Samuel Huron
email: samuel.huron@cybunk.com

Romain Vuillemot
email: romain.vuillemot@inria.fr

Jean Daniel Fekete

Bubble-TV: Live Visual Feedback for Social TV Broadcast

Keywords: Social TV, Information Visualization, Backchannel, Live Tagging, Data Stream, Twitter, Poll ACM Classification H.5.m [Information interfaces and presentation (e.g., HCI)]: Miscellaneous

Live visualizations connected to Twitter are an opportunity to engage television (TV) viewers by providing them with visual feedback, social awareness and the possibility to interact with others. In this paper we describe our experience in deploying Bubble-TV, an extension of Bubble-T [3], intended for live visualization of TV viewers' Tweets. It was used as a background for the french TV show: "Le grand Webzé", allowing its hosts to explore and comment the social activity that took place around the show. In addition, we found that Bubble-TV impacted the viewers' experience, since half of all the viewers who Tweeted actively used the system guidelines that were given to them.Yet as effective as Bubble-TV was, we believe more research and different applications are needed to identify best practices and develop general guidelines.

Context

What is Bubble-TV? Bubble-TV is a dynamic visualization that encodes Tweets as small bubbles which continuously fall from the top of the screen and fill up bins of a bar chart. After a small amount of time, each bin shows the total number of Tweets (Figure 1), divided into 1) the latest bubbles (that stay visible for 30 seconds), and 2) an aggregation of older ones below (that is updated every time a bubble disappears). This offers a double reading: latest Tweets are expressed by the density of bubbles, and the total count by the bar chart beneath. Thus one can easily visualize social networking activities. This visualization technique has already been used to monitor real time evolution of 2012 French presidential candidates' popularity on Twitter [START_REF] Vuillemot | Et si twitter votait[END_REF]; and is based on the metaphors introduced in our visual sedimentation toolkit [START_REF] Huron | Towards visual sedimentation[END_REF].

For which live TV show?

The live TV show in which Bubble-TV was deployed, was called "Le Grand Webzé". It was aired on "France 5" (National Public TV channel) one Friday per month at 11pm and lasted 1h30min. It was presented by two hosts and a community manager, and had an average of 115 060 viewers, with peaked at 708 000. The main topic was to promote emerging talents on the Web (YouTubers, bloggers, ..), which is why Bubble-T [START_REF] Vuillemot | Et si twitter votait[END_REF] was picked up. The edition in which Bubble-TV appeared aired on February, 24th 2012.

Our position

Our work started when the Innovation services of the French national television network asked us to adapt Bubble-T for "Le Grand Webzé". This re-design forced us to consider new types of users, i.e., TV viewers, but also the people involved in the production of the show. As far as we know, such an experiment has never been discussed, and we found no guidelines to follow. We want to take the opportunity of the workshop to share our experience, discuss potentially similar ones, and eventually establish guidelines for Social TV scenarios using visualisations.

Design for the TV Show

TV shows have a well established complex production chain. Many people are involved: scenarists, directors, producers, TV hosts, guests, and in our particular case, a community manager. The first preparation meeting we had with these people was held 45 days before the show. They were interested in using Twitter to engage users in an active process by including them in the TV show. Traditionally, this is done by inviting people to be physically present, or by getting them to phone or send SMS or Emails. More recently however, the use of Twitter has been emphasized to capture viewers' feelings and feedback. Yet this collected information has mostly been presented in aggregated forms, i.e., total number of Tweets, or one Tweet at a time. Bubble-TV shows both in a dynamic way. It also indicates provenance of every Tweet with individual avatar faces on each bubble. Furthermore, no specific client application (e.g. second screen to send Tweets) is needed, and the only visualization provided by Bubble-TV is broadcasted. Our design and deployment of Bubble-TV was decomposed into the following three steps:

1. Preparation of the TV Show (Weeks before).

We discussed with the scenarists and the directors when Bubble-TV would appear on screen, when the TV hosts and community manager would have to introduce it, what role the visualization would have, and what guidelines would be given to viewers.

2. Before the TV Show (Hours before). We set the system up on stage and in the video control room. We explained to the community manager how to interact with the visualization feature by showing her how to point at and display details of an individual Tweet. 3. During the TV Show. We gave the community manager, TV hosts, and directors autonomy. They followed the initial script we agreed upon, but had room to improvise.

Specific interfaces dedicated to each actor

A series of iterations were performed to make Bubble-TV compatible with the different roles of each actor of the TV show, i.e, the hosts', scenarists' and directors'.

Stability was a prime issue since no crash, freeze or reboot was allowed. This design process resulted in the development of three different interfaces dedicated to the viewers and hosts, the community manager and the producers. These are:

• The stage visualization (Figure 2),which used the Bubble-TV visualization introduced earlier. It presented Twitter activity in real time. • The community manager interface (Figure 3), which was similar to the stage visualization but fit for a computer screen, and augmented with interactive features used to monitor, read, select, and display Tweets. This interface also controled the visualization on stage. • The counter of Tweets (Figure 4), which allowed the viewers, hosts, and producers to know the exact volume of Tweets throughout the show.

Scenario for the TV broadcast

Explaining Bubble-TV to a very diverse audience is not straightforward. The wording to describe it has to be short, easily understandable, regularly repeated and consistent throughout the show.

Focus on a scenario

Instead of monitoring the whole Twitter activity, a specific scenario was decided upon: a real time poll system would be used during the TV show. This is quite common, but is usually done with phone calls or SMS, which are hard to visualize collectively and expensive.

At the beginning of the show, the speaker introduced Bubble-TV (Figure 5, duration 2min15), asked the poll question to the public ("Does the second host have to be fired?"), gave four possible answers (#yes, #no, #hehastochange, and #whoisthisguy), and quickly explained how to send tweets with hashtags and how to read Bubble-TV. During the show, the community manager made quantitative and qualitative reports (Figure 6, between 30 and 50 seconds longs). At the end of the show, the hosts and the community manager discussed the final results of the poll (they ended up keeping the second host).

Talking to the audience with Bubble-TV support During the broadcast, the hosts commented Bubble-TV as if it were a weather forecast, with the difference that they had to introduce what a Tweet was and its meaning in the context of the question being asked. They had to repeat both questions and instructions frequently as the show was quite long and people could join in at any time.

The community manager reported several interesting Tweets and interacted them live.

Interesting observations from the TV show

During the approximate 20 minutes (out of 1h30) Bubble-TV1 was visible and in focus Figure 1, a series of unexpected events occurred. For instance one of the two hosts voted on Twitter to fire the other (Figure 6); at one point the visualization suddenly refreshed while a host was pointing a specific bubble, making it disappear; and at another, one of the hosts made a connection between an avatar and a person in the audience.

After the TV broadcast

During the show in which Bubble-TV was deployed, twice as many Tweets were sent compared to the previous one (4658 versus approximately 2000). 23% (1094) of these were sent using the answer hashtags accounting for 518 out of the 1268 active Twitter users. We believe that this high level of adoption (40% of different Twitter accounts) is linked to the poll scenario, but also to viewers' appeal to see their avatar on TV. Overall, we received positive feedback and congratulations from the producers, viewers and broadcaster. Sadly the show was cancelled after that, but Bubble-TV appeared in the France Television 2012 innovation teaser for programs, and is still under consideration for further use.

Conclusion

Our experience with Bubble-TV indicate that social networking activity could be highly impacted by the experience provided by TV broadcasting. We believe that live social network interactions driven by a broadcaster will allow to achieve tasks such as live tagging. Indeed people seem motivated to tag their own tweets if their opinion is asked for [START_REF] Huron | User-supplied sentiments in tweets[END_REF]. The benefits of this include providing a realtime feedback, an accuracy that other systems may not deliver, and quantitative and qualitative data that broadcasters could benefit from. For example, such data could be used for sentiment analysis, video annotation, or specific metadata collection for future applications. We believe visualizing this in real time will have an important role to play but will also require careful designs and well thought scenarios.

