Amir Yahyavi

Kévin Huguenin

Bettina Kemme

AntReckoning: Dead Reckoning using Interest Modeling by Pheromones

In games, the goals and interests of players are key factors in their behavior. However, techniques used by networked games to cope with infrequent updates and message loss, such as dead reckoning, estimate a player's movements based on previous observations only. The estimations are typically done using dynamics of motion, taking only inertia and external factors (e.g., gravity, wind) into account while completely ignoring the player's goals (e.g., chasing other players or collecting objects).

This paper proposes AntReckoning: a dead reckoning algorithm, inspired from ant colonies, which models the players' interests to predict their movements. AntReckoning incorporates a player's interest in specific locations, objects, and avatars in the equations of motion in the form of attraction forces. In practice, these points of interest generate pheromones, which fade and spread in the game world, and are a source of attraction.

Our simulations using mobility traces from World of Warcraft and Quake III show that AntReckoning improves the accuracy by up to 30% over traditional dead reckoning techniques.

I. INTRODUCTION

Interactive games have become very popular reaching an unprecedented scale, and therefore, forcing major on-line multi-player gaming platforms to develop a range of techniques to increase scalability. In interactive games, position update messages account for the largest portion of the network traffic [START_REF] Knutsson | Peer-to-Peer Support for Massively Multiplayer Games[END_REF], calling for techniques that predict player movements in order to reduce the update rate while keeping the error on player position low: the current position of an avatar is usually estimated from previous positions; only when the error is higher than a threshold a new position update is sent, thus reducing the update rate [START_REF] Fujimoto | Parallel and Distributed Simulation Systems[END_REF][START_REF] Aggarwal | Accuracy in Dead-Reckoning Based Distributed Multi-Player Games[END_REF]. Upon reception of a new update a convergence step is performed to hide the estimation errors from the player in rendering the motion [START_REF] Murphy | Believable Dead Reckoning for Networked Games[END_REF]. Such techniques also help in coping with message loss or delay by extrapolating the new position when the new update is not received in time.

Dead reckoning estimates the position of an object from the equations of motion, based on previous observations, and has been successfully used in a number of areas including distributed simulations [START_REF] Fujimoto | Parallel and Distributed Simulation Systems[END_REF][START_REF] Mccoy | Multistep-Ahead Neural-Network Predictors for Network Traffic Reduction in Distributed Interactive Applications[END_REF] and games [START_REF] Aggarwal | Accuracy in Dead-Reckoning Based Distributed Multi-Player Games[END_REF][START_REF] Murphy | Believable Dead Reckoning for Networked Games[END_REF]. While the performance of dead reckoning, in its current form, is good for vehicles moving smoothly [START_REF] Berman | The Role of Dead Reckoning and Inertial Sensors in Future General Aviation Navigation[END_REF], it may degrade in games where players, driven by their short-term environment-related goals, make frequent and sudden changes to their movements.

A typical example of this is a wounded player, moving in a given direction, having both an attacker shooting at him and a health pack in his vision field: he tends to maintain the same motion (because of inertia), while trying to move towards the health pack and to evade from the attacker. As games generally have relaxed physical rules sudden drastic changes in movements (e.g., rapid U-turn) can occur. These unpredictable changes may dramatically reduce the performance of dead reckoning as it only takes mechanics into account.

Motivated by this example, we argue that key factors in an avatar's motion are not only inertia but also the objectives of the game as well as entities in his vicinity that we refer to as points of interest. Following this line of reasoning, we propose AntReckoning. To the best of our knowledge it is the first interest-based approach to dead reckoning. The main concepts involved in AntReckoning are as follows:

• Each entity is assigned a given attractiveness leading to the generation of pheromones that fade and spread in the world; • Pheromones in the vicinity of an avatar exert attraction on it. Attraction is integrated in the equations of motion, under the form of forces, to estimate its future position. The main contributions of AntReckoning are: (1) to incorporate players' interests into the equations of motion used for dead reckoning, and (2) to use pheromones to model such interests, taking temporal and spatial aspects into account. Moreover, pheromones offer a practical solution to the decentralized implementation of interest-based dead reckoning.

We evaluated AntReckoning using mobility traces from World of Warcraft and Quake III. Our simulation results show that AntReckoning consistently outperforms dead reckoning for a carefully chosen set of parameters, and can improve the average accuracy of the estimation by up to 30% over traditional dead reckoning. Since AntReckoning involves several parameters we identify the key ones and perform a preliminary sensitivity analysis to evaluate their respective impact on the accuracy. We also discuss solutions to set game-related parameters, such as attractiveness of objects and avatars.

II. BACKGROUND

In multi-player games, players control their avatars which evolve in a virtual space called the game world. Clients regularly exchange the states of their avatars, including their position. They do so directly or through servers. The objective of the game is to accomplish missions such as going to a given location, collecting objects, or killing other entities.

In networked games, dead reckoning exploits information contained in the last state updates to extrapolate the timedependent future state of entities. Dead reckoning enables less frequent exchange of state updates and also helps coping with update message loss. A typical dead reckoning problem is the estimation of the position of a moving entity, which is required for rendering the virtual world at the clients, between two successive updates. In this situation, the key variables are the kinematic ones: the last position x t and velocity v t = ẋt of the entity and possibly its acceleration a t = ẍt (as defined by the IEEE Standard for Distributed Interactive Simulation [START_REF]IEEE Standard for Distributed Interactive Simulation -Application Protocols[END_REF]), where t represents time. Extra information that helps estimate the forces the entity is subject to can also be included.

The study of the trajectory of objects rely on the dynamic equations of motion, and more specifically, on Newton's second law which links the acceleration of an object, its mass and the forces it is subject to: a t = 1 m f . When a closed form expression of the (sum of the) forces is known, the ordinary differential equation characterizing the trajectory of the object can be obtained from this relation, and formally or numerically solved. The future position of the object is thus fully determined by its initial position and velocity.

In practice, a approximation derived from Taylor series expansion of the position, as a function of time, is used to predict the position in a near future. For instance, the second-order polynomial predictor is given by:

x t+δt = x t + v t δt + 1 2 a t δt 2 (1)
Note that such predictors are accurate only for small values of δt (compared to the rate at which players move and change their direction). It has been shown that using derivatives of orders higher than two usually results in a negligible improvement in the prediction [START_REF] Singhal | Networked Virtual Environments: Design and Implementation[END_REF][START_REF] Pantel | On the Suitability of Dead Reckoning Schemes for Games[END_REF]. As a result, the use of first and second order derivatives is usually preferred and estimating the velocity and acceleration and sending them with the current position is sufficient for short-term dead reckoning.

Estimating velocity and acceleration is commonly done from previous observation using exponential moving average (EMA). In short, EMA estimates the velocity by a weighted sum of its current value, namely the difference between the current position x t and the last position x t-δt divided by the time interval, and the last estimation:

v t = α v x t -x t-δt δt + (1 -α v ) v t-δt (2)
a t = α a v t -v t-δt δt + (1 -α a ) a t-δt (3)
Such an approach, taking into account previous estimations, has proven to have a beneficial smoothing effect [START_REF] Brown | Smoothing, Forecasting and Prediction of Discrete Time Series[END_REF].

III. MOTIVATION AND DESIGN RATIONALE When using a first order predictor, the velocity of the avatars is usually estimated from short term history of their states, thus taking into account only their inertia in the prediction. To increase the accuracy of dead reckoning, one needs to incorporate the second derivative (i.e., the acceleration) and estimate it from the forces the avatar is and will be subject to.

Estimating the forces an avatar is subject to is a difficult problem since it depends on the player's decisions: For instance, a player can suddenly accelerate to have his avatar in the game world chase another avatar. The intuition behind this reasoning is that a player is more likely to follow another player or to go to pick up a game item (e.g., a weapon) rather than just continuing on its current path. Key here is the fact that players' moves are usually driven by specific goals and interests that are themselves related to features of the virtual world. Indeed, in games such as World of Warcraft, players are interested in specific locations, certain objects, and other avatars, referred to as points of interest (POI).

More specifically, an interest-based dead reckoning algorithm should handle the following situations: (1) Game objects attract players specially if they are valuable or when the player is in urgent need of them. For example if a player comes across a powerful weapon he will most likely move towards it and pick it up. Similarly, players running out of ammo or wounded would pick up ammunitions or health packs. Attraction therefore depends on both the objects of interest and the moving avatar. ( 2) Players are attracted by the avatars they are chasing or they want to trade with, and repulsed by the avatars that are chasing them. (3) Interesting and popular locations (e.g., top of a hill, corner, etc.) in the game, namely hotspots, are a source of attraction. Such attraction points can be inferred from the history of the movements of all players.

In order to use the framework of dynamics while considering game strategy for predicting avatar movement, we incorporate player interest in the second order predictor in the form of attraction forces. The intensity of the attraction forces exerted by POIs on a given avatar depends on their relative attractiveness given the current state of the avatar and can be determined or learned in most games.

