excess by the father constitute block 2 (Figure 1c). Regarding the 8-SNPs haplotype in RAN, in comparison to the maternal over-transmission (p=0.02, OR=2.1, CI95=1.1-3.8), we found a higher statistical significance for the paternal overtransmission (p=3.10 -5 , OR=3.7, 95%CI=1.9-7.3) (Figure 1a).

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ESR1 association with an independent RAN German cohort

As a second step, we attempted to replicate the association by genotyping ESR1 SNPs in an independent German cohort of 41 RAN trios (Table 4). Although no allele was transmitted in excess in the probands of this replication cohort, we found a preferential paternal over-transmission of the same SNP which was initially associated in our sample, namely the rs726281 (p=0.025), and a trend of significance for rs3798577 (p=0.059), conferring a higher risk for RAN in this sample (OR=3.0, 95%CI=1.1-8.3, and OR=2.6, 95%CI=0.9-7.3, respectively).

ESR1 association with eating disorders in an independent population-based sample

In a population-based sample of 693 young French Caucasian women (mean age 20.30 ± 0.05 years), tagged-SNP rs3798577 was found associated with the presence of eating disorders (Additive model: p=0.008) (Table 5).

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DISCUSSION

In the current study, we found an association between ESR1 gene and AN, mainly observed in the restrictive subtype of anorexia nervosa. We showed no association of ESR2 with AN, nor with RAN or BPAN subgroups. Furthermore, we did not identified ESR1-ESR2 gene-gene interaction with either AN or restrictive subtype.

Only two works of AN with ESR1 and ESR2 genes were previously published [START_REF] Rosenkranz | Systematic mutation screening of the estrogen receptor beta gene in probands of different weight extremes: identification of several genetic variants[END_REF][START_REF] Eastwood | Variation in the ESR1 and ESR2 genes and genetic susceptibility to anorexia nervosa[END_REF]. The initial study has screened for mutation in ESR2 gene [START_REF] Rosenkranz | Systematic mutation screening of the estrogen receptor beta gene in probands of different weight extremes: identification of several genetic variants[END_REF] and found different distribution of the variant G1082A (rs1256049) in AN compared to BN or to obese/underweight subjects. In the second study, no association was reported between AN and 3 markers, or haplotypes, of ESR1 gene, but a significant association was reported with the rs1256049 SNP of ESR2 [START_REF] Eastwood | Variation in the ESR1 and ESR2 genes and genetic susceptibility to anorexia nervosa[END_REF]. Furthermore, an association was also reported with rs4986938 and rs928554 (but not with rs1256049) in bulimia nervosa and eating disorders not otherwise specified [START_REF] Nilsson | Association of estrogen receptor beta gene polymorphisms with bulimic disease in women[END_REF]. In the present study, no association was found between ESR2 SNPs, which are in linkage disequilibrium (D'>0.9) with rs1256049 according to databases, and AN, RAN or BPAN subsets. Noteworthy, our screening of 321 AN families using the transmission disequilibrium test was more powerful (1-β = 89%) than the two previous case-control studies (1-β = 18% and 63%, respectively) and distinguished RAN and BAN.

We reported a strong association of specific SNPs and haplotypes of the ESR1 gene and AN, and RAN subgroup, with a preferential paternal over-transmission. While we genotyped a large cohort of families and performed transmission disequilibrium tests that reduce the sex and ethnic stratification bias, the probability of a false positive finding in the present study cannot be excluded due to the number of tests performed. After a Bonferroni Versini et al.

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15 correction taking into account the 13 SNPs within ESR1 gene for the RAN subgroup, we found only trends of association for two SNPs, rs726281 p corrected =0.065 and rs2295193 p corrected =0.091, but still observed a strong statistical significance for the 8-SNPs haplotype (p corrected =0.00008). It must be kept in mind that the Bonferroni correction is relevant for independent tests. Given that linkage disequilibrium between the 13 SNPs are mainly above zero in our sample, this correction is probably over-conservative. In order to assess a more appropriate p-value corrected for multiple testing for single SNP association, we carried out the Single Nucleotide Polymorphism Spectral Decomposition (SNPSpD) method [START_REF] Nyholt | A simple correction for multiple testing for single-nucleotide polymorphisms in linkage disequilibrium with Each Other[END_REF]. Significance threshold required is a p<0.0051 (rs726281) and effective number of independent SNP is 10 instead of 13. Thus, we found a significant association for rs726281 p corrected =0.049 and a trend for rs2295193 p corrected =0.07.