During the workshop we would like to discuss the following questions: (1) How can these live social TV systems be designed in order to achieve more complex tasks? (2) How can visualisation and scenario design improve users' incentive? (3) What is the best way to instruct a new user, even if he/she joins the show in progress?

Figure 2 :

 2 Figure 2: The stage with Bubble-TV as a background.

Figure 3 :

 3 Figure 3: The community manager screen control.

Figure 4 :

 4 Figure 4: The Tweet counter embedded in the stage furniture.

Figure 5 :

 5 Figure 5: Speaker present and explain how the visualization will work.

Figure 6 :

 6 Figure 6: The community manager reporting Twitter activity.

A montage of interesting sequences is available here (in French): http://www.youtube.com/watch?v=jn9ief5O_gQ

Acknowledgements

We thank France 5, France Television Innovation who hosted this experiment; ANR project Eulalie and Periplus for the funding; Grigolini Antonio, Cyrille de Lasteyrie, Florence Porcel and "Le Grand Webzé"'s production crew; IRI team: Nicolas Sauret, Raphael Velt, Yves Marie Haussonne, Vincent Puig; Jeremy Boy for his help.


Mehdi Benallegue

Adrien Escande

Sylvain Miossec

Abderrahmane Kheddar

Fast C 1 Proximity Queries using Support Mapping of Sphere-Torus-Patches Bounding Volumes

STP-BV is a bounding volume made of patches of spheres and toruses. These patches are assembled so that a convex polyhedral hull is bulged, in a tunable way, into a strictly convex form. Strict convexity ensures at least C 1 property of the distance function -and hence, its gradient continuity. STP-BV were introduced in our previous work [1], but proximity distance queries were limited to pairs of STP-BV covered objects. In this work we present an alternative to achieve fast proximity distance queries between a STP-BV object and any other convex shape. This is simply made by proposing a support mapping for STP-BV to be used with GJK algorithm [2]. Implementation and experiments of the proposed method and its performance are demonstrated with potential applications to robotics and computer graphics.

I. INTRODUCTION

The distance function, its properties and its potential application in robotics planning and optimization were nicely studied by the seminal work of Gilbert and Johnson [START_REF] Gilbert | Distance functions and their application to robot path planning in the presence of obstacles[END_REF]; they also elegantly proved the existence, under certain conditions, of generalized gradients and directional derivatives of the distance function that can be used efficiently in optimized trajectories generation. Another of their result proved -as we motivated differently and independently in [START_REF] Escande | Continuous gradient proximity distances for humanoids free-collision optimized-postures generation[END_REF]-that the gradient continuity of the distance function is guaranteed if one object, from the pair being tested, is strictly convex. In [START_REF] Gilbert | Distance functions and their application to robot path planning in the presence of obstacles[END_REF], they revealed about achieving such a property by slightly budging objects within a given tolerance margin. However, they did not provide a method to achieve practicly this property. In our previous work [START_REF] Escande | Continuous gradient proximity distances for humanoids free-collision optimized-postures generation[END_REF], we proposed a new method to implement this idea by wrapping sets of 3D points cloud -representing vertices of a graphical geometric model of a given object (e.g. any robot's link)-with a new bounding volume called STP-BV having the following properties:

• it is build from patches of spheres and toruses (STP);

• it is at least C 1 ;

• it can be seen as a tunable regularization of the polyhedral convex hull as it can be continuously morphed from the convex polyhedral hull to the sphere that includes all the object; In fact our BV can be seen as a merging of two properties which can not be found together in any existing known BV taken alone (see [START_REF] Ericson | Real-time collision detection[END_REF] for a list of BVs): it merges the smoothest and simpler know convex BV (spheres), with the best known volume-ratio convex-fit of any object: the polyhedral convex hull (PCH).

Yet, in our previous work [START_REF] Escande | Continuous gradient proximity distances for humanoids free-collision optimized-postures generation[END_REF], a construction method for STP-BV was proposed. Then, we used V-Clip [START_REF] Mirtich | V-Clip: fast and robust polyhedral collision detection[END_REF] as a basis for distance queries which were restricted only on a pair of STP-BV. This drawback must be discarded since it is sufficient to have only one object as strictly convex to ensure the continuity of the distance's gradient. This is very important because it has a nice consequence in robotics: it is indeed enough to cover any robot with STP-BV to guarantee the gradient continuity of the distance function computed with any other obstacle. Indeed, the continuity of the gradient induces continuity of the low level velocity control in any tracking task which makes use of the proximity distance. Examples of such tasks could be reaching a target with auto-collision and collision avoidance [START_REF] Stasse | Real-time (self)-collision avoidance task on a HRP-2 humanoid robot[END_REF] plus the included references, tracking a trajectory with a distance clearance [START_REF] Patoglu | Feedback-stabilized minimum distance maintenance for convex parametric surfaces[END_REF], making a contact with the environment by reducing the distance to zero [START_REF] Escande | Planning support contact-points for acyclic motion and experiments on HRP-2[END_REF]... The space limitation does not allow to discuss many other remarkable work in the field.

This paper proposes a new implementation of STP-BV proximity queries using a hierarchical approach instead of a feature-based approach, yet we keep track of the coherence and spatial properties to speed distance queries. Our novel contribution in this paper solves the following:

• In [START_REF] Escande | Continuous gradient proximity distances for humanoids free-collision optimized-postures generation[END_REF], the distance query was made only between a pair of STP-BV covered objects. This is because we used a feature-based approach in which distance computation are based on properties of the related voronoi region structure. It is easy to draw such properties between pairs of voronoi region representing the same geometrical features (pairs of STP-BV or pairs of PCH) and exploit neighboring region for time and spatial coherence. This generalization would have been extremely difficult to do if each object of a pair has a different model representation and a different topology for the related voronoi regions respectively.

• A consequence of the previous remark is that in [START_REF] Escande | Continuous gradient proximity distances for humanoids free-collision optimized-postures generation[END_REF], the distance computation was restricted to pairs of STP-BV objects and was achieved in two steps: the first step uses the underlying polyhedron convex hull (PCH) -obtained from the STP-BV vertices (the center of the small spheres)-and use V-Clip to find the closest features of a pair of underlying PCH. Once found, the pair underlying PCH features allows knowing the potential closest pair of STP-BV features (small sphere, big sphere or torus) respectively; this is made through heuristic association rules between STP-BV features and the underlying Fig. 1. STP-BV construction steps, from left to right: point clouds (vertices of an object), building vertice-spheres (small radius spheres for security margin), linking vertices-spheres with face-sphere (big radius spheres), closing neighboring face-spheres by edge-toruses (equivalently, the edge-torus is obtained by rotating one face-sphere arc toward the neighboring one).

CPH features. Finally the distance is computed between thre possible cases: two spheres, two toruses or a torus and sphere. First, even if they are very rare, there are cases where (i) the vertices used for STP-BV might not be convex, and (ii) the heuristics association rules might fail. These degenerate cases suggest particular programming efforts for their identification and treatment.

These drawbacks are definitely solved in this work. This is made thanks to a hierarchical approach of the distance computation such as the well known GJK algorithm [START_REF] Gilbert | A fast procedure for computing the distance between complex objects in three-dimentional space[END_REF], upto-date implementation of which allows fast distance queries between any convex shapes, as far as a support function exists for these shapes [START_REF] Gilbert | Computing the distance between general convex object in three-dimentional space[END_REF] [START_REF] Van Den Bergen | Collision detection in interactive 3D environments, ser[END_REF]. We thus propose a support function for STP-BV. We also made several optimizations in the STP-BV and GJK implementation and improved the performance of distance queries as will be seen in benchmark instances. Namely, we also make use of time and spatial coherence when this is allowed.