IV. THE ANTRECKONING ALGORITHM

In AntReckoning, points of interest are treated as ants that generate pheromones modeling their relative attractiveness. Pheromones are chemicals that exert attraction forces on players, integrated in a second order predictor. They spread in the game world, and fade over time, therefore taking geometrical and temporal aspects into account. Throughout this section, we use the example depicted in Figure 1 to illustrate the different mechanisms involved in AntReckoning. Table I summarizes the parameters of AntReckoning together with a brief description and the value used in the evaluation. We discuss how to tune these parameters in Section V. Model Consider a game evolving in discrete event loops called frames. In each frame each player needs to know the positions of other avatars, which he receives through position updates. Consider player Q who seeks to estimate the position x t+δt of the avatar of player P in frame t + δt while the last update received contains the position x t (and possibly the estimated velocity v t and acceleration a t ) of P in frame t. Dead reckoning AntReckoning makes use of a second order predictor where the second order term is a weighted sum of the acceleration of the avatar and the attraction forces. The estimated position therefore writes: where δt is the number of frames elapsed since the last position update, F t is the sum of the attraction forces exerted by pheromones on P and other forces (e.g., gravity), and v t (resp. a t ) is the estimated velocity (resp. acceleration) of P .

x t+δt = x t + v t δt + 1 2 α 1 m F t + (1 -α) a t δt 2 , (4)
In AntReckoning, the estimation of velocity and acceleration is performed from previous observations using EMA as described in §II with parameters α v and α a respectively. Figure 1 illustrates the estimation of the position of P for the next frame using the current velocity alone (i.e., α v = 1) and attraction forces alone (i.e., α = 1). Pheromones As common to most games, AntReckoning assumes a game world divided into non overlapping cells, e.g., Delaunay triangulation, Voronoi tessellation, binary space partitioning, or regular grids (e.g., square grid in Figure 1) typically used for tasks such as path finding, collision detection, or graphical rendering. The management of pheromones and the computation of attraction forces exerted by them is performed at the granularity of a cell: for each avatar P for which Q performs dead reckoning, Q computes the concentration of pheromone (represented in grayscale in Figure 1) in each cell and computes and sums the corresponding attraction forces. For the sake of scalability, only the cells in a limited region around P , called the attraction region and denoted by R, are considered, e.g., a fixed-size square represented with dashed lines in Figure 1. Since pheromones spread, even points of interest outside R are taken into account.

For each P for which player Q has to perform dead reckoning, the concentration of pheromone inside a cell that is part of the attraction region R of P is calculated as follows:

• Generation: in each frame, each point of interest within a cell, be it an avatar or an object, generates a given amount of pheromone related to its attractiveness to P . Attractiveness is a function of the characteristics of the object and the current state of the considered avatar (as in the wounded player example). This amount is added to the concentration of the cell. The maximum concentration of a cell can be capped to limit the attractiveness of any single cell. • Evaporation: in order to limit in time the attraction of previous positions of points of interest, pheromones fade in time, meaning that their concentration is decreased at the beginning of each frame. Exponential decays, i.e., removing a fixed percentage of the old pheromones at the beginning of each frame, have been successfully used in previous work on ant colonies (e.g., Max-Min ant colonies [START_REF] Stützle | Max-Min Ant System[END_REF]). Beyond its simplicity and its effectiveness, such an evaporation model ensures that the total number of pheromones in the game world does not grow to infinity over time. • Dissemination: since pheromones spread, the concentration of pheromone in neighboring cells are mutually dependent. At the beginning of each frame (after the evaporation step), a given amount of pheromone is removed from each cell and evenly dispatched to its neighboring cells. The size and shape of this neighborhood depend respectively on the speed of pheromones and the world map (e.g., wall, hills, etc.). These phenomena are captured by the following recursive expression of the concentration of pheromone in a cell, for a given player P , at frame t:

ph t (cell) = evaporation ε ph t-δt (cell) + generation entity∈cell attractiveness(entity, P ) + c∈N (cell) ε • γ |N (c)| ph t-δt (c) incoming dissemination -ε • γ ph t-δt (cell) outgoing dissemination , (5)
where ε is the evaporation factor, γ is the dissemination factor, and N (•) is the set of a cell's neighboring cells.

The attractiveness of a player to itself is set to zero. These phenomena can be observed in Figure 1 around the trajectory of a moving avatar: some pheromones remain and some spread around its previous positions; all pheromones fade over time.

To better understand the evolution of the concentration of pheromone described by Equation ( 5), consider the central cell c in the simplified example depicted in Figure 2. Cell c contains an object (depicted with a triangle), its neighborhood is composed of the four adjacent cells, and its current concentration of pheromone is 32. Assuming an evaporation factor ε of 0.5 the concentration is first reduced to 16. Considering a dissemination factor γ of 0.5, another 8 pheromones are then removed and evenly dispatched to the four neighboring cells. As a result of pheromone dissemination from the neighboring cells, cell c receives a total of 1 + 4 + 2 + 4 = 11 incoming pheromones. Finally the pheromones generated by the object in c, say 5, are added to its concentration yielding a total of 16 -8 + 11 + 5 = 24 pheromones in cell c at the next frame.

To further improve AntReckoning's scalability, concentrations of pheromone lower than a given threshold are ignored, since their attraction power is negligible. Attraction In physics, attraction forces between two bodies are generally directed along the line connecting them and their intensity is a decreasing function of the distance between them. In the case of spring attraction, the force is inversely proportional to the distance between the two bodies while it is inversely proportional to the square of the distance for gravitational and electromagnetic attractions. In AntReckoning, the Illustrative example of the evolution of the concentration of pheromone inside a cell with an evaporation factor of ε = 0.5 and a dissemination factor of γ = 0.5: half of the pheromones are removed due to evaporation and half of the remaining pheromones are evenly dispatched to the four neighboring cells. attraction force exerted by a cell on an avatar is directed along the line connecting the position of the avatar, i.e., x t , to the center of the cell. The intensity of the attraction force is proportional to the concentration of pheromone in the cell divided by the distance raised to a certain power:

f t (cell, x t ) = ph t (cell) d(cell, x t ) k , ( 6
)
where k is a parameter of the system. Attraction forces of various intensities originating from P and directed towards cells containing pheromones can be observed in Figure 1.

Throughout this section, we considered solely players attracted by objects and other players, through pheromones. However, repulsion, e.g., of players by one another as described in the motivation section ( §III), can easily be incorporated in the force model of AntReckoning: making repulsive objects (e.g., time bomb) or avatars (e.g., an attacker) generate pheromones with negative values would result in repulsive forces moving P away from them in the predictions.

V. PARAMETRIZATION AND IMPLEMENTATION

In here we discuss practical considerations about AntReckoning, more specifically the tuning of its parameters and its implementation in a decentralized setting.

A. Parametrization

Defining parameters of AntReckoning are as follows: Attractiveness of points of interest can be divided into two categories: (1) game objects and (2) players:

• Game objects: Most games are able to define the attractiveness of the game objects based on their value or power in the game. In addition, the attractiveness of objects can be defined as a function of key factors in the player's current state, estimated from the analysis of game play traces. For instance, one can experimentally estimate the probability that a player with a given health level having a health pack in his sight picks it up within the next δt seconds. This estimation can then be used to define the attractiveness of a health pack as a function of the current health of an avatar. • Players: Attractiveness of players for one another can be based on their recent interactions, e.g., trading or fighting, and built into the equations as follows: the attractiveness of a player Q to a player P is a function of the time t P,P elapsed since their last interaction. An exponentially decreasing factor (i.e., e -t P,P ) takes the pace of game into account. The type of interaction (e.g., shooting or being shot) determines the sign of attractiveness, i.e., attraction or repulsion. Other factors such as the items a player is carrying, e.g., flag, can be incorporated in his attractiveness.

Mass modulates the effect of attraction forces on avatars. Avatars with higher masses are less subject to attraction than others. Different mass levels can be used to capture the relative attraction of avatars by objects: for instance, heroes may move only to achieve important goals and should therefore be assigned a high mass while regular units which move to achieve secondary goals (e.g., collect resources) should be assigned small masses. Note that the scale of mass is proportional to that of attractiveness: doubling the mass of all avatars is equivalent to halving the attractiveness of all objects.

Attraction region & cell size

The size of the attraction region, in game world distance unit, and the size of each cell affects the accuracy of predictions. Larger attraction regions take into account farther objects and smaller cells compute the direction of attraction forces at a finer granularity, thus providing better accuracy. This, however, comes at the cost of computational and memory overheads. More precisely, the computational and space complexities of dead reckoning the position are proportional to the number of cells inside the attraction region. Note that since attraction decreases rapidly with the distance, increasing the size of the attraction region beyond a certain point may bring only a negligible improvement.

In games where players see the world through the eyes of their avatars, the attractiveness of objects should be weighted based on their relative positions to the avatar. The rationale is that players would be more attracted by objects they can actually see, which depends on their vision field and on the world map (e.g., walls). Also, taking into account the game map for dissemination allows to prevent avatars from being attracted by objects they cannot reach, e.g., behind an obstacle.

B. Implementation

Players have access to information about other avatars and objects in their vicinity in order to render the game world. This information is received from the server, other players, or can be extracted from maps. Therefore, if P is in the vicinity of Q, Q has access to information about the points of interest in a limited vicinity around P . For reasonably sized attraction regions, Q has access to all the necessary information and history to run AntReckoning at no additional network cost. Because it uses cells and pheromones instead of maintaining the precise current and past positions of points of interests, AntReckoning provides a lightweight implementation of interest-based dead reckoning. For each avatar for which dead reckoning is performed, AntReckoning uses a single fixed-size data structure, i.e., the map of pheromones around the avatar, that maintains the amount of pheromone in each cell. The map captures the entire temporal and geographical information within a fixed amount of memory, independent from the number of players and from time. By including the amount of pheromone a cell contains in the partition structure provided by the game, and by performing the pheromone generation step during the iteration over the entities required by the game rendering, the overhead of AntReckoning would remain low.

