Hye Young Kim
email: hye.young.kim@ens.fr

Knots and Consciousness: Knotted Models Applied to Uriah Kriegel's "Consciousness, Permanent Self-Awareness, and Higher-Order Monitoring"

This paper is a response to Uriah Kriegel's "Consciousness, Permanent Self-Awareness, and Higher-Order Monitoring" (Kriegel 2002) interpreted with my knot models of consciousness. In his paper, Kriegel argues that permanent self-awareness accompanies every conscious state, which I present in a trefoil knot model that provides some features of consciousness which were not captured in the preexisting models of consciousness. By doing so, I will also show that the core of the consciousness discussion is related to the structure and the relationship between the observing and the observed self.

Introduction

1-1. Consciousness, Self-Awareness, and Knots

This paper is a response to Uriah Kriegel's "Consciousness, Permanent Self-Awareness, and Higher-Order Monitoring" (Kriegel 2002) interpreted with my knot models of consciousness.

Kriegel refers to the phenomenon that one with a conscious experience is aware of oneself as the experience owner having permanent self-awareness which is differentiated from introspective awareness (Kriegel 2002, 518). The main object of a permanent self-awareness involving experience is whatever external condition is experienced, while the main object of introspective awareness is the subject's internal experience (Kriegel 2002, 518). One of the differences between these two phenomena, Kriegel explains, is that permanent self-awareness accompanies every conscious state, while introspective awareness is rare (Kriegel 2002, 519). The other difference is that the focus of the experience of introspective awareness is directed at oneself, while permanent self-awareness is typically a peripheral component of conscious state, which means one's awareness of oneself as the experience owner remains peripheral (Kriegel 2002, 519). Permanent self-awareness is not introspective this wayin the way that it consumes the subject's attention (Kriegel 2002, 519). However, a single state cannot involve permanent selfawareness, rather there is a temporally extended, permanent self-awareness (Kriegel 2002, 520).

And each particular mental state takes part in this stretch of self-awareness (Kriegel 2002, 520).

Therefore, even if a particular state does not permanently involve self-awareness, the selfawareness it involves is permanent. This is what Kriegel refers to as "a state involving permanent self-awareness" or "a permanent self-awareness involving state" (Kriegel 2002, 520).

I second Kriegel's argument and will try to visualize his models anew by utilizing knots, which could capture some features of consciousness that were not so clearly presented or slipped out in the pre-existing models provided by Kriegel. But why knots? What can knots say, or rather, show about consciousness? Following the progression of Kriegel's arguments, I will summarize and introduce his models of consciousness and show the possibility of applying my knot-models to his consciousness model. And in the end, I will present the trefoil knot as an alternative model of the structure of consciousness, which is a state involving permanent self-awareness.

1-2. The Paradox of Self: Problem of the PSA Model

One could still ask though, why consciousness? Or rather, knots and consciousness?

Consciousness indicates an awareness of something, either awareness of an object or awareness of self. Being aware of something is related to, roughly speaking, knowing and knowing that we know. The act of seeing as the most primitive perception represents this 'knowing' as being aware. This seeing is not only seeing an actual object in reality, but it includes the meta level of seeing, which points at self-observation. This means seeing myself, or seeing myself seeing (an object).

Observation is the beginning of not only understanding, but also understanding understanding in knot-theory-represented topological space. Knots and consciousness share their fundamental domain in the act of seeing, therefore, knots could be useful for mapping the theoretical models of consciousness.

do not show this relationship nor explain the act between these differentiated yet identical self(s). What we need to be able to represent is a structure of self that is two-fold.

(1) Seeing (one)self always comes with seeing not-self.

Therefore, this is a two-layered seeing: seeing an object (not-I) and seeing myself (I). This seen self is always an othered self.

(2) Seeing an object always comes with seeing myself. (Permanent Self-Awareness) (Even if we are not necessarily aware of this meta-seeing (seeing myself) every time I see an object.) These two are fundamentally linked. Or, it could be stated they are two contents of one and the same mental state. This paradoxical structure of self in the process of "self-awareness" is not captured in the PSA models. It is difficult to visualize this, because (1) it is in the structure of a paradox, and (2) the double layers of one process need to be presented intertwined. The one layer is the structure of the observer and the object, and the other is the intrinsic structure of self both as the observer and the observed. Each layer could be presented and connected to the other, while each layer is still presented as a separate mental content. This connection is weak, i.e. external. The connection of these two different things does not guarantee that these contents are the two contents of one and the same state. With knots, however, it is possible to visualize (1) the paradox model, and (2) the multi-layered relationship in a unitary structure (process as a whole).

A Higher-Order Monitoring Model of Permanent Self-Awareness

Kriegel introduces a Higher-Order Monitoring model of permanent self-awareness (Kriegel 2002, 520). It is yet to be proven whether the Higher-Order Monitoring theory can be successfully interpreted as an illuminating model of permanent self-awareness (Kriegel 2002, 520).

According to Higher-Order Monitoring theories, for my experience of an object to be conscious, is for it to be accompanied by a suitable second-order state representing it (Kriegel 2002, 520). In this context, however, the second-order state must be both roughly simultaneous with the firstorder state and formed non-observationally and non-inferentially (Rosenthal 1990, also see Kriegel 2002, 520). Higher-Order Monitoring theorists are still divided as far as their interpretation of what kind of second-order state this might be. According to Higher-Order Perception theory, second-order state is a perception-like state, while for Higher-Order Thought theorists, it is a thought (Kriegel 2002, 521). Here, Kriegel focuses on David Rosenthal's Higher-Order Thought account.

Let's say there is a purple cube as an object of a conscious experience. "According to Rosenthal, having a conscious experience of a purple cube is a psychological structure involving the concurrence (more or less) of two mental states" (Kriegel 2002, 521): first-order state (S 1 ) and second-order state (S 2 ). The content of a first-order state is purple cube and the content of a suitable second-order state is I am seeing a purple cube. S 2 represents not only the occurrence of S 1 , but also its occurrence in the subject. "This means that having conscious experiences requires the possessionand deployment -of a concept of self" (Kriegel 2002, 521). Kriegel applies this aspect of the theory to account for permanent self-awareness. The idea is that S 1 involves permanent self-awareness because it is accompanied by a mental state that represents its occurrence in the self (Kriegel 2002, 521) as described explicitly by Rosenthal: "A strong intuitive connection obtains between being in a conscious state and being conscious of oneself.

[…] Higher Order Thought theory explains the phenomenon […] successfully, since one's Higher Order Thoughts refer to oneself" (Rosenthal 1990, 744-45; see also Kriegel 2002, 521).

Kriegel visualizes this as below (Kriegel 2002, 521). 2 It is also because layers provide borders which illuminate the distinctive ontological status of consciousness itself as the subject of the perceived, differentiating itself from the perceived (observed), yet in the perceived as part of themselves as well.

permanent self-awareness and introspective awareness (Kriegel 2002, 521). The problem of this model is, however, that in this model, S 2 represents the property, an extrinsic property of S 1 which makes S 1 involve permanent self-awareness. Therefore, S 2 itself is not conscious (Kriegel 2002, 521). Kriegel shows that a third-order thought (S 3 ) is required, for S 2 to be conscious (Kriegel 2002, 521). This is what happens in cases of introspective awareness (Kriegel 2002, 521). This means that one has a second-order thought as "I am seeing a purple cube" accompanied by a third-order thought as "I am thinking that I am seeing a purple cube" (Kriegel 2002, 522). And Kriegel presents the following figure to visualize this structure (Figure 2, Kriegel 2002, 522).

2-2. Belongingness (Mutuality) of the Layers

This model, however, comes with two conspicuous defects. First, in the case of the conscious experience of the purple cube, in this model, "neither the monitoring state S 2 nor the monitored state S 1 is in and of itself conscious. The consciousness of S 1 derives from its embedding in a relational structure, it is not intrinsic to it. Taken out of this structure, S 1 becomes non-conscious.

But if neither S 1 nor S 2 is in itself conscious, then it is conceivable that there should be a zombie who harbours both states but has no PSA [permanent self-awareness] whatsoever" (Kriegel 2002, 522). Second, "the second-order state S 2 , in virtue of which S 1 is conscious, is itself a nonconscious state. So, the fact that S 2 represents the self does not imply that, by having S 2 , the self is conscious of itself, for S 2 is not a conscious representation of the self" (Kriegel 2002, 522-523).

Taking into consideration that consciousness of self requires that the self be in the content of a conscious state, there is no real self-awareness in the Higher Order Thought model, because this model attributes to the subject a presentation of itself, but a non-conscious one (Kriegel 2002, 523).

If these problems are interpreted in the grammar of belongingness4 , whether the layers of orders statesare in themselves conscious, the question is whether the layers belong to each otherfor instance, the layer S 1 belongs to S 2, and S 2 to S 3 , or in a reversed wayand/or if they belong to one's consciousness. The inevitable temporal gaps between different layers, monitoring and monitored states, must be somehow reconciled in order to guarantee the consistency and the identity of these layers as layers of one's conscious experience as a whole. In other words, these separate layers need to belong together to constitute a conscious experience. And this belongingness resolves the difference of the temporal gaps.

The Brentanian Model of Permanent Self-Awareness

3-1. Permanent Self-Awareness and Introspective Awareness in Brentano's Model

The belongingness solution can be better applied and represented in accordance with the next model that Kriegel presents, a model that preserves many of the theoretical resources of the Higher Order Thought model but still attempts to satisfy the further demands, namely the Brentanian model of permanent self-awareness (Kriegel 2002, 523). Kriegel explains that "according to Brentano, a conscious experience of a purple cube has two representational contents. The primary content is given by the purple cube. The secondary content is given by the experience of the purple cube. Thus, the experience represents primarily the cube and secondarily itself. More specifically, it represents itself precisely as a representation of the cube, and its primary content is embedded in its secondary content. Thus, the representation of the cube, and the representation of the representation of the cube, are wrapped up together in a single mental act" (Kriegel 2002, 524; emphasis added). Therefore, this experience is both a perception of itself and a thought about itself (Kriegel 2002, 524). The emphasis lies on "all wrapped up together in a single mental act" (Kriegel 2002, 524). In other words, they belong together to a single mental act.