II. BACKGROUND: STP-BV

A. Basics

A STP-BV is a bounding volume made of parts of spheres and toruses. The basic idea behind it is to round-off the flat parts of a polyhedron convex hull (edges and faces) from which distance gradient discontinuities are originated. To do so, we perform, in first approximation the following:

• each vertex is replaced by a sphere with small radius r, called small sphere, • each face is associated with a part of big sphere with a radius R, that is tangent to the small spheres attached to the vertices of this face, • each edge is recovered by a part of torus connecting the big spheres of the adjacent faces. Parts of STP-BV are illustrated on Fig. 1, while a full STP-BV is depicted on Fig. 2. This description is only an approximation because, due to the curvature of the big spheres, some small spheres are not part of the STP-BV while their associated vertices were part of the original PCH. The big spheres define triple of small spheres and thus triple of vertices and faces. The polyhedron associated to the STP-BV might thus be different from the original PCH. We call this new polyhedron the underlying PCH.

B. Construction

The STP-BV building is similar to the gift wrapping algorithm (or Jarvis march) for PCH, Fig. 1. For given r and R, we start from a cloud of points that have been covered by small spheres. We first look for a triple of small spheres such that there exists a big sphere tangent to them and containing all the other small spheres. The vertexes define three edges. We turn the big sphere around one of them until it becomes tangent to another small sphere. This defines two new edges. Turning the sphere around the edge defines an inner volume that is the part of torus we need. By turning around each new defined edge until we reach edges we already met, we completely wrap the cloud of points and end up with its STP-BV.

III. STP-BV SUPPORT FUNCTION

Prior to further discussion, we recall quickly the definition of the key concept and step in GJK that is the support mapping, which is made through as fast as possible support function.

A. Support function

The support function of a compact A is the mapping s A which associates to each vector v the point of A such as:

v.s A (v) = max{v.a : a ∈ A}
where s A (v) is the support point of the object in the direction v. In other words, the support mapping gives the farthest point on the object's surface in this given direction.

For convex objects, the support mapping also associates to each vector the point of the object which admits this vector as normal on the surface; for strictly convex objects, this point is unique. The computation of the support function reduces therefore to find the point which admits v as normal.

Since STP-BV are made from bounded patches of spheres and toruses as primitives (i.e. basic geometric features), we divided in two steps the computation of the support point of an STP-BV in the direction v:

1) find out what primitive (i.e. what STP-BV's patch) contains v as normal, and then 2) calculate the support mapping of this primitive. The second step is reduced to use the support function for a sphere or that of a torus; both are very fast. The first step is less trivial; let us define basic data structures that are necessary for the STP-BV's features search. Based on these data structure, several feature search method will be presented.

B. Basics and data structures 1) STP-BV Voronoi Diagram:

The voronoi diagram of an STP-BV is a division of the outside space in many cells or regions such as each feature F of the STP-BV has its cell C F so that a point p outside the STP-BV belongs to C F iff p is closer to F than any other STP-BV features.

Several observations can be made at this stage:

• C F is the set of points whose projection on the STP-BV is on F ; • the vector -→ p ′ p, p ′ being the projection of p on the STP-BV, is normal to the STP-BV at p ′ , so that any point

q = p ′ + k • -→ p ′ p, k ∈ R + lies in C F ;
• any Voronoi cell is limited by straight line beams passing by the points of the feature border and following the directions of normal vectors at these points.

2) The Vector Voronoi Diagram: The Vector Voronoi Diagram of an STP-BV is a division of the unit sphere S 2 in cells, such that each feature F has its cell C F and that C F = Γ(F ) where Γ is the Gauss map [START_REF] Banchoff | Cusps of the gauss map[END_REF]. Thus, a unit vector v belongs to the C F iff there is a point on F such that the unit normal vector to the STP-BV at this point is equal to v. A stereographic illustration (2D projection) of the vector voronoi regions is illustrated by Fig. 5 for clarity.

C. Feature search methods

The feature search step reduces to finding which VVR contains a given direction vector v. We have seen previously that the VVR of STP-BV's features are limited by a finite set of cones and planes. We can check if a given vector is within a VVR simply by testing if the vector lies in the right side of each boundary. This is made simply using a dot product between the vector and the axis of the cone or the plane's normal (we consider the plane as a particular cone having π/2 angle). Indeed, for a cone c with normalized axis a and angle θ, we have :

v inside c ⇐⇒ v.a v > cos θ
This evaluation allows also having an evaluation of the distance between the vector and the violated boundary. We noticed that a VVR may be expressed exclusively with its boundaries, and each boundary simply with its axis and its angle cosine. Now that we have a method to check if a vector lies inside a VVR, it remains to find to which VVR a given vector belongs to. We propose hereafter three non-exclusive methods which resolve this.

1) Naive method: It consists simply in checking for each VVR if the vector is inside or not. This technique always finds the feature in demand. The complexity of this method is however O(n), n being the number of features in the STP-BV, and it cannot be easily used to take advantage of time and spatial coherences. A possible method would be a spiral march around the last feature found, which is really difficult in such irregular patches. This naive method is certainly not optimal, but since it is very robust, we used it to check the results of the following optimized ones.

2) Guided march method: This method is inspired by the hill climbing-based polyhedron support function. When we know that a vector does not belong to a given VVR, we also know to which boundary the vector is on the wrong side. Thus it is natural to check if the vector belongs to the VVR of the feature lying in the other side of this boundary. The problem is when many boundaries are violated; the choice of the neighbor must not be arbitrary, because infinite loops may occur. The experience has shown that the following choice always reaches the right VVR whatever the beginning feature:

• Big spheres: choose any neighbor of the good side of a boundary.

• Torus: go prior to big spheres nearby if one of them is in the right side of its limit plan. Otherwise, go to small sphere. • Small sphere: take the torus nearby whose common limit with the small sphere is the farthest from the given vector. The infinite loop case, although it has never been met in real situation, could be easily detected after n tests, n being the number of features of the STP-BV, then the algorithm would behave like the naive method that always finds the right feature.

There is no theoretical complexity calculation about this method, but we can evaluate it to O( √ n), because if the algorithm behaves like expected, it is a march guided by a potential field in a two-dimensional manifold divided into cells.

3) The underlying polyhedron convex hull method: It is an acceleration technique to the guided march method. It works in two steps; the first is to find the support point for the underlying polyhedron convex hull, that can be considered to be always a vertex on the polyhedron. The next step is to start the guided march method from the small sphere corresponding to the support vertex.

The idea of this method is that the support point in the STP-BV for a given direction can not be far from the farthest small sphere in this direction. We know also that the farthest vertex according to a given direction corresponds exactly to the farthest small sphere, so if we find this vertex, we can be sure to start the guided march from the closest small sphere. Hence, the underlying polyhedron structure allows us to accelerate the farthest point search. However, we can not use directly the STP-BV underlying polyhedron (i.e. the polyhedron having the center of the small spheres as vertexes which are linked by edges by keeping torus patches' topology); because there are some extreme cases where it is not convex. Thus we have to use the underlying polyhedron convex hull recomputed from the small sphere centers, and use it to find the farthest vertex.

The VVR of the small sphere is always strictly contained in the VVR of the corresponding vertex of the underlying polyhedron convex hull. It means that the second step, starting from a small sphere, never reaches another one, and it can find the searched feature at distance less than 4 from the initial small sphere.

