Maher Hatab

Abderrahmane Kheddar

GJK for Deformable Object Collision Detection

GJK is one of the main methods for distance calculations between convex objects. In this article, the adaptation of GJK for deformable object collision detection is proposed. Although the original method is only suited for distance calculations, the proposed method is capable of ˇnding the colliding triangle pairs between two continuously deforming virtual objects in real time. Furthermore, it handles all deformation types at no extra time cost and it allows the client application to add, or remove triangles from the considered object meshes at run time with no extra overhead for the collision detection. The proposed method is very exible in many aspects, making it an ideal choice for virtual reality and haptic applications.

I. INTRODUCTION

Computer simulated scenes gained in complexity and realism over the years. It is crucial for real time applications to develop fast and reliable algorithms, capable of providing high fidelity multimodal rendering at interactive rates. This is even more crucial in interactive simulations such as the ones using haptic feedback. Physically based simulations are gaining in acceptability because they use rigorous mathematical basis to drive graphical animation. In all these applications, collision detection (CD) is an important unavoidable step, but it is still the bottleneck process of any implementation. There are several important methods that have been proposed for CD with rigid or deformable models and in robotic planning. We refer the reader to the following surveys [START_REF] Jimnez | 3D Collision Detection: A Survey[END_REF][START_REF] Teschner | Collision detection for deformable objects[END_REF].

One of the main advantages in targeting a standard CD module is its potential to be ported to a dedicated hardware card which will free developers in various domains from this recurrent problem. Recent methods are trying to use nowadays GPU computation capabilities [START_REF] Govindaraju | Cullide: Interactive collision detection between complex models in large environments using graphics hardware[END_REF][START_REF] Knott | Cinder: Collision and interference detection in real-time using graphics hardware[END_REF]. The problem is that as far as we focus on particular category of objects, any method would not open hardware implementation perspectives. The hardware implementation of the hidden surface removal algorithm (the well known Z-buffering) was made possible because the algorithm revealed to be generic, simple and applicable to any kind of objects. It is in this spirit that we are developing research on CD.

The rest of the paper is organized as follows. In the next section, we start by a brief reminder of the main collision detection methods. Next we explain in greater details the GJK algorithm and some of its modifications that are directly related to * e-mail: hatab@iup.univ-evry.fr † email: kheddar@ieee.org our method. Then we introduce the cut procedure. This simple procedure is at the heart of the improved version of GJK, which is presented in section 4. In section 5 we show how to include the combined GJK of section 4 in a recursive procedure, capable of finding the colliding triangle pairs of the objects in a similar manner to bounding volume hierarchies. We finish the article by the implementation results and performance comparison against the AABB method and a discussion of the obtained figures. We conclude by interesting future enhancements of the proposed algorithm.

II. RELATED WORK

Traditionally CD occurs in two main phases (or passes): (i) an acceleration phase in which objects shapes are approximated with a succession of rough to relatively more tiny bounding volumes, called bounding volume hierarchy (BVH) and (ii) an exact, precise collision checking computation that takes place at the lower level of the BVH and made on the actual object's shape. None of existing papers demonstrates a clear and plausible relation between the nature of objects, the number of vertices and the recommended level of the BVH trees. There is indeed an optimum, but very dependent on various parameters.

Bounding volumes hierarchies (BVH) have been used for solid objects CD long ago. Spheres [START_REF] Hubbard | Approximating polyhedra with spheres for time critical collision detection[END_REF], OBBs [START_REF] Gottschalk | Obbtree: a hierarchical structure for rapid interference detection[END_REF], k-DOPS [START_REF] Klosowski | Efficient collision detection using bounding volume hierarchies of k-dops[END_REF] are among the proposed basic shapes to enclose the objects.

Strategies for tree construction such as bottom-up, top-down, or insertion [START_REF] Goldsmith | Automatic creation of object hierarchies for ray tracing[END_REF] produce variably fit hierarchies, traversed using depth first, level first, bigger volume first, or interruptible strategies. The latter is used for time critical applications [START_REF] Hubbard | Collision detection for interactive graphics applications[END_REF][START_REF] Mendoza | An interruptible algorithm for collision detection between deformable objects[END_REF].

The adaptation of BVH to deformable objects mainly focused on refitting previously constructed hierarchies instead of completely rebuilding them. Thus Van Den Bergen [START_REF] Van Den Bergen | Efficient collision detection of complex deformable models using aabb trees[END_REF] proposed a way to refit the AABB hierarchy which is made possible by the preparation of an AABB for each object with respect to its own reference. The tree starts by refitting the leaves, containing one polygon each, and then refits the higher levels of the tree by adjusting the size of each AABB to contain its child boxes. He also proved that refitting the tree can produce less optimized hierarchies than rebuilding them, but the overall CD process is up to 15 times faster. More recently, [START_REF] Larsson | Collision detection for continuously deforming bodies[END_REF] considered several factors in building and traversing BVH for deformable object collision detection, and James and Pai [START_REF] James | Bd-tree: output-sensitive collision detection for reduced deformable models[END_REF] proposed to adjust the sphere hierarchies using the reduced deformable models. We refer the reader to this recent survey [START_REF] Teschner | Collision detection for deformable objects[END_REF] on deformable objects CD techniques.

The first collision detection techniques only operated on convex objects since they present many exploitable advantages. The two main convex-based methods are the GJK [START_REF] Gilbert | A fast procedure for computing the distance between complex objects in threedimensional space[END_REF] and the LC [START_REF] Lin | Efficient algorithms for incremental distance computation[END_REF]. GJK finds the separation distance between the convex hulls of two point clouds at linear time. LC on the other hand only operates on convex hulls, and that at constant time.

It walks on the surface of the hulls jumping between vertices, edges and faces in order to converge to the minimum separation distance. Convex hulls are rarely used as bounding volumes in real time application involving deformable objects, due to the extensive building time they require. Furthermore, the object decomposition into its convex subparts is not unique and usually requires a large number of objects to completely cover the original ones. One solution is to implement acceleration levels, capable of selecting pairs of convex subparts for the exact CD process [START_REF] Cohen | I-collide: an interactive and exact collision detection system for large-scale environments[END_REF][START_REF] Ehmann | Accurate and fast proximity queries between polyhedra using convex surface decomposition[END_REF] but are not suited for deformable objects. The next section contains a more detailed explanation of GJK's general algorithm and its main modifications that have been proposed over the years.

[18] developed a fast triangle-triangle test that we chose to use in our implementations.

Our Contribution

We introduce an adaptation of the known GJK in conjunction with a recursive procedure for deformable object collision detection. Its main characteristics are the following:

• It runs in real time for a pair of meshes of moderate sizes while deterministically finding the colliding triangle pairs.

• No restrictions are imposed on the deformation types or amounts, furthermore, such changes do not require additional computation time for CD.

• Its performance is not affected by triangle creation or removal. In fact, the client application can have a giant triangle pool, and can choose at each time step the triangles for which the CD should be performed.

III. GJK BASICS

The original GJK [START_REF] Gilbert | A fast procedure for computing the distance between complex objects in threedimensional space[END_REF] is capable of finding the separation distance between the convex hulls of a couple of point clouds in case the objects are disjoint. Even though the convex hulls are not actually built, the algorithm can find the separation distance in O(n + m) where n and m are the clouds' point counts.

Internally, it uses simplices, and a distance sub-algorithm for finding the minimum distance between them. It starts by choosing a support direction, and then finds the support vertices in that direction on both objects. The newly found vertices are added to the simplices, and the simplices results form the new support direction to be used in the next iteration. The algorithm iterates in that manner until the minimum separation distance is found. The termination condition is a comparison between the current iteration's simplices result and the minimum theoretical distance at that iteration, while accounting for computational errors. When the objects are colliding, the method can find an upper bound for the minimum penetration distance. We refer the reader to the original paper for more details.

A first modification was proposed in [START_REF] Chung | Quick elimination of non-interference polytopes in virtual environments[END_REF] where the simplices and the distance sub-algorithm were replaced by a formula for guessing iteration i+1 support direction based on the iteration i support direction and support vertices. The main gain is the ability to find the new direction without having to solve the simplices. The termination condition was also changed to accommodate for the simplices removal.

Another modification was brought by [START_REF] Den Bergen | A fast and robust gjk implementation for collision detection of convex objects[END_REF] where many optimizations were introduced. We are particularly interested by the separating axes terminating condition. In fact, Van Den Bergen proposed to terminate the GJK iterations when the support direction is a separating direction, i.e. the projections of both objects on this direction are disjoint. This terminating condition can be used when the exact value of the separation distance is not needed, allowing early termination of the iterative procedure.

In summary, the overall structure of GJK based methods is presented in algorithm 3. Now that we reviewed the related existing methods, we will introduce our algorithm. The main idea is to safely eliminate at every step, the triangles that lie far from the collision region. The triangle elimination algorithm is described in the next section. In fact, you will notice that it has a common part with the general GJK of algorithm 3.1. We will show how to exploit this feature for finding all colliding triangle pairs between the objects.

v 1 ← any point of VL 1 ; 2 v 2 ← any point of VL 2 ; 3 SupDir ← v 2 -v 1 ; 4 Terminate ← 0; 5 while Terminate = 1 do 6 v 1 ← SupportVertex(VL 1 ,SupDir); 7 v 2 ← SupportVertex(VL 2 , -SupDir);

IV. THE CUT PROCEDURE

The main idea of the proposed method is to eliminate the triangles that are completely outside the potential collision region. A potential collision region exists for each direction. The ideal direction which yields the smallest collision region is usually referred to as minimum penetration direction. Finding such a direction is time consuming, and its good cutting performance does not compensate for the big amount of time needed for the search. It is also effective to use any direction, if it can be easily found and if it allows the removal of non colliding triangles.