The three SNPs of ESR1 associated with RAN in our sample (rs726281, rs3798577 and rs2295193) are located in introns and 3' UTR region. To date, they have no known functional consequences (Ascenzi, et al 2006). However, the associated haplotype block of 8 SNPs covers the C terminal E/F region of ESR1 protein, which corresponds to the ligand fixation domain of nuclear receptor. So, it is tempting to speculate that the association of these SNPs with RAN could suggest changes of ligand fixation in RAN patients.

We also attempted to replicate our results in an independent German cohort of 41 RAN trios, but failed to confirm significant associations between ESR1 SNPs and RAN. Surprisingly, participants in the German RAN cohort showed a significant higher mean of minimal lifetime BMI compared to the French RAN cohort, while they were significantly younger and had shorter disease duration. As up to half of the restrictive AN patients crossover to binge eating/purging subtype in a 7 years follow-up study [START_REF] Eddy | Diagnostic crossover in anorexia nervosa and bulimia nervosa: implications for DSM-V[END_REF], this difference may explain the absence of replication in the German sample, since, in the latter, young RAN patients could still switch to the BPAN phenotype. While this difference between the two cohorts decreases any chances of replication, we were able to observe the excess of paternal transmission of the main SNP associated with anorexia nervosa in the first sample. Due to a small sample size, the RAN German cohort provided a reduce power (power=33%) compared to the RAN French cohort (power=59%) that can explain the low significance of association.

Finally, we tested a tagged-SNP of the ESR1 gene in a large population based sample, and found an association with eating disorders, as defined by a SCOFF score equal or above 2. However, it should be noted that the SCOFF scale is a screening tool for eating disorders rather that a diagnostic instrument for AN, and therefore no direct comparison should be made between the two first clinical samples and this population based sample. At most, this epidemiological sample gives indirect evidence for replication, which is usually regarded as needed for genetic association studies in complex disorders.

There are several limitations of this study. Firstly, the instruments assessing the eating disorders are different in the three cohorts. French and German trios families were assessed with semi-structured interview, respectively, DIGS and CIDI, while the self-evaluation SCOFF scale was used to screen epidemiological eating disorders in a large woman population sample. Secondly, the sample size of the German trios is small with a shorter disease evolution period, although a cohort with a larger sample size and a disease duration equivalent to the French cohort is recommended to replicate our results. Thirdly, the three SNPs of ESR1 (rs726281, rs3798577 and rs2295193), associated with RAN, have no known functional consequences up to now and are located in non-coding regions. These SNPs required a functional analysis regarding their potential effects of associated alleles in ESR1 receptor proprieties.

Versini et al. NPP-09-0894 Neuropsychopharmacology 17

Although there is a lack of report on the genetic aspects of hormonal status as a risk factor for anorexia nervosa, recent investigations suggest that some hormonal environment might be associated with eating disorders [START_REF] Procopio | Intrauterine hormonal environment and risk of developing anorexia nervosa[END_REF][START_REF] Young | Estrogen and the etiology of anorexia nervosa[END_REF].