The complexity of this method depends on the complexity of the first step, as the second one has constant time. There exists a O(log n) complexity polyhedron support function computation method (see a thorough discussion in [START_REF] Van Den Bergen | Collision detection in interactive 3D environments, ser[END_REF]) but it does not take profit from the time-space coherence. Thus we use the Hill climbing method which is easily adapted to keep the latest support data.

D. Support functions for STP-BV features

Any previously chosen feature search method returns a sphere (big or small) or a torus.

The support function of a sphere S c,l (with a center c and a radius l) is known and simply computes in:

s S c,l (v) = c + l.v
v For the case of torus features, we must keep in mind that the word "torus" is a misnomer. Indeed, we consider in the torus the inter-penetrated part [START_REF] Escande | Continuous gradient proximity distances for humanoids free-collision optimized-postures generation[END_REF]. We can compute the support function of this entire portion, but we know that the belonging test automatically excludes the peaks. The torus portion is the result of a big sphere rotation around an edge, this makes the center of the big sphere form a circle C. The support point of the considered part for a vector v is given by the sum of the support point of the circle C according to the vector -v, and the support point of the big sphere with radius R and centered in the origin O according to the direction v; that is:

s A (v) = s C (-v) + s SO,R (v) = s S s C (-v),R (v)
IV. IMPLEMENTATION AND PERFORMANCES Previous theoretical results have been implemented in C++ into a packaged library called SPQ for Smooth Proximity Queries. It is has been implemented as a standalone code so that it can be integrated to several applications, but it has been optimized to run in real-time since our primary focus is to use it in the low-level control of humanoid robots. Data structure is also enhanced to contain additional information for exploiting space and time coherencies (e.g. last visited feature, last distance witness points, etc.). The library is modular enough to be extended to any other convex geometry [START_REF] Gilbert | Computing the distance between general convex object in three-dimentional space[END_REF] and BVs such as OBB, AABB, Spheres, STP-BV, PCH-BV, and superellipsoids (SE-BV).

A. Performance study

At first, performances of the support function methods have been tested separately. All the tests have been run on a Pentium 4 PC 3.8GHz and 2GO RAM. We chose a complex object of 1100 vertexes (that represent a link of the HRP-2 humanoid robot) as bench; in order to have a variable number of features, we simply changed the ray of the big sphere of the STP-VB. These tests allow to confirm that the complexity of the support function computation is sub-linear. In the following we undergo the performance evaluation of the complete proximity query. We used an object having 300 vertexes, which is also an HRP-2 link. Fig. 8 shows obtained performances of the overall query without spatial and temporal coherence (i.e. the worst case) and using the guided march method for computing the support function of the STP-BV. The precision asked for the query is 10 -6 (which can be quoted in meters for our case studies, clearly this is far too much from what one requires to avoid collision in robotics!). Again the overall complexity is sub-linear relatively to the complexity of the object.

B. Comparative study

Table I relates obtained performance results in terms of number of proximity queries for different convex volume bounded objects. This object has been covered with three different bounding volumes: the polyhedral convex hull (PCH), our proposed STP-BV, and a best fit convex superellipsoid (CSE-BV). The support function for the SE is computed analytically 1 and not obtained from its polyhedral approximation. Tests have been performed on randomly positioned and oriented pairs of the same object. The results show that faster queries can be obtained using pairs of PCH-BV but without guarantee of distance gradient continuity. For this object, it appears that STP-BV queries would require 39% more time then PCH-BV whereas CSE-BV queries would require 145% more time than PCH-BV. But this is only a tendency that is likely to change depending on the complexity of the object and the application requirements. In another hand, there is actually a benefit in using a double STP-PCH BV representation for each robot's link. The reason why this is interesting appears clearly for humanoid autocollision avoidance. For a distance query between a given pair of bodies, it is better to choose an STP-BV representation for the body containing less STP-BV features, and a PCH-BV representation for the other. This reasoning certainly extends to any pair of bodies, i.e. including the objects of the environment. This also means that both BV need to be stored in memory to use the appropriate one at will.

V. APPLICATION EXAMPLES

Our method is packaged into a C++ code and integrated to a humanoid avatar interactive simulator framework we have developed. It can also be used as a standalone code to be integrated in any other application. The Fig. 9, is a screen snapshot of the video attached to the paper. In this simulation, all the 31 links of the HRP-2 humanoid robot are randomly moving and proximity distances are computed between all pairs of objects. For the example of the Humanoid HRP-2, we are able to compute necessary pairs for auto-collision (here we took the worst case) in less then 0.7msec of time. When temporal and spatial coherences are taken into account, this time reduces to 0.5msec for the overall robot. This means that we are able to integrate auto-collision into the low-level control.

The Fig. 10 illustrates pairs of distance proximity queries for a virtual avatar, here, the obtained STP-BV are rendered in transparency to see the under-covered avatar. The distance is illustrated by the (red) line linking computed witness points for each selected pairs of body.

VI. CONCLUSION

We present a substantial improvement of our STP bounding volume [START_REF] Escande | Continuous gradient proximity distances for humanoids free-collision optimized-postures generation[END_REF] which allows fast C 1 proximity queries between convex shapes. Provided that (i) any object can potentially be decomposed into a collection of convex sub-objects, and (ii) it suffices that only one object be strictly convex to ensure continuous gradient of the distance function [START_REF] Gilbert | Distance functions and their application to robot path planning in the presence of obstacles[END_REF], this method has certainly potential use in robotics, humanoids and virtual avatar whole-body free-collision motion generation control or optimization. For the time being, we proved that the obtained performance are satisfactory and the implementation is robust. As future work, this software will be further code-optimized and integrated in a low level control of a real humanoid robot as a continuation of [START_REF] Stasse | Real-time (self)-collision avoidance task on a HRP-2 humanoid robot[END_REF].

r

  is the minimal distance between the original PCH and the STP-BV. It defines a security margin for the collision detection. R controls the curvature of the STP-BV, and thus the regularity of the distance gradient. When r → 0 and R → ∞, the STP-BV tends to the original PCH, Fig.2.

Fig. 2 .

 2 Fig. 2. A robot part (humanoid chest): the polyhedral convex hull bounding volume (PCH-BV), left; and the sphere torus patches bounding volume (STP-BV), right: light pink (big spheres patches), pink (toruses patches), red spots (small sphere patches).

Fig. 3 .Fig. 4 . 3 )•

 343 Fig. 3. Obtaining vectorial Voronoi diagram.

Fig. 5 .

 5 Fig. 5. Steregraphic projection of vectorial voronoi regions.

Fig. 6 .Fig. 7 .Fig. 8 .

 678 Fig. 6. Performance for the guided march based function support computation.

Fig. 9 .

 9 Fig. 9. STP-BV covered HRP-2 links, distance query is performed between all pairs of links.

Fig. 10 .

 10 Fig. 10. Auto-collision avoidance with a virtual avatar.

TABLE I NUMBER

 I OF PAIR PROXIMITY QUERIES PER SECOND.

		PCH-BV	STP-BV	CSE-BV
	PCH-BV	795123
	STP-BV	584567	525394
	CSE-BV	319216	286368	187429

This is the object of another paper.

ACKNOWLEDGMENT

This work is partially supported by grants from the ImmerSence EU CEC project, Contract No. 27141 (FET-Presence) under FP6 www.immersence.info.