A fast way for identifying a potential collision region is by isolating the space delimited by the maximum extents of both objects on the considered direction. The main function of our method (algorithm 4.1) operates as follows: given TL 1 and TL 2 two triangle lists, and given CutDir, the cut direction going from TL 1 to TL 2 , it starts by finding the support vertex v 1 of TL 1 in the direction CutDir, and the support vertex v 2 of TL 2 in the direction -CutDir. It removes from TL 1 the triangles having all vertices located before v 2 in CutDir's direction, and it removes from TL 2 the triangles having all vertices located after v 1 in CutDir's direction. We are currently investigating the use of adapted data structures for accelerating this process. At the first glance, this expensive operation seems only profitable if it removes a relatively large number of triangles, and thus, one might think that it might slow down the overall process if the objects are deeply inter penetrating (since in such situations, many cuts will not be able to remove a big percentage of the existing triangles). We found out in our experiments, that it is always advantageous to perform the cut, even for deeply inter penetrating objects. The related graph and discussion are presented in section 6 of this paper. This is furthermore practical, since the client application doesn't have to implement a cut decision making scheme any more, thus avoiding further complexity and sources of error.

A sample cut is shown in figure 1. In the first part, the initial positions of the objects are shown, along with the maximum extents of both objects with respect to a chosen cut direction. In the second, we can see the remaining triangles of both objects after the cut is performed.

Both presented algorithms need to perform support vertex calculations. The combined GJK with the cut code of algorithm 4.2 operates as follows: once the support vertices corresponding to the support direction are found, we can use them to perform the cut operation by using the support direction as the cut direction. This reduces the triangles count and accelerates the support vertex operation for the following iterations.

The CutList(TL, v) function performs the elimination of the triangles having all vertices before v. The function does not need to have the cut direction as an input since the dot product for all the vertices was already calculated by the support Although it is not shown in the above algorithm, the code terminates anytime a cut removes all the triangles from a list. For faster performance, our implementation uses a vertex list that contains the triangle lists vertices. The support vertex operation is performed on the vertex list rather than on the triangle list since less dot product operations have to be operated. The formula shown in line 15 of algorithm 4.2 is the one introduced by [START_REF] Chung | Quick elimination of non-interference polytopes in virtual environments[END_REF]. The choice of the terminating condition will be explained in the next section.

8 v 2 ← SupportVertex(VL 2 , -SupDir); 9 SupDir ← SupportDirection(SupDir, v 1 , 10 v 2 ); cut 1 ← CutList(TL 1 ,v 2 ); 11 cut 2 ← CutList(TL 2 ,v 1 ); 12 temp = v 1 -v 2 ;

V. THE RECURSIVE ALGORITHM

The combined GJK algorithm presented above gives a predicate if the convex hulls of the triangles collide. It also keeps in the final triangle lists, only those situated in the collision region. At this point, it is possible to perform a split of both triangle lists in the same manner used for building top-down bounding volume hierarchies. Once the two pairs of lists are produced, we can perform pair wise checks between the produced lists using the combined GJK method in a recursive manner. In fact, the corresponding operation is an on line partial built of the hierarchy. Every iteration, many non-colliding triangles are removed, and the remaining ones are split into two, and so on, until the lists contain one triangle each. In this case, a triangle-triangle test decides whether the triangle pair should be added to the results list. Algorithm 5.1 presents the corresponding procedure. This algorithm has the same overall structure as the recursive collision detection procedure for BVH but presents some key modifications. First we check TL 1 and TL 2 for collision. If they do not collide, we stop the process at this level. If they do collide and they can be split, we check the produced splits against each others using recursive function calls. On the other hand, if the current nodes are leaves, all the contained triangles are checked for collision, and the found colliding pairs are added to the results list. Typically each leaf only contains one triangle. In algorithm 5.1, when a split operation is not successful, all the triangles of the original list TL 1 will be placed in TL [START_REF] James | Bd-tree: output-sensitive collision detection for reduced deformable models[END_REF] . TL 12 will be empty. When RecursiveCheck(TL 1 , TL 2 ) is called on an empty list, it will exit directly with a negative result. This handles the case where only one list could be split.

It is not crucial for the CombinedGJKcollide() to remove all non colliding triangles. Those will most probably be removed at later iteration, or in the worst case, during the triangletriangle test. For this reason, it is not critical to use a nonoptimal terminating condition in algorithm 4.2. In fact, the iterations for that algorithm terminate when it fails to perform a list cut. Although it might be possible to remove more triangles if the procedure is not stopped, we chose to stop it because from the moment where a cut is unsuccessful, the next ones have a high probability of failing again. The time consumed by the cut operation is not balanced out by a reduction of the number of triangles, and the cut is actually slowing the overall process instead of accelerating it. Stopping the iterative process will avoid such situations. If all cuts are unsuccessful, then the algorithm is actually performing the complete construction of the hierarchy plus the CD. Fortunately, such cases never occur. Even if the root nodes present a high inter penetration level, it regresses while descending the tree due to the split operation. The regression speed has the same relation to the configuration of the objects as the depth of tree traversal in standard BVHs.

The split is the operation of separating the original list into two sub-lists. Several splitting heuristics were proposed over the years. In general, they compute a threshold on the splitting direction, and then put all the triangles having their barycenter before this value in the first sub-list, and the others in the second one. A common choice of threshold is the median of all the polygon points. This produces balanced lists. The choice of the splitting direction is also an important one and comes just after the cut in the dir direction. Due to the nature of the cut, the remaining triangles usually form oblong shapes. Any orthogonal direction to SupDir would make a good splitting direction.

As one can see, the algorithm operates in a single shot: it takes the two triangles lists, and operates on the current positions of their vertices. If the objects deform, the algorithm does not need to perform additional operations. Even if polygons are added or removed from the original objects, the algorithm finds the colliding triangle pairs at that iteration, since it considers the polygons currently in the list, and not those of previous iterations.

VI. RESULTS AND DISCUSSIONS

The tests were conducted on an Intel Centrino 1.7 GHz with 1Gbytes of RAM and an ATI X700 graphics card.

The aim of our first experiments was to determine the applicability of the cut with respect to the percentage overlap region. In other words, we wanted to verify if we should always perform a cut, even when it has a low probability of actually eliminating triangles. As a fast indicator of such a probability, we considered the ratio of the projections on the cut direction (dir) of:

• The common region of the two objects delimited by the max 1 and max 2 , the maximum values of O 1 and O 2 in dir and -dir respectively.

• The object that need to be cut, delimited by max and min, the maximum and the minimum of O in dir.

Please note that all the above max values are the same that need to be found to perform the cut and thus do not present an extra cost. The min search on the other hand, is an additional operation, and will be the major factor for the high computational cost of the decision making process.

We implemented the above ratio in a test version, and allowed the cut to be performed if the overlap is less than the T max . While moving the object pair, we varied T max between 40%, 55%, 70%, 85% and 100% for each position of the objects (where 100% means that the cut is always performed), and we plotted the time needed in each case to find the colliding triangle pairs. The corresponding graph is graph 2.

It is very clear from the graph that it is always beneficial to perform the cut. Except for very few exceptions, the 100% curve is always the fastest. This result can be explained by the fact that the cut operation consists of two main parts: The dot products, and the list split which only consists of pointer assignments. The dot products are by far, the most time consuming. The modified version with the implemented threshold contains more dot products. In fact, a decision can be made once the maximum and minimum were calculated, while the cut only required calculating the max. To be able to make the decision, the procedure has already consumed the most of the time that the cut would have needed, that performing the cut at this stage will only be a waste if fails to remove any triangles.

The above result is only valid of course, if our decision making criteria is used. However, we did not find a faster choice for the modified GJK method that is capable of justifying the implementation of decision module.

The next test investigates the effect of the on line triangle removal from the objects while performing the collision detection. To be able to compare and scale up the results, we decided to disable the physical engine, and to fix the positions of a pair of bulls in a high collision setup. Such a configuration is non realistic because the physical engine will not allow the inter penetration to happen. Please note that the objects will not be moving with respect to each other, but their triangles will be randomly removed until there are no more left. The plotted timings are the needed ones to find all the colliding triangle pairs. Since the algorithm does not require any additional time to update the hierarchy, those timing show the needed time to perform the complete collision detection process. Initially, there are 258 colliding triangle pairs, but the number decreases when a colliding triangle is removed. The X axis indicates the number of remaining triangle in both objects. Since we are removing the same quantities of triangles at each step, and the objects had initially the same number of triangles, then the number of triangles of each object at each given X value is half of that value. Figure 3 shows 4 instances with decreasing triangles and their collisions, while graph 4 shows the timings plot.

The first observation from graph 4 is the big fluctuations occurring at many instances. Although it might seem contradictory that removing triangles from a pair of fixed position objects is slowing the collision detection process, it has a simple explanation: removing triangles has the same effect as changing configuration. A new configuration implies a new set of cutting directions and iterations, which might be slower than the first one if it follows a more problematic path. This is actually the same effect that involves the standard bounding volume hierarchies, and that makes their behavior highly dependent on their configuration at each iteration. The sudden drop at 8000 triangles happened when most of the colliding triangles were Due to the properties of the algorithm and the implementation, the effect of adding triangles is almost exactly the inverse of graph 4 and will not be plotted again.