Kriegel shows this in the following figure (Figure 3, Kriegel 2002, 525) and explains: "Whatever the subject's experience is primarily directed at (whether the sight of a purple cube or the sound experience (see Figure 3). Hence, the subject's permanent self-awareness. In the Brentanian model, then, an experience is conscious just in case it represents (secondarily) that the subject herself is having that very experience" (Kriegel 2002, 524-525).

Figure 5 5

This self-awareness involved in ordinary conscious experience is differentiated from introspective awareness, because the self-awareness experience represents itself only secondarily, while introspective awareness would be awareness in which the mental act would be its own primary object, according to Brentano (Kriegel 2002, 525). Introspective awareness in Brentano's model looks as below: This solution is also the very difficulty of the Brentanian model -the "mysteriousness" of the model. "What is mysterious about Brentanian experiences is specifically the fact that they represent themselves" (Kriegel 2002, 526;emphasis added). The riddle of Brentanian model that we need to solve is that of self-representation. 7

3-2. Paradox: Self-Representation and Self-Membership

The problem of the Brentanian model lies the intuitive difficulty to understand the mechanisms underlying this capacity for self-representation. "What exactly is this capacity is supposed to amount to?" (Kriegel 2002, 526). How can two different mental contents be carried by one and the same mental state? In other words, one mental state is one, but at the same time not one. I restructure this problem in the framework of belongingness and mutuality. Namely, two different mental contents (seeing a thing and seeing oneself) belong together to one mental state. This unitary mental state represents a process itself as a whole, not two separate processes combined together.

More precisely, seeing oneself in this process means seeing oneself seeing a thing. Therefore, the two mental contents of seeing a thing and seeing oneself should be reformulated as "seeing oneself seeing a thing." In this context, the problem seems to be focused upon "seeing oneself," because the "oneself" that is seen includes not only the self but also the self's act of seeing at the same time. This is the core problem of self-representation: How can one represent oneself? In other words, how can one be the observer and the observed at the same time? This observed self is the observer of a thing and itself at the same time. The core of this problem is the problem of self-membership. How can one be the container and the member at the same time? I attempt to suggest a way to logically comprehend this structure of self-representation or resolve this paradox by applying knot-logic by Louis Kauffman and present a new model which is knot-7 Knotted models applied to Brentano's models are to be presented in a separate paper with a detailed explanation of the related knot logic.

shaped. This is a paradox, because two different mental contents are presented by one and the same state. They are different yet the same. This paradox can be resolved in a knotted model.

For example, here is a modified model of the Brentanian one with a twist which creates a knot link on it 8 .

Figure 7

Or, one can present the same model as below as well:

Figure 8 8 The knot link logic is to be also discussed in another paper along with the logic of belongingness.

The crucial point of this model lies in the loop. This is one seamless ring that is twisted once in the middle. This twist creates a crossing on the ring. At this crossing, this one ring becomes two.

The line that goes on the top and the line that goes on the bottom at the crossing are still the same ring. In other words, at each crossing a membership relationship is created. Membership is indicated by the diagram shown below (Kauffman 1995, 33).

Figure 9

Here, Kauffman shows that 'a' belongs9 to 'b' (a ↋ b). The arc 'b' is unbroken, while the arc 'a' is broken. "Following the pictorial convention of illustrating one arc passing behind another by putting a break in the arc that passes behind one, one says that a passes under b" (Kauffman 1995, 33). At the crossing, in both Figure 7 and 8, this membership relationship is created by a loop, but note that it is still one single ring. Therefore, in the above models, S 1 and S 2 belong together.

Let's say one walks on this twisted ring. At the crossing, one who started walking on the S 1 side could see oneself on the other side S 2 which is either above or under where one stands. Here a transformation of the status of the one who walks on the ring happens: one goes from an observer to the observed, i.e. the container becoming the member.

What is significant about Figure 7 and the Figure 8 is that in these models, S 1 and S 2 are different and identical at the same time. In other words, the two different states S 1 and S 2 are wrapped up in and indicate a single mental act. Both figures, Figure 7 and 8, are a single ring but with a twist that creates a self-mutual relationship within itself.

In this model, the first order state (seeing a purple cube) and the second order state (seeing myself seeing a purple cube) can appear to be conscious at the same time, i.e. belong together in the same (identical) consciousness, yet they are two different stages of a conscious act. 10 This solution can explain the belongingness of the different layers of mental states that are temporally separated as in Figure 3 andFigure 4.

One More Representational Attempt by Kriegel

Kriegel also presents a new model to overcome the difficulty of the Brentanian model. Namely, he attempts to find a model where a PSA-involving experience involves a conscious representation of the self without representing itself. He suggests a three-step psychological process model. "A three-step psychological process takes place in the subject. First, there is a non-conscious purely sensory reaction, S 1 which registers the presence of a purple cube. Second, the occurrence of S 1 brings about a second-order state, S 2 , which represents the occurrence of S 1 in the subject. Third, S 2 also comes to represent the purple cube itself. At this stage, then, S 2 represents both that there is a purple cube and that one is, oneself, seeing the purple cube, but without representing itself. S 2 is the PSA-involving conscious experience" (Kriegel 2002, 527).

See the following figure .   10 Kauffman approaches Russell's paradox from a different point of view with this logic of self-membership: Let R be the set that contains all the sets that do not include themselves. If R contains itself, R does not include itself, but if R does not include itself, R should be a member of itself. S 1 and S 2 are different yet the same. We can resolve this paradox in the domain by having every set as a member of itself and not a member of itself (Kim forthcoming, see also Kauffman 1995, 40), which is visually represented on the loop created by a twist on a ring. Russell's paradox becomes meaningful in the knot set domain (Kauffman 1995, 39) in the framework of membership and belongingness discourse. This is valid in the discussion of knot set theory as a radical variant of a set theory. I elaborate this logic more specifically in "An Application of Kauffman's Knot Logic to the Brentanian Model of Permanent Self-Awareness" (Kim).

Figure 10 11

Concerning the difference between PSA and introspective awareness, he suggests that "we can avail ourselves of the Brentanian notions of primary and secondary content. When the primary content of S 2 is the external cube, S 2 involves only PSA; when its primary content is the internal cube sensation, S 2 constitutes introspective awareness" (Kriegel 2002, 527).

In effect, the knotted model with one crossing resolves the paradox of self-representation by having two different mental states belonging to each other, i.e. a unitary mental process.

However, this knotted model still suffers another shortcoming. Namely, it is only two-fold, which is again problematic, because only the self-mutuality of the observing and the observed self is represented by this model. Which means, this model is not based on the necessary relationship between the process of seeing oneself and the process of seeing a thing. In other words, one can be aware of oneself without seeing a thing at the same time. The two-fold knotted model is good enough for representing the relationship between the observing self and the observed self, but it is not enough for representing the observation of an external object (purple cube) necessarily included in the process of self-awareness. In other words, the two-fold models are good for representing self-awareness but not a PSA-involving conscious experience.

The whole point of the permanent self-awareness lies in that one is permanently aware of oneself when seeing an object that is not myself (or the othered self). The key point is that these models are supposed to show the necessary relationship between the process of seeing a thing and the process of seeing myself seeing it.

Trefoil Knot Model of Consciousness I

Kriegel's model of a three-step psychological process could be a basis for a more advanced knotted model of a conscious experience. A simple self-membership created by a loop on a ring is applied to knot-models in order to help us comprehend the self-mutual and mutual 11 "Figure 6. One more model of permanent self-awareness" (Kriegel 2002, 528). membership relationship of knots. The trifold relationship between the states in Kriegel's One more model of permanent self-awareness could be represented in a trefoil knot model.

When I see a thing: (a) A thing is sensed (as a non-conscious sensory reaction).

(b) I see the sensed thing (represented in my consciousness).

(c) I see myself seeing a thing. This is a three-fold process. Kriegel's three-step psychological process model (figure 10) is the representation of these three steps. And this is one process, i.e. one mental act. In other wordsin the sense of knot logicthey belong together to one mental state. This model includes the moment of 'seeing a thing' in its process. The problem of this model, however, as with the previous models, is that this model does not present the self-mutual relationship between the self as the observer, the self as the observed, and the process between these two othered selves. The self-mutuality means that it is in fact one and the same self. As mentioned above, the two-fold knot models with one crossing in the middle show the relationship between the observing and the observed self, but not the process12 nor the othered self while seeing an object. The defect of the earlier presented knotted models with one loop was that they had only two differentiated sides in one complete structure. We need three. This is where we can think of a trefoil knot.

A trefoil knot is the simplest example of a nontrivial knot, which means that it is not possible to untie this knot in three dimensions without cutting it. It is one and the same ring. As the name of the knot indicates, this knot has three differentiated sides. Compare it to the above-presented knots with one twist with two differentiated sides (see figure 7,8). These three steps do not happen one by one after one another in a temporal sequence, but rather happen all at once when I see a thing. Therefore, this can represent the complete inner-structure of the conscious act of seeing a thing. When I see a thing, it's not only a thing that I see, but it's a thing and myself at the same time that I see. Here, one twist wouldn't do anymore, we need more than one crossing to include all three steps in one process. The three-step psychological process could fit the trifold structure of a trefoil knot, because these three different steps have to belong together, and the model needs to be able to show the self-mutuality of the different steps.

So, here is a trefoil knot: Figure 12 "This shows the self-mutuality, because a trefoil knot consists of one seamless ring. Therefore, a trefoil knot represents a stable self-mutuality in three loops about itself: a = {a}" (Kim forthcoming). The self-mutual relationship at each crossing are as appears in the following table (Kim forthcoming):

Crossing Belongingness Α A Є A A = {A} Β A Є A A = {A} Γ A Є A A = {A}
form a single mental actperception of a purple cube. All three steps belong to one process in a trefoil knot. Therefore, the model (Figure 10) could be modified with a trefoil knot as below: 1) The first step of the three-step psychological process as a purely sensory reaction is not conscious yet, therefore, it is questionable if this stage could be included in this consciousness model.

2) Without the first step as a purely sensory reaction, this model does not differentiate itself much from the Brentanian model. This means that a one loop knot model would still do for this three-step process model.