Keywords: myocardial infarction, exercise, obesity, kinases, protein phosphatases

Obesity is a major health issue that impedes the ability of preconditioning and postconditioning to protect the myocardium against infarction secondary to dysregulation of kinase signalling pathways. Moreover, exercise decreases cardiovascular mortality in obese patients but the mechanism remains to be established. Wild-type (WT) and obese (ob/ob) mice were assigned to sedentary conditions or regular treadmill exercise (1h/day, 5 days/7, 4 weeks, 4° slope, 10-30 cm/s) and underwent 30 min of coronary artery occlusion followed by 24 h of reperfusion for infarct size measurement. In WT, exercise reduced infarct size by 60% and increased phosphorylation of kinases such as Akt, ERK 1/2, p70S6K, AMPK and GSK31. Importantly, the level of corresponding phosphatases PTEN, MKP-3 and PP2C was decreased. Calcium concentration inducing opening of mitochondrial permeability transition pore (mPTP) was increased by exercise. In ob/ob, regular exercise induced a robust cardioprotection by reducing infarct size (-67%), increasing kinase phosphorylation, decreasing phosphatase levels and improving the resistance to mPTP opening. However exercise did not modify hyperglycemia, hypercholesterolemia, hyperinsulinemia, fat mass and body weight in obese mice. In conclusion, regular exercise induces cardioprotection against myocardial infarction despite obesity and restores pro-survival signalling pathways with simultaneous increase in kinase phosphorylations, decreased levels of phosphatases and increased resistance of mPTP opening, independently from improvement in associated comorbidities.

ABBREVIATIONS

ACC: acetyl-Co A Carboxylase; Akt: protein kinase B, ERK: extra-cellular signal regulated kinase; Ex: exercised animals; GSK3β: glycogen synthase kinase 3β; MKP-3: mitogenactivated protein kinase phosphatase-3, mPTP: mitochondrial permeability transition pore; ob/ob: leptin deficient mice; P-: phosphorylated form; PI3K: phosphatidylinositol-4,5biphosphate 3-kinase; PTEN: Phosphatase and tensin homologue deleted on chromosome 10; PP2C: protein phosphatase 2C, p70S6K : p70S6 kinase; Sed: sedentary.

INTRODUCTION

Cardiovascular diseases are a major cause of death in industrialized countries with coronary artery disease being the most prevalent manifestation. Despite reperfusion, coronary artery disease involving myocardial ischemia can result in myocardial infarction associated with elevated morbi-mortality. Consequently, several strategies, pharmacological or not, have been proposed to induce cardioprotection. Among them, regular exercise has been shown to reduce cardiovascular morbi-mortality [START_REF] Sofi | Physical activity during leisure time and primary prevention of coronary heart disease: an updated meta-analysis of cohort studies[END_REF][START_REF] Thompson | Exercise and physical activity in the prevention and treatment of atherosclerotic cardiovascular disease: a statement from the Council on Clinical Cardiology (Subcommittee on Exercise, Rehabilitation, and Prevention) and the Council on Nutrition, Physical Activity, and Metabolism (Subcommittee on Physical Activity)[END_REF] and is considered as the only practical and sustainable countermeasure capable of providing cardioprotection against myocardial infarction. Interestingly, clinical investigations have demonstrated that exercise is a cardioprotective factor, independent of the presence of other risk factors [START_REF] Bijnen | Physical inactivity as a risk factor for coronary heart disease: a WHO and International Society and Federation of Cardiology position statement[END_REF][START_REF] Blair | Influences of cardiorespiratory fitness and other precursors on cardiovascular disease and allcause mortality in men and women[END_REF][START_REF] Fletcher | Statement on exercise. Benefits and recommendations for physical activity programs for all Americans. A statement for health professionals by the Committee on Exercise and Cardiac Rehabilitation of the Council on Clinical Cardiology, American Heart association[END_REF].

Obesity is also a major health issue in western countries and its importance is constantly growing. According to the World Health Organization, this disease has reached epidemic proportions with more than 1 billion overweight adults and at least 300 million of them are clinically obese. Obesity is a major and independent risk factor for coronary heart disease and increased waist-to-hip ratio is associated with greater occurrence of myocardial infarction [START_REF] Yusuf | Obesity and the risk of myocardial infarction in 27,000 participants from 52 countries: a case-control study[END_REF].

Most animal studies investigating cardioprotective strategies have been performed in young healthy animals but it is well known that co-morbidities such as obesity impede the ability to protect the myocardium against infarction. Indeed it has been previously reported that both pre-and postconditioning failed to reduce infarct size in obese animals probably because of their inability to activate the cardioprotective signalling pathways through kinase phosphorylations. [START_REF] Ferdinandy | Interaction of cardiovascular risk factors with myocardial ischemia/reperfusion injury, preconditioning, and postconditioning[END_REF][START_REF] Peart | Clinical cardioprotection and the value of conditioning responses[END_REF][START_REF] Bouhidel | Myocardial ischemic postconditioning against ischemia-reperfusion is impaired in ob/ob mice[END_REF]. Nevertheless, it is known that exercise is able to decrease cardiac events and mortality in obese or overweight patients [START_REF] Blair | Effects of physical inactivity and obesity on morbidity and mortality: current evidence and research issues[END_REF][START_REF] Savage | Reduction in obesity and coronary risk factors after high caloric exercise training in overweight coronary patients[END_REF][START_REF] Singh | Effect of diet and moderate exercise on central obesity and associated disturbances, myocardial infarction and mortality in patients with and without coronary artery disease[END_REF].

In lean conditions, Golbidi et al. [START_REF] Golbidi | Molecular mechanisms in exercise-induced cardioprotection[END_REF] have proposed to divide the potential beneficial mechanisms of exercise into two large categories: mechanisms that decrease reactive oxygen species production and others that repair cellular damages. Among them, mitochondrial adaptations seem to be crucial in exercise-induced cardioprotection [START_REF] Kavazis | Exercise training induces a cardioprotective phenotype and alterations in cardiac subsarcolemmal and intermyofibrillar mitochondrial proteins[END_REF][START_REF] Kavazis | Exercise induces a cardiac mitochondrial phenotype that resists apoptotic stimuli[END_REF]. Indeed, these organelles, in particular their mitochondrial permeability transition pore (mPTP), represent a major target for protecting the myocardium against infarction [START_REF] Lim | Preconditioning and postconditioning: the essential role of the mitochondrial permeability transition pore[END_REF]. The signalling pathway including PI3K-Akt, ERK 1/2 or GSK3β, the so-called Reperfusion Ischemia Salvage Kinases (RISK) pathway has been identified to converge toward the mitochondria and to induce cardioprotection during both pre-and postconditioning [START_REF] Hausenloy | Reperfusion injury salvage kinase and survivor activating factor enhancement prosurvival signaling pathways in ischemic postconditioning: two sides of the same coin[END_REF][START_REF] Heusch | Cardioprotection: nitric oxide, protein kinases, and mitochondria[END_REF]. However, this signalling pathway has not been extensively studied for understanding exercise inducedcardioprotection, in particular in obese subjects.

Accordingly, our aim was to investigate whether regular treadmill exercise was able to condition the heart against myocardial infarction through pro-survival signalling pathways during obesity. For this purpose, we investigated in a mouse model of obesity 1) the effects of regular exercise against myocardial infarction and 2) the subsequent activation of the RISK and AMPK pathways as well as mitochondrial adaptations.

METHODS

Animals

Male 5 to 10 week-old wild-type C57BL/6J (WT) and obese (ob/ob) mice were used (R. Janvier, Le Genest St Isle, France). Mice were housed in an air-conditioned room with a 12 h light-dark cycle and received standard rodent chow and drinking water ad libitum. The authors have been granted a license from the institutional office "Préfecture du Val de Marne" (France) to conduct animal research (agreement A94-028-28). The investigation conformed to the Guide for the Care and Use of Laboratory Animals published by the US National Institute of Health.