The next two tests involve two pairs of continuously deforming objects. At every iteration, we applied a wave function to deform all the triangles of both objects. In addition, we were moving the objects with a haptic device to obtain different degrees of collision. These tests were meant to compare the performance of our method to the AABB hierarchies. Since we were unable to find an implementation of the AABB where it is possible to deform the meshes and to update the hierarchies accordingly, we implemented the AABB as presented in [START_REF] Van Den Bergen | Efficient collision detection of complex deformable models using aabb trees[END_REF].

It was brought to our attention that our implementation might be slower than other existing AABB implementations, but the faster implementations we found did not take the deformations into account, and had to rebuild the hierarchies. Graph 5 shows the performance of AABB and the modified GJK on objets of about 1500 triangles each. Graph 6 shows the performance on the pair of bulls of about 13000 triangles each.

As can be seen, the modified GJK is faster than our implementation of the AABB method. The green curve represents the AABB performance including the time it took to refit the hierarchies and is basically a shift of the blue curve that represents the AABB performance while excluding the refit operation.

VII. CONCLUSION

We presented a modification to the known GJK method, enabling it to be used for exact collision detection by finding all colliding triangle pairs. The new method is suitable for continuously deforming objects, and for adding or removing triangles at run time. It is capable of satisfying high demanding virtual reality application such as haptic simulations dealing with moderate sized objects and requiring the exact list of colliding triangles. Next we will be investigating the use of this method for multi-resolution collision detection: an increase in the resolution can be regarded as the removal of few rough triangles, and the addition of many fine ones. Since the method can easily handle both cases, it is a very good candidate.

8

  SupDir ← SupportDirection(SupDir, v 1 , 9 v 2 ); Terminate ← CheckTermination(Result); 10 end 11

Algorithm 4 . 1 : 1 v 1 ← 2 v 2 ← 7 if 10 The

 411122710 CutAlongDirection input : CutDir is the cut's direction input : TL 1 and TL 2 are two triangle lists output: TL 1 and TL 2 only contain the potential collision region's triangles begin SupportVertex(CutDir, T L 1 ); SupportVertex(-CutDir, T L 2 ); 3 for every polygon t 1 of T L 1 do 4 if All t 1 's vertices are before v 2 on CutDir then 5 RemovePolygonFromList(t 1 ,TL 1 ); 6 for every polygon t 2 of T L 2 do All t 2 's vertices are after v 1 on CutDir then 8 RemovePolygonFromList(t 2 ,TL 2 ); 9 end above algorithm runs in O(n + m) where n and m are TL 1 and TL 2 vertex counts. If the provided meshes present a high vertex sharing level among neighboring polygons, then the vertex number is smaller and the performance is optimal.

Figure 1 :

 1 Figure 1: L 1 and L 2 cut with respect to CutDir

Algorithm 4 . 2 : 1 v 1 ← 2 v 2 ← 3 SupDir ← v 2 -v 1 ; 4 cut 1 ← true; 5 cut 2 ← true; 6 while cut 1 = 7 v 1 ←

 4211223241526171 Combined GJK with cut input : TL 1 and TL 2 are two triangle lists input : VL 1 and VL 2 are the point lists of TL 1 and TL 2 output: L 1 and L 2 only contain their common region's triangles begin any point of VL 1 ; any point of VL 2 ; true and cut 2 = true do SupportVertex(VL 1 ,SupDir);

13 normalize(temp); 14 SupDir

 1314 = SupDir -temp× (temp• SupDir) × 2 15 end 16

Figure 2 :

 2 Figure 2: The effect of the threshold on the CUT operation

Figure 3 :Figure 4 :

 34 Figure 3: 4 instances of random triangle removal

Figure 5 :Figure 6 :

 56 Figure 5: Speed comparaison between AABB and the modified GJK while operating on 1500 triangles objects

  1. The SupportVertex(VL, SupDir) function finds VL's vertex in SupDir's direction. It runs in O(n), where n is VL vertex count. It can be brought down to a constant time if the convex hull is used. The SupportDirection(SupDir, v 1 , v 2 ) finds the support direction based on the previous support direction, and on the current support points. As explained above, several criteria were used over the years for obtaining the next support direction and for termination condition.

Algorithm 3.1: General GJK algorithm input : VL 1 and VL 2 are two point lists output: minimum separation/penetration distance or a predicate of collision begin 1

  Algorithm 5.1: RecursiveCheck input : TL 1 and TL 2 are triangle lists. output: Obtain RL, the list of TL 1 's and TL 2 's colliding triangle pairs begin

1 if CombinedGJKcollide(TL 1 ,TL 2 ) then 2 if Split(TL

1 ,TL 11 ,TL 12 ) = false And 3 Split(TL 2 ,TL 21 ,TL 22 ) = false then Check all triangles of TL 1 against all 4 triangles of TL 2 else 5 RecursiveCheck(TL 11 ,TL 21 ); 6 RecursiveCheck(TL 12 ,TL 21 ); 7 RecursiveCheck(TL 11 ,TL 22 ); 8 RecursiveCheck(TL 12 ,TL 22 ); 9 end 10

ACKNOWLEDGEMENTS The work presented in this paper is sponsored by a ph.D grant to Mr. Hatab offered by the Lebanese National Council for Scientific Research.


M Noc

M Ginet

& Deslauriers-Varin

The Cognitive Interview for Suspects: A Test with Customs Officers

Keywords:

The current study aimed to test the impact of the Cognitive Interview for Suspects (CIS) used by trained custom officers on the quantity of gathered details, compared to a control Standard Interview (SI) used by untrained officers. Forty-five mock-suspects were required to perform a series of actions and each was interviewed by a pair of customs officers. Participants had to give statements containing truthful parts and deceptive parts. The CIS elicited significantly more details than the SI. Truthful parts of the statements contained more details than deceptive parts. An interaction effect revealed that the CIS elicited a higher number of action details in truthful parts. It is worthwhile for professionals in the field to adopt the CIS, which provides valuable benefits for information gathering. Moreover, the increase in action details raise the question of considering it as a possible lie detection tool.

Investigators may have various objectives when interviewing a suspect: to obtain as much details as possible, to distinguish between lies and truth, and to obtain a confession.

Interrogation models considered as accusatory, such as the Reid technique, tend to emphasize only one of these goals, namely obtaining a confession [START_REF] Inbau | Criminal interrogation and confessions[END_REF]. This may also be the case for standard interviews, i.e. interviews conducted by untrained interviewers [START_REF] Snook | Let'em talk!: A field study of police questioning practices of suspects and accused persons[END_REF]. Typically, these interview models are constructed on the basis of a short questions/short answers interaction (Kebbel et al., 2001) and can contain 'psychologically manipulative tactics that are designed to elicit compliance from a suspect in the form of a confession to the crime' (Meissner et al., 2014: 462). This quest for a confession often limits the volume of details obtained due to its narrow focus [START_REF] Gudjonsson | The psychology of interrogations and confessions: A handbook[END_REF]. However, the quantity of gathered details is crucial for case solution and effective criminal prosecution since, on the one hand, it makes it possible to obtain valuable information on a criminal event and, on the other, permits the emergence of inconsistencies that result in the detection of lies [START_REF] Dando | Maximising opportunities to detect verbal deception: training police officers to interview tactically[END_REF][START_REF] Geiselman | Interviewing witnesses and victims[END_REF].

By contrast with the accusatory models, the Cognitive Interview for Suspects (CIS, Geiselman, 2012) is a more recent interview method, inspired by 'witness interview dynamics', that focuses on gathering information and identifying deception. However, to our knowledge, very few studies have been conducted on the CIS, and none when it is used by professionals and compared to a standard interview. Furthermore, none have assessed its benefit in gathering more details. Considering the potential value of this method, the current study aims to test the efficacy of the CIS compared to a standard interview (SI) conducted by customs officers and to evaluate its benefits in gathering a significant amount of information about the criminal event.

The Cognitive Interview for Suspects

The CIS is an adaptation of the Cognitive Interview (CI, Fisher & Geiselman, 1992), which was initially developed for interviewing witnesses and victims. The core elements of the CI draw on theoretical principles such as Tulving's theory of multiple access to memory and specific encoding [START_REF] Tulving | Elements of episodic memory[END_REF]. As proposed in [START_REF] Deslauriers-Varin | Criminal investigation of sexual offenses. Sexual offending: A criminological perspective[END_REF], the theoretical bases are grounded in three basic psychological processes, namely: memory and cognition, social dynamics, and communication. More specifically, memory-enhancing techniques (e.g., Mental context reinstatement, Reverse order) are often combined with methods for improving social dynamics (e.g. Rapport building, encouraging active participation) in order to develop a communication environment that is most likely to allow victims and/or witnesses to provide the most detailed, comprehensible, and accurate account of what they experienced [START_REF] Fisher | Memory-enhancing techniques for investigative interviewing: the cognitive interview[END_REF]. To date, the CI is the interview technique that has undergone the most scientific testing [START_REF] Geiselman | Interviewing witnesses and victims[END_REF]. Many studies have shown that, significantly, the CI elicits between 25%-50% more correct information from witnesses or victims than the comparison interview, including details related to actions, people, objects, and locations, and does so at a comparable accuracy rate [START_REF] Memon | The cognitive interview: a meta-analytic review and study space analysis of the past 25 years[END_REF]. The CI or its components are now part of many police training programs and are the recommended police practices in numerous countries [START_REF] Deslauriers-Varin | Criminal investigation of sexual offenses. Sexual offending: A criminological perspective[END_REF].