3) Therefore, this model does not seem to overcome the shortcoming of the previous models, which do not show the structure and the necessary relationship of the observing and the observed self.

Instead, I suggest another three-step process:

(a′) I see a thing.

(b′) I see(know) that I see a thing.

(c′) I see(know) that I see(know) that I see a thing. One might still ask whether the stage (c′) is not superfluous. No, it is not. This step (c′) is what brings about the trifold structure. This step is the binder 14 of the other two steps (a′) and (b′) and represents the understanding of the whole process as a whole. The three steps on each arc of a trefoil knot are the different states of one act, but note that this is one and the same act, as a trefoil knot is one seamless ring.

Figure 16

14 As the ultimate glue! Der Ursprung der Einheit des Prozesses.

20

When I see that I see a thing, the I who is observed by the first I is the observer of the thing that is observed. The point where these two states, "I see myself" and "I see a thing" is bound and therefore becomes one process, is the second I, who is observed by the first I and observing an object at the same time. The (c′) manifests the moment of seeing this process. Therefore, (c′)

represents the act of observation itself.

Figure 17

In fact, this trifold structure manifests the inner structure of self. Let me reformulate the threestep process as following: let's say that I is the observing self, I′ is the observed self, and O is a thing (object). The arrow (→) represents the act of seeing. This featurethe inner structure of selfwas not captured in the previous PSA models, which enables (justifies) the self-representational process of PSA in a trifold structure. The trefoil knot model not only represents its trifold structure, but also reveals16 the structure of self within itself.

Conclusion

The logic of mutuality and self-mutuality in the trefoil knot enables the visualization of the fundamental inter-relations of a subject's conscious experience of self and others and their structure. This explains how we can be aware of myself and others at the same time. Conscious experience is possible through an interaction of the perception of self and the perception of notself (including other objects and observed self). This double perception occurs simultaneously.

*Reference

Kim, Hye Young. Forthcoming. "A Topological Analysis of Space-Time-Consciousness: Self, Self-Self, Self-Other." When Form Becomes Substance. Power of Gesture, Grammatical Intuition and Phenomenology of Space, Basel: Birkhäuser-Springer.

  (a) Self (the observing) = Self (the observed) (b) Self (the observing) ≠ Self (the observed) *(a) and (b) are the same and different at the same time.

  Figure 1 1

Figure 2 1"

 2 Figure 2

Figure 3 3

 3 Figure 3 3

Figure 4

 4 Figure 4

Figure 6 6

 6 Figure 6 6

Figure 11

 11 Figure 11

Figure 13

 13 Figure 13

Figure 14 6.

 14 Figure 14

Figure 15

 15 Figure 15

  Figure 18 15

  Kim, Hye Young. An Application of Kauffman's Knot Logic to the Brentanian Model of Permanent Self-Awareness (unpublished). Kauffman, L. (1995) Knot Logic. in Kauffman, L (ed.) Knots and Applications. Series on Knots and Everything Vol. 6. Singapore: World Scientific. Kriegel, U. (2002) Consciousness, Permanent Self-Awareness, and Higher-Order Monitoring. Dialogue. XLI. pp. 517-40.

"Figure 2. Introspective awareness in the HOT model" (Kriegel 2002, 522).

The notion of belongingness in knot logic is to be discussed in a detailed manner in a separate paper, "An Application of Kauffman's Knot Logic to the Brentanian Model of Permanent Self-Awareness."

"Permanent self-awareness in Brentano's model"(Kriegel 2002, 525).

"Figure 4. Introspective awareness in Brentano's model" (Kriegel 2002, 525).

This notion of belongingness is used in the domain of the knot set theory (seeKauffman 1995).

The act of seeing an object

The differentiation refers not only to the differentiation of the observing self from the observed self, but also the differentiation of the self from the not-self, i.e. the observed external object.

By "reveal" I mean, "makes visible, therefore, comprehensible."


L J Niccolai

L Debeffe

G Gonzalez

Ontogeny of personality in roe deer (Capreolus capreolus)

Personality is often described as individual differences that are consistent across time and context [1]. Numerous traits are often used to characterize personality, such as sociability, aggressiveness, exploration, boldness and neophobia [2]. The existence of personality in the animal kingdom is not yet admitted by the entire research community, and relatively few studies have investigated the ontogeny of personality [3]. This longitudinal study explored if roe deer (Capreolus capreolus) exhibited consistent individual differences (personality) in a neophobic situation, and if said personality evolved throughout the years (fawn to adulthood).

1/ We first hypothesized that roe deer would indeed exhibit consistent individual differences and confirm the existence of personality in this species.

2/ Secondly, we hypothesized that personality would stay consistent across time (both fawns and adults would show unique personality profiles).

The findings of our longitudinal study of the existence and ontogeny of personality in roe deer exposed to a novel object context show a time consistency of distinct behavioral profiles [4]. This experiment is part of a larger ongoing project as multiple cohorts are being tested at 1 and 3 years old both in novel object and isolation context at the CEFS. Roe deer behavior is thus being studied in different contexts and at different life stages which could bring us an answer on the existence and ontogeny of personality in this species.

Behavioral profiles

Behavioral tendencies : comparison at 1 and 3 years old.

▪ Axis 2 captures individuals' activity, opposing reactive individuals on its positive pole (avoid stimulus, focus on feeding) and proactive individuals on its negative pole (actively seek to interact with object).

▪ Comparison showed that boldest and shyest behavioral profiles stayed consistent over time.

Results confirmed hypotheses as individual differences were found to be consistent across time (fawn to adult) and relevant behaviors to neophobia were repeatable. Our results suggest that roe deer have different behavioral profiles that are consistent in their lives in relation to their reaction to novelty.

▪ Repeatability (R = 0.276, 95% CI [0, 0.592], p = 0.008).

Materials and Methods

Introduction

Results and Discussion

Conclusion

▪ "Novel object" test : a novel object was placed in a familiar environment ▪ The behavior of six females was recorded using the "continuous recording" method for 5 minutes.

▪ Total of 42 videos (6 females, 7 sessions)

▪ Behavioral repertoire of 18 behaviors ▪ PCA (Principle Component Analysis) to visualize correlations between behaviors and identify potential profiles.

▪ Repeatability of relevant behaviors to neophobia.

Experimental setting Analyses

  Gardouch experimental station, INRA (National Agronomy Research Institute) near Toulouse, France. ▪ Comparison of cohort at 1 and 3 years old to show consistency in time.

Subjects 1 year old (2013) 3 years old (2015)

	Maïs	Bold -low feeding	Shy
	Mica	Shy	Shy
	Mollo	Shyest	Shyest
	Mousse	Shy	Bold -most vigilant
	Minnie	Shy	Bold
	Mylène	Boldest -low locomotion	Boldest -low feeding

Acknowledgements

Thanks to Professors Gilles Gheusi and Jean-Luc Durand. Special acknowledgement to the INRA and CEFS.

* laura.niccolai@yahoo.fr


Matthias Baessler

Md Delwar

Hossain Bhuyan

Falk Hille

Eva Viefhues

Michael Döhler

Laurent Mevel

Impact of environmental based effects on SHM strategies

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

INTRODUCTION

In Structural Health Monitoring (SHM) of civil engineering structures, the information value of the measured data is often limited by the effects of environmental characteristics. In this context, the structure's temperature driving parameters air temperature and solar radiation have the most significant influence.

Especially SHM methods for the identification of structural damage are prone to false alarms, when temperature affects the static and dynamic behavior in different ways or simply influence the measurement. In general, temperature-based effects on features indicating SHM damage are more significant than local structural damage in an early stage [START_REF] Farrar | Variability of modal parameters measured on the Alamosa Canyon bridge[END_REF][START_REF] Peeters | One-year monitoring of the Z24-Bridge: environmental effects versus damage events[END_REF][START_REF] Rohrmann | Structural Causes Of Temperature Affected Modal Data Of Civil Structures Obtained By Long Time Monitoring[END_REF]. For that reason, the environmental variability is a crucial issue for the practicability of SHM.

To eliminate the masking effect of temperaturebased variations on damage detection and localization procedures in SHM different approaches have been proposed in the last decades by the research community. Generally, two different approaches are pursued, first utilizing physical models to compute the effect of varying temperature on the structural response and second, statistical models to filter out the temperature induced perturbations on the monitoring data.

Physical model-based approaches are closely connected with the structural circumstances and described in several publications. [START_REF] Meruane | Structural damage assessment under varying temperature conditions[END_REF] developed a physical model-based damage detection procedure which employs a genetic algorithm for optimization to solve the inverse problem. They successfully tested the method on simulated and experimentally generated data of the steelconcrete composite I-40 bridge.

On the other hand, statistical methods are solely based on measurement data without using any geometrical or material information describing the behavior of the observed structure. To eliminate the effect of varying environmental perturbation in signals of damage indicating features, the data is processed utilizing statistical models.

At present, several methods utilizing different statistical models are developed and adapted by the SHM community. Generally, two different approaches can be distinguished, those including and those not including the measured environmental parameters into the statistical analysis. A general summary including simple regression based methods is given in [START_REF] Baeßler | A study on diverse strategies for discriminating environmental from damage based variations in monitoring data[END_REF].

In this paper an overview of the different physical as well as statistical model-based approaches is given, and two statistical algorithms are described. As a basis, firstly the influence of the several mechanisms of a relation between the temperature field in a structure and its response are addressed. Thereafter, the paper introduces physical model-based approaches for With the background of increasing affordability of sensing and computing technology, effort should be made to increase sensitivity, reliability and robustness of procedures, separating environmental from damage caused changes in SHM measures. The contribution describes an attempt to evaluate both general strategies, their advantages and drawbacks. In addition, two vibration monitoring procedures are introduced, allowing for temperature-based perturbations of the monitoring data. different structural issues. Based on simulated measurement data, the allowance of temperature-based variations on two subspace-based indicators for first, damage detection and second, damage localization is demonstrated in the paper. Namely, the robustness of the Stochastic Subspace-based Damage Detection (SSDD) [START_REF] Döhler | Subspace-based damage detection under changes in the ambient excitation statistics[END_REF][START_REF] Viefhues | Stochastic subspace-based damage detection with uncertainty in the reference null space[END_REF] and of the Statistical Stochastic Dynamic Damage Locating Vector method (S-SDDLV) [START_REF] Bhuyan | Statistical damage localization with stochastic load vectors using multiple mode sets[END_REF][START_REF] Döhler | Statistical decision making for damage localization with stochastic load vectors[END_REF] on varying temperature is increased by statistical model-based analysis.