The complexity of AntReckoning can be optimized in two ways: (1) If a player performs dead reckoning for himself and sends the prediction to other players, he can use a single map of pheromones, thus significantly reducing the complexity. Also, since he has access to more information about the points of interest around his avatar and its current state, the computation is more accurate; [START_REF] Fujimoto | Parallel and Distributed Simulation Systems[END_REF] In case where players also perform dead reckoning for other players, the complexity can be reduced by making the attractiveness a function of only the points of interest, regardless of the state of the dead reckoned avatar, as then only one pheromone map would be needed.

VI. EVALUATION

The goal of the evaluation is two-fold: (1) perform preliminary experiments comparing AntReckoning to traditional dead reckoning in order to validate our approach and estimate the potential gains it conveys; (2) perform a sensitivity analysis of AntReckoning to identify its key parameters and evaluate their individual impact on the performance.

We evaluated AntReckoning using traces collected from Quake III and World of Warcraft. The first consists of the positions of the 48 players and entities (e.g., ammunitions) in the game world, in q3dm1 and q3dm17 maps, for each frame as well as the map information (e.g., walls). The second consists of sparse position information about more than 200 players in the Wintergrasp region, and has been obtained from [START_REF] Miller | The Near-Term Feasibility of P2P MMOG's[END_REF].

The methodology used for the evaluation was as follows. We divided time in frames and set the players' positions for each frame as their last position updates in the corresponding time interval. We estimate the position of players δt frames ahead with both traditional second-order dead reckoning, i.e., based on both the estimated velocity and acceleration, and AntReckoning, and compare their performance with respect to the relative error, knowing the actual position of the players at this frame. More specifically, we compute the Euclidean distance between the estimation and the actual position, i.e., the error, and look at the ratio between the errors of AntReckoning and traditional dead reckoning. A value of 0.8 for this metric means that AntReckoning decreases the estimation error by 20% over traditional dead reckoning. That is, values smaller than 1 denote an improvement in accuracy.

For the sake of simplicity, we used a basic version of AntReckoning: only players generate pheromones (since no information about the objects were available in the World of Warcraft trace) and all players generate the same amount λ of positive pheromones regardless of the state of the avatar for which dead reckoning is performed. Consequently a single pheromone map is used for all avatars. We used a square region of attraction and took into account pheromone evaporation. However, we did not consider pheromones dissemination: only cells players go through contain pheromones.

For our sensitivity analysis, we considered the following parameters: (1) the diameter of the region of attraction, denoted by |R|; (2) the attractiveness of players for each other, denoted by λ; (3) the evaporation factor, denoted by ε; (4) the duration of the prediction step, denoted δt. Other parameters were fixed to the values specified in Table I. The results from our trace-driven evaluation are compiled in Figure 3.

The effect of the size of the attraction region is shown in Figure 3(a). By increasing the size of the attraction region, a larger number of attraction forces are taken into account, therefore, improving the quality of predictions. However, increasing the size beyond a certain point results in negligible performance gains, confirming our intuition. This allows to perform efficient interest-based dead reckoning at no network cost with limited information locally available at each player and with limited computational and memory overhead.

Figure 3(b) demonstrates the effect of attractiveness on the performance of dead reckoning: while taking attraction forces into account improves the accuracy, over-estimating their influence and disregarding inertia decreases the accuracy.

Figure 3(c) shows that evaporation has little effect on the performance of the algorithm: players' actions are mostly driven by other avatars' recent positions. This is most likely due to the fact that Quake III is a fast paced game. However, in World of Warcraft where the pace of the game is slower and players are more motivated by long term goals, evaporation has a higher impact: larger values of ε, which characterize a slower evaporation, significantly increase the performance. Human interactions are an order of magnitude slower than game events. Therefore, in very short periods of time (e.g. 50 ms), avatars movements are mostly a function of their inertia. However, in longer periods (e.g., one second) they follow players' interests. This fact is illustrated in Figure 3(d) where AntReckoning performs better when prediction is done farther into the future. Given that many protocols (e.g., Donnybrook) rely on dead reckoning to increase the delay between sending updates to up to seconds, AntReckoning will be of use.

Our experiments on traces from World of Warcraft showed a slightly lower improvement over dead reckoning, i.e., up to 20%. In addition, the optimal set of parameters was different from Quake III showing the importance of fine tuning AntReckoning parameters based on the game. In world of Warcraft, players are motivated by longer term objectives and interactions happen at a lower pace, highlighting the effects of the evaporation factor and the length of the prediction step.

VII. RELATED WORK

A number of techniques improving the performance of dead reckoning have been proposed. In [START_REF] Cai | An Auto-Adaptive Dead Reckoning Algorithm for Distributed Interactive Simulation[END_REF] the threshold above which a new update is sent is adapted to the precision requirements, determined by the relative position of the entities. In [START_REF] Roberts | Bounding Inconsistency Using a Novel Threshold Metric for Dead Reckoning Update Packet Generation[END_REF], the metric used to evaluate the prediction error takes temporal aspects into account in order to optimize the perceived inconsistency. These techniques are orthogonal to our approach and could be used together with AntReckoning to increase the performance of dead reckoning.

In [START_REF] Mccoy | Multistep-Ahead Neural-Network Predictors for Network Traffic Reduction in Distributed Interactive Applications[END_REF] neural networks are trained and used, instead of instantaneous estimates, to predict changes of the entity velocity. ARIVU [START_REF] Anand | ARIVU: Power-Aware Middleware for Multiplayer Mobile Games[END_REF] predicts the next player actions in mobile games, using historical data, to determine if the wireless interface can be put into sleep mode, thus saving energy. These techniques could be incorporated in AntReckoning to help estimating velocity and acceleration, and player actions respectively.

Ant colony optimization has been successfully used to solve a wide range of problems, e.g., the traveling salesman problem [START_REF] Stützle | Max-Min Ant System[END_REF][START_REF] Dorigo | Ant System: Optimization by a Colony of Cooperating Agents[END_REF]. AntReckoning is inspired from these techniques, e.g., the concepts of evaporation, spreading, etc., however it is, to the best of our knowledge, the first application of pheromones to interest modeling and dead reckoning.

Beyond predicting avatar position, the interest model of AntReckoning, e.g., attractive pheromones, can be used to make convergence, path-finding (e.g., A * ), and artificial intelligence [START_REF] Murphy | Believable Dead Reckoning for Networked Games[END_REF][START_REF] Bai | Offloading AI for Peer-to-Peer Games with Dead Reckoning[END_REF] algorithms exhibit human-like behavior.

Fig. 1 .

 1 Fig.1. Overview of AntReckoning: the game world is divided into cells using a regular square grid. Each cell contains a certain amount of pheromone reflected in grayscale. To estimate the current position of P , one adds (1) his velocity, estimated from his trajectory, and (2) the sum of the attraction forces generated by cells inside a square region around him, to the position of P in the last frame. Attraction forces are directed towards the attracting cells and their intensity is proportional to the amount of pheromone they contain.

  Fig.2.Illustrative example of the evolution of the concentration of pheromone inside a cell with an evaporation factor of ε = 0.5 and a dissemination factor of γ = 0.5: half of the pheromones are removed due to evaporation and half of the remaining pheromones are evenly dispatched to the four neighboring cells.

Fig. 3 .

 3 Sensitivity analysis of AntReckoning around point (|R|, λ, ε, δ) = (60, 1.2, 0.8, 60) for Quake III and (60, 0.8, 0.9, 70) for World of Warcraft.

TABLE I IMPORTANT

 I PARAMETERS IN ANTRECKONING.

	Parameter	Description	Value
	δ	# of frames since last position update	variable
	α	weighting coef. acceleration v.s. forces	1
	αv	weighting coef. in EMA of velocity	0.8
	αa	weighting coef. in EMA of acceleration	0.8
	R	region for attraction	variable
	ε	evaporation factor	variable
	γ	dissemination factor	0
	k	decreasing power of attraction forces	2
	attractiveness(•) attractiveness of avatars and objects	variable

ACKNOWLEDGEMENTS

Amir Yahyavi was funded by NSERC Strategic Grant STPGP/350626-2007. Kévin Huguenin was partially funded by a scholarship offered by University of Rennes I.

VIII. CONCLUSION

This paper proposed AntReckoning, an interest-based algorithm to improve dead reckoning. AntReckoning models a player's interest in other players and game objects in the form of attraction forces exerted by pheromones at a low computational and memory overhead. Preliminary results on Quake III and World of Warcraft have shown improvements up to 30% in accuracy over traditional dead reckoning, even in basic settings, demonstrating a great potential. Future work includes measuring bandwidth saved by AntReckoning using thresholdbased dead reckoning as well as refining the execution of the algorithm with the notions of repulsion, map features, and vision. We also plan to develop techniques to parametrize AntReckoning with offline trace-driven analysis and online learning as well as applying it to convergence algorithms.


Kévin Huguenin

Amir Yahyavi

Bettina Kemme

Cheat Detection and Prevention in P2P MOGs

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.

I. INTRODUCTION

Scalability and fairness are keys to the success of massively multi-player on-line games. The first is necessary for the technical viability of the game while the latter is required for the wide adoption by players. Although they achieve better scalability, peer-to-peer games are more prone to cheating as players have access to and manipulate sensitive game data [START_REF] Kabus | Addressing Cheating in Distributed MMOGs[END_REF].

While in centralized games cheat detection and prevention can be achieved by having the server verify the players' actions and reduce the information sent to players to the minimal amount required to render the game world, in decentralized games, it is more difficult as natural trade-offs between responsiveness, scalability, verification and information disclosure appear together with the issues of trust and collusion [START_REF] Baughman | Cheat-Proof Playout for Centralized and Peer-to-Peer Gaming[END_REF].