In a way similar to the CI, the CIS is an information-gathering approach based on scientifically derived principles of memory and communication theory. In the CIS, the suspect is encouraged to provide a large amount of details that may be relevant for a police investigation. As presented by [START_REF] Geiselman | The cognitive interview for suspects (CIS)[END_REF], the CIS consists of eight stages: (1) Rapport building / Introduction. During this stage, the interviewer develops a rapport with the suspect while talking about neutral topics in order to put them in a psychologically comfortable state and thus make the interview more productive; (2) Narrative. The suspect is encouraged to freely report as many details as possible (Report everything instruction) and to mentally recreate the context of the crime (Mental context reinstatement instruction); (3) Drawing / sketch. In this stage, the suspect has to sketch/draw the crime scene or a part of this scene; (4) Follow-up, open-ended questions. Questions are asked using an information-gathering approach rather than a confrontational one; (5) Reverse order mnemonic. The suspect is instructed to recall the criminal event backward; (6) Challenge. In this stage, the suspect is gradually confronted with evidence and incriminating contradictions. The interviewer remains respectful and presents the weakest evidence first; (7) Review. The interviewer reviews the suspect's statements and asks them to correct any errors or omissions; (8) Closure. At this stage, cooperative suspects can be thanked. To those who appear to have lied, the interviewer may 'express disappointment and disrespect' (Geiselman, 2012: 5).

Note that six of these stages are adapted from the CI method for witnesses, whereas the Drawing and the Challenge stages are two new techniques that are intended to improve lie detection [START_REF] Dando | Maximising opportunities to detect verbal deception: training police officers to interview tactically[END_REF]Vrij et al., 2010a). Indeed, one of the major differences between witness and suspect interviews is the truthfulness of the statements. Witnesses are assumed to produce 'honest' errors (e.g. caused by misperception, interferences, retrieval failures) while suspects tend to lie intentionally [START_REF] Yarmey | Truthfulness in witnesses' and suspects' reports[END_REF]. These differences have led to the protocol being adapted to a potentially less cooperative and more deceptive population. In particular, the protocol includes some components whose purpose is to detect deception (i.e.

Drawing, Reverse-order and Challenge).

Empirical assessment of the CIS protocol and deception detection

In the first study conducted by [START_REF] Geiselman | The cognitive interview for suspects (CIS)[END_REF], CIS-trained college students conducted interviews with participants who had been instructed to describe a recent autobiographical or a completely fabricated event. The interviewers had to rate the likelihood of the participant's truthfulness at each stage of the protocol. The results from this study showed that the interviewers were able to discriminate truth from lies in the CIS context and that their accuracy increased as they progressed through the various stages of the protocol.

Two other studies have assessed the ability to discriminate between truth and lies in the CIS protocol [START_REF] Frosina | The effect of cognitive load on nonverbal behavior in the cognitive interview for suspects[END_REF][START_REF] Logue | Using reality monitoring to improve deception detection in the context of the cognitive interview for suspects[END_REF]. In these studies, the participants in the truthful condition had to play a game with a confederate, whereas those in the deceptive condition had to steal $10 from a confederate's wallet, while pretending that they had also played the game. They were then interviewed by CIS-trained college students. Deception was rated by means of two methods: verbal cues [START_REF] Logue | Using reality monitoring to improve deception detection in the context of the cognitive interview for suspects[END_REF] and physiological cues [START_REF] Frosina | The effect of cognitive load on nonverbal behavior in the cognitive interview for suspects[END_REF]. The results showed that these lie detection methods were effective and applicable in the CIS context. According to the authors, the CIS may lead to better deception detection due to the information-gathering style of this protocol and to the increase in the suspects' cognitive load. However, in all three studies cited, the CIS was not compared with a control group. Furthermore, only deception detection was evaluated and the amount of information contained in the suspects' statements was not assessed. However, it is important to verify that the CIS can provide valuable details for investigative purposes, while at the same time increasing the number of opportunities for signs of deception to emerge. Finally, given the applied aim of the CIS, it seems particularly important to assess whether it can be beneficial in the field when used by professionals who regularly interview suspects.

Hypotheses

In the current study, the investigators were customs officers. Indeed, this is a population that has been insufficiently studied in the scientific literature compared to police officers, even though interviewing suspects is also one of a customs officer's tasks [START_REF] Granhag | Crime on the border: Use of evidence in customs interview[END_REF].

Trained or untrained customs officers had to gather details in a mock-suspect interview.

The experimental design involved mock-suspects in order to verify the accuracy of the gathered information, which is an important element to be taken into account in the field. In order to mimic a real-life situation, the participants were asked to lie about some parts of their actions and to tell the truth about others [START_REF] Vrij | Outsmarting the liars: toward a cognitive lie detection approach[END_REF]. More specifically, it was expected that, compared to a SI, the CIS would help the interviewers gather more details (i.e. more action, person, object and location details) without increasing the number of incorrect and confabulated details. Moreover, as was found in [START_REF] Geiselman | The cognitive interview for suspects (CIS)[END_REF], the CIS-trained interviewers were expected to detect lies better than untrained ones.

Method

Participants and Design

Interviewees

Our initial sample was composed of 48 French undergraduate students (14 men and 34 women). However, three participants were excluded because of recording failures during the interview process. The final sample consisted of 45 participants (13 men and 32 women). An a priori power analysis established with the Superpower package in R [START_REF] Lakens | Simulation-Based Power Analysis for Factorial Analysis of Variance Designs[END_REF] for within-between interactions on ANOVAs had indicated a necessary sample size of 70 participants to allow an effect size of f = 0.16 (estimated from [START_REF] Vrij | Translating theory into practice: Evaluating a cognitive lie detection training workshop[END_REF] study), with α = .05 and a 87% power. However, the size of the sample was determined by the constraints of the customs service and the number of investigators available .The participants were aged between 18 and 38 with a mean age of 19.93 (SD = 3.73) and all used French as their first language. All the participants received course credits and a €10 reward for their participation. They were randomly assigned within a 2 (interview: CIS vs. SI) x 2 (veracity: lie, truth) mixed design, with veracity as a within-subject variable.

Confederates

Two female research assistants (aged 21 and 38 years) acted as confederates. One of them acted as an experimenter, spending most of the time during the experiment with the participant, while the other acted as a laboratory member, who was met only briefly during the 'criminal' stage of the experiment. Each experimenter learned the two roles, which were pre-determined, and played them in equal proportions.

Interviewers

This study was conducted in collaboration with a French customs service, which is a service that investigates fraud and trafficking offences and realises suspects interviews. The interviewers were 12 French volunteer customs officers: 3 women and 9 men, whose ages ranged from 30 to 61 years (M = 48.56, SD = 8.38), and who used French as their first language. They were recruited on a voluntary basis after a collaborative training project presented by their department head, who wanted some officers to be trained in interview methods. The officers had all been trained in customs missions at the National Customs School. However, this did not include training in interview methods. Their seniority within the customs service ranged from 6 to 40 years, with an average of 23.33 years of experience (SD = 8.75).

Training

Cognitive Interview for Suspects

Six interviewers received CIS training and the six remaining interviewers had no interview training (the experimenter asked them to conduct the interview as they usually did.

It should be noted that they received the CIS training three months after the experiment was over.). The latter group was used as a control group for the current study. The distribution of interviewers to training conditions was random.

The training lasted 10 hours and was given by the first author of this paper at the university. Three weeks before the training, the interviewers received an academic booklet including theoretical information on the CIS (e.g. advantages of rapport building, questioning styles, CIS mnemonics), a quiz, documents and exercises. They were asked to read and complete the booklet before the intervention took place. The training included exercises, formal presentation, and role-playing games followed by detailed feedback. In order to avoid biasing the results of the study, the trained interviewers were asked not to talk about the CIS method to the untrained interviewers until after the end of the experiment.

To assess their self-reported interviewing ability, the CIS-trained interviewers had to answer the question: 'On a 1 to 5 scale, with 1= not at all and 5= absolutely, how experienced do you feel in interviewing suspects?' before and after the training. A Paired-sample t.test showed that the interviewers trained in the CIS reported being more skilled in interviewing after the training (M = 3.38, SD = 0.52, 95% CI [2.94,3.81]) than before it (M = 2.63, SD = 0.74, 95% CI [2.00, 3.25]), t(5) = -4.58, p = .003, d = 3.46.

In order to verify that the interviewers had actually used the components/strategies learned during training, they were coded based on the audio recordings of the interviews. This coding revealed that the trained interviewers were fairly accurate in following the taught protocol (see supplemental online material for more information). Such an observation was also made in the SI. Although SI are 'instinctive' interviews conducted by untrained interviewers, and therefore normally all different, there were similarities between these practices. In general, the SI did not include a rapport building, and the interviewers asked many closed, leading, and repeated questions. In addition, they directly accused the interviewees and regularly cut them off.

Lie detection

In order to limit motivational effects due to the CIS training, all the interviewers received lie detection training prior to the current study. Moreover, because the study aimed to test the potential benefit of CIS in improving lie detection among interviewers, it was necessary to ensure that the investigators had a minimum shared level of knowledge in this area.