PHYSICAL BEHAVIOR

Influences on the temperature field in bridge structures

To include the effect of temperature loading to the computation of structural responses it is necessary to account for the influencing thermal processes and principles. For determination of the temperature field in a structure, the heat transfer on the structures surfaces together with the boundary conditions by the surrounding environment is decisive. Heat transfer describes the exchange of thermal energy between the physical systems and consists out of the three general parts: conduction, convection and radiation. The heat transfer of a structure exposed to the natural atmosphere is dependent on the following influences: ambient air temperature, wind speed, rain, ice, humidity, global radiation of the sun (direct and diffuse radiation), reflection of the global radiation of the sun, atmospheric radiation, radiation of the environment and reflection of the radiation, heat radiation of the component as well as evaporation and condensation.

To determine the temperature field of a structure, the knowledge of the measured meteorological data in its characteristic course of the day and of the year as well as data of the thermo-physical material characteristics such as emission coefficients, thermal conductivity or specific heat capacity are necessary.

But even accounting for the general thermal parameters in the temperature field computation, especially for comparative studies one should be aware, that most of the processes are transient and thus two equal states of temperature distribution on a bridge structure are hardly feasible.

Thermal structural behavior

Table 1 summarizes the influence of seasonal changes on structural members with respect to its physical origin. (a) describes the well-known fact that bridges with asphalt layer react far stiffer in cold season than in summer. In general, if the material behavior of a homogeneous region itself is temperature-dependent, additional considerations are necessary to assess the effect of the temperature field. (b) addresses the seasonal impact on concrete structures truly affecting the capacity (c) [START_REF] Gonzales | Seasonal effects on the stiffness properties of a ballasted railway bridge[END_REF] investigated a ballasted concrete railway bridge in north Sweden and proved large dependencies of the dynamic response by the temperature variations in the ballast and the ground, especially during frost. (d) and (f) give examples for the impact of temperature on the support conditions. Finally, there is a possibility that slender members are affected by stress softening (or stiffening) (e).

Requirements on physical models

For design and structural assessment physical models are a relevant precondition to relate the structural response to a meaningful statement on the structure's behavior. Physical models verified from SHM results can be either used for the assessment of bearing capacity or the structures dynamic behavior:

-

Assessment of load bearing capacity

The aim of Structural Health Monitoring (SHM) is the measurement-based assessment of the load-bearing capacity of a structure.

N N

In detail that means to detect damage, to identify changes in load bearing capacity and to determine the safety level. It is essential to correctly evaluate temperature influences. Generally, the main challenge of a global state monitoring is the provision of an adequate sensitivity of the damage detection methodology for essential damage scenarios. Damages in their initial stage on robust structures as reinforced and prestressed bridges are normally not activated by existing traffic load. Accordingly, no changes in the stiffness ratios are detectable, and thus the damage cannot be detected by means of a measurement of global structural parameters based on the dynamic response. This situation must always be considered in planning monitoring systems for bridge structures. For a physical model-based monitoring of the structural state, a model in high quality is required to provide a connection between system identification and monitoring variables on the one hand and the related load-bearing evaluation on the other hand. For a typical reinforced concrete cross section, this also means that temperature dependent changes in the load bearing behavior must be assessed correctly. Figure 1 shows two cases: In case (1), the structure reacts stiffer due to the carrying effect of the asphalt layer. In terms of safety evaluation, however, this stiffness share is not taken into account. In case (2), the change in the load bearing behavior during crack formation, for example from temperature dependent constraints and inherent stresses, is shown. In the sense of safety assessment, this leads to a reduction of the load bearing capacity in the sense of stability assessment. Those distinctions are elementary for an evaluation. (Baeßler and Hille, -System identification for dynamic verification Measurements are carried out to identify a dynamic structural behavior. In the case of a dynamic structural analysis, there is no verification to the safer side, the dynamic behavior of the structure must be considered in its actual limits to take account of resonance effects, for example to verify the dynamic behavior of railway bridges during train crossing. Particularly, fatigue and the limitation of maximum acceleration amplitudes of the bridge deck are considerably dependent on modal parameters of the bridge structure.

Physical Testing

Data on temperature dependent physical behavior of building materials is rare [see e.g. [START_REF] Eisenmann | Beitrag zur Ermittlung der Werkstoffeigenschaften und des Verformungsverhaltens von bituminös gebundenen Straßendecken[END_REF][START_REF] Simonsen | Resilient properties of unbound road materials during seasonal frost conditions[END_REF][START_REF] Welsch | Zentrischer Temperaturzwang von Stahlbeton und Spannbeton bei Abkühlung auf sehr niedrige Temperaturen[END_REF]. The focus of interest is often restricted to extreme conditions like fire or severe frost conditions. A current research interest is a better understanding of the behavior at "normal" seasonal conditions. Furthermore the structural behavior is not universal (variability e.g. due to specific mixtures, fabrication, age). This leads to a second focus on the determination of site-specific characteristic values. For the various open questions a large climate chamber has been developed for further investigation (Figure 2). In that respect the scope of research is focused on the following topics: -Material level: characteristic values for stiffness and damping in correlation to temp. and humidity -Full specimen level: constraints and bonding and its impact on fracturing as well specific contact nonlinearities -Testing methods: Role of excitation; stationary or moving load. -Evaluation of site-specific properties -Damage detection and localization -Model updating for changing structural conditions although it has to be stretched, that research is ongoing.

STATISTICAL METHODS UTILIZING VIBRATION MONITORING

In addition to simple statistical tools using linear regression models for removing effects of environmental variations on the monitoring data we utilize statistical vibration-based damage diagnosis methods which provide the rejection of environmental influences as method inherent feature. On the common base of the stochastic subspace-related system description two different methods for damage diagnosis are introduced, both allowing for environmental perturbations.

Damage detection allowing for environmental perturbation

Statistical approaches are promising when it comes to damage diagnosis using temperature afflicted vibration data. In the stochastic subspace-based damage detection (SSDD) the careful choice of an adequate reference system enables the formulation of algorithms robust to temperature variation.

The basic idea of the method is to exploit a Hankel matrix ℋ, which contains the cross-covariances of the output signal at different time steps in the reference state. For its left null space S it holds 𝑆 𝑇 ℋ= 0. By definition, ℋ depends on the system matrices of the state-space representation of the dynamical system, namely the state transition matrix A and the observation matrix C. Therefore, changes in the dynamical system will result in a change of ℋ. In the monitoring state, S is confronted to ℋ in a data-based residual vector 𝜁 = √𝑁 vec(𝑆 𝑇 ℋ) .

(1)

ℋis built from data in the monitoring state. The value of the residual will be different from 0, if H has changed significantly. This is tested statistically in a hypothesis testing framework. From test values in the undamaged case a threshold is computed. If the test value in the monitoring state exceeds the threshold a damage is detected.

In the context of temperature rejection, the challenge is, to choose a good reference system, to enable a proper threshold, which enables high probability of detection but few false alarms. Three approaches will be introduced shortly.

A simple temperature rejection approach is proposed in [START_REF] Balmès | Merging Sensor Data from Multiple Temperature Scenarios for Vibration Monitoring of Civil Structures[END_REF]. The reference null space and the residual covariance for the hypothesis tests are computed on an averaged Hankel matrix in the reference state. The averaged Hankel matrix is obtained from a big data set 𝑌 ̅ = [𝑌 1 𝑌 2 ⋯ 𝑌 𝑚 ] merged from 𝑌 𝑗 = [ 𝑦 1,𝑗 𝑦 2,𝑗 ⋯ 𝑦 𝑁,𝑗] at j = 1, …, m different reference temperatures Tj . The whole test can be performed without any information about the reference temperatures.

If temperature measurement information is taken into account, a reference system can be computed piecewise for a specific temperature range, as proposed e.g. in [START_REF] Fritzen | Elimination of temperature effects on damage detec-tion within a smart structure concept[END_REF]. The reference null space matrices Sj and corresponding covariances Σ ℋ 𝑗 are estimated on reference data Yj at a reference temperature Tj . In the monitoring state, the nearest reference null space with respect to the current testing temperature is used for the damage diagnosis.

In another approach presented in [START_REF] Viefhues | Subspace-based Damage Detection with Rejection of the Temperature Effect and Uncertainty in the Reference[END_REF] the reference null space and the residual covariance are based on an interpolation step. An interpolated Hankel matrix

ℋ(𝑇) = ∑ 𝜌 𝑗 2 𝑚 𝑗=1 (𝑇)ℋ 𝑗 (2)
for the testing temperature T with bell-shaped weighting functions 𝜌 𝑗 (𝑇) leads to the null space matrix 𝑆(𝑇) and the corresponding covariance of the interpolated Hankel matrix

Σ ℋ (𝑇) = ∑ 𝜌 𝑗 4 𝑚 𝑗=1 (𝑇)Σ ℋ 𝑗 .
(3) Figure 3 shows the undamaged and damaged test values at different testing temperatures for the three temperature rejection approaches. For an 8-mass-spring damper the temperature variations were simulated as stiffness increasing (lower temperatures) or reduction (higher temperatures). 5 reference temperatures are considered. A global damage is modeled as stiffness reduction of 2% at every element. With the average and the piecewise method, it will be impossible to find a good threshold for damage detection, as the test values in the damaged state sometimes exceed the undamaged values and sometimes fall below them. The approaches are not able to decide if temperature or damage affected the stiffness of the system, as they do not consider the right reference system for the specific testing temperature. The interpolation method, however, can provide a proper reference system for each testing temperature. This results in a clear shift of the test values in case of damage and thus enables a definition of a threshold for damage detection.