Common decentralized approaches include mutual verification, auditing, agreement protocols, and information filtering [START_REF] Kabus | Addressing Cheating in Distributed MMOGs[END_REF][START_REF] Baughman | Cheat-Proof Playout for Centralized and Peer-to-Peer Gaming[END_REF][START_REF] Webb | Secure Referee Selection for Fair and Responsive Peer-to-Peer Gaming[END_REF]. However, most protocols have one of the following drawbacks: they (1) rely on a central server or trusted third parties; (2) do not deal with collusion; (3) detect cheaters a posteriori; (4) fail to provide responsiveness and scalability.

Based on Donnybrook [START_REF] Bharambe | Donnybrook: Enabling Large-Scale, High-Speed, Peer-to-Peer Games[END_REF], a distributed version of Quake III, we propose the following techniques to detect and prevent cheating while avoiding the aforementioned pitfalls:

• vision-based filtering and indirect communication to reduce the information available at each player close to the minimum amount necessary to render the game world; • assign each player a proxy player in charge of update dissemination and action verification. Proxies are chosen at random and dynamically renewed to limit the impact of collusion while allowing on-the-fly mid-term verifications.

II. BACKGROUND

Games usually run in a discrete event-loop, meaning that in each frame the states of the avatars and objects are updated and updates may be sent. In a centralized game, all objects in the game world are owned by the server and players send updates about their avatars to the server. The server verifies each update and sends it, given its global knowledge, to only those players who need it. In a P2P game, however, each client usually owns his avatar and some of the other objects. A simple P2P game lets each player send all changes directly to all other players. However, because of resource limitation, the following techniques are used: Kévin Huguenin was partially funded by a scholarship offered by University of Rennes I and an Explorateur grant offered by INRIA. Amir Yahyavi was funded by NSERC Strategic Grant STPGP/350626-2007. An extended version is available as a Technical Report [START_REF] Huguenin | Cheat Detection and Prevention in P2P MMOGs[END_REF].

• Dead reckoning consists in predicting the state of an avatar, thus allowing to reduce the frequency of position updates while keeping the display smooth. In Donnybrook, guidance messages containing the avatar's expected next position and aim (computed locally) and its current position, aim, rate of fire, etc. are used by AI to simulate the avatar's action. • Area of interest filtering consists in limiting the information a player receives about other avatars. Donnybrook distinguishes between the set of the top-5 avatars (with respect to an attention metric based on proximity, aim and interaction recency), called interest set (IS), and other avatars. In Donnybrook, a player receives frequent updates only about avatars in his IS and guidance messages about all other avatars. This is implemented through a publish-subscribe scheme, in which each player manages the subscriptions to his avatar, with two subscriptions types (i.e., IS and others).

The cheating opportunities a player can exploit to help him achieve his goal (i.e, kill other players' avatars and avoid being killed in a typical deathmatch scenario) are to: (1) delay, drop or corrupt updates in order to confuse other players; (2) delay the updates he sends to base his actions on those he receives from others; (3) tamper with the game code to circumvent the game physical laws (e.g., limited velocity) and unduly change his state (e.g., increase his health); (4) increase his score by unduly claiming he has killed some other player; (5) exploit information available but not supposed to be disclosed (e.g., position of players not visible, expected position contained in guidance messages, and subscriptions from other players) to increase his chances to kill other players and foresee danger.

III. CHEAT DETECTION AND PREVENTION

We propose a cheat detection and prevention approach based on mutual verification, indirect communication, and vision-based information filtering. These key mechanisms are facilitated by a dynamic randomized proxy architecture. Proxy architecture In any frame, a player has a single designated proxy. To prevent collusion, proxies are chosen in a randomized but verifiable way. In order to limit in time the impact of collusion between a player and his proxy, the effects of a malicious proxy, and unnecessary information disclosed to proxies, proxies are periodically renewed. This is achieved by making each player maintain, for each player including himself, a pseudo-random number generator that he initializes with the player's id. At the beginning of each new period, a player determines both his own and the other players' proxies by picking a player id with the associated generator. Subscriptions To prevent players from cheating the information received by players from updates is reduced to the minimum amount required to render the game world, from the standpoint of his avatar. This is achieved by means of different subscription types based on the relative positions and aims of the avatars (Fig. 1). We used three subscriptions types: • Interest set (IS): it contains the top-5 (with respect to an attention metric) avatars about who a player receives frequent state updates (just as in Donnybrooke). • Vision set (VS): it contains the avatars the player can see, i.e., those within a spherical cone, defined by a given radius and angle (e.g., 50 meters and ±45 degrees), centered on the avatar and not behind obstacles (e.g., walls). For VS subscription, a player receives infrequent guidance messages.

Vision -Spherical cone Interest -Top-5 inside vision Other + Fig. 1. Subscription-types and corresponding areas.

• Others: In order to determine the subscription type he needs, the player receives infrequent position updates about avatars neither in IS nor in VS. This is the default type and, thus it does not require explicit subscription. To make the multi-type subscription management cheat-proof and hide from players the subscriptions from other players, subscriptions are handled by proxies and through proxies (see Fig. 2). A player's proxy relays (and verifies) the subscriptions the player does. Subscriptions to a player are sent to his proxy, which maintains the list of subscribers on the player's behalf. All updates are then published by players through their proxies: the player sends the three types of updates to his proxy which then dispatches them accordingly. Verifications In our verification scheme, all players verify each others' actions, with a special attention from proxies to the players they are in charge of:

• Subscriptions are done through proxies who assess the validity of their types (e.g., the target of a VS-subscription is indeed in the player's vision field). Proxies have sufficient information to perform such verifications (i.e, frequent position updates about the players they are in charge of and infrequent position update about the target). • State updates are published through the proxies which verify that players' actions follow games physics (e.g., limited velocity) and game rules (e.g., decreasing health after a fall) by comparing successive state updates. Proxies also verify, a posteriori, that actual movements are consistent with predictions included in guidance messages. All players can verify another player's actions but with relative accuracy depending on the information they have. Proxies also check that players do send timely updates. • Interactions such as hit and kill-claims can be verified by proxies as well as by players acting as witnesses.

To prevent players from tampering with the messages they forward, updates and subscriptions are signed. Misbehaviors detected upon verifications are reported under the form of blames that eventually lead to sanctions. Ill-founded blames (e.g., purposeful, message loss) are dynamically filtered out.

IV. EVALUATION

We built our solution in Quake III and performed our evaluation with 48 players in the q3dm17 map. We compared our solution against Donnybrook along the following aspects:

• Mutual verifications We evaluated, for a given cheater, the average number of honest players that: act as proxy for him, have him in their IS, or have him in their VS. The results foresee a great potential for verifications: when the cheater colludes with 3 other cheaters, he is assigned an honest proxy in 93% of the cases and 10 players witness his actions (4 through frequent updates and 6 through guidance). • Information disclosure: We observed that, despite the use of proxies, information disclosure is significantly reduced when compared to Donnybrook. For instance, a coalition of three cheaters has minimum information (i.e., infrequent position update alone) for 31% of the honest players while in Donnybrook, it has guidance message about 99% of them. • Responsiveness The use of proxies increases the delays because of forwarding. Another source of delay is when an avatar enters in a player's IS or VS while only a possibly outdated position update is available. This phenomenon is however infrequent: in a frame, on average 88% of the players in IS were already in IS in the previous frame, 8.5% were in VS and only 3.5% would suffer from a slight delay.

Fig. 2 .

 2 Fig. 2. Role of proxies: manage subscriptions and verify and forward updates.


Nader ; Perroud
email: nader.perroud@hcuge.ch

Isabelle Jaussent

Sébastien Guillaume

Frank Bellivier

Patrick Baud

Fabrice Jollant

Marion Leboyer

Cathryn M Lewis

Alain Malafosse

Philippe Courtet

Isabelle Guillaume

Sebastien Bellivier

Frank Baud

Patrick Jollant

Fabrice Leboyer

Marion Lewis

Cathryn Malafosse

Alain Courtet

COMT but not serotonin-related genes

Keywords: comt, serotonin, genes, trait anger, suicidal behaviors, sexual abuse COMT, serotonin, genes, trait anger, suicidal behaviors, sexual abuse

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

Anger is a basic, commonly experienced emotional state that consists of feelings of variable intensity, from mild irritation to intense fury and rage. Anger has been related to several phenomena in medicine and several behavioral and psychiatric conditions [START_REF] Chida | The association of anger and hostility with future coronary heart disease: a meta-analytic review of prospective evidence[END_REF][START_REF] Lara | Toward an integrative model of the spectrum of mood, behavioral and personality disorders based on fear and anger traits: II. Implications for neurobiology, genetics and psychopharmacological treatment[END_REF]. A high level of anger traits has indeed been associated with eating disorders [START_REF] Fassino | Anger and personality in eating disorders[END_REF], borderline personality disorder [START_REF] Zanarini | Borderline psychopathology in the first-degree relatives of borderline and axis II comparison probands[END_REF], drug addiction [START_REF] De Moja | Anger and drug addiction[END_REF], and suicidal behaviors [START_REF] Baud | Personality traits as intermediary phenotypes in suicidal behavior: genetic issues[END_REF][START_REF] Baud | Catechol-Omethyltransferase polymorphism (COMT) in suicide attempters: a possible gender effect on anger traits[END_REF]. For the latter, in comparison to controls suicide attempters have indeed been shown to express higher level of anger [START_REF] Baud | Personality traits as intermediary phenotypes in suicidal behavior: genetic issues[END_REF][START_REF] Baud | Catechol-Omethyltransferase polymorphism (COMT) in suicide attempters: a possible gender effect on anger traits[END_REF].