The training lasted 4 hours and was given by the first author of this paper on the university premises. Three weeks before the training, the interviewers received an academic booklet including theoretical information on deception detection (e.g. 'pitfalls and opportunities' presented in the scientific literature; [START_REF] Vrij | Detecting lies and deceit: pitfalls and opportunities[END_REF], a quiz, documents and exercises. They were asked to read and complete the booklet before the intervention took place. The training included exercises and role-playing games followed by detailed feedback.

Procedure

It should be noted that for the purposes of the following procedure, the motivational incitement of the participants to lie, the interview length, the contextual background given to the interviewer, and the lie detection assessment were inspired by the study conducted by [START_REF] Vrij | Translating theory into practice: Evaluating a cognitive lie detection training workshop[END_REF], which aimed to compare a trained and an untrained group of interviewers. Their procedure was then adapted to the context of our study.

Interviewees

The participants were recruited on a voluntary basis by asking them to enter their names on a list posted in the laboratory. After arriving at the university, the interviewees completed an informed consent form and were then told that they would perform a series of actions, and then help us to analyse customs interviewers' lie detection abilities by lying them about some of these actions. This series of actions constituted a complete scenario consisting of four sequences lasting about 8 minutes each. The complete scenario lasted about 32 minutes, and the participants had to tell the interviewers the whole scenario after having lived it.

Because we wanted participants of our study to mimic real-life suspects who may lie about some aspects of the to-be-remembered event and tell the truth about other aspects, each participant was instructed to tell the interviewers the truth about two of the four sequences they experienced and to lie about the other two sequences.

So that it is not always the same sequences, for all the participants, which are the object of a lie or of the truth, we carried out a counterbalancing. To do this, we created a true version and a deceptive version of each sequence (see table 1). We then created four possible combinations of truthful and deceptive sequences, corresponding to four possible scenario versions (see Table 2).

INSERT TABLE 1 ABOUT HERE INSERT TABLE 2 ABOUT HERE

For example, a participant who lived scenario C had to go with a confederate to pick up a document in an unknown room of the university, then sat in a corridor and completed a logic questionnaire, then read a text describing the truthful car park sequence and had to imagine s/he performed it so s/he can convince the interviewer that s/he really did so, and finally met a confederate to exchange an envelope with cash, but s/he was asked to pretend that s/he completed the quiz and convince the interviewer.

The interviewees were equipped with video-recording spy glasses during all the sequences so that the experimenters could check the veracity of their interview statements.

The glasses were worn on the nose of the participants, and recorded what they saw with an angle of 180°. Thus, it was possible to observe their movements through the different buildings, and also the objects and people they met. Moreover, the glasses also recorded the sound, allowing to hear the various noises and conversations to which they were exposed.

After the first part of the experiment, the participants were told that the purpose of the study was to assess the ability of customs officers to detect lies. The participants were thus informed that, to this end, they would be interviewed about the event and have to lie about its 'lie sequences' and tell the truth about the 'truth sequences'. In order to enhance motivation during the interviews, they were also told that it was important to convince the officers that they were telling the truth, and that they would receive a €10 reward if they were successful in doing so. Moreover, they were told that if the interviewers were not convinced, they would have to send an e-mail dissertation on their lying skills. The aim of this methodological choice was to mimic the real-life situation of a suspect as much as possible (i.e. more motivated to lie than to tell the truth about their wrongdoing because of the potential consequences they may face).

The interviewees were taken to the interrogation room and interviewed. They were then debriefed and they all received a €10 reward for their participation.

Interviewers

After arriving at the university, pairs of customs officers (both trained or both untrained to CIS) were assigned to an interrogation room in the same way as when they are used to conducting interviews in the field. They were told that a mock-crime had been committed in the university (i.e. that a transcript had been stolen from a teacher's office and sold for money) and that they had to find out what happened by interviewing students. Each customs officer in each pair of interviewers had to interview four participants. In these four interviews, only the interviewer talked with the interviewee, while the other officer just listened. They were asked to interview the mock-perpetrator for a maximum of 45 minutes in the light of the length of the scenario experienced by the participants. The actual average length of the interviews was finally 24 minutes and 36 seconds (SD = 7.14). In the SI condition, the interviews were longer (M = 27.97; SD = 6.27; 95% CI [25.12,30.82]) than in the CIS condition (M = 21.69; SD = 3.58, 95% CI [20.19,23.21]), t(44) = 4.04, p < .001, d = 1.28.

The interviewers and interviewees gave their prior consent for the interviews to be audio-recorded. The officers were not aware of which scenario had been played out by the mock-suspects. The interviewers were given the contextual background to the events (cf.

Appendix A) to enable them to organize their interview as they would do in a real case. When the interview was over, the officers had to assess whether the interviewee was lying or telling the truth for each of the four sequences. The pair of investigators deliberated together before giving a common judgment for each sequence, in a dichotomous manner (e.g. this sequence about the car park is truthful or is deceptive). The number of errors was counted for each of the four participants interviewed by the same interviewer (min.: 0, max.: 16). More precisely, two types of errors were possible: 'truth' errors (thinking that the sequence is deceptive when it is actually truthful) and 'deception' errors (thinking that the sequence is truthful when it is actually deceptive). Moreover, the correct answers were counted in the same way: the 'truth' correct answers (thinking that the sequence is truthful when it is in reality truthful) and the 'deception' correct answers (thinking that the sequence is deceptive when it is in reality deceptive).

Coding of the statements

The interviews were audio-recorded and transcribed verbatim. All the details reported by the participants were coded by the first author of the study, with one point being given for each detail. They were only scored the first time they were reported (repeated details were ignored). In a way that is consistent with the CI literature [START_REF] Holliday | Reducing misinformation effects in older adults with cognitive interview mnemonics[END_REF][START_REF] Stein | Testing the efficacy of the cognitive interview in a developing country[END_REF], each detail was classified into one of the following four categories: actions (details describing something that the participant or another person did, e.g. 'I walked'), objects (details describing an object, e.g. 'the logic test sheet'), locations (details describing a location, e.g. 'the third floor corridor'), and persons (details describing the participants themselves or another person, e.g. 'the small experimenter'). Video records were used to code the quality of details in the truthful parts of the statements. Each detail was coded as correct (i.e. describing something that corresponded exactly to what actually occurred), incorrect (i.e. wrongly describing something that actually happened) or confabulated (i.e. describing something that did not occur at all). Twenty-three interviews (i.e. 51.11 %) were coded by a second independent coder in order to assess coding reliability. A series of two-way mixed intraclass correlations (ICC) revealed a high degree of reliability between the two raters for all the measures (all ICC (1,2)

≥ .78).
Moreover, the number of questions asked was also coded. The analyses showed that three times as many questions were asked in the standard interviews, (M = 173.52, SD = 55.60, 95% CI [148.21,198.83]), than in the CIS (M = 47.63, SD = 24.14, 95% CI [37.43,57.82]), t(44) = 9.62, p < .001, d = 3.07. The number of questions will be taken into account in order to calculate the ratio of the number of recalled details to the number of questions asked.

Results

Position of the participant in the interview set and influence of the scenarios

Each interviewer conducted four successive interviews, each involving different participants. In order to check the potential effect of the participant's position in the series of interviews depending on the type of interview used, three 2 (interview: SI vs. CIS) x 4 (interviewee position: 1 vs. 2 vs. 3 vs. 4) ANOVAs were conducted, with both factors as between-subject variables. There was no significant effect of position on the total number of details (i.e. the sum of correct, erroneous and confabulated details) and the number of correct details provided, Fs ≤ 0.59, ps ≥ .624. There was also no effect of the interaction between interview style and interviewee position on the total number of details and the number of correct details, Fs ≤ 1.59, ps ≥ .208.

In addition, the participants experienced one of the four versions of the scenario (depending on the counterbalancing). To check the effect of this variable on the main measures, three 2 (interview: SI vs. CIS) x 4 (scenario counterbalancing: A vs. B vs. C vs. D) ANOVAs were conducted, with both factors as between-subject variables. There was no significant effect of the scenario counterbalancing on the total number of details and the number of correct details, Fs ≤ 1.37, ps ≥ .266. There was also no effect of the interaction between interview style and scenario counterbalancing on the total number of details and the number of correct details, Fs ≤ 0.70, ps ≥ .561.

The interviewee position and scenario counterbalancing variables were therefore not included in the subsequent main analyses. All results for the main effects of interview style are discussed below.

Total number and type of details recalled

A series of 2 (interview: CIS vs. SI) x 2 (veracity: truth, lie) mixed ANOVAs with the last factor as a within-subject variable were conducted on the total number and type of details recalled. Descriptive statistics and analyses are presented in Table 3.

Overall, the analysis revealed a significant main effect of interview style, with CIS eliciting more details than SI. Furthermore, there was a main effect of the interview style on the number of details recalled in relation to actions, objects, and locations, with CIS eliciting more such details than SI. However, no significant effect of interview style was observed on the number of details recalled in relation to persons.

The analysis also revealed a significant main effect of veracity, with the truthful parts of the statements containing more details than the deceptive parts. Furthermore, there was a main effect of veracity on the action, object, and person-related details recalled, with the truthful parts of the statements containing more details of these types than the deceptive parts.

No significant main effect of veracity was observed for location-related details.