Experimental protocol

Both WT and ob/ob mice were randomly subjected to regular treadmill exercise (Ex-WT and Ex-ob/ob) or to sedentary conditions (Sed-WT and Sed-ob/ob). Exercised animals have run 5/7 days during 4 weeks. The first week was an adaptation period with gradual speeds during 30 min [START_REF] Blair | Effects of physical inactivity and obesity on morbidity and mortality: current evidence and research issues[END_REF][START_REF] Kavazis | Exercise training induces a cardioprotective phenotype and alterations in cardiac subsarcolemmal and intermyofibrillar mitochondrial proteins[END_REF][START_REF] Heusch | Cardioprotection: nitric oxide, protein kinases, and mitochondria[END_REF][START_REF] Moien-Afshari | Exercise restores coronary vascular function independent of myogenic tone or hyperglycemic status in db/db mice[END_REF][START_REF] French | Exerciseinduced protection against myocardial apoptosis and necrosis: MnSOD, calcium-handling proteins, and calpain[END_REF], and 30 cm/s, 4° slope, 5 min each step for WT and 8, 8, 10, 14, 18, and 20 cm/s, 4° slope, 5 min each step for ob/ob). For the three other weeks, mice ran during one hour per day (30 and 20 cm/s for WT and ob/ob, respectively, 4° slope) without any exhaustion. To take into account the differences in body weight, the speed was different between the two strains in order to obtain similar vertical work [START_REF] Massett | Strain-dependent differences in responses to exercise training in inbred and hybrid mice[END_REF]. After these 4 weeks of exercise or sedentary conditions, mice were subjected to 30 min of ischemia followed by reperfusion. Infarct sizes were measured at 24 h of reperfusion. Additional mice were used for Western blot experiments and investigating mPTP opening by calcium. In this case, the heart was excised at 10 min of reperfusion. All these final experiments were performed 24h after the last bout of exercise. Additional mice were used for biological and morphological analyses.

Morphometry

Mice were anesthetized by intraperitoneal injection of pentobarbital sodium (60 mg/kg).

Fat and lean masses were determined by means of a PIXImus (Lunar Corporation, Madison, WI, USA) using dual-energy x-ray absorptiometry.

Blood measurements

Blood glucose and cholesterol levels were measured using a multiparametric automat (Automat type AU-400, Olympus, Hamburg, Germany). Insulin level was determined using the Rat/Mouse Insulin ELISA kit (Millipore, Billerica, MA, USA). All these parameters were obtained from fed animals.

Myocardial infarction

Mice were anesthetized by intraperitoneal injection of pentobarbital sodium (80 mg/kg), intubated and ventilated mechanically. The body temperature was maintained at 37°C. A left thoracotomy was performed in order to realize the sequence of coronary artery occlusion followed by reperfusion with an 7-0 Prolene thread placed around the left coronary artery as previously described [START_REF] Michael | Myocardial infarction and remodeling in mice: effect of reperfusion[END_REF]. Myocardial ischemia was confirmed by the occurrence of regional cyanosis. Reperfusion was confirmed by visualisation of an hyperemic response and the chest was closed in layers.

After 24 h of reperfusion, mice were reanesthetized. The chest was opened, the coronary artery was re-occluded at the same location than previously performed and Evan's blue solution was injected through the apex to delineate the area at risk. The heart was excised, the left ventricle was cut into 6 slices and the infarct area was identified by 2,3,5triphenyltetrazolium chloride (TTC) staining. The area at risk was identified as the non-blue region and expressed as a percentage of the left ventricle weight. The infarcted area was identified as the TTC positive zone and expressed as a percentage of area at risk.

Mitochondria

For measurement of mPTP opening, areas at risk were placed in medium containing 220 mM mannitol, 70 mM sucrose, 10 mM HEPES, 1 mM EGTA (Sigma-Aldrich, St. Louis, MO, USA), pH 7.4 at 4°C. The tissues were minced with scissor and homogenized on ice using a Teflon Potter homogenizer and were centrifuged at 1000 g for 5 min. Supernatants were centrifuged at 10000 g for 10 min. The final pellets were resuspended in the homogenization buffer including 0.01 mM EGTA. Protein concentration was determined by the method of Lowry et al. [START_REF] Lowry | Protein measurement with the Folin phenol reagent[END_REF].

Mitochondrial Ca 2+ retention was monitored as an index of mPTP opening.

Mitochondria were loaded with increasing concentrations of Ca 2+ until the load reached a threshold where mitochondria underwent a fast process of Ca 2+ release due to mPTP opening. Cardiac mitochondria (0.8 mg/ml), energized with 3.3 mM pyruvate/malate, were incubated in a buffer (50 mM sucrose, 100 mM KCl, 10 mM HEPES and 5 mM KH 2 PO 4 ) containing 3.3 µM Ca 2+ Green-5N fluorescent probe (Interchim, Montluçon, France). The reaction was started by the addition of successive 2.5 µM Ca 2+ pulses. After each addition, a rapid uptake was observed and was followed by a dynamic steady state corresponding to the equilibrium between the influx and the efflux of Ca 2+ . When maximal Ca 2+ -loading threshold was reached, this equilibrium was disrupted and Ca 2+ was released. The concentration of Ca 2+ in the extra-mitochondrial medium was monitored by means of a Perkin-Elmer LS 50B fluorescence spectrometer (Perkin-Elmer, Waltham, MA, USA) at excitation and emission wavelengths of 506 and 532 nm, respectively.

Western Blot analysis

Areas at risk were placed in medium containing 220 mM mannitol, 70 mM sucrose, 10 mM HEPES, 1 mM EGTA, 5µl/ml of protease inhibitor cocktail, 1 mM sodium orthovanadate, 5 mM sodium fluoride, 1 mM sodium Na 2 1-glycerol phosphate (Sigma-Aldrich, St. Louis, MO, USA), pH 7.4 at 4°C. The tissues were scissor minced and homogenized on ice using a Teflon Potter homogenizer. The homogenates were centrifuged at 17600 g for 30 min at 4°C to collect the cytosol. The protein concentrations were determined by the BCA Protein Assay kit (Pierce, Rockford, IL, USA).

Extracted protein samples were denatured at 90°C for 5 min. Proteins (25 µg/lane) were separated by SDS-polyacrylamide gel electrophoresis, transferred to PVDF membranes and probed with primary antibodies for phospho-Akt (Serine 473), phospho-ERK 1/2 (Threonine 202/Tyrosine 204), phospho-p70S6K (Threonine 389), phospho-p70S6K (Threonine 421/Serine 424), phospho-AMPK (Threonine 172), phospho-GSK3β (Serine 9), phospho-ACC (Serine 79), total Akt, total ERK1/2, total p70S6K, total AMPK, total GSK3β, total ACC, PTEN (all from Cell Signaling Technology, Danvers, MA, USA), MKP-3 (Epitomics, Burlingame, CA, USA), PP2C (Abcam, Cambridge, UK). Blots were washed and then incubated with goat anti-rabbit IgG secondary antibody conjugated to horseradish peroxidase (Santa Cruz Biotechnology, Santa Cruz, CA, USA). Blots were finally incubated using the ECL detection system (Pierce, Rockford, IL, USA) and exposed to ECL chemiluminescence film (Hyperfilm ECL, Amersham, Buckinghamshire, UK). Bands of interest were scanned and quantified in a blinded manner using gel analysis software Image J-1.37 (National Institute of Health, Bethesda, MD, USA).

RESULTS

Morphological and biological parameters

As shown in Table 1, body weights and fat masses were increased by 1.7-fold and 4.3fold respectively in ob/ob as compared to WT sedentary mice (p<0.05). Blood glucose, cholesterol and insulin levels were significantly higher in ob/ob as compared to WT sedentary mice. Regular exercise had no effect on these three biological parameters either in ob/ob or in WT animals. In addition, body weights and fat masses were not affected by regular exercise.