Anger is part of the brain's fight-or-flight response to a perceived threat. This multidimensional structure is composed of physiological, behavioral and cognitive aspects that have been shown to correlate positively with aggression, hostility and impulsivity [START_REF] Ramirez | Aggression, and some related psychological constructs (anger, hostility, and impulsivity); some comments from a research project[END_REF]. From this perspective, particular attention has been paid to anger in the field of suicidal behaviors. Indeed, subjects with a history of suicide attempts have been shown to display a greater tendency towards anger or greater difficulty in outwardly expressing anger than control [START_REF] Baud | Personality traits as intermediary phenotypes in suicidal behavior: genetic issues[END_REF][START_REF] Baud | Catechol-Omethyltransferase polymorphism (COMT) in suicide attempters: a possible gender effect on anger traits[END_REF].

Knowledge of the sources of individual differences in anger remains sparse but includes genetic and environmental factors. Twin and family studies have indeed suggested that anger-related traits are inheritable [START_REF] Rebollo | Genetic analysis of anger: genetic dominance or competitive sibling interaction[END_REF][START_REF] Sluyter | Genetics of testosterone and the aggression-hostility-anger (AHA) syndrome: a study of middle-aged male twins[END_REF].

Several genes involved in serotoninergic and catecholaminergic neurotransmissions have recently been associated with anger traits and/or related measures of anger such as aggression or impulsivity, including tryptophan hydroxylase 1 (TPH1) [START_REF] Baud | Modulation of anger control in suicide attempters by TPH-1[END_REF][START_REF] Manuck | Aggression and anger-related traits associated with a polymorphism of the tryptophan hydroxylase gene[END_REF][START_REF] Rujescu | Association of anger-related traits with SNPs in the TPH gene[END_REF], several serotonin receptors (5-HTR) [START_REF] Giegling | Anger-and aggressionrelated traits are associated with polymorphisms in the 5-HT-2A gene[END_REF][START_REF] Serretti | HTR2C and HTR1A gene variants in German and Italian suicide attempters and completers[END_REF][START_REF] Zouk | The effect of genetic variation of the serotonin 1B receptor gene on impulsive aggressive behavior and suicide[END_REF], the monoamine oxidase A (MAOA) [START_REF] Alia-Klein | Brain monoamine oxidase A activity predicts trait aggression[END_REF][START_REF] Manuck | A regulatory polymorphism of the monoamine oxidase-A gene may be associated with variability in aggression, impulsivity, and central nervous system serotonergic responsivity[END_REF] and the catecholamine O-methyl transferase (COMT) genes (Alia- et al., 2008[START_REF] Baud | Catechol-Omethyltransferase polymorphism (COMT) in suicide attempters: a possible gender effect on anger traits[END_REF][START_REF] Baud | Modulation of anger control in suicide attempters by TPH-1[END_REF][START_REF] Giegling | Anger-and aggressionrelated traits are associated with polymorphisms in the 5-HT-2A gene[END_REF][START_REF] Manuck | Aggression and anger-related traits associated with a polymorphism of the tryptophan hydroxylase gene[END_REF][START_REF] Rujescu | Association of anger-related traits with SNPs in the TPH gene[END_REF][START_REF] Serretti | HTR2C and HTR1A gene variants in German and Italian suicide attempters and completers[END_REF][START_REF] Zouk | The effect of genetic variation of the serotonin 1B receptor gene on impulsive aggressive behavior and suicide[END_REF] Environmental factors such as childhood maltreatment, lack of social support and negative life events were also found to predict high levels of anger [START_REF] Springer | Long-term physical and mental health consequences of childhood physical abuse: results from a large populationbased sample of men and women[END_REF].

Finally, the effects of gene-environment interaction (GxE) on measures of anger are also taken into account although this area has not been thoroughly investigated to date. Exactly how GxE modulates anger related traits is not yet understood. Some studies such as those published by Caspi et al. [START_REF] Caspi | Role of genotype in the cycle of violence in maltreated children[END_REF] provide some preliminary evidence pointing to the interaction of MAOA and early maltreatment on aggression and anti-social personality traits.

In this study, we intend to explore the extent to which some GxE underlies interindividual differences in the expression of anger in a population of suicide attempters. In view of the importance of childhood maltreatment in the development of suicidal behaviors [START_REF] Dube | Childhood abuse, household dysfunction, and the risk of attempted suicide throughout the life span: findings from the Adverse Childhood Experiences Study[END_REF], the close relationship between suicidal behaviors and anger [START_REF] Horesh | Anger, impulsivity and suicide risk[END_REF] and the existence of a genetic component in suicidal behaviors [START_REF] Bellivier | Association between the TPH gene A218C polymorphism and suicidal behavior: a meta-analysis[END_REF], a population composed of suicide attempters is ideal to unravel the environmental and genetic components of anger-related traits.

Materials and Methods

Subjects

Suicide attempters (N=875) were included after informed written consent was obtained. Suicide attempters were recruited from consecutive admissions to the psychiatric units of three university hospitals -Montpellier and Créteil (France), and Geneva (Switzerland) -between 1994 and 2006. Suicide attempt was defined as the occurrence of self-harming acts with an intent to end one's own life [START_REF] Mann | Neurobiology of suicidal behaviour[END_REF]. Suicide attempters were all of European ancestry for at least two generations. Suicide attempters were assessed for psychiatric diagnoses using either the French version of the Diagnostic Interview for Genetics Studies (DIGS) or the Mini International Neuropsychiatric Interview (MINI) [START_REF] Nurnberger | Diagnostic interview for genetic studies. Rationale, unique features, and training. NIMH Genetics Initiative[END_REF][START_REF] Preisig | Diagnostic interview for genetic studies (DIGS): inter-rater and test-retest reliability of the French version[END_REF][START_REF] Sheehan | The Mini-International Neuropsychiatric Interview (M.I.N.I.): the development and validation of a structured diagnostic psychiatric interview for DSM-IV and ICD-10[END_REF]. The study protocol was approved by research ethics committees in each centre.

Behavioural and Childhood trauma assessments

Anger-related traits were assessed with the State-Trait Anger Expression Inventory (STAXI) [START_REF] Spielberger | State-Trait Anger Expression Inventory, Research Edition. Professional Manual. Psychological Assessment Resources[END_REF]. The STAXI is a 44-item self-report questionnaire measuring the experience and expression of anger in accordance with the state-trait personality theory [START_REF] Norlander | Anger, hostility, and male perpetrators of intimate partner violence: a meta-analytic review[END_REF]. The experience of anger comprises State Anger (the current feelings experienced by an individual) and Trait Anger (individual disposition to experience anger or the ease, frequency and intensity of becoming angered), whereas the expression of anger comprises the three components of Anger-In (which measures the individual tendency to suppress angry feelings), Anger-Out (the tendency to outwardly express anger towards people or objects) and Anger control (the capacity of an individual to regulate or control his/her anger).

The Childhood Trauma Questionnaire (CTQ) [START_REF] Bernstein | Childhood Trauma Questionnaire. A Retrospective Self-Report[END_REF] [START_REF] Bernstein | Initial reliability and validity of a new retrospective measure of child abuse and neglect[END_REF]. It comprises 28 items and each item is rated from 1 (never) to 5 (very often). Scores range from 5 to 25 for each type of abuse. According to Bernstein and Fink, thresholds or cut scores have been set for each type of trauma at four levels of maltreatment: None, Low, Moderate and Severe (see Table 1 for cut-off scores for each of the five CTQ subscales). The different cut-offs have been shown to have good specificity and sensitivity [START_REF] Bernstein | Childhood Trauma Questionnaire. A Retrospective Self-Report[END_REF].

Genotyping

The following polymorphisms previously associated with related measures of anger were chosen for the analyses: the TPH1 rs1800532 (A218C) polymorphism [START_REF] Jollant | The influence of four serotonin-related genes on decision-making in suicide attempters[END_REF][START_REF] Manuck | Aggression and anger-related traits associated with a polymorphism of the tryptophan hydroxylase gene[END_REF][START_REF] Rujescu | Association of anger-related traits with SNPs in the TPH gene[END_REF]; the MAOA variable number of tandem repeat polymorphisms in the promoter region (MAOA-u-VNTR) [START_REF] Jollant | The influence of four serotonin-related genes on decision-making in suicide attempters[END_REF][START_REF] Shih | MAO-A and -B gene knock-out mice exhibit distinctly different behavior[END_REF]; the functional rs6295 (C-1019G) promoter polymorphism in the 5-HTR1A gene [START_REF] Keltikangas-Jarvinen | Serotonin receptor genes 5HT1A and 5HT2A modify the relation between childhood temperament and adulthood hostility[END_REF][START_REF] Serretti | HTR2C and HTR1A gene variants in German and Italian suicide attempters and completers[END_REF]; the 5-HTR2A rs6311 (A-1438G) and rs6313 (C102T) polymorphisms [START_REF] Keltikangas-Jarvinen | Serotonin receptor genes 5HT1A and 5HT2A modify the relation between childhood temperament and adulthood hostility[END_REF][START_REF] Turecki | Prediction of level of serotonin 2A receptor binding by serotonin receptor 2A genetic variation in postmortem brain samples from subjects who did or did not commit suicide[END_REF]; the 5-HTR1B promoter rs130058 (A-161T) and rs6296 (G861C) polymorphisms [START_REF] Zouk | The effect of genetic variation of the serotonin 1B receptor gene on impulsive aggressive behavior and suicide[END_REF]; and COMT rs4680 (Val158Met) polymorphism [START_REF] Rujescu | A functional single nucleotide polymorphism (V158M) in the COMT gene is associated with aggressive personality traits[END_REF] and with suicidal behaviors: three TPH2 polymorphisms: rs11179000 and rs11179001 in the intron 4 and rs7305115 in exon 7 [START_REF] Jollant | The influence of four serotonin-related genes on decision-making in suicide attempters[END_REF]; the 44 base pair insertion/deletion polymorphism within the serotonin transporter gene (5-HTTLPR) [START_REF] Jollant | The influence of four serotonin-related genes on decision-making in suicide attempters[END_REF][START_REF] Roy | Interaction between childhood trauma and serotonin transporter gene variation in suicide[END_REF]; and the Brain Derived Neurotrophic (BDNF) rs6265 (Val66Met) polymorphism [START_REF] Perroud | Interaction between BDNF Val66Met and childhood trauma on adult's violent suicide attempt[END_REF]. All primers and genotyping conditions were carried out as previously [START_REF] Baud | Catechol-Omethyltransferase polymorphism (COMT) in suicide attempters: a possible gender effect on anger traits[END_REF][START_REF] Etain | Lack of association between 5HT2A receptor gene haplotype, bipolar disorder and its clinical subtypes in a West European sample[END_REF], Jollant et al., 2007[START_REF] Paoloni-Giacobino | Identification and analysis of new sequence variants in the human tryptophan hydroxylase (TpH) gene[END_REF][START_REF] Perroud | Interaction between BDNF Val66Met and childhood trauma on adult's violent suicide attempt[END_REF] or are available upon request.