No overall significant effect of the interaction between interview style and veracity was found for the total number of details, F(1, 45) = 0.52, p = .477. However, a significant interaction effect was observed for action details, F( 1

INSERT TABLE 3 ABOUT HERE

Considering the number of questions asked, the ratio of gathered details was 3.65 details per question for the CIS (130.71 details for an average of 47.63 questions asked), and 0.58 details per question for the SI (101.24 details for an average of 173.52 questions asked).

Accuracy of truthful statements

To compare the accuracy of the gathered statements, the effect of interview style on the number of correct, erroneous and confabulated details reported in truthful parts was analyzed with an independent samples t.test (the deceptive parts were not concerned, as they were entirely inaccurate). Descriptive statistics and analyses of these results are presented in Table 4.

There was a significant main effect of interview style on the number of correct details recalled, with CIS statements containing more correct details than SI statements. Furthermore, there was a main effect of interview style on the number of correctly recalled action, object, and location details, with CIS significantly outperforming SI. There was no difference between CIS and SI for correct person-related details.

Overall, there was no significant difference between CIS and SI on the number of erroneous or confabulated details produced. However, there was a significant main effect of interview style on the number of erroneous and confabulated person-related details produced, with CIS eliciting more errors and confabulations than SI. There were no differences between CIS and SI for the erroneous and confabulated details produced in relation to actions, objects and locations.

INSERT TABLE 4 ABOUT HERE

The accuracy rates (correctly recalled details as a proportion of total details provided) were, respectively, 93.86% vs 93.96% for CIS and SI, and were not significantly different, t(44) = 0.08, p = .935.

Interviewers' lie detection skills

In total, the CIS-trained interviewers made 10 lie detection errors, whereas the untrained officers made 11 errors. The interviewers' lie detection accuracy rates were calculated by dividing the number of correctly identified truthful/deceitful sequences by the total number of sequences in the statements. These rates were, respectively, 89.58% and 83.82% for CIS and SI, and did not differ significantly, t(44) = -0.78, p = .235.

Furthermore, the number of errors made by CIS-trained interviewers and SI interviewers did not differ for truth errors and deception errors. It was the same for truth correct judgements, Fs ≤ 0.69, ps ≥ .410. However, analyses revealed a difference in deception correct judgements: CIS-trained interviewers gave more deception correct judgements (M = 1.83, SD = 0.38, 95% CI [1.67, 1.99]), compared to SI interviewers (M = 1.47, SD = 0.80, 95% CI [1.06, 1.88]), t(44) = -1.74, p = .049, d = 0.62.

Discussion

The aim of the study was to provide knowledge about the benefits of the CIS used by field professionals, compared to officers using their own interview techniques. The broad hypothesis of this study was that CIS-trained customs officers would gather more detailed statements from the participants compared to the untrained officers using SI, without increasing the number of erroneous and confabulated details. The results of our study support this hypothesis, and are described more precisely in the sections below.

Details gathering

As expected, the analyses revealed that the customs officers collected more details when using the CIS than the standard interview. These results provide information about the advantage of the CIS for details gathering compared to a SI conducted by professional interviewers. More precisely, the CIS made it possible to gather 29% more details than the SI.

In terms of quantity of details, the increase was high for the following categories: the actions, objects, and locations (respectively 32%, 19% and 29% more with CIS). These results are consistent with observations made concerning the benefit of using CI rather than SI for witnesses/victims in terms of the quantity of gathered details [START_REF] Colomb | Back to the real: Efficacy and perception of a modified cognitive interview in the field[END_REF][START_REF] Memon | The cognitive interview: a meta-analytic review and study space analysis of the past 25 years[END_REF]. However, we did not observe any such increase for person-related details. This result has already been found in studies of CI used for witnesses/victims, and even for lying witnesses. In the study by [START_REF] Bembibre | Differential effectiveness of the cognitive interview in a simulation of a testimony[END_REF], CI revealed fewer person-related details than SI, but as many object and more action details. The authors explained that these results could be due to the general context of criminal investigations, in which it seems more important for interviewees to describe actions (elements that could inculpate or exonerate a suspect), rather than people and their physical appearance [START_REF] Bembibre | Differential effectiveness of the cognitive interview in a simulation of a testimony[END_REF][START_REF] Milne | Back to basics: A componential analysis of the original cognitive interview mnemonics with three age groups[END_REF]. It is also possible that the absence of improvement for the person details category is due to the event chosen for this study. Indeed, the participant was alone in most of the scenario events: only one of the sequences involved an interaction with an unknown person, and not all the participants had to meet this person. A floor effect could therefore explain this lack of difference.

Despite this issue concerning person-related details, the overall increase for details quantity is all the more noteworthy when we consider that the interview duration was shorter with the CIS than with the SI. These results for interview lengths are due to the number of questions asked by the interviewers across the conditions. Indeed, SI contained more than three times as many questions as CIS. Considering that the CIS made it possible to obtain 29% additional details, the details/questions ratio (i.e. 6.29 times more details with the CIS) highlights a high increase for details gathering with this interview method. These results reflect prior observations from SI which have been analyzed in the literature. Indeed, SI

contain very few open-ended questions and many closed-ended questions, the answers to which are not very informative. Interviewers therefore spend a lot of time during the interview asking questions in an attempt to obtain more details, sometimes in vain [START_REF] Snook | Let'em talk!: A field study of police questioning practices of suspects and accused persons[END_REF].

These findings are of interest to field investigators in that the majority of professionals cite time constraints as a barrier to the application of lengthy protocols, such as the Cognitive Interview [START_REF] Dando | The cognitive interview: The efficacy of a modified mental reinstatement of context procedure for frontline police investigators[END_REF].

As expected, analyses of the truthful parts of the statements revealed an improvement in the gathering of correct details with the CIS (23% more details), without any increase in the number of errors and confabulations. More precisely, the beneficial effect of CIS was found on action, object, and location details. However, and as in the analysis of the amount of details, this improvement in the number of correct details was not present for person-related details. In addition, the analyses revealed an increase in the number of errors and confabulations affecting the descriptions of persons in CIS compared to SI, even if the volume of incorrect information was globally very low (i.e. less than one item per interview). In the literature, person-related details have already been found to be a category that is affected by many errors. In a study by [START_REF] Sauerland | Speaking is silver, writing is golden? The role of cognitive and social factors in written versus spoken witness accounts[END_REF], in which participants were asked to produce a free recall preceded by a report-everything mnemonic, the person-related details category exhibited a lower accuracy rate (71.55%) than the other event-related categories of details (i.e. action, object and location details: 94.39%). Indeed, [START_REF] Meissner | Person descriptions as eyewitnesse vidence[END_REF] showed that the person-related details category was of particular interest to the interviewers and that the latter tended to ask more leading and repeated questions on this subject, despite their training in interview methods such as the CI. However, these observations do not explain why the number of errors on person-related details is higher in CIS than in SI. Future research should explore this phenomenon more closely and analyze the joint impact of the interviewers' interest in this category of detail, the type of questions arising from this interest and instructions such as those present in the CIS (e.g. Mental context reinstatement) on the potential for person-related errors and confabulations.

In suspect interviews, it is also useful to be able to detect deception in a statement. Lie detection studies generally show that truthful statements contain more details than deceptive ones (e.g. [START_REF] Bogaard | Using the Reality Interview improves the accuracy of the Criteria Based Content Analysis and Reality Monitoring[END_REF][START_REF] Masip | The detection of deception with the reality monitoring approach: a review of the empirical evidence[END_REF]. As expected, this is the case in the present study, in which the total number of details was higher in the truthful parts (20% more details) than in the deceptive parts of the statements. In particular, the truthful parts contained more action, object, and person-related details. However, the truthful parts did not include more location details than the deceptive ones. This phenomenon may be due to a strategy adopted by the participants in order to produce credible lies. Indeed, although they could not anticipate the objects, actions and people they were going to meet during this experiment, the students knew the university's rooms, corridors, stairs and car park (where the experiment took place).

Therefore, the deceptive parts could include as many location details as the truthful parts because the participants could describe the places precisely, even if they had not been there that day.

Furthermore, and with regard to the action details, an interaction effect between veracity and interview style highlighted the fact that a difference between truth and lies was only present for the statements gathered with the CIS (and not for the statements in response to the SI). In view of the recommendation made in the study by [START_REF] Masip | The detection of deception with the reality monitoring approach: a review of the empirical evidence[END_REF], according to whom verbal cues to deception are particularly visible in 'information gathering style' interviews, these results suggest that action details could be considered as a verbal truth/lie discriminant criterion to be integrated into verbal lie detection tools such as the Reality Monitoring list (see [START_REF] Izotovas | Facilitating memory-based lie detection in immediate and delayed interviewing: The role of mnemonics[END_REF].

Apart from the number of actions, the results did not indicate any other effect of an Interview Style x Veracity interaction on the details gathered. This means that the observed increase in the quantity of details obtained with the CIS (compared to the SI) also concerned the deceptive statements. This is potentially problematic from the perspective of interviewers, who may be misled by more detailed lies. Indeed, there are many misleading beliefs about lying [START_REF] Bond | Accuracy of deception judgments[END_REF]. Although the quantity of information is a criterion of the CBCA list, which allowed for some accuracy in discriminating lying and truthfulness [START_REF] Vrij | Criteria-based content analysis: a qualitative review of the 13 first studies[END_REF], more recent studies have shown that a strategy sometimes used by liars is to mix lying and truthfulness in their statements, which tends to result in more detailed lying parts [START_REF] Verigin | The interaction of truthful and deceptive information[END_REF]. Thus, interviewers should be informed that a testimony gathered using the CIS is likely to be more detailed, even when it is untrue.