Myocardial infarct sizes

The areas at risk were similar among all groups (41±1%, 41±3%, 38±1% and 38±3% for Sed-WT, Ex-WT, Sed-ob/ob and Ex-ob/ob, respectively). Infarct size was significantly increased in ob/ob vs WT sedentary mice (Figure 1). In exercised WT mice, infarct size was reduced by 60% (43±3% vs 17±2% for Sed-WT and Ex-WT, respectively, p<0.05). In ob/ob mice, regular exercise elicited a major cardioprotective effect as infarct size was significantly reduced by 67% (58±3% vs 19±1% for Sed-ob/ob and Ex-ob/ob, respectively).

Signalling pathways

In exercised WT mice (Figure 2), the phospho-Akt/Akt ratio was significantly increased after ischemia-reperfusion. As p70S6K is known to be phosphorylated at Threonine 389 through the Akt pathway, we examined its phosphorylation. Western blot revealed a raise in phosphorylated p70S6K/p70S6K ratio by exercise (+65%, p<0.05). Concomitantly, PTEN which participates to Akt inactivation was significantly decreased in exercised as compared to sedentary animals. Interestingly, all these effects were also observed in ob/ob mice.

As illustrated in Figure 3, exercised WT mice elicited major increases in the phosphorylated form of ERK 1/2 and of one of its downstream kinase, i.e., p70S6K (Thr 421/Ser 424) while the ERK 1/2 corresponding phosphatase MKP3 levels were simultaneously reduced as compared to sedentary WT mice. In ob/ob animals, exercise allowed once again to induce major significant increases in the level of these phosphorylated kinases and decrease in phosphatase levels.

Then we examined AMPK that plays a critical role in maintaining energy homeostasis and cardiac function during stress situations such as ischemia (Figure 4). We found that phosphorylation of AMPK and one of its characterized targets ACC, were significantly increased after ischemia-reperfusion in exercised as compared to sedentary WT mice. Concomitantly, levels of PP2C which inactivates AMPK, were significantly reduced. Similar pattern of phosphorylation and phosphatase variation was observed in exercised vs sedentary ob/ob animals.

We also investigated GSK3β, one of the downstream target of ERK 1/2 and Akt signalling pathways that is known to play a role in mPTP opening (Figure 5A). We found that phospho-GSK3β/GSK3β ratio was significantly increased by exercise. In ob/ob animals, regular exercise also induced significant and similar increase in phosphorylation of GSK3β.

Finally, we evaluated the adaptation in mPTP opening by assessing its susceptibility to calcium overload. The Ca 2+ concentration required to open mPTP was significantly improved by 95% in exercised as compared to sedentary WT mice (Figure 5B). Improved resistance to mPTP opening was also observed in exercised ob/ob animals.

DISCUSSION

The present study demonstrates that regular treadmill exercise induces protection against myocardial infarction despite obesity and activates cellular cardioprotective kinases, independently from improvement in associated co-morbidities. Therefore, regular exercise is a powerful cardioprotective strategy that restores the activation of pro-survival signalling pathways and protects cardiac mitochondria. This is of major importance as both pre-and postconditioning failed to reduce myocardial infarct size in obese animals because of their inability to activate these cardioprotective pathways in obese conditions (for review, [START_REF] Peart | Clinical cardioprotection and the value of conditioning responses[END_REF]).

Importantly, the variations in phosphatase levels mirrored those of kinase phosphorylations as the increased amount of phosphorylated forms of survival kinases was accompanied by a reduction in phosphatases expression, i.e., PTEN, MKP-3 and PP2C. The mechanisms of this protection also involved major cardiac mitochondrial adaptations illustrated by an increased capacity of mitochondria to retain calcium showing a greater resistance to mPTP opening.

In the present study, we used the ob/ob mice model of obesity characterized by hyperphagia with increased body weight and metabolic abnormalities. With regular exercise, we did not however observe any significant changes in body weight, fat mass, glycemia, cholesterolemia and insulinemia, probably related to maintained hyperphagia although individual food intake was not measured in the present study. This is an important feature of our experimental setting that allowed to avoid any confounding effect induced by changes in these biological parameters. This latter point is in agreement with previous studies. Moien-Afshari et al. [START_REF] Moien-Afshari | Exercise restores coronary vascular function independent of myogenic tone or hyperglycemic status in db/db mice[END_REF] have shown that exercise restores coronary vascular function independently of changes in hyperglycaemic and hyperinsulinemic status in db/db mice. In another study, treadmill exercise failed to restore body weight in the db/db mouse model [START_REF] Sennott | Treadmill exercise training fails to reverse defects in glucose, insulin and muscle GLUT4 content in the db/db mouse model of diabetes[END_REF]. Therefore, exercise induced-cardioprotection in these obese animals was independent from any improvement in associated co-morbidities.

Numerous experimental studies have reported cardioprotection with exercise and it has been proposed that it could improve myocardial antioxidant capacity, increase cardiac ATPsensitive potassium channel expression, prevent calpaïn activation and decrease calcium overload [START_REF] Brown | Susceptibility of the heart to ischaemia-reperfusion injury and exercise-induced cardioprotection are sex-dependent in the rat[END_REF][START_REF] Domenech | Exercise induces early and late myocardial preconditioning in dogs[END_REF][START_REF] French | Exerciseinduced protection against myocardial apoptosis and necrosis: MnSOD, calcium-handling proteins, and calpain[END_REF][START_REF] Soufi | Role of 12-week resistance training in preserving the heart against ischemia-reperfusion-induced injury[END_REF]. To our knowledge, although several pro-survival kinases and mitochondria are described as major actors of cardioprotection [START_REF] Hausenloy | Reperfusion injury salvage kinase and survivor activating factor enhancement prosurvival signaling pathways in ischemic postconditioning: two sides of the same coin[END_REF][START_REF] Heusch | Cardioprotection: nitric oxide, protein kinases, and mitochondria[END_REF], no study has investigated their role in exercise-trained animals, either healthy or obese, during myocardial ischemia-reperfusion.

Only Zhang et al [START_REF] Zhang | Long-term aerobic exercise protects the heart against ischemia/reperfusion injury via PI3 kinase-dependent and Aktmediated mechanism[END_REF] have described that long term aerobic exercise alleviated cardiac dysfunction following myocardial infarction through a PI3K-Akt and GSK3β dependent mechanism in rats. One major insight of the present study is the concomitant investigation of the RISK pathway as well as its downstream target, the mitochondria but also AMPK and several phosphatases. Indeed following ischemia-reperfusion in WT and ob/ob mice, we observed that regular exercise induced activation of the RISK pathway through phosphorylation of its components, i.e., Akt, ERK 1/2 and their common downstreams, p70S6K and GSK 3β. In parallel, the variations of phosphatase levels mirrored those of corresponding kinase phosphorylations as PTEN and MKP-3 were concomitantly decreased by regular exercise. This point is of major importance as it is known that phosphatases limit the efficacy of some cardioprotective strategies such as pre-or postconditioning during aging or obesity [START_REF] Bouhidel | Myocardial ischemic postconditioning against ischemia-reperfusion is impaired in ob/ob mice[END_REF][START_REF] Fenton | Inhibition of phosphatase activity enhances preconditioning and limits cell death in the ischemic/reperfused aged rat heart[END_REF][START_REF] Przyklenk | Aging mouse hearts are refractory to infarct size reduction with post-conditioning[END_REF]. One could suggest that reduced phosphatases expression would be responsible for the activation of survival kinases which is known to be a crucial event for protecting the myocardium against myocardial infarction. Indeed, it has been clearly demonstrated for other cardioprotective strategy that phosphorylation of kinases at reperfusion is essential for inducing cardioprotection independently from cellular events that could occur prior to reperfusion [START_REF] Hausenloy | Ischemic preconditioning protects by activating prosurvival kinases at reperfusion[END_REF]. Blockade experiments were not performed and will require other studies. Moreover, the use of inhibitors of ERK and Akt pathways might be complicated as compensatory mechanisms and crosstalks between signalling pathways could exist.

Activation of these signalling pathways is well known to target mitochondria by protecting against mPTP opening and ultimately from cell death. Indeed, the critical role of mPTP has been demonstrated during cardioprotection elicited by ischemic and pharmacological pre-and post-conditioning [START_REF] Lim | Preconditioning and postconditioning: the essential role of the mitochondrial permeability transition pore[END_REF][START_REF] Heusch | Cardioprotection: nitric oxide, protein kinases, and mitochondria[END_REF]. Accordingly, we evidenced that regular exercise increased the capacity of mitochondria to retain calcium in WT but also similarly in obese animals during ischemia-reperfusion. These findings are in accordance with the prevention of the release of proapoptotic proteins from mitochondria by treadmill exercise [START_REF] Lee | Exercise protects cardiac mitochondria against ischemia-reperfusion injury[END_REF]. Another point deserves to be discussed. In sedentary animals, myocardial infarct sizes were greater in ob/ob vs WT mice while the capacity of mitochondria to retain calcium was similar. This apparent discrepancy might be related to the difference in calcium handling between WT and ob/ob mice and therefore to a greater level of mPTP opening stimulation by calcium in the cardiomyocyte. Indeed, calcium leak from sarcoplasmic reticulum through the ryanodine channel and altered calcium reuptake could occur in ob/ob as previously reported in db/db mice, these alterations being normalized by exercise [START_REF] Stolen | Interval training normalizes cardiomyocyte function, diastolic Ca2+ control, and SR Ca2+ release synchronicity in a mouse model of diabetic cardiomyopathy[END_REF].

We also investigated AMPK that plays a critical role in maintaining energy homeostasis and cardiac function during stress situations such as ischemia. Indeed AMPK plays an important protective role in limiting damage associated with ischemia-reperfusion in the heart [START_REF] Russell | AMP-activated protein kinase mediates ischemic glucose uptake and prevents postischemic cardiac dysfunction, apoptosis, and injury[END_REF]. Exercised mice exhibited increased phosphorylations at Thr172 of AMPK and of one of its characterized targets ACC. AMPK activation may protect the heart through improved preservation of cardiac energetics. Once again, this activation was observed in both strains.

These results are in agreement with previous findings demonstrating that improving AMPK activation protects the diabetic heart against ischemia-reperfusion [START_REF] Paiva | Enhancing AMPK activation during ischemia protects the diabetic heart against reperfusion injury[END_REF]. Similarly to the balance between kinases and phosphatases for the RISK pathway, the phosphatase PP2C level, which is known to inactivate AMPK, was reduced while the phosphorylated form of AMPK was increased in exercised mice.

Other aspects deserve to be discussed. We can hypothesize that a small amount of reactive oxygen species produced during each bout of exercise may trigger the cardiac adaptations. Indeed, studies have demonstrated that cardioprotective effects of exercise or tachycardia were abolished when anti-oxydants are given during exercise [START_REF] Akita | Exercise-induced activation of cardiac sympathetic nerve triggers cardioprotection via redox-sensitive activation of eNOS and upregulation of iNOS[END_REF][START_REF] Lucats | Rapid ventricular pacing induces delayed cardioprotection against myocardial stunning[END_REF][START_REF] Sanchez | Exercise and tachycardia increase NADPH oxidase and ryanodine receptor-2 activity: possible role in cardioprotection[END_REF].

Furthermore, reactive oxygen species are able to stimulate the PI3K-Akt, ERK1/2 and AMPK pathways [START_REF] Barbosa | Acute exercise induce endothelial nitric oxide synthase phosphorylation via Akt and AMP-activated protein kinase in aorta of rats: Role of reactive oxygen species[END_REF][START_REF] Clerk | Stimulation of multiple mitogen-activated protein kinase sub-families by oxidative stress and phosphorylation of the small heat shock protein, HSP25/27, in neonatal ventricular myocytes[END_REF][START_REF] Nelson | Effect of N-2mercaptopropionyl glycine on exercise-induced cardiac adaptations[END_REF]. This might partly explain potential beneficial adaptations of calcium handling with exercise. Indeed, it has been previously reported that exercise increases ryanodine-S-glutathionylation which inhibits ryanodine-mediated calcium leak [START_REF] Sanchez | Exercise and tachycardia increase NADPH oxidase and ryanodine receptor-2 activity: possible role in cardioprotection[END_REF].

CONCLUSIONS

Independently from improvement in associated co-morbidities, regular treadmill exercise induces cardioprotection against myocardial infarction in obese mice. Despite obesity, exercise is able to restore similar capacity to lean animal at activating pro-survival signalling pathways, contrasting with other conditioning strategies. This mechanism might participate to the beneficial effects of regular exercise against myocardial events in obese or overweight patients. Western blot analysis of Akt and its phosphorylated form (panel A), p70S6K and its phosphorylated form at Thr 389 due to the effect of Akt (panel B) as well as PTEN (panel C) in wild-type (WT) and ob/ob mice in sedentary conditions (Sed) or after regular exercise (Ex).

Values are expressed as mean ± SEM (n=3 in WT groups and 4 in ob/ob groups). * p<0.05 vs corresponding sedentary group. † p<0.05 vs corresponding WT group.

Figure 3

Western blot analysis of ERK 1/2 and its phosphorylated form (panel A), p70S6K and its phosphorylated form at Thr 421 and Ser 424 due to the effects of ERK1/2 (panel B) as well as MKP-3 (panel C) in wild-type (WT) and ob/ob mice in sedentary conditions (Sed) or after regular exercise (Ex). Values are expressed as mean ± SEM (n=3 in WT groups and 4 in ob/ob groups). * p<0.05 vs corresponding sedentary group. † p<0.05 vs corresponding WT group.

Figure 4

Western blot analysis of AMPK, ACC and their phosphorylated forms (panels A and B) as well as PP2C (panel C) in wild-type (WT) and ob/ob mice in sedentary conditions (Sed) or after regular exercise (Ex). Values are expressed as mean ± SEM (n=3 in WT groups and 4 in ob/ob groups). * p<0.05 vs corresponding sedentary group. † p<0.05 vs corresponding WT group. 4.9 ± 0.6 † 13.9 ± 3.5 † 17.5 ± 2.1 † 5.0 ± 0.5 † 12.9 ± 2.9 † 18.8 ± 2.5 †

Figure 1

 1 Figure 1

Figure 2

 2 Figure 2

Figure 5 Fat 6 †

 56 Figure 5

  Figure 1

  Figure 5

Table 1 .

 1 Morphological and biological parameters

	Glycemia (mmol/L)
	Cholesterolemia (mmol/L)
	Insulinemia (ng/mL)

ACKNOWLEDGEMENTS

The authors are greatly indebted to Dr M. Longchampt (Institut de Recherche Servier) for dual-energy x-ray absorptiometry measurements and to the laboratoire de biochimie (ICB-IFR2, Université Paris Diderot-Paris 7) for blood analyses.

DISCLOSURES

None declared.

Statistical analysis

All values were expressed as mean ± SEM. Comparisons were performed using a Kruskal-Wallis analysis followed by Mann-Whitney tests. Statistical significance was defined as a value of p<0.05.

SOURCES OF FUNDING

This study was supported by a grant from the Fondation de France (2008-002688).

Lolita Portal was a recipient of a grant from the Region Ile de France (CODDIM, 2010).