Damage Localization allowing for environmental perturbation

In a second development, the statistical extension of the Stochastic Dynamic Damage Locating Vector (S-SDDLV) approach has been utilized [START_REF] Bhuyan | Statistical damage localization with stochastic load vectors using multiple mode sets[END_REF][START_REF] Döhler | Statistical decision making for damage localization with stochastic load vectors[END_REF]. The SDDLV is an outputonly damage localization method based on both a finite element model of a structure and modal parameters estimated from output-only measurements in the reference and damaged states. A statistical version of the approach takes into account the inherent uncertainty due to noisy measurement data. Therefore, the effect of temperature variations on the performance of the method is analyzed in a model-based approach using a finite element model with temperature dependent parameters. For robust damage localization, the temperature effect on the identified modal parameters in the damaged state is rejected by sensitivity analysis.

Numerical application: Beam model

The method is applied on a simulated structure as shown in Figure 4 with temperature dependent parameters [START_REF] Gautier | An experimental setup for subspace based damage identification methods[END_REF]. The structure is modeled with 4 main beam elements of length 1m. The mass density, Young modulus and Poisson ratio are 7800 kg/m3, 70 GPa (at 20°C) and 0.33, respectively. In the Finite Element (FE) model, each main beam element is discretized into 5 small elements and hence, the total number of elements is 30, and the number of degrees of freedom of the structure is 180.

Damping is defined such that the damping ratio of all modes is 0.2 %. Note that the damaged position is modeled at elements 12-14 (1.45 m from left end) by decreasing 30 % stiffness loss. For the damaged and undamaged states, the acceleration data length for each simulated set is N = 100,000, generated from collocated white noise excitation using four sensors in the Y-direction at 0.43 m, 1.49 m, 2.49 m, and 3.47 m from the left support end with a sampling frequency of 2000 Hz, and 5 % white noise was added to the output data.

After applying a heat source at element 17, the temperature field is computed at the elements of the finite element model. Their stiffness is then computed from the obtained temperatures and used for the data simulation for different magnitudes of the heat flux. Moreover, Figure 5 shows that how the first modal frequency is varying in terms of increasing heat flux for both healthy and damaged states.

Figure 5. Temperature effect on the first modal frequency for both healthy and damaged states. Damaged at elements 12, 13 and 14 (30% stiffness loss).

Performance evaluation of damage localization with and without temperature rejection

To analyze the performance of the SDDLV method under temperature variation, the success rate (or probability) of damage localization is evaluated for 100 sets of simulated measurement data in a Monte Carlo experiment. In order to make decision if an element is potentially damaged or not, the 𝜒 𝑡 2 value is tested for each structural element. For each Monte Carlo realization, damage localization is seen as successful when the smallest 𝜒 𝑡 2 value among all elements is indeed at the damaged element, and the success rate is the percentage of realizations for which the 𝜒 𝑡 2 value at the damaged element is the smallest 𝜒 𝑡 2 value. The success rate depends on the chosen value for Laplace variable s and serves as the performance indicator for the method. Notice that the generation of several datasets allows the evaluation of the success rate, while usually only one dataset is available.

In Figure 6, the mean of the success rates of damage localization (e.g. both estimated stress and its statistical evaluation) for values of Laplace variable s with Im(s) = 100, 150, ... ,1300 are shown in dependence of the heat flux in the damaged state with and without the temperature rejection approach. Without using rejecting the temperature effect, it is seen that the success rate decreases when the heat flux increases, since no heat flux is present in the healthy state. The performance of the localization results is significantly improved by using the temperature rejection strategy. Considering temperature rejection, figure shows that the success rate is constantly high and nearly independent of the heat flux.

CONCLUSIONS

As basis, a review on relevant case studies and methods was conducted. The aim of the study is to classify the specific problems and to outline briefly SHM strategies for environmental based perturbations.

Secondly, a summary is given on the physical behavior of bridge structures and its components based on material testing. Better knowledge of material behavior affected by environmental conditions like temperature distribution and humidity is generally seen as crucial for assessment strategies for the loading bearing behavior of bridges.

On the common base of the stochastic subspacerelated system description three different methods for damage diagnosis are introduced. Especially the algorithm, where the reference null space and the residual covariance are based on an interpolation step shows promising results in eliminating environmental perturbations.

With the Stochastic Dynamic Damage Locating Vector (SDDLV) method another statistical approach is introduced. This vibrational damage localization method is based on a finite element model of a structure as well as output-only measurements in both reference and damaged states. In simulations the effect of the temperature rejection could be shown.

Table 1 .

 1 Temperature influence on structural components. a) Asphalt layer: strong dependency of stiffness on temperature b) Reinforced and prestressed concrete: stiffness can vary for E depends on temperature and humidity and cracks or coupling joints might open with temperature c) Ballasted Track: stiffness changes with temperature d) Structure soil interaction: stiffness at columns and at abutments can be frost dependent e) Axial forces: for constrained slender structures, axial forces and vibration modes are coupled f) Bearings: typical bearing materials can behave temperature dependent 3 METHODS BASED ON PHYSICAL MODELS

Figure 1 .

 1 Figure 1. Stiffness changes with different relevance for structural safety.

Figure 2 .

 2 Figure 2. Climate chamber [temperature -40°C up to 60°C; variable humidity 10% to 80%].

Figure 3 .

 3 Figure 3. Test values in undamaged and damaged case for different temperature rejection approaches.

Figure 4 .

 4 Figure 4. 3D Model with 30 beam elements.

Figure 6 .

 6 Figure 6. With/without temperature rejection: Success rates of damage localization for different heat flux. Damaged elements are 12, 13 and 14.

  Impact of environmental based effects on SHM strategies M. Baeßler, D. Bhuyan, F. Hille & E. Viefhues Bundesanstalt für Materialforschung und -prüfung, Berlin, Germany M. Döhler & L. Mevel Inria, Ifsttar, Univ. Rennes, Rennes, France ABSTRACT: Environmental based perturbations influence significantly the ability to identify structural damage in Structural Health Monitoring. Strategies are needed to classify such effects and consider them appropriately in SHM. It has to be considered if seasonal effects just mask the structural response or if temperature itself correlates to a weakening of the structure. Various methods have been developed and analyzed to separate environmental based effects from damage induced changes in the measures. Generally, two main approaches have emerged from research activity in this fields: (a) statistics-based tools analyzing patterns in the data or in computed parameters and (b) methods, utilizing the structural model of the bridge considering environmental as well as damage-based changes of stiffness values.


Alexia Carrizales
email: alexia.carrizales@u-bordeaux.fr

Cyrille Perchec

Lyda Lannegrand-Willems

Brief report: How many dimensions in the prosocial behavior scale? Psychometric investigation in Frenchspeaking adolescents

Keywords: prosocial behavior, adolescence, confirmatory factor analysis, measurement invariance

The purpose of the study was to evaluate the factor structure and the reliability of the Prosocial Behavior Scale (PBS). To our knowledge, no factorial validity of the multifactorial structure of PBS has been published to date. The psychometric characteristics of the PBS were examined in several samples of French adolescents (aged 11-19, N1 = 1141, N2 = 1071, and N3 = 1640) using Confirmatory factor analyses (CFA). The original four-factor structure was not confirmed due to lack of discriminant validity. CFA led us to retain a two-factor solution with a good fit and a satisfactory reliability. Furthermore, the results support the convergent validity of the PBS: helping and caring dimensions were positively correlated with empathy. In addition, partial measurement invariance across gender and grade was attested. In conclusion, the results indicate that the French version of the PBS is a useful instrument for the assessment of prosocial behaviors in adolescence.

Research on the development and correlates of prosocial behaviors (i.e., behaviors intended to benefit others) has been an active field of study for the last three decades. Prosocial behaviors have been theoretically and empirically linked to a variety of positive cognitive, socioemotional and psychological outcomes for personal and social adjustment during adolescence [START_REF] Alessandri | Prosociality during the transition from late adolescence to young adulthood: The role of effortful control and ego-resiliency[END_REF][START_REF] Gregory | Behavioral genetic analyses of prosocial behavior in adolescents[END_REF]. Although the importance of understanding behaviors that benefit society has been highlighted, surprisingly few measures are available, and none in French for evaluating prosocial behaviors.

While some measures do exist, they are typically characterized by a conceptualization of prosocial behaviors as a unidimensional global construct [START_REF] Ladd | The child behavior scale: A teacher-report measure of young children's aggressive, withdrawn, and prosocial behaviors[END_REF][START_REF] Rushton | The altruistic personality and the self-report altruism scale[END_REF]. However, the developmental literature has shown different types of prosocial behaviors to be associated differently with other psychological constructs [START_REF] Batson | Altruism and prosocial behavior[END_REF][START_REF] Padilla-Walker | Prosocial development: A multidimensional approach[END_REF]. For example, prosocialness is primarily expressed in the actions of helping, sharing, taking care of, and feeling empathic with others. [START_REF] Caprara | A new scale for measuring adults' prosocialness[END_REF] proposed a new scale for measuring these four behavioral expressions of prosocialness. Its properties were examined using an item response theory (IRT) approach. Specifically, unidimensional IRT models were used; hence, the multifactorial structure was not tested. To our knowledge, the factorial validity of the multifactorial structure has not been assessed to date. Moreover, it has mainly been used with late adolescents and emerging adults (college students). However, from early -middle to late adolescence, we consider that the socialization experiences and cognitive abilities may lead to changes in the internalization of culturally related values and in prosocial behaviors [START_REF] Calderón-Tena | The socialization of prosocial behavioral tendencies among Mexican American adolescents: The role of familism values[END_REF]. Therefore, studies focusing on early-to-late adolescence should be conducted.

The aim of our study was to investigate whether the factor structure of the Prosocial Behaviors Scale (PBS) identified by Caprara and colleagues (2005) in adults would be the same in a French sample of early and late adolescents. To this end, we proceeded by translating and assessing the factorial validity, reliability, convergent validity (with empathy), and measurement invariance of the French PBS.