Statistical analyses

Demographic and clinical characteristics of the study population were described using mean and standard deviation for quantitative variables and proportions for categorical variables. We used a linear regression model to test for the main effect of genes. P-values were two-tailed, and p< 0.05 was considered to indicate statistical significance. The statistical package STATA V.10 and PLINK software [START_REF] Purcell | PLINK: a tool set for whole-genome association and population-based linkage analyses[END_REF] were used for the analyses.

For statistical purposes and to enhance the power of tests, all cases of childhood trauma were pooled in two categories: not-abused or not-neglected versus abused or neglected individuals (by pooling low, moderate and severe abused/neglected subjects) [START_REF] Perroud | Interaction between BDNF Val66Met and childhood trauma on adult's violent suicide attempt[END_REF]. Sex, age at interview, diagnosis, and the recruitment centre were added as confounding variables because there were significant associations for each of these variables with at least one of the STAXI subscales, the childhood trauma items and/or the genetic polymorphisms.

When a significant main effect for a genetic polymorphism was detected on a STAXI subscore, we tested for an interaction between polymorphism and childhood maltreatment on this STAXI sub-scale.

The one-sample Kolmogornov-Smirnov test was used to investigate whether STAXI sub-scale distributions were normally distributed. The Trait Anger scale was normally distributed and therefore used without any transformation in our analyses. As regards other subscales, since no transformation was able to normalize them, we firstly used the robust command (provided with STATA) in order to take into account skewed distributions.

Secondly we used a permutation test that randomly assigned STAXI sub-scales to subjects whilst keeping each subject's genotype and environmental variable fixed. These permutation

F o r R e v i e w O n l y
procedures have been shown to relax assumptions about the normality of continuous phenotypes and to be robust against abnormal distribution patterns [START_REF] Epstein | Inference on haplotype effects in case-control studies using unphased genotype data[END_REF][START_REF] Purcell | PLINK: a tool set for whole-genome association and population-based linkage analyses[END_REF][START_REF] Zhao | Model-free analysis and permutation tests for allelic associations[END_REF]. For each analysis, the empirical p value was based on 10 000 permutations. Results were then compared to those obtained with the original distribution in order to verify the accuracy of our model.

In a second step and if an interaction was observed for a polymorphism, we tested for a possible evocative correlation association (evocative rGE) by determining with a chi-square test if the genetic polymorphism could be involved in evoking or eliciting maltreatment exposure. If so, we used logistic regression to adjust on sex, age at interview, recruitment centre and diagnosis.

Since we compared genotypic and allelic distributions of 13 polymorphic markers between non-maltreated and maltreated individuals on five STAXI sub-scales, a correction for multiple testing was required. It is difficult to correct for multiple testing in a multi-stage analysis. The primary purpose of our research was to detect interactions between the STAXI anger sub-scales and the childhood abuse and neglect measures in association with the genetic polymorphisms tested. We initially tested for the main effects of association with the five STAXI sub-scales. For genetic variants with a liberal p-value threshold of p=0.05, we then proceeded to test for interaction with the five childhood trauma items. We used a more stringent p-value threshold for the interactions. We tested 9 independent polymorphisms (since there is strong linkage disequilibrium (LD) between the polymorphisms within TPH2, 5-HRT2A, and 5-HTR1B); the childhood trauma items are all highly correlated, and we therefore consider this to be equivalent to two independent measures. For a Bonferroni correction on the p-values for interaction, we therefore used p=0.05/(9*2) = 0.0028 as a threshold for significance. Power analysis was performed using the QUANTO program [START_REF] Gauderman | QUANTO 1.1: A computer program for power and sample size calculations for genetic-epidemiology studies[END_REF].

Power calculation

We aimed to detect genetic effects accounting for at least 2% of variance in the various STAXI sub-scales under a dominant genetic model for a polymorphism with a minor allele frequency of 0.2. The power for detecting such an effect was calculated for the nominal significance level α = 0.05. The sample of 875 individuals had 0.99 power to detect an effect of a genetic marker accounting for 2% of the variance for the studied trait at an α level of 0.05.

Assuming that 40% of the subjects are exposed to childhood maltreatment and that the latter accounts for at least 1% of the variance of the trait, the GxE analysis had a power of 0.88 to detect an interaction effect accounting for more than 3% of the variance at an α level of 0.0028.

In short, our study is sufficiently powered to detect not only the clinically significant effects of genes on STAXI sub-scales but also GxE.

Results

Genotype and allele frequencies of genetic polymorphisms in suicide attempters were in Hardy-Weinberg equilibrium and similar to the frequencies reported in other clinical samples (Table 2) [START_REF] Roy | Interaction between childhood trauma and serotonin transporter gene variation in suicide[END_REF][START_REF] Rujescu | Association of anger-related traits with SNPs in the TPH gene[END_REF][START_REF] Rujescu | A functional single nucleotide polymorphism (V158M) in the COMT gene is associated with aggressive personality traits[END_REF][START_REF] Serretti | HTR2C and HTR1A gene variants in German and Italian suicide attempters and completers[END_REF][START_REF] Spurlock | A family based association study of T102C polymorphism in 5HT2A and schizophrenia plus identification of new polymorphisms in the promoter[END_REF][START_REF] Thorisson | The International HapMap Project Web site[END_REF][START_REF] Zalsman | Relationship of MAO-A promoter (u-VNTR) and COMT (V158M) gene polymorphisms to CSF monoamine metabolites levels in a psychiatric sample of caucasians: A preliminary report[END_REF][START_REF] Zouk | The effect of genetic variation of the serotonin 1B receptor gene on impulsive aggressive behavior and suicide[END_REF]. There were more females (N=471, 73.8%) in Montpellier than in Creteil (N=70, 61.4%) and Geneva (N=78, 63.4%) (X2=10.9; df=2; p=0.004). Moreover subjects recruited in Geneva scored significantly higher on Anger Control subscale than individuals from Creteil (21.8 [5.0] vs 20.5 [4.7]; b=1.33; t=2.17; 95%CI from 0.12 to 2.53; p=0.031). For these reasons, recruitment centre was added as confounding variable in all the analyses. No other variables distinguished individuals from the different center of recruitment. 3. Interestingly, neither sexual abuse nor emotional neglect had an effect on any of the STAXI sub-scales. However, other forms of maltreatment had a principal effect on most of the different STAXI sub-scales (Table 3).

Effect of childhood abuse on anger traits

Effects of genotypes and GxE on anger traits COMT Val158Met

As previously described [START_REF] Baud | Catechol-Omethyltransferase polymorphism (COMT) in suicide attempters: a possible gender effect on anger traits[END_REF], we found that COMT Val158Met had a principal effect on the Trait Anger sub-scale. Individuals carrying the high activity Val allele scored significantly higher on the Trait Anger scale than individuals homozygous for the low activity Met allele (Val/Val=24.9 [5.6]; Val/Met=24.1 [6.2]; Met/Met=23.4 [6.1]), (b=-0.85; t=-2.96; 95%CI from -1.35 to -0.19; p=0.003) (Table 4).

On the same lines, we also noted that COMT Val158Met had a main effect on Anger Out scores, (Val/Val=17 [4.8]; Val/Met=16.8 [5.1]; Met/Met=16 [4.7]), (b=-0.48; t=-2.05; 95%CI from -0.98 to -0.03; p=0.041) (Table 4). COMT genotypes did not affect other STAXI sub-scales.

We found a significant interaction between COMT Val158Met and sexual abuse on Trait Anger (F (2,762) =6.96; p=0.001) (Figure 1). This interaction was highly significant when looking at individuals with a Met/Met genotype compared to those carrying a Val allele (F (1,764) =13.13; p=0.0003). This result was significant even after correction for multiple testing. In patients reporting sexual abuse, this interaction was explained by a significantly lower Trait Anger score among individuals carrying a Met/Met genotype (22.3 [5. To less of an extent but along the same lines as the results obtained for Trait Anger, COMT Val158Met also interacted with sexual abuse when considering Anger Out scores (F (2,760) =3.38; p=0.035). However, this interaction was no longer significant following adjustment for multiple testing.