Observations between same-sex and opposite-sex twins allowed to find a high AN prevalence in adult life in female compares to male, suggesting an influence of intrauterine exposure level to sex hormone [START_REF] Procopio | Intrauterine hormonal environment and risk of developing anorexia nervosa[END_REF]. Interestingly, significant deficiency of serum levels for estradiol, the ligand of estrogen receptor, has been described in AN patients compared to controls, and a lower concentration in restrictive subtype rather than the binge eating/purging subtype has been reported [START_REF] Ohwada | The relationship between serum levels of estradiol and osteoprotegerin in patients with anorexia nervosa[END_REF]. It is tempting to speculate that the association between ESR1 gene and RAN may lead to specific biological effects, such as a modified expression and/or an altered function of the estrogen receptor alpha. Furthermore, the paternal transmission of the association that we observed also supports a genetic imprinting, which might be influenced by sex hormones. Also, it is important to consider DNA methylation in psychiatric disorder because it could help to the understanding of mechanism of the pathology and could constitute potential therapeutic targets. Acute administration of a selective ER alpha agonist leads to ovariectomized rats that showed a decrease in daily food intake and body weight [START_REF] Santollo | Acute activation of ER alpha decreases food intake, meal size, and body weight in ovariectomized rats[END_REF]. Furthermore, in female mice, agonists of ER receptors produce different effects on social learning of food preferences [START_REF] Clipperton | Differential effects of estrogen receptor alpha and beta specific agonists on social learning of food preferences in female mice[END_REF]. Then, ER alpha antagonist treatment failed to reduce food intake decrease in chemically ovariectomized rats [START_REF] Santollo | Effect of a putative ERalpha antagonist, MPP, on food intake in cycling and ovariectomized rats[END_REF]. Finally, in female rat, the level of ESR1 protein expression and estrogen sensitivity are modulated by oxytocin [START_REF] Perry | Neonatal oxytocin alters subsequent estrogen receptor alpha protein expression and estrogen sensitivity in the female rat[END_REF]. Thus, it is difficult up to now to suggest a pharmacological treatment for AN. Further functional studies are needed to

  the RAN subsetLinkage disequilibrium analysis of pairwise SNPs revealed several haplotype blocks across the 296 kb of ESR1 gene (Figure1c). Over-transmissions in the RAN subset were found for common haplotypes based on five SNPs (Block 1: rs726281*A-rs3020407*A-rs17080994*T-rs2982712*T-rs3020371*C, 0.503 frequency, p=0.06), three SNPs (Block 2: rs2228480*G-rs3798577*T-rs2295193*G, 0.410 frequency, p=0.002), and the eight SNPs of the two blocks merged (rs726281*A-rs3020407*A-rs17080994*T-rs2982712*T-rs3020371*C-rs2228480*G-rs3798577*T-rs2295193*G, 0.230 frequency, p=6.10 -6

aOT:

  Over-transmitted allele. b T:U: Transmitted versus untransmitted allele. c OR [CI 95 ]: odds ratio and the 95% confidence interval. d Significant p values are indicated in bold.

Table 1 : Demographic and clinical data for the French and German family-based cohorts and the French RAN and BPAN subgroups

 1 effect of the association identified in our study which may influence the number or affinity of ESR1 receptor in restrictive AN patients.Data are indicated as N, % or mean ± standard deviation. a Significant difference between RAN and BPAN from the French cohort. b Significant difference between French RAN subset and German RAN cohort. c Eating Attitude Test. Significant difference indicates a p value inferior at 0.05 in one-way analysis of variance or t-test. Not available, n.a.

	Versini et al.

Table 2 : Transmission disequilibrium test of ESR1 SNPs with AN in the French family-based cohort

 2 Minor allele and its frequency in the parentheses. b OT: Over-transmitted allele. c T:U: Transmitted versus untransmitted allele. d OR [CI 95 ]: odds ratio and the 95% confidence interval. e Significant p values are indicated in bold.

	TDT

a MAF:

Table 3 : Transmission disequilibrium test of ESR1 SNPs with restrictive AN subset of French family-based cohort

 3

	TDT	Maternal TDT	Paternal TDT

ACKNOWLEDGMENTS

Overall, we acknowledge the kind assistance of the families, students and patients who participated in the studies. This work received grants from EC Framework V "Factors in Healthy Eating" (a consortium coordinated by Janet Treasure and David Collier), and from INRA/INSERM (4M406D). AV is supported by grants from "Région Ile-de-France". YLS is funded by the "Société Française de Tabacologie". The SAGE study was supported by grants from the Institut de Recherche sur les Boissons (IREB), and from the « Mission Interministérielle de Lutte contre la Drogue et la Toxicomanie » (MILDT).

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Zehr JL, Culbert KM, Sisk CL, Klump KL (2007). An association of early puberty with disordered eating and anxiety in a population of undergraduate women and men. Horm Behav 52: 427-435.

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