Method

Participants

Three independent samples were used for the analyses, Sample 1 (N = 1141, M age = 14.35, SD = 1.69) and Sample 2 (N = 1071, M age = 15.19, SD = 2.27) used in the EFA analyses and Sample 3 (N = 1640, M age = 14.58, SD = 1.88) used in the CFA analyses. Specifically, participants from Sample 3 came from an ongoing longitudinal study. They were divided into two groups based on educational grade. The first one included 867 junior high school adolescents (grade 6-9, 51% females, M age = 13.11; SD = 1.17) and the second one included 773 high school adolescents (grade 10-12, 43% females, M age = 16.22; SD = .93). The data are a nationally representative sample of adolescents in Secondary school: 84.39% were from public schools and 15.61% from private ones, 47.07% were from High School including 21.35% vocational education. Adolescents reported on the highest education level obtained by either parent, there were as follows: 34% Master level, 26% Bachelor's level, 18% upper secondary general education, 14% upper secondary vocational education, 3% lower secondary education, 5% primary education. Parents were informed of the study and provided consent. Students completed self-report questionnaires during lesson time, with one hour reserved for completion. They were informed that participation was voluntary and that their responses were anonymous.

Measures

The PBS [START_REF] Caprara | A new scale for measuring adults' prosocialness[END_REF] is a 16-item questionnaire rated on a 5-point Likert scale ranging from 1 (never/almost never true) to 5 (almost always/always true) that assesses four types of prosocial behaviors (sharing, helping, taking care of, and feeling empathic; 4 items per dimension). The translation from English to French by three independent researchers was made according to the recommendations of the International Test Commission [START_REF] Hambleton | The next generation of the ITC test translation and adaptation guidelines[END_REF].

The Basic Empathy Scale (BES) is a 20-item questionnaire rated on a 5-point Likert scale ranging from 1 (strongly disagree) to 5 (strongly agree) developed by [START_REF] Jolliffe | Development and validation of the basic empathy scale[END_REF] and adapted in French by [START_REF] Carré | The basic empathy scale in adults (BES-A): Factor structure of a revised form[END_REF]. It includes three dimensions: emotional contagion (6 items), cognitive empathy (8 items) and emotional disconnection (6 items). Its internal consistency was satisfactory in our sample (see Table 3).

Analytic strategy

Three sets of analyses were performed: (1) CFA for testing the original factor using Sample 1, (2) EFA for investigating the factor structure using Sample 2 and (3) CFA for testing the two-factor solution obtained by EFA using Sample 3 and Convergent Validity. In order to account for the ordered -categorical nature of the scale items, Weighted Least Square Means-Variance (WLSMV) and theta parameterization (for multiple group models) were performed using Mplus 7.3.

In total, missing data ranged from 0 to 3.75% across all samples. No missing data in Sample 1, 3.75% in Sample 2 and 3.72% in Sample 3. The percentage of missing values across the prosocial behaviors and empathy variables ranged between .57 and 6.63% in Sample 2 and .26 and 4.75% in Sample 3. In order to deal with the missing data, the WLSMV Multiple Imputations procedures were applied [START_REF] Asparouhov | Weighted least squares estimation with missing data[END_REF].

Exploratory factor analysis (EFA) and factor analyses replication were performed using Sample 2. Concerning the EFA, the factor retention methods used included scree test and Velicer's MAP criteria [START_REF] Velicer | Component analysis versus common factor analysis: Some further observations[END_REF]) using an oblique rotation. For the factor analyses replication, internal replicability analyses were performed, data was randomly split, and the same number of factors were extracted using the same rotation (Geomin) and extraction procedures in order to compare standardized factor loadings [START_REF] Osborne | replication analysis in exploratory factor analysis: What it is and why it makes your analysis better[END_REF].

Measurement Invariance across gender and grade through a series of multiple group models with progressively more stringent constraints were performed using Sample 3. A more constrained solution was rejected when: (a) the chi-square difference test (Δχ²) had a probability lower than .05 1 [START_REF] Byrne | Testing for measurement and structural equivalence in large-scale cross-cultural studies: Addressing the issue of nonequivalence[END_REF], (b) the decrease in the Comparative Fit Index criterion (ΔCFI) was higher than .01 2 [START_REF] Cheung | Evaluating goodness-of-fit indexes for testing measurement invariance[END_REF][START_REF] Vandenberg | A review and synthesis of the measurement invariance literature: Suggestions, practices, and recommendations for organizational research[END_REF], (c) an increase in ΔRMSEA was higher than .015, indicating non-invariant loadings, thresholds or residuals [START_REF] Chen | Sensitivity of goodness of fit indexes to lack of measurement invariance[END_REF].

Results

CFA for testing the original four factor structure

Confirmatory factor analyses of the original four factor structure yielded an acceptable fit χ² = 1026.661 (98), p < .001, RMSEA = .076 [.072-.080], CFI = .93 and WRMR = 1.920. The main concern of this original structure is the high factor correlations among latent variables (r = . 87 and .86, respectively). Taking into consideration items similar wording and modification indices, 3 error covariances were added. Model fit was χ² = 806.488 (95), p < .001, RMSEA = .068 [.036-.072], CFI = .95 and WRMR = 1.687. Although a better fit was achieved, this resulted in an inflated estimate of the factors correlations (all above .85). In light of these issues, we decided to test a second -order model, this lead to an inadmissible parameter solution. Despite the good model fit, the discriminant validity is too low to accept the four-factor solution [START_REF] Brown | Confirmatory factor analysis for applied research[END_REF].

EFA for investigating the factor structure

Taking into account the exploratory factor analyses factor retention results and internal replicability analyses, we report the two-factor solution which provided much more statistically and theoretically coherent and interpretable factors than did the other solutions. EFA replicability suggested that 2 items (2, 11) failed to meet the initial criteria, i.e., the structural replication 3 ; these two items were removed from further analyses. 1 owing to the Wlsmv estimator used here, the change in χ² and degrees of freedom cannot be calculated in a straightforward fashion. "the difference in chi-square values for two nested models using the […] Wlsmv chi-square values is not distributed as chi-square" (muthén & muthén, 2017). therefore, a scaling correction (DIfftEst function) is used, of which only the p-value should be interpreted.

2 the Δχ² and ΔcfI may sometimes suggest different conclusions. clear rules on how to proceed in such a situation are lacking [START_REF] Byrne | Testing for measurement and structural equivalence in large-scale cross-cultural studies: Addressing the issue of nonequivalence[END_REF]. researchers can opt to describe the conclusions of both approaches or choose one over the other, based on the admissibility of the solution and examination of the modification indices.

3 specifically, looking at the factor loadings, item 2 "I share what I like with my friends" has the highest factor loading on factor #2 in the first analysis and on factor #1 in the second analysis; and item 11 "I easily lend money or other things" has the highest factor loading on factor #1 in the first analysis and on factor #2 in the second analysis. all other items have their strongest loading on congruent factors, so if we delete these two items, we would say that the factor structure of the scale meets the basic level of replication. the next step was to look at the squared differences in the factor loadings; these were within reasonable range (.0000-.0324), indicating that the largest difference between the standardized factor loadings is |.18|.

CFA for testing the two factor structure and Convergent validity

Confirmatory Factor Analyses using Sample 3 for testing the two-factor structure obtained by EFA was performed; due to similar wording and underlying motivation, three error covariances were added (see Table 1). This two factor-solution had an acceptable discriminant validity (see Table 3). This solution was tested to be invariant across gender and grade. The results confirmed partial measurement invariance for the two-factor model. All factor loadings (except notes: χ² = chi-square; df = degrees of freedom; rmsEa = root mean square Error of approximation; cI = confidence Interval; Wrmr = Weighted root mean square residual; cfI = comparative fit Index; tlI = tucker lewis Index. cov. Error = errors of items 1 and3, 8 and5, 12 and8 item 6 across grade) proved to be invariant over gender and grade, and since at least two items for which all thresholds were invariant [START_REF] Steinmetz | Testing measurement invariance using multigroup CFA: Differences between educational groups in human values measurement[END_REF], meaningful latent mean comparison using the partially invariant factor are still possible, as it was suggested by [START_REF] Byrne | Testing for the equivalence of factor covariance and mean structures: The issue of partial measurement invariance[END_REF] that it "makes substantive sense to do so" (p. 465). Fit indices are shown in Table 2. We labeled the first factor "Helping" (6 items; items 1, 3, 4, 6, 7, and 9) on which people who scored high reported being helpful and sharing with others. We labeled the second factor "Caring" (8 items; items 5, 8, 10, 12, 13, 14, 15, and 16) on which people who scored high were likely to feel responsibility for and concern about the welfare of others (see Supplementary material). The omega coefficients4 for the two dimensions were satisfactory and the two-factor solution did have an acceptable discriminant validity (see Table 3).

Convergent validity

Finally, we examined the convergent validity of the dimensions of the PBS and BES using CFA (i.e., latent correlations). The results revealed that Helping and Caring were positively associated to BES factors. The correlations between Caring and BES were higher than the correlations between Helping and BES (see Table 3). These results demonstrated convergent validity and were in line with those reported in the literature [START_REF] Eisenberg | Empathy-related responding: Associations with prosocial behavior, aggression, and intergroup relations[END_REF].

Discussion

In the present study, we investigated the psychometric properties of the French version of the PBS in a large age range sample covering early and late adolescence. First, we tested the original four-factor structure, but decided not to retain this structure due to low discriminant validity. Secondly, Replication Analysis in Exploratory Factor Analysis suggested a two-factor solution. Third, Confirmatory Factor Analyses showed that the two-factor model had a good fit. The internal consistency of Helping and Caring were good. In addition, Helping and Caring were positively associated with empathy dimensions. This is in concordance with previous studies that reported a positive link between these two constructs [START_REF] Eisenberg | Empathy-related responding: Associations with prosocial behavior, aggression, and intergroup relations[END_REF]. Finally, our findings of partial measurement invariance across gender and grade confirm the relevance of the two-factor solution.

Further investigations with other samples (e.g., emerging adults and adults) compared to adolescents are needed in order to test whether the two-factor model is the best one across age, or whether this structure in two dimensions of prosocial behaviors is specific to the period of adolescence. Indeed, several theories on the development of social cognition posit that during adolescence important steps forward are made in social perspective-taking [START_REF] Hoffman | Toward a comprehensive empathy-based theory of prosocial moral development[END_REF], thereby fostering prosocial behaviors [START_REF] Eisenberg | Prosocial development[END_REF]. Meanwhile, the capacities of internalized / self-reflective other-oriented modes of reasoning observed across the 20s and into the early 30s might lead to a finer distinction of different dimensions of prosocial behaviors [START_REF] Eisenberg | The development of prosocial moral reasoning and a prosocial orientation in young adulthood: Concurrent and longitudinal correlates[END_REF]. These considerations support our findings and other investigations across age from a developmental perspective.