We did not observe any interaction between other types of maltreatment and COMT Val158Met for Trait Anger and Anger Out.

TPH1 A218C

THP1 A218C was found to have a main effect on Anger Control scores (Table 3).

Subjects carrying the AA genotype displayed lower Anger Control scores than the AC and CC carriers (20.3 [4.4] vs. 21.5 [4.4] and 21.3 [4.9] respectively; b=0.51; t=2.19; 95%CI from 0.14 to 2.00; p=0.029) (see Table 4). Other STAXI sub-scales were not influenced by THP1 A218C.

There was no significant interaction between childhood maltreatment and TPH1 A218C polymorphism on the Anger Control sub-scale.

MAOA u-VNTR

MAOA u-VNTR was found to have a significant effect on the Anger State STAXI subscale among male suicide attempters. Individuals carrying the H allele scored significantly higher on this sub-scale (b=1.89; t=2.05; 95%CI from 0.05 to 4.11; p=0.041) (Table 4). An interaction between MAOA u-VNTR and sexual abuse on Anger State scores was observed but did not survive correction for multiple testing (data not shown). Savitz et al. [START_REF] Savitz | The relationship between childhood abuse and dissociation. Is it influenced by catechol-O-methyltransferase (COMT) activity?[END_REF] found that Val/Val genotype, and not Met/Met genotype, was associated with increasing levels of dissociation in subjects exposed to higher levels of childhood trauma. Thapar et al. [START_REF] Thapar | Catechol O-methyltransferase gene variant and birth weight predict early-onset antisocial behavior in children with attention-deficit/hyperactivity disorder[END_REF] found that Val/Val genotypes are particularly susceptible to the effects of lower birth weight in developing anti-social behavior.

And finally Stefanis et al. [START_REF] Stefanis | COMT Val158Met moderation of stressinduced psychosis[END_REF] showed that carriers of the Val allele were more sensitive to the effect of stress on the development of psychosis than those with the Met/Met genotype. Overall, these findings support the involvement of COMT Val158Met in mediating the relationship between early traumas and psychopathology during adulthood with the Val allele being more sensitive to environmental influences.

The current findings partly contrast with those from other studies showing increased sensitivity to stress in carriers of the Met as opposed to the Val allele [START_REF] Drabant | Catechol O-methyltransferase val158met genotype and neural mechanisms related to affective arousal and regulation[END_REF][START_REF] Smolka | Catechol-O-methyltransferase val158met genotype affects processing of emotional stimuli in the amygdala and prefrontal cortex[END_REF]. Moreover, as the Met allele has been associated with violent suicide attempts and a greater tendency towards external expression of anger [START_REF] Rujescu | A functional single nucleotide polymorphism (V158M) in the COMT gene is associated with aggressive personality traits[END_REF], one would have expected to find this allele associated with a high level of anger. The results of direct association studies between COMT Val158Met and psychiatric disorders have been inconsistent with some involving the Met allele [START_REF] Park | Functional catechol-O-methyltransferase gene polymorphism and susceptibility to schizophrenia[END_REF][START_REF] Rujescu | A functional single nucleotide polymorphism (V158M) in the COMT gene is associated with aggressive personality traits[END_REF] and others the Val allele [START_REF] Glatt | Association between a functional catechol O-methyltransferase gene polymorphism and schizophrenia: meta-analysis of casecontrol and family-based studies[END_REF][START_REF] Wonodi | Association between Val108/158 Met polymorphism of the COMT gene and schizophrenia[END_REF]. Val158Met polymorphism certainly appears to have a pleiotropic effect on human behavior and various cognitive functions [START_REF] Mier | Neural substrates of pleiotropic action of genetic variation in COMT: a meta-analysis[END_REF]. Partly for this reason, several recent studies have focused on GxE rather than the principal genotypic effect. Although contrasting evidences have emerged from these findings, most of the interactions (ours included) conducted with this polymorphism provided evidence of synergism between the Val allele and environmental exposure [START_REF] Caspi | Moderation of the effect of adolescent-onset cannabis use on adult psychosis by a functional polymorphism in the catechol-O-methyltransferase gene: longitudinal evidence of a gene X environment interaction[END_REF][START_REF] Henquet | An experimental study of catechol-o-methyltransferase Val158Met moderation of delta-9-tetrahydrocannabinol-induced effects on psychosis and cognition[END_REF]. It can be assumed that both the Val and Met alleles are involved in the development of psychopathology through different interactions with specific environmental factors but with more environmental susceptibility in Val carriers.

The inconsistencies in studies analyzing the effect of Val158Met polymorphism have been the subject of many debates. Some authors proposed that COMT Val158Met may modulate the balance of tonic and phasic dopamine function in different areas of the brain depending on specific environment [START_REF] Bilder | The catechol-Omethyltransferase polymorphism: relations to the tonic-phasic dopamine hypothesis and neuropsychiatric phenotypes[END_REF]. According to this hypothesis, the Val allele is associated with decreased tonic dopamine but increased phasic dopamine neurotransmission subcortically. The predominance of phasic over tonic dopamine in Val allele carriers may explain reduced stability of neural networks but an increase in cognitive flexibility. The opposite effect is put forward for the Met allele [START_REF] Nolan | Catechol Omethyltransferase Val158Met polymorphism in schizophrenia: differential effects of Val and Met alleles on cognitive stability and flexibility[END_REF][START_REF] Rosa | New evidence of association between COMT gene and prefrontal neurocognitive function in healthy individuals from sibling pairs discordant for psychosis[END_REF]. From this perspective, the Val allele, which is associated with increased COMT activity [START_REF] Shield | Human catechol O-methyltransferase genetic variation: gene resequencing and functional characterization of variant allozymes[END_REF], may result in reduced dopamine neurotransmission in the prefrontal cortex associated with deficits in working memory, attention and executive functioning [START_REF] Bilder | The catechol-Omethyltransferase polymorphism: relations to the tonic-phasic dopamine hypothesis and neuropsychiatric phenotypes[END_REF], Goldberg et al., 2003). Our finding confirms the hypothesis that lower levels of tonic dopamine, associated with the Val high activity allele, have less control over phasic (subcortical) dopamine release resulting in an abnormally high phasic dopamine response in the nucleus accumbens [START_REF] Bilder | The catechol-Omethyltransferase polymorphism: relations to the tonic-phasic dopamine hypothesis and neuropsychiatric phenotypes[END_REF][START_REF] Meyer-Lindenberg | Midbrain dopamine and prefrontal function in humans: interaction and modulation by COMT genotype[END_REF]. It is therefore tempting to presume that, with equal environmental exposure, stressinduced phasic dopamine release will be greater in Val allele carriers than in Met/Met individuals. This would also explain why most of the interactions found the Val allele to be An inverted 'U'-shape relationship between dopamine levels and prefrontal cortex function could provide another related explanation for the paradoxical findings [START_REF] Mattay | Catechol O-methyltransferase val158-met genotype and individual variation in the brain response to amphetamine[END_REF]. In this model it is postulated that both excessive and insufficient dopamine levels impair working memory performance and that only a narrow range of dopamine levels offer optimal functioning. The pleiotropic effect of Val158Met polymorphism could be explained by the position of each allele on this particular 'U'-shaped curve where the Val/Val genotype is positioned in a less favorable position compared to the Met allele carriers (Meyer-Lindenberg & Weinberger, 2006[START_REF] Mier | Neural substrates of pleiotropic action of genetic variation in COMT: a meta-analysis[END_REF]. In Goldman's 'warrior/worrier' model [START_REF] Goldman | The genetics of addictions: uncovering the genes[END_REF], each allele is supposed to be maintained in the population because each confers an environmental-specific advantage. In Goldman's view, the Val allele is useful in threatening environments where maximal performance is required despite threat and pain (a warrior strategy), whereas the Met allele may be useful in complex environments where maximal performance is required in terms of memory and attention tasks (a worrier strategy). The high level of anger observed in Val allele carriers sexually abused in childhood could be the surviving response of this warrior strategy to this particularly threatening environment.

Val158Met polymorphism is not the only variation in the COMT gene. Considerable complexity in haplotypes and LD patterns exist across this gene and vary among populations around the world [START_REF] Mukherjee | The complex global pattern of genetic variation and linkage disequilibrium at catechol-O-methyltransferase[END_REF]. Inconsistencies regarding association studies may be due to the haplotypic combination of alleles comprising the Val158Met and several other SNPs across the gene. Several studies also revealed that sub-stratification in the investigated population could also be responsible for discrepancies between studies [START_REF] Bray | A haplotype implicated in schizophrenia susceptibility is associated with reduced COMT expression in human brain[END_REF][START_REF] Mukherjee | The complex global pattern of genetic variation and linkage disequilibrium at catechol-O-methyltransferase[END_REF]. Given the recent investigations showing moderate stratification in 18 even closely related populations, this hypothesis is not to be ruled out [START_REF] Novembre | Genes mirror geography within Europe[END_REF].

Finally and as evidenced in our previous finding [START_REF] Baud | Catechol-Omethyltransferase polymorphism (COMT) in suicide attempters: a possible gender effect on anger traits[END_REF], the moderating effects of the COMT Val158Met may be sex-specific. We have also highlighted that the observed interaction was present only in the female sample, which corroborates the idea of the sex-specificity of this polymorphism. This could also partly explain the discrepancies noted in studies concerning Val158Met polymorphism.

Limitations

The measurement of childhood maltreatment was retrospective -hence recall bias may have influenced the reports. Sample size is another issue in GXE studies [START_REF] Hunter | Gene-environment interactions in human diseases[END_REF].