Deception detection

We expected that the CIS-trained interviewers would be better lie-detectors than the untrained ones, given that Geiselman (2012) has already stated that the interview method would facilitate lie detection. The results did not show a significant difference in the number of errors made in lie detection as a function of the type of interview. This could be due to the fact that there were only very few lie detection errors: ten errors for the CIS trained officers and eleven errors for the untrained ones, corresponding to accuracy rates of 89.58% and 83.82%, respectively. These are among the highest accuracy rates to have been found in deception detection studies and they may be related to the repetition of interviews regarding the same events and to the material evidence provided. Firstly, each pair of customs officers had to interview eight participants, and the officers were therefore able to construct an idea of the four scenarios acted out by the interviewees. This does not reflect the procedure in real cases. Secondly, items of material evidence were given to the interviewers in the study, as in [START_REF] Vrij | Translating theory into practice: Evaluating a cognitive lie detection training workshop[END_REF]. For example, two pictures -one of the room and one of the car -were given to the interviewers, thus making it possible for them to know when the interviewees were lying about these two aspects. In further studies, less critical evidence, or no evidence at all, should be given to the interviewers in order to make it possible to analyze their real deception detection abilities.

However, considering the type of detection judgments, results showed a benefit of CIS in identifying deception. More precisely, CIS-trained interviewers made more correct deception judgments than SI interviewers, which could be interpreted as CIS more clearly identifying deceptive statements compared to SI. These results would be in line with those described by [START_REF] Geiselman | The cognitive interview for suspects (CIS)[END_REF], who found that interviewers using the CIS were good at identifying deception as the interview progressed. However, if the CIS made it easier to identify deceptive statements, this would not explain the lack of significant differences observed for deception errors and truth errors in our study. Indeed, if the CIS improves the possibility of detecting deceptive parts, it should also make it possible to avoid mistaking deceptive parts for truthful parts, and mistaking truthful parts for deceptive ones. However, this is not the trend found in the present study. In any case, our small sample size does not allow us to draw conclusions from these analyses and to obtain a sufficient Cohen's d [START_REF] Lakens | Simulation-Based Power Analysis for Factorial Analysis of Variance Designs[END_REF]. A replication of the study focusing on interviewers' lie detection skills, with a larger sample size, would allow for analysis of the results for this particular issue.

Limitations

As described in the previous section, the first limitation of our study was the small sample size. Indeed, as in the study conducted by [START_REF] Vrij | Translating theory into practice: Evaluating a cognitive lie detection training workshop[END_REF] with police officers, practical constraints meant that the sample size was small and thus that the effect sizes in our analyses of the results were also small. A replication of the study with a larger sample size would increase the effect sizes associated with the significant results.

A second major limitation of our study is the absence of a third comparison group, using for example another interview protocol than the CIS. Indeed, the results presented here suggest a benefit of the CIS protocol on the number of gathered details. However, we compared a group of interviewers trained in an interview protocol with a group of untrained interviewers. It is then possible that another interview method could have the same beneficial effects as the CIS.

To investigate this question, further replications of this study should include a third group, such as interviewers trained in the PEACE protocol [START_REF] Walsh | What really is effective in interviews with suspects? A study comparing interview skills against interview outcomes[END_REF] or in the structured interview (i.e., CIS without the Mental Context Reinstatement, Report-Everything, Drawing and Reverse Order mnemonics).

In addition, the majority (71%) of the participants in this study were women, and all of the participants were first-year psychology students. Since this sample is not representative of the population typically interviewed in customs suspect interviews, this study should be replicated with a more heterogenous population. However, studies have shown that CI (for witnesses/victims) remain effective when used with populations of different ages or socioeconomic status. For example, [START_REF] Stein | Testing the efficacy of the cognitive interview in a developing country[END_REF] pointed out that CI improved the amount of correct information gathered, without increasing the number of errors, from people with a low level of education. Furthermore, a study by [START_REF] Wright | Enhancing the recall of young, young-old and oldold adults with cognitive interviews[END_REF] showed similar results in terms of information gathering compared to standard interviews when a CI was used with individuals of various ages (young adults, adults and elderly persons). Even so, it would be necessary to confirm these results with suspects, since the studies previously cited involved witnesses and victims.

Finally, as discussed below, the interviews in this study were adapted to the customs environment, since the participating investigators belonged to a customs service with specific missions (i.e. mostly drugs and money-related crimes). Thus, the training provided and the study conducted should be repeated with other law enforcement agents, such as police officers. Indeed, the dynamics of other crimes, such as murder or violent crime, may lead to differences in information gathering and the obtaining of confessions. For example, suspects of non-violent crime are more likely to confess their crimes and provide information about them, whereas drug trafficking suspects tend to give few details and are less likely to confess [START_REF] Deslauriers-Varin | Confessing their crime: Factors influencing the offender's decision to confess to the police[END_REF]. In addition, customs officers have generally been the object of little interest on the part of researchers and have received little training in the area of suspect interviews [START_REF] Granhag | Crime on the border: Use of evidence in customs interview[END_REF]. Thus, customs officers' SI include behaviors that can be detrimental to information gathering, such as asking a large number of questions, interrupting the interviewees, portraying oneself as an authoritative figure, maximizing, and so on [START_REF] Noc | Perceptions des pratiques en matière d'audition de suspects: une évaluation auprès des agents des douanes françaises[END_REF]. Further studies should be conducted to compare the benefit of CIS in standard police interviews, for example. The participant sits in a corridor and completes a logic questionnaire

The participant is asked to steal a transcript from a professor's office, but s/he will have to convince the interviewer that s/he completed the logic questionnaire

Sequence 3

The participant goes with a confederate to record a license plate number in the university car park

The participant reads a text about this event and has to imagine s/he performed it so s/he can convince the interviewer that s/he really did so Sequence 4

The participant sits in a corridor and completes a general knowledge quiz

The participant meets a confederate to exchange an envelope with cash, but s/he will have to convince the interviewer that s/he completed the quiz 34.29 10.16 [30.00, 38.58] 23.33 6.73 [20.27, 26.40] 17.63

  , 45) = 5.87, p = .020, d = 0.74. Truthful parts of the statements contained more action details (M = 18.92, SD = 5.15, 95% CI [16.74, 21.09]) than the deceptive parts (M = 15.37, SD = 6.29, 95% CI [12.72, 18.03]), in the CISgathered statements, t(24) = 3.23, p = .002, d = 1.35, but not in the SI-gathered statements (truthful: M = 11.02, SD = 3.67, 95% CI [9.85, 13.19], deceptive: M = 11.81, SD = 4.67, 95% CI [9.64, 13.98]), t(21) = 0.25, p = .803 , d = 0.11. There were no interaction effects between interview style and veracity on the recalled object, location, or person-related details, Fs < 0.854, ps > .360.

Table 1 .

 1 True and deceptive version of each of the 4 sequences corresponding to a complete

	scenario
	Truthful version	Deceptive version
		The participant reads a text about
	The participant goes with a
		this event and has to imagine s/he
	confederate to pick up a transcript
	Sequence 1	performed it, so s/he can convince
	in an unknown room of the
		the interviewer that s/he really did
	university
		so
	Sequence 2

Table 2 .

 2 Quantity of details in function of interview style and veracity

	Interview style

Two criminal events were committed inside the University: a transcript has been stolen from a professor's office, and this document has been sold in exchange for cash. You are going to interview four suspected students. Each of the students may have committed one of these crimes, or both of them, or no crime at all.

Your objective is to find out the truth about what happened. To do this, you will conduct four 45-minute interviews with these students. After the interviews, you will have to judge if each student is guilty or not of the crimes described. You will also have to judge which parts of her/his statement were truthful, and which parts were deceptive.

Two pictures are available to help you prepare your interviews:

Picture of a third-floor room Picture of cars in the parking lot


Jianyong Xue

Frédéric Alexandre

Developmental Modular Reinforcement Learning

In this article, we propose a modular reinforcement learning (MRL) architecture that coordinates the competition and the cooperation between modules, and inspire, in a developmental approach, the generation of new modules in cases where new goals have been detected. We evaluate the effectiveness of our approach in a multiple-goal torus grid world. Results show that our approach has better performance than previous MRL methods in learning separate strategies for sub-goals, and reusing them for solving task-specific or unseen multi-goal problems, as well as maintaining the independence of the learning in each module.

Introduction

Traditional reinforcement learning algorithms have been proven successful in solving complex, single-goal tasks; yet they perform badly in multi-tasks and non-stationary environments with hidden states. Modular reinforcement learning (MRL) provides one solution that decomposes a complex problem into a collection of concurrently running RL modules, each of which learns a separate policy to solve a portion of the original problem.

MRL has been studied not only for the decomposition of complex tasks into modules, but also for the reusability of separately learned modules in new strategies for other tasks that have never been solved before [START_REF] Simpkins | Composable modular reinforcement learning[END_REF]. Focusing both on the optimality of the composite strategy for the entire task and on the independence of learning in separate modules, [START_REF] Samejima | Inter-module credit assignment in modular reinforcement learning[END_REF] introduced a specific concept of "modular reward" to propagate local rewards toward the entire task achievement between modules. Considering the performance degradation in the composability of modules that have incomparable reward scales, [START_REF] Simpkins | Composable modular reinforcement learning[END_REF] proposed a model, Arbi-Q, that recruits an additional module of command arbitrator to assign probabilities to the selection of a module for each state; then the selected module's preferred action becomes the agent's action in that state. However, one limitation of Arbi-Q is that the agent's action always comes from one of the modules.

In this article, we adopt the idea of multiple model-based reinforcement learning from [START_REF] Doya | Multiple modelbased reinforcement learning[END_REF] and present a new MRL architecture that addresses all the concerns mentioned above by borrowing principles and mechanisms from the mentioned models. Additionally, a particular component of "coordination module" is introduced, to mediate the competition and the cooperation between different modules, and inspire the learning system to create new modules in circumstances where current modules are not capable of handling unseen tasks.

Figure 1 shows the overall organization of the proposed Developmental MRL (DMRL) architecture, which is composed of a coordination module plus a list of n model-based RL (MBRL) modules. Each MBRL module shares the same inputs and has an identical structure that consists of three components: the reward predictor, the RL controller and the state predictor [START_REF] Doya | Multiple modelbased reinforcement learning[END_REF]. The coordination module will be activated to create new modules whenever the summation of errors from each state predictor reaches a threshold. Furthermore, learning in each component is gated by a "responsibility signal" [START_REF] Doya | Multiple modelbased reinforcement learning[END_REF], which comes from the gaussian softmax function of prediction errors and determines how much the modules are responsible for the current task. Fig. 1: . Schematic diagram of the DMRL structure.

State predictor and the responsibility signal

The state prediction function F i (s t+1 , s t , a t : θ) gives the probability distribution of the newly observed state s t+1 ∈ S based on the previous state s t ∈ S and the action a t ∈ A performed by the agent at step t, where S and A are the set of state space and action space, i ∈ {1, . . . , n} is the index of modules. Specifically, the dynamic function is realized through a three-layers neural network, where the vector of parameters θ represents the weights of the network. This network is trained by a collection of pairs of inputs (s t , a t ) and their corresponding output labels s ′ t+1 from trajectories τ = {s 0 , a 0 , . . .

, s T -2 , a T -2 , s T -1 } of length T [4]
. Initial parameters in this neural network are set as a small random value with uniform distribution between 0.0 and 1.0. With the newly observed state s t+1 , the state prediction error δ i st of module i is calculated as follows:

δ i st = F i (j, s t , a t : θ i ) -c(j, s t+1 ), j ∈ S (1)
where c(j, s t+1 ) is 1 if j = s t+1 and 0 otherwise. Along with state prediction errors, the responsibility signal λ i t for each module is formulated as an output of the gaussian softmax function:

λ i t = λi t e -1 2σ 2 δ i st 2 n j=1 λi t e -1 2σ 2 δ j st 2 , λi t = λ i t-1 ρ n j=1 λ j t-1 ρ (2)
where λi t represents the prior knowledge about module selection, which was used to maintain the temporal continuity of the selected module [START_REF] Doya | Multiple modelbased reinforcement learning[END_REF]. Parameter σ controls the sensitivity of responsibility signals to state prediction errors, and ρ (0 < ρ < 1) indicates the effects of past module selections on current decisionmaking. The parameter vector θ is updated as follows:

θ i = θ i + αλ i t δ i st ∂F i (s t+1 , s t , a t : θ i ) ∂θ i (3)
where 0 < α < 1 is the learning rate.

Reward predictor

The reward predictor R i (r ′ , s t , a t ) provides an expected reward r ′ t based on the previous state s t and the action a t selected at step t. The modular reward ri t is formed as the sum of immediately received reward plus an extra bonus for rewarding the module that better fits the current sub-goal. Specifically, this bonus is calculated from the product of modular value function and the temporal difference in the responsibility signals; then we have the reward prediction error:

δ i rt = ri t -R i (r ′ , s t , a t ), ri t = r t + (λ i t+1 -λ i t )V i (s t+1 ) (4)
therefore, parameters in the reward predictor are updated by: R i (r ′ , s t , a t ) = R i (r ′ , s t , a t ) + αλ i t δ i rt (5)

RL controller

The RL controller in module i provides two functions: the state-value function V i (s t ) and the state-action-value function Q i (s t , a t ). Combined with the state transition function F i (s t+1 , s t , a t ) and the reward function R i (r ′ , s t , a t ), we have the full Bellman equation [START_REF] Richard | Reinforcement learning: An introduction[END_REF] of value function:

V i π (s t ) = at∈A π i t (a t |s t )[R i (r ′ t , s t , a t ) + γ st+1∈S F i (s t+1 , s t , a t : θ i )V i π (s t+1 )] ( 6
)
where γ is the discount factor that controls the effects of future rewards. Furthermore, we recorded the eligibility traces e i t s for each state s, which are updated as:

e i t (s) = ηγe i e-1 (s) if s = s t ηγe i e-1 (s) + 1 if s = s t (7)
then the state value V i (s t ) will be updated by:

V i (s t ) = V i (s t ) + αλ i t δ i vt e i t (s), δ i vt = ri t + γV i (s t+1 ) -V i (s t ) (8)
where δ i vt is the temporal-difference (TD) error with modular reward ri t .

Action selection

For each candidate action a j ∈ A, (j = 1, . . . , M ), their preferences are calculated by:

Q(s t , a j ) = n i=1 λ i t [R i (r ′ , s t , a j ) + γ j∈X F i (s j , s t , a j : θ i )V (s j )] ( 9
)
where X is the set of possible states that the agent observed after taking action a j in state s t . We use a softmax function as a stochastic version of the greedy policy, where the action a t is selected by

P i (a j |s t ) = e βQ(st,aj ) M k=1 e βQ(st,a k ) (10)
where β was set as trials/500, which controls the stochasticity of action selection.

The coordination module

The coordination module (CM) is designed to (a) prevent learned modules for specific subs-tasks from being modified, and (b) inspire the learning system to create new modules in circumstances where current modules are not capable of handling tasks that they never experienced before. In order to keep modules independent in learning their own policies, the CM modulates the sensibility of responsibility signals to smaller predictions errors by adjusting the value of the parameter σ, as:

σ t = - n i=1 log(δ i st ) (11)
In situations where the system detects a new sub-task that has never been solved before, or when current modules are not capable of solving them, the watch list records the sum of prediction errors in κ steps and calculates the average value se t to compare with the threshold. When se t reaches the threshold, the coordination module will directly duplicate the module that has the least prediction error from current list of modules, and then train it through trajectories observed in experimental data.

Experiments

Settings

We investigate the performance of DMRL in a torus grid world derived from [START_REF] Doya | Multiple modelbased reinforcement learning[END_REF]. In this hunter-prey world, the hunter agent chooses one of five possible actions: {north (N), east (E), south (S), west (W), stay}, and tries to catch multiple preys in a 7x7 torus grid world (as shown in Figure 2). Meanwhile, preys move in either one of four directions: {N E, N W, SE, SW }, which are represented as four different kinds of targets: G = {g 1 , g 2 , g 3 , g 4 }. The experiment is divided into two parts: (a) all of 4 targets appear cyclically in a fixed order, which is G 1 = (g 1 , g 2 , g 3 , g 4 ) (as shown in Fig. 2). At the beginning of each trial, the hunter and the prey are placed at a random position and the prey's movement follows the first target g 1 . When the hunter catches the prey, another prey appears at an other position and moves in the direction of the next target. A reward r = 10 is given only when the last target g 4 is caught, which terminates this trial; a cost for each movement is set as -0.01. (b) Four different tasks are designed in the order of increasing complexity: T = {T 1 = (g 1 ), T 2 = (g 1 , g 2 ), T 3 = (g 1 , g 2 , g 3 ), T 4 = (g 1 , g 2 , g 3 , g 4 )}.

Results

In the first experiment, we compare the performance of DMRL with other MRL approaches. Left three figures in Fig. 4 shows the average number of steps, the averaged reward, and the total value of states respectively during 2000 trial epochs in 20 simulation runs. It can be seen that the DMRL works significantly better than Arbi-Q and Inverse Arbi-Q (an adaptation we made, where action preferences are evaluated by a joint policy, instead of coming from a single module); also it converges faster than the MBRL and MBRL with modular reward (MR). Fig. 3 shows examples of the value functions and the prediction models learned by the DMRL. It can be seen that modules 1, 2, 3, 4 are specialized for the prey moving to the NW, NE, SW, and SE, respectively. The landscapes of the value functions are coherent with preys' movement directions.

Fig. 4: Performance of DMRL compared with previous MRL approaches.

In the second experiment about increasing complexity reported in the figure on the far right of Fig. 4, the DMRL gradually learns modules as new sub-problems appear in the tasks, and amplitude of the spikes representing the maximum of error decreases as the complexity of the tasks increases, which indicates that the architecture is capable of reusing previously learned modules for solving new problems.

Conclusion and future work

In summary, we present the simple yet effective architecture DMRL to enable evolving multiple-goal tasks. Specifically, the responsibility signal was used to gate the learning of components in each module, and a particular coordination module is introduced to mediate the competition and the cooperation between different modules, and inspire the learning system to create new modules as needed. Nevertheless, a number of questions stands out as important targets for the next stage of research, such as (i) the planning strategy or the proactive way in modular reward; (ii) the top-down and bottom-up approaches for task decomposition. Inspirations from continual learning approaches will be a promising direction for learning tremendous task effectively without creating discrete modules.

Fig. 2 :

 2 Fig. 2: The pursuit experiment in the torus grid world.

Fig. 3 :

 3 Fig. 3: Value functions and prediction models learned by the DMRL.