Table 1 .

 1 fit indices for the different factor models of the pBs.

Table 2 .

 2 , are allowed to covary. multiple-group confirmatory factor analyses of the two-factor + 3 cov. error model for measurement and structure invariance across gender and grade (N = 1640). : χ² = chi-square; df = degrees of freedom; rmsEa = root mean square Error of approximation; cI = confidence Interval; Wrmr = Weighted root mean square residual; cfI = comparative fit Index. Δχ² = Delta chi-square; ΔcfI = Delta comparative, ΔrmsEa = change in rmsEa. fit Index. **p < .01. ***p < .001.

	Model		χ²	df	RMSEA [90 CI %]		WRMR	CFI	TLI
	two factor model		700.369 76	.071 [.066-.076]		1.74	.95	.94
	two factor model + 3 cov. errors	505.39	73	.060 [.055-.065]		1.46	.97	.96
								ΔRM-
	Model	χ² (df )	RMSEA [90% CI] WRMR CFI	Δχ² Δdf p ΔCFI	SEA
	MG-CFA Gender
	invariance m 1 . configural	609.69 (146) .062 [.057-.067] 1.65 .959	-	-	-	-
	invariance m 2 . metric	578.75 (158) .057 [.052-.062] 1.67 .963	9.63 12 .65	.004 .005
	invariance m 3 . scalar	677.61 (198) .054 [.050-.059] 1.92 .958 135.16 40 *** .005 .003
	scalar m 3a . partial	571.90 (182) .051 [.046-.056] 1.73 .966 31.25 24 .15	.003 .006
	invariance
	invariance m 4 . strict	691.08 (215) .052 [.048-.056] 2.02 .958 48.28 17 *** -.008 .001
	MG-CFA Grade
	invariance m 1 . configural	592.69 (146) .061 [.056-.066] 1.61 .965	-	-	-	-
	invariance m 2 . metric	584.49 (158) .057 [.052-.062] 1.67 .966 25.47 12 **	.001 .004
	iance (except m 2 . metric invar-	568.13 (157) .056 [.052-.062] 1.64 .967 13.75 11 .25	.001 .001
	Item 6)
	invariance m 3 . scalar	685.77 (198) .055 [.050-.059] 1.92 .961 137.98 40 *** .005 .002
	scalar m 3a . partial	569.29 (180) .051 [.047-.056] 1.72 .966 30.41 22 .11	.000 .006
	invariance
	invariance m 4 . strict	800.16 (215) .058 [.053-.062] 2.19 .954 243.83 35 *** -.007 .003

notes

Table 3 .

 3 Descriptive statistics and correlations between pBs and BEs dimensions.

	Measure	M	SD	ω s	2	3	4	5
	1. pBs -helping	3.47	.68	.79	.79*	.35*	.41*	.34*
	2. pBs -caring	3.58	.72	.81	-	.60*	.55*	.52*
	3. BEs -Emotional contagion	3.52	.82	.70		-	.68*	.54*
	4. BEs -cognitive empathy	3.93	.66	.74			-	.50*
	5. BEs -Emotional disconnection	3.73	.87	.80				-
	note: ω, = omega coefficient.
	*p < .0001.

open source software Jasp was used to calculate omega coefficients.

Disclosure statement

No potential conflict of interest was reported by the authors.


Static Hysteresis modelling of FeSi NO sheets in rolling and transverse directions Fabien SIXDENIER (1) , Riccardo SCORRETTI (1) Atef LEKDIM (2) ( 1) : Univ Lyon, Université Claude Bernard Lyon 1, INSA Lyon, ECLyon, CNRS, Ampère, F-69100, Villeurbanne, France (2) : LEM TECH FRANCE,575-655-LES ALLEES DU PARC,69800 SAINT PRIEST, France Context and objectives 1. predict magnetic losses or magnetic weveforms in NO FeSi sheets when excited in both rolling (RD) and transverse direction (TD). 2. Need for a vectorial hysteresis model 3. Modification of the vector play model [START_REF] Bergqvist | Magnetic vector hysteresis model with dry friction-like pinning[END_REF] improved by [START_REF] Fran¸ois-Lavet | Vectorial incremental nonconservative consistent hysteresis model[END_REF] Original isotropic Model

h = h re + h ir (1)
.

h re = N k=1 ω k h k re (2) h k re = h k re0 if ||h -h k re0 || < χ k h -χ k • h-h k re0 ||h-h k re0 || otherwise (3)
M = M an (||h re ||) • h re ||h re || (4) b = µ 0 (M + h) (5)
χ k : maximum pining field of the k th cell ω k : weight of the k th cell

χ h re = h re0 h h ir h re0 h re h |h ir | = χ

Modifications to include anisotropy

Modifications prosposed in [START_REF] Steentjes | Energy-based ferromagnetic material model with magnetic anisotropy[END_REF] to take into account magnetic anisotropy in FeSi NO sheets. 1. Modifications of the anhysteretic curve (4)

M = M an (||h re ||)G (γ) h re ||h re || (6)
with γ, a scalar parameter to identify

G (γ) h re ||h re || = 1 0 0 γ e RD e TD (7)
2. Modifications of the coercivity (pining field) by making cells ellipsoidal.

χ k (α, β) = χ k RD 1 + (β -1) 1 -α 2 (

Identification Results

the (ω k , χ k ) sets have been identified following the protocol described in [START_REF] Jacques | Representation of microstructural features and magnetic anisotropy of electrical steels in an energy-based vector hysteresis model[END_REF]. identification of first cells following [START_REF] Jacques | Representation of microstructural features and magnetic anisotropy of electrical steels in an energy-based vector hysteresis model[END_REF] may be inaccurate. Following [START_REF] Sixdenier | Numerical model of static hysteresis taking into account temperature[END_REF] can improve accuracy in this region as recently shown in [START_REF] Roberta Longhitano | Comparison of identification protocols of a static hysteresis model[END_REF]. Proposed modifications are sufficient to qualitatively take into account of the anisotropy Losses behaviour vs angle is quatitatively well retrieved. Accuracy of computed losses should be improved.

Conclusions and perspectives

A readily vectorial hysteresis model including anisotropy has been tested. Better identification of (ω k , χ k ) or/and improvements of the original model must be made (constant coercivity assumption) for FeSi materials More complex modifications can be imagined to improve the accuracy such as Test this approach with FeSi GO materials -----------

Figure 1 :

 1 Figure 1:Example of the two situations of (3)

Figure 2 :

 2 Figure 2:Illustration of ellispoidal spheres

Figure 3 :Figure 4 :Figure 5 :Figure 6 :Figure 7 :

 34567 Figure 3:Measured and simulated anhysteretic functions in RD and TD

Figure 9 :

 9 Figure 9:Assumption to respect[1]

  M = M an RD (||h re ||) M an TD (||h re ||) h re ||h re || (9)inverse the model to have h(b)

Table 1 :

 1 Values of ω k and χ k sets in RD

	ω k 0.021 0.237 0.3954 0.1681 0.1773
	χ k 0 25.1 51.2 70.4 127.7
	γ 0.965	β	1.3

http://www.LaTeXTemplates.com john@smith.com


Christophe Le Bourlot
email: christophe.le-bourlot@insa-lyon.fr

Amin Azman

Jérôme Adrien

Éric Maire

E Maire

An example of in situ ductile damage analysis by tracking algorithm

Keywords: X-ray tomography, in situ, ductile damage, particle tracking

INTRODUCTION

Damage evolution in ductile metals is characterized by the nucleation, growth and coalescence of small internal voids. Many laws and studies have been developed to understand and predict damage. Numerical modeling, based on full field microstructure acquisitions have proven also to be quite efficient. [START_REF] Hannard | Characterization and micromechanical modelling of microstructural heterogeneity effects on ductile fracture of 6xxx aluminium alloys[END_REF] Real microstructure input are of utmost importance as some studies have shown that the deviation from the average behavior for voids growth can be huge and therefore allows a single cavity to drive the damage behavior and lead to failure. [START_REF] Lecarme | Heterogenous void growth revealed by in situ 3-d x-ray microtomography using automatic cavity tracking[END_REF] In order to develop such approach, proper input data are needed. High energy X-ray contrast tomography allowed to work on large samples and avoid size and shape effect from samples. The next step is to follow and correlate damage evolution during in situ traction test with numerical modeling. Voids nucleation and growth used to be characterized statistically as their number can be quickly very high [START_REF] Lecarme | Heterogenous void growth revealed by in situ 3-d x-ray microtomography using automatic cavity tracking[END_REF][START_REF] Withers | Quantitative x-ray tomography[END_REF] (few thousands on each tomographic volume acquisition). In such condition, the initial state is important but not enough to characterize the sample and be used as input. Following individually each cavity all along the mechanical test is of the utmost importance.

New generation synchrotrons allow fast acquisition and make it possible to easily collect few dozens of tomographic volume sets, often in situ with dedicated environments. [START_REF] Withers | Quantitative x-ray tomography[END_REF] But the analysis of such large amount of data requires then dedicated tools: an example is presented in this paper.

DATASET ACQUISITION

In situ traction test experiment

Interrupted in situ tensile tests have been performed on different materials (titanium, iron or aluminum alloys), to collect sets of tomographic volumes. The present paper focuses on the case of a titanium alloy, the T 40. A home made tensile machine is used, 4 mounted directly on the rotation stage.

Only large scale synchrotron facilities can allow simultaneously fast, efficient as well as high resolution tomography needed. High energy (≈ 80/85 keV ) is required to have a descent transmitted signal through thick samples. High brilliance is also needed to perform a single tomography acquisition in a short enough amount of time (few seconds to minutes) in order to minimize setup vibrations, sample relaxation,... Many volumes per samples (from 10 to 20) are acquired to properly describe the tensile curve. Acquisition have been acquired at SLS TOMCAT and Soleil PISCHE beamlines.