In the present study, the power was enhanced by the accurate measurement of the phenotype and childhood maltreatment and the fact that we explored biologically plausible candidates.

Moreover, our study is sufficiently powerful to detect such an interaction. Another limitation is that we only considered SNPs that reached a specific level of significance for the interaction analyses, excluding potential significant interactions. COMT Val158Met does not account for all the genetic variation in the COMT activity [START_REF] Nackley | Human catechol-O-methyltransferase haplotypes modulate protein expression by altering mRNA secondary structure[END_REF] and, future studies genotyping further SNPs within the gene could help to disentangle the complex relationship between COMT gene and outcome. We however did not genotype other SNPs in this gene and were therefore not able to perform such analysis.

Although the direct association between COMT Val158Met and Anger Trait was significant, this association was not as strong as in our previous article [START_REF] Baud | Catechol-Omethyltransferase polymorphism (COMT) in suicide attempters: a possible gender effect on anger traits[END_REF]. Indeed, when looking only at the new sample of suicide attempters (448 subjects), the results were not significant. In the present study, the two samples were pooled as there was no heterogeneity between them. However, in both samples, the interaction was significant and in the same direction. This suggests that it is crucial to take into account environmental factors to consistently detect a significant association.

Interestingly, sexual abuse did not significantly influence Anger dimensions on itself.

One explanation for this intriguing result could be that we are looking at an enriched population for history of childhood sexual abuse and anger related traits and therefore at the right end of the distribution for both variables. It could be therefore more difficult to highlight a potential association. The other possible explanation is that the retrospective investigation of sexual abuse could have increased either false positives or false negatives and secondarily led to a loss of significant association.

Conclusions

To the best of our knowledge, this is the first study showing an interaction between COMT Val158Met polymorphism and childhood sexual abuse in modulating anger-trait levels in adulthood. These are important findings as they point towards sexual abuse as main environmental factors over other types of maltreatment, interacting with susceptibility genes.

Recent studies suggest that the early environment acts through epigenetic modifications in order to modify behavior [START_REF] Mcgowan | Epigenetic regulation of the glucocorticoid receptor in human brain associates with childhood abuse[END_REF][START_REF] Weaver | Epigenetic programming by maternal behavior[END_REF]. It could be hypothesized that early and repeated exposure to adverse environmental factors may elicit permanent changes in gene expression patterns via epigenetic modifications. From this perspective, Val allele carriers could be more susceptible to these epigenetic modifications, which would explain why most of the studies found this allele to be associated with increased psychopathology when exposed to an adverse environment. Table 1: Clinical and demographic characteristics of the 875 suicide attempters

  Results of the regression analyses estimating the effect of childhood trauma on STAXI sub-scales are shown in Table

  7])compared to carriers of a Val allele(ValVal (25.9 [6.1]) orValMet (25.4 [6.3]) (b=-3.75; t=-3.79; 95%CI from -5.70 to -1.81; p<0.0001 and b=-3.61; t=-4.00; 95%CI from -5.38 to -1.83; p<0.0001). We also found a significant three-way interaction with sex (F (5,757) =2.81; p=0.016) above interaction was mainly explained by the female population of suicide attempters (Figure2).

  A-161T, 5-HTR1B G861C, 5-HTR2A A-1438G, 5-HTR2A C102T, TPH2 rs11179000, TPH2 rs11179001, TPH2 rs7305115, 5-HTR1A, BDNF Val66Met and 5-HTTLPR These polymorphisms were not found to have any principal effect on STAXI scores. rGE Finally we tested for a possible evocative genotype-environment correlation (evocative rGE) between COMT Val158Met and sexual abuse. No evocative rGE was found.

  COMT Val158Met polymorphism modulates the association between childhood sexual abuse and adulthood anger-trait level. In the presence of sexual abuse, individuals carrying the Val allele display a higher disposition towards anger than individuals homozygous for the Met allele. Our results corroborate the findings of three recent investigations analyzing the modulating effect of COMT Val158Met on different outcomes.

  to psychopathologies when exposed to adverse environmental conditions.

Figure 1 :

 1 Figure 1: Trait Anger scores by sexual abuse and COMT Val158Met polymorphism in 822 suicide attempters (Ns: Val/Val=159, Val/Met=228, Met/Met=106 for individuals without history of sexual abuse; Ns: Val/Val=93, Val/Met=159, Met/Met=77 for individuals with history of sexual abuse).

Figure 2 :

 2 Figure 2: Trait Anger scores by sexual abuse and COMT Val158Met polymorphism for males (N=239; Val/Val=67, Val/Met=74, Met/Met=34 for males without history of sexual abuse; Val/Val=11, Val/Met=38, Met/Met=15 for males with history of sexual abuse) and females (N=583; Val/Val=92, Val/Met=154, Met/Met=72 for females without history of sexual abuse; Val/Val=82, Val/Met=121, Met/Met=62 for females with history of sexual abuse) respectively

  is a retrospective self-report questionnaire that examines the traumatic childhood experiences of adults and adolescents. It assesses five types of childhood trauma: emotional abuse, emotional neglect, physical abuse, physical neglect and sexual abuse. CTQ has demonstrated excellent test-retest reliability and convergent validity

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Table 1

 1 displays the demographic and clinical characteristics and rates of childhood abuse and neglect in suicide attempters. Most of the suicide attempters suffered from major depressive disorder (68.8%), were female (70.7%), and displayed non-violent suicide attempt (75.4%). The majority of suicide attempters revealed that they had suffered from childhood abuse of at least minor severity: 38.2% of suicide attempters reported a history of physical abuse, 39.9% sexual abuse, 51.1% physical neglect, 67.9% emotional abuse and 84.7% emotional neglect. Women scored significantly higher on the Trait Anger sub-scale (24.5

	[6.1] vs. 23.4 [5.8]; b=0.89; t=2.02; 95%CI from 0.01 to 1.79; p=0.044) and lower on the
	Anger Control sub-scale (21 [4.7] vs. 21.8 [4.4]; b=-0.76; t=-2.22; 95%CI from -1.42 to -0.09;
	p=0.027) than men. Moreover, age was negatively correlated to Trait Anger and Anger Out
	scores (b=-0.05; t=-3.26; 95%CI from -0.08 to -0.02; p=0.001 and b=-0.05; t=-4.13; 95%CI
	from -0.07 to -0.02; p<0.0001 respectively).

Table 1 Clinical and demographic characteristics of the 875 suicide attempters

 1

	N	%

Table 2 :

 2 Genotypes in all suicide attempters

Table 3 :

 3 STAXI by childhood trauma

	Table 2			Genotypes in all suicide attempters
			N	%				N	%
		ValVal	252	30.66			CC	209	25.61
	COMT Val158Met	ValMet	387	47.08	5-HTR1A 1019G	C-	CG	430	52.7
		MetMet	183	22.26			GG	177	21.69
		LL	266	32.56			AA	125	23.11
	5HTTLPR	LS	399	48.84	5-HRT2A 1438G	A-	AG	267	49.35
		SS	152	18.6			GG	149	27.54
		AA	152	18.51			CC	57	25.91
	TPH1 rs1800532	AC	393	47.87	5-HRT2A C102T	CT	118	53.64
		CC	276	33.62			TT	45	20.45
		AA	517	63.05			AA	400	48.9
	TPH2 rs11179000	AT	259	31.59	5-HRT1B 161T	A-	AT	331	40.46
		TT	44	5.37			TT	87	10.64
		AA	10	1.22			CC	49	5.98
	TPH2 rs11179001	AG	89	10.84	5-HT1B C861G	CG	321	39.19
		GG	722	87.94			GG	449	54.82
		AA	124	15.14	MAOA u-VNTR	L	82	34.6
	TPH2 rs7305115	AG	398	48.6	male		H	155	65.4
		GG	297	36.26
							LL	70	12.05
		MetMet	41	4.98	MAOA u-VNTR female	LH	237	40.79
	BDNF Val66Met	ValMet	270	32.81			HH	274	47.16
		ValVal	512	62.21

Table 4 :

 4 Significant associations between SNPs and STAXI sub-scales

	Table 3

Table 4 Significant associations between SNPs and STAXI sub-scales

 4

			N	mean (SD)	b; t; adjusted p for allele comparisons
				Trait Anger
		ValVal	240	24.9 (5.6)
		ValMet	368	24.1 (6.2)	-0.85; -2.96; 0.003
	COMT	MetMet	171	23.4 (6.1)
	Val158Met			Anger Out
		ValVal	239	17 (4.8)
		ValMet	367	16.8 (5.1)	-0.48; -2.05; 0.041
		MetMet	171	16 (4.7)
				Anger Control
	TPH1	AA	144	20.3 (4.4)
	A218C	AC	369	21.5 (4.4)	0.51; 2.19; 0.029
		CC	265	21.3 (4.9)
				State Anger
	MAOA uVNTR male	L H	78 150	18.9 (6.1) 21 (7.4)	1.89; 2.05, 0.041

345x215mm (72 x 72 DPI)

Genes, Brain and Behavior

Acknowledgments

This study received financial support from the CHU Montpellier (PHRC UF 7653) and Agence Nationale de la Recherche (NEURO 2007 -GENESIS). This study was also funded by the Swiss National Fund for Scientific Research grant 320000-112084 awarded to Alain Malafosse. Nader Perroud was funded by the Swiss National Science foundation: PASMA-118605. We would like to thank Camille Laurent and Claire Belloc for collecting the data.

The authors have no conflicting financial interests.