Fig. 1 shows a picture of the tensile rig, a sketch of the sample's geometry and a tensile curve of a T40. The samples are first machined as M3 screws, then a notch is machined to localized strain and therefor damages. The initial smallest diameter in the region of interest is 1 mm, large enough to be sure to collect elementary representative volumes of each sample. Different radii are used for the notch in order to change the initial triaxality in the neck. [START_REF] Bridgman | Studies in Large Plastic Flow and Fracture: With Special Emphasis on the Effects of Hydrostatic Pressure[END_REF][START_REF] Bai | On the application of stress triaxiality formula for plane strain fracture testing[END_REF] A complete slice of the sample in the region of interest, where damage occurs, can be acquired with a lateral voxel size of 1 µm. An example of tensile curve is shown in Fig. 1 on the right. The tensile test is done with constant displacement of the upper sample grip, at 0.5 µm/s. The displacement is stopped during the acquisition. The acquisition are done at the red dots, after relaxation and stabilization.

Volume preparation and voids characterization

The tomographic volumes are post-treated using the open source Fiji software. [START_REF] Schindelin | Fiji: an open-source platform for biological-image analysis[END_REF] The volumes are 3D filtered before segmentation and binarization of the different phases. Each features are then labeled and series of characteristics are calculated, including: position, volume, shape, inertia, equivalent ellipsoid, surface,... First the surface of the sample is extracted. Potential open cracks at the surface are filled. From the evolution of the sample shape, the equivalent triaxality at the center of the sample is estimated (cf. Fig. 1

right).

The voids features are defined as void within the sample mask. Therefore a crack is counted as a void, and characterized as well.

The whole post-treatment process results in the creation of a database of all the voids in all the different acquisitions, with the associated parameters, and mesh-files with the sample shape and all the cavities shape. An example is shown on figure 2(left) with a zoom on the right.

STATISTICAL CHARACTERIZATION

A simple quantification of the damage can be done by analyzing this database.

Nucleation, growth and germination estimation

The distribution of the void size for each acquisition is presented in Figure 3. The number of voids per acquisition is given in the legend (in parenthesis). It is clearly visible that nucleation is very important, and that new nucleated voids are small. Void growth is visible by the shift of the voids distribution. Few very large voids would suggest coalescence events. When all the voids are taken into account, the average void size is almost constant: the growth of the void is compensated by the nucleation of new small voids. But the influence of these voids (the n largest) on the ductile damage and especially to the finale failure is unknown.

The void growth behavior is then difficult to evaluate directly as all nucleation, growth and coalescence events happen simultaneously. A classical approach 4, 8, 9 is to follow the n largest voids assuming that the largest voids remain the same at each step, with different possible values for n. The result is shown on Figure 3(right). Whatever the number of voids taken into account, their average size increases during the experiment, confirming void growth.

Limitations

Despite all the information collected, the characterization of the 3 stages of ductile damage (nucleation, growth and coalescence) is not clearly possible. For example, nucleation and coalescence have an inverse effect on the number of cavities and occur at the same time.

When acquisitions are limited to the central area of the sample, called local tomography, cavities may enter or exit the field of view during acquisition (the material moves during the tensile test).

Therefore, the only way to properly separate the different steps is to have a full knowledge of the behavior of each void ; which means being able to follow each of them. This can be achieved by using the tracking algorithm described below.

TRACKING ALGORITHM 4.1 Principle

The theory of the tracking algorithm is classical (also named Particle Image Velocimetry 10 ), and widely used in different fields: biology to follow cells evolution in situ using time-lapse videos, [START_REF] Meijering | Tracking in cell and developmental biology[END_REF][START_REF] Chenouard | Objective comparison of particle tracking methods[END_REF][START_REF] Brandes | Automated segmentation and tracking of non-rigid objects in time-lapse microscopy videos of polymorphonuclear neutrophils[END_REF][START_REF] Ulman | An objective comparison of cell-tracking algorithms[END_REF][START_REF] Al-Zaben | Automated tracking of label-free cells with enhanced recognition of whole tracks[END_REF] structural timber engineering, [START_REF] Ottenhaus | Use of particle tracking velocimetry in timber material and connection testing[END_REF] and much more... The algorithm used here is an extension of previous publications, [START_REF] Lecarme | Heterogenous void growth revealed by in situ 3-d x-ray microtomography using automatic cavity tracking[END_REF][START_REF] Brandes | Automated segmentation and tracking of non-rigid objects in time-lapse microscopy videos of polymorphonuclear neutrophils[END_REF] adapted to tomographic datasets.

The principle is to build a directed graph with each voids as nodes. The edges are computed between nodes with weights. The weight is the probability for the two nodes to be the same at consecutive time steps. Two more virtual nodes are added with which all nodes are connected: a black hole (representing the possibility for a track to get out of the field of view) and a white-fountain (this represent the possibility for a void to nucleate from nowhere).

Once build, all the voids tracks are extracted by a shortest path algorithm, using the black hole as an end target (by construction of the graph, all the tracks have to end in the black hole).

Weight estimation

Before any analysis, rigid body corrections are applied to each volume to correct possible movements during the tomographic acquisition (translations and rotations).

Simplest case

The simplest case happens when all voids are perfect spherical voids during an in situ tensile test of a perfect elastic material. In that case, the macroscopic deformation of the sample is due to the tensile applied along one direction, and the Poisson effect for the two others. Geometrical corrections are simple.

Then the probability computed between two voids can be simply based on the distance between the geometrically corrected positions of the voids: voids would not move within the mater.

Real case As soon as the voids shape is no more spherical this approach is limited. For example, coalescence events produce highly non-spherical voids. To improve the weight estimation, few steps are added.

First, links between features should be computed only if the features are of same type (there could be no link between a void and a second phase inclusion for example).

Second, distance can be computed between surfaces of the voids rather than the center. As soon as superposition/intersection is detected between two voids of successive acquisition, their probabilities to be linked is very high (and the distance null). This computation used to be quite long, as it involves to load two meshes and compute distance between all their nodes.

If only ductile damage happens, the voids should grow only, they have no reason to shrink. Therefore if a link between two voids implies a volume diminution, this link should be remove (null probability).

Of course, these computations can be very quickly time consuming. To limit the memory usage and fasten the process, a cutting radius is defined: if the distance between two voids center is too high, the probability for these two to be linked is null, therefore there is no need to compute the distance between their surface.

APPLICATION TO TITANIUM T40 SAMPLE

The tracking algorithm is applied here to a T40 sample, deformed in situ. The figure 4 illustrates the result. Each line (or track) corresponds to the displacement of a cavity during tomographic acquisition. The cavities are connected to highlight this link. The color code is the acquisition step, from blue (first acquisition) to red (last acquisition). The vertical axis corresponds to the tensile direction clearly visible. The Poisson effect is also clearly visible (contraction along the two other directions).

The figure 5(left) illustrate the void growth on a single track due to damage: nucleation happens at acquisition step 3 and is followed during the next 5 steps. On the right is an example of a coalescence event: two cavities (in blue) coalesce giving the red one. The ligament between the two cavities is clearly visible (black arrow). Once the tracking done, nucleation and coalescence events are easy to separate. The Figures 6 illustrate: on the left the evolution of nucleation and coalescence events during the acquisition, and on the right the void growth.

As expected, nucleation is very important for this sample, but there is very few coalescence (about a dozen altogether). The interesting information comes from the voids growth evolution: some cavities are stable and do not show any growth evolution during deformation; on the other hand, others show a very high growth rate. This very large dispersion is independent of the initial volume of each cavity, or even its position in the sample. Therefore, the dispersion is in contradiction with the classical theory of void growth. This result has already been shown in 2, but this study generalizes the result: the dispersion of growth law was observed on all studied samples.

Once known, the evolution of the center of mass of each cavity and its surroundings provides access to the local deformation environment. Figure 7(left) illustrates the T40 sample using each cavity as a node of a Delaunay mesh generated using the Paraview application. [START_REF] Ayachit | The ParaView guide: updated for ParaView version 4.3 , Kitware[END_REF] The figure on the right shows the amplitude of the local equivalent elastic deformation brought back to a homogeneous and regular cubic mesh grid (voxels). The resolution of the resulting field depends on the cavity density (high in the center, low at the periphery of the 7. Left: based on the tracked-voids position a mesh is generated using a Delaney tessellation ; Right: using finite element approach, the strain field associated to the mesh evolution/distortion between two acquisition is measured.

sample).

The local elastic deformation field can therefore be used as local information.

Figure 1 .

 1 Figure 1. Left: picture of the in situ device mounted at TOMCAT beamline, as used in 4 ; Middle: shape of the sample with R1 = 1 mm as described in 2 ; right: strain/stress curve and associated triaxality calculated based on the acquired tomographic volumes.

Figure 2 .

 2 Figure 2. Left: voids segmented (4501) within the sample mask, for the last acquisition ; right: zoom at the center of the sample.

Figure 3 .

 3 Figure 3. T40 sample voids statistics. left: voids distribution for the different acquisitions ; right: evolution of the average size of the n largest voids for each acquisition. The fluctuation of the blue curve is due to segmentation uncertainties.

Figure 4 .

 4 Figure 4. Tracks of the voids in the T40 sample. The color code is the acquisition step: from blue (first acquisition) to red (last one). The initial diameter is 1 mm. The vertical axis corresponds to the direction of traction. The Poisson effect is clearly visible (extension along one axis, contraction along the other two).

Figure 5 .

 5 Figure 5. Left: example of a simple track, the color correspond to time step, the voids are linked to highlight the track. Right: the blue and red colors correspond to two successive acquisition time step. The black arrow point on the ligament.

Figure 6 .

 6 Figure 6. Left: evolution of nucleation and coalescence as function of the acquisition steps. Right: evolution of the volume of each cavity according to the effective deformation of the cavity (normalized with respect to the measured strain at nucleation).

Figure

  Figure 7. Left: based on the tracked-voids position a mesh is generated using a Delaney tessellation ; Right: using finite element approach, the strain field associated to the mesh evolution/distortion between two acquisition is measured.

ACKNOWLEDGMENTS

The acquisitions have been done on TOMCAT beamline at SLS and PSICHE beamline at Soleil synchrotron facilities. Nothing would have been possible without the help of the beamline